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Can stop be light enough?
Ph),~tcs Letters B 31q ( Iq93 ) 355-364 Norlh.i Iolland
PHYSICS LETTERS B
Can stop be light enough? T a d a s h i K o n a.t a n d T o s h i h i k o N o n a k a b.? Pacult.r ofEng+neermg. Setket Umverstty. Tokyo 180. Japan u Department ofPhystcs. Rddc)'o I.'mverstt.r. Tokyo 171. Japan
•
Received 23 September 1993 Ed,tor L. Montanet
We examme a possibthty for the extstence of a hght supers)mmctric partner of the top quark (slop) walh mass 15-20 GcV m the framework of the minimal supcrgravtty GUT model. Such light stop could explain the slight excess of the htgh PT cross section of the D "~-meson production m the two-photon process at TRISTAN. We point out that the extstence of such a stop could change the dominant decay mode of some panicles and could weaken substantially present experimental bounds on the supersymmelric parameter space. It seems that lherc is a finite parametcr region allowing the existence of the hght stop even ff we consider the present experimental data. Inversely, tf the light stop was dtscovered at TRISTAN. masses and mixing parameters of the other SUSY partners as well as masses of the Higgs and the top wdl be severely constrained, for example, rn k " 75 CrcV, ma < 55 GeV. 90 GeV < ml < 130 GcV, 100 GeV < m~ < 150 GeV, m h < 60 GeV and 115 GeV < mf < 135 ~,cV. Some phcnomenologtcal implications on the present and future experiments arc also discussed.
!. Introduction Reccntly, Enomoto et al. in the T O P A Z group at TRISTAN have reported a slight excess of the high Pt cross section of D ' ± - m e s o n production in a twophoton process [ I ]. While the d~sagrcement between the measured value and the standard model prediction is at I.Sa level, there is a exciting way to interpret this enhancement. It is the pair production of the supers.vmmetnc {SUSY) p a n n e r of the top quark {stop) at e + e - collision, e * e - - - t', t'[ [ 2-4 I. Since the stop wdl decay into the charm quark plus the hghtest neutralino [ 2 ]. which can be regarded as the lightest SUSY particle (LSP). the signature of events will be the charm quark pa~r plus large missing momentum. This signature would resemble the charmed-hadron production in the two-photon process at e * e - colhders. Enomoto et al. have pointed out that the stop with mass about 15 GeV and the neutralino with mass about 13 GeV could well explain the experimental data.
I -'
E-mad address: d34477~jpnac.bimet. mtsk ~jpnkektr b=tnet. E-mail address: rra0OIc~.jpnrky00.btmct.
Else,,tcr Science Pubhsher~ B.V. .KSD!0370-2ht,~3( 93 IF 1405.M
It is natural to ask: "Have not such a light stop and neutralino already been excluded by LEP or Tevatron experiments?" and "Could such a hght stop be favored theoretically?" in this paper we examine the possibilit) for the existence of the light stop and the neutralino in the minimal supcrgravity G U T ( M S G U T ) scenario [ 5,6 ] taking into account the present experimental bounds on the SUSY parameter space. Here we consider onl) the bounds from collider data and do not conmder rather model dependent bounds from the proton decay' experiments and the dark matter searches.
2. Light stop: its theoredcal bases In the framework of the MSSM [ 7 ]. the stop mass matrix in the {IL. l'R ) basis is expressed by .~p
=
(
,,,+; \ a,m,
,~,m,
nil=
)
.
(i)
where m, is the top mass. The SUSY mass parameters m~m, and a, arc paramctrized in the following way [8l:
355
Volume 319. number 1.2.3 •
~
•
,,,'~ = .,~,,
•
PIIYSIC'S LI: I-rFR.',;B
23 Lk~cmber 19~3
•
+ .z:, cos 2,8 ( ! - i' sin"' O, ) + m;.
(2)
m,~ = mb~ + inC, cos2,gsin:O~ + roT.
(3)
a, = ..1~ + ~cot,8.
(4)
where tan,8.1~ and ..I, denote the ratio of t~,o Higgs vacuum expectation values ( = v:/t,~ ). the SUSY Higgs mass parameter and the trilinear coupling constant, respectively. The soft breaking masses of the th,rd generation doublet ~¢~ and the up-type singlet ~ht.~ squarks are related to those o f the first (and second) generation squarks as
and the corresponding mass eigenstates are expressed by
)
sinO, + .7~ cosO, ~ '
(9)
where 0, denotes the mixing angle of stops: tan Ot =
at mt
,n~,
- mi, "
(105
We see that ff the SUSY mass parameters and the top mass are of the same order o f magnitude, small m h is possible owing to the cancellation in the expressmn (8) [2,101
(s)
=
~,~., = ,~.,
-
16)
2t,
where I is a function proportional to the top quark Yukawa coupling ¢,, and is determined by the renorrealization group equations in the MSGUT. Throughout this paper we adopt the notation of ref. [9]. There are two origins for lightness of the stop compared to the other squarks and slcptons. ( t 5 smallness of the diagonal soft masses m,~ and nh~ and (ii) the left-right stop mixing. Both effects originate from the large Yukawa interaction of the top. The origin (i) can be easib seen from eqs. ( 2 ) - ( 6 5 . The diagonal mass parameters m,;t and m~ in eq. ( I ) h a v c possibly small values owing to the negati~ e large contributions o f / p r o p o r t i o n a l to ,~t in eqs. (51 and (6)• It should be noted that this c o n t n b u t m n is also important in the radmtive SU(2)~, LI(I ) breaking ,n the MSGUT. The Higgs mass squared has an expression simdar to eqs. 15) and (6). mh: = m~_, - 31.
(75
where rh~., denotes the soft breaking mass of first generation doublet slepton. The large contribution of I enables n~l, to become negative at an appropriate weak energy scale. In order to see another origin (n) we should diagnnalize the mass matrix { 15. The mass eigenvalues are obtained by --
+
i,
' .t50
+ ( 2 a : m , ) ' ] I -'}.
(8)
After the mass diagonahzatmn we can obtain the interactmn Lagrangian in terms of the mass eigenstate t'~. We note. m particular, that the stop coupling to the Z-boson (tli'~Z) depends sensitively on the mixing angle 0,. More specifically, it is proportional to
C'i, - i sm" 0u - .~cos" 0,.
(I I )
Note that for the s p e o a l value of 0r -,, 0.98. the Z boson couphng completely vanishes [ 3 ].
3. Present bounds on stop mass
Before a d,scusston of experimental bounds on the stop mass mi,, we examine the decay modes o f the stop. In the MSSM. the stop lighter than the other squarks and gluino can decay into the various final states t'l - - t 2 1 (a). bll'l ( b ) . b f b ( c ) . b v [ ( d ) , b W 2 1 (el. t , f f ' 2 t (f), c2t (g). where 21, fli, b and t'. respectively, denote the hghtest neutralino, the lighter chargmo, the sneutrino and the charged slepton. If we consider the hght stop with mass smaller than 20 GeV. the first five decay modes (a) to (e) are kinemat~cally forbidden due to the model independent lower mass bounds for the respective particles: rn, ;~ 90 GeV, mD~, ;~ 4 5 G e V . mi ;~ 4 5 G c V a n d m , ~ > 4 0 G e V . So If) and (g) are left. Hikasa and Kobayashi [2] have shown that the one-loop mode t'l ~ c~..t (g) dominates over the f o u r - M y mode ,;~ ~ b.f.f'2~ (f). This is absolutel.~ true in the case considered here. because the mode (f) is negligible b) the kinematical suppressmn, m 6 ",- m2, + m~,. So we can conclude that such a light stop will decay into the charm quark jet plus the missing momentum taken awa.~ by the
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PHYSICS LEI'I-F.RS B
bounds, however, are invalidated if mo - m~.~ < 8 GeV. in addition, the mass bound mi~ ~ 37 GeV from the direct stop search by the DELPHI group at LEP is valid only for mi, - m2, > i 7 GeV [ 14 ]. Recentb Okada [i 5] has investigated possible bounds on masses of the stop and the neutralino from the exIxrimental data of the b ~ s7 decay. He has shown that the light stop with mass m h < 20 GeV has not been excluded by the data. After all. we can conclude that there ~s no bound on the stop mass for m,~, 10 GeV and 0, ;~ 0.6 ifm~, - m,~, < 8 GeV.
i .i
i
._,,
23 December 1993
. [El'
1 + ,
..,
. , ,
. . . . . .
°
Ftg. I. Excluded region in (Or. mi.) plane by LEP ~ath A/~ < 35.1 MeV.
neutralino with almost 100% branching ratio. Note that the width of stop in this cave is xer3' small, i.e., of the order of magnitude of eV. Naively. it will be expected that Tevatron a n d / o r LEP can set severe bounds on the stop mass through the processes .gg - - tt t; . c'72, 21 (Tevatron) a n d / o r Z --/'j/'~
4. Present bounds on gaugino parameters
In the MSSM. masses and mixing parameters of the gaugino-higgsino sector are determined b~ three parameters, ~. tan ,8 and M:, where M,, denotes the soft breaking S U ( 2 ) gaugino mass. Some regions in 1/,, tan ,8..*,!2) parameter space have already excluded by the negative searches for the SUSY particle's at some collider experiments. First, we consider the experimental data at LEP: (i) lower bound on the mass of lighter chargino, mih ;~ 45 GeV, (ii) upper bound on the branching ratio of the visible neutralino modes of the Z. B R ( Z - - vis.) - ~ ,., F ( Z - - 2 , 2 j ) / 1 " , , ~ i~/vI
< 5 × l0 -~ [18]. and (iii) upper bound on the invisible width of the Z . F { Z ~ 2,21) < 16.2 MeV [I 2]. In fig. 2 we show the region excluded by the experimental data ( i ) - { i i i ) in the (#. M 2 ) plane for tan,8 = 2. We also plot a contour of m,~, = 13 GeV which can explain the TRISTAN data as mentioned above. First we realize that the neutralino with mass 13 GcV can be allowed in the range - 1 6 0 GeV £ - I I 0 GeV for tan ,8 = 2. Note that the contour of m~, = 13 GeV lies in the excluded region for/~ > 0. If we take larger {smaller) values of tan ,8, the allowed region becomes narrower {wider). We find that the allowed region disappears for tan ,8 ;~ 2.3. Second ~e see that oh,: = 13 GeV corresponds to M , ~- 22 GeV in the allowed region and we can find that this correspondence is independent of the values of tan ,8. Con,~quently, we can take M: = 22 GeV as an input value in the follovdng calculation. The allowed region in the (1~, tan ,8) plane fixed by M: = 22 GeV is shown in fig. 3. Additional bounds on the (,u. tan,8) parameter space from the negative search for the neu357
Volume 319. number 1.2.3
PHYSI( .'S I.E VIERS B
23 rx"gx-mbcr1993
m i = .ll~ = "...! sm'OwAI2. _.
.~
.,
.
-
.
:
I
! ','"
i
[ 7 F-
in the M S G U T . the gluino mass m i bounds from the hadron collidcrs could be converted into the bounds on M : [ 16 ]. The gluino mass bound at C D F taken into account of the cascade decays ,~ ~ q~2:.~., and ~? -- udll].2 [17] as well as the direct deca) ,~ q ~ 2 f has been reported as [191
:
-,.
,
m i ~ 95GeV
.',
I •
!
].1 '( i~\'. Fig. 2. Contour of m 2. = 13 G e V m the ( p . M2 ) plane for tan B = 2. The excluded rcgaon b) LEP ns also depicted.
-.
"
I
Xl -22(;.\
• -.
"-"'~.':t't,i
. . . . . n,
rl't"x,.
.
.
.... .
.
~T . . . . .
:
vt~V----,r--~,
(90%C.L.)
t.
.
Fig. 3. Allowed revon nn the (/a. tanB) plane for . t / : = 22 GeV. The dashed Inneand the dotted hne correspond to the contourofBR(Z ~ vis.) = 5 x 10 -5 and that o f m ~ L = 45 GeV, respecllveb. tral Higgs boson at LEP will be discussed below. It us worth mentioning that the lightest neutralino 2, is almost the photino ~'. in the allowed parameter range in fig. 3. In fact, the photmo component of the neutralino is larger than 99% in the range. Next we should discuss bounds on the gauglno parameters from the hadron collider experiments. If we assume the G~'I" relation,
(13)
for p = -250 GeV and tanB = 2. This bound can easily be converted into the bound on M: by eq. ( ! 2 ) as M: ;~ 28 GeV. which rejects the above fixed value. M: = 22 GeV. (Note that the G U T relation (121 depends sensitively on sin: 0,. and ,,,. Here we take s i n : 0 w = 0.232 and n, = 0.113. ) We must consider, however, the fact that the bound 113) is obtained based on the assumption that m h > m i and the 81uino cannot decay into the stop. This is not the case we consider here. In fact• the gluino can decay into the stop pair. ~ - - ?~?~2t. which becomes another seed for the cascade decay. In fig. 4 we show the m i dependence of the branching ratio of 81uino. where we include the mode ~ - and sum up quark flavors q . q ' = u . d . c , s . W e t a k e t a n f l = 2,,u = - 1 5 0 G e V . mr, = 15 GeV. 0, = 0.7. m, = 135 GeV and .it: = 22 GcV. and take m i as a free parameter. The squark masses are taken as m# = 2 m i Ca) and m# = 3ink (b),where m # - m..LR = mdt., = m 6 . j = m h ~ . The arrow in the figure denotes the rni value determined by the G U T relation. The branching ratio of the direct decay mode .~ - - q ~ , . which is important in the search in terms of large ~'~ signature, is reduced substantially as BR(~ ~ q~ZT, ) < 50% (15%). even for the hght gluino w,th mass rni ;~ 60 GeV for rn~ = 2m i (m~ = 3 m i ) . Therefore. we should reconsider the UA2 bound n q ;~ 79 GeV [20] obtained under the assumption BR(,~ ~ qq.~,) .-- 100% as well as the CDF bound (13). For the v a l u e m i = 74 GeV determined by the GLIT relation. BR(~, ~ q ~ 2 ~ ) ,~ 20% ( 4 % ) f o r m 4 = 2 m i (mo = 3 m i ) . w h i c h should be compared with BR(,~ ~ q ~ ) -,- 70% obtained when there is no stop mode. We can find that if we take larger values of mo. BR(~ ~ q~2.~ ) is reduced rapidly. In this case the Tevatron bound (13) would Ix" d~minished s,gnificantly. This ,s because the width of the stop mode F ( ~ ~ ?~?72~ ) does not depend on
~,?~2,
. r.I
:.
358
(12)
.
.!
M 't ic\
. . . .
Volume 319. number 1.2.~
PHYSICS LETTERS B
23 December 1993 m;-m~M.)
mf-m~M:, I F ........ [ ......
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Ftg. 4. m i dependence of the branchmg ratios of the glumo. The sum over quark flavors q . q ' = u . d , c . s Is taken. Input Darametcrs are tan// = 2. t~ = -150 GeV. m h = 15 GcV. 0t = 07. mt = 135 GeV..it'_, = 22 GcV and m# = 2rn i la) and m d = 3m k (b} The arro~ tn the figure denotes the m i value determined by the GUT relation. m# but all the other widths become smaller for larger values of rod. While all squark masses are independent parameters in the MSSM. they are d e t e r m i n e d by small n u m b e r s of input parameters in the M S G U T . Hereafter we adopt the G U T relation a n d will reconsider the T e v a t r o n b o u n d after presenting the results of the M S G U T analyses. Note that if we remove the G U T relation, the gluino can be hear,, with no relation with 312 and m 2 , a n d BR(,~ - - q~2.t) can be small.
t a n / / is not too large (<< m , / m ~ ) , which is the case we consider here, tan # < 2.3. As for the e v o l u t i o n o f t h e gauge couplings ¢,, (t) a n d the gauglno masses M , ( t ) . we take the input values , - I ( m , , ) = 128.8 a n d s i n ' 0 , . = 0.232. A s s u m i n g that the SUSY scale is not too different from r n z . we may use the SUSY beta function at all scales above m z for simplification. T h e n one finds M,. = 2.1 x 10 .6 GeV. ,~.l 1= a~ l ( M x ) = ~ T l ( M ~ .) = a ~ - I ( M ¢ ) ) = 24.6 and n 3 l m z ) = 0.113. Moreover. the R G E for gaugino masses are easily solved as M:,.
5. M S G U - r analysis Before presenting our results for analysis, we wtll s u m m a r i z e briefly the calculational scheme in the M S G U T [9]. In this scheme the i n d e p e n d e n t parameters, besides the gauge a n d Yukawa couplings, at G U T scale M r are the SUSY Higgs mass p a r a m e t e r u ( M r ) = l l x and three soft breaking mass parameters: the c o m m o n scalar mass th} ( M r ) = rh]h (.tit') =
m~.. the c o m m o n gaugino mass A t 3 ( M t . ) = = M l i A t . r ) = M.~ a n d the t r i h n e a r coupling A , ( . l t t . ) = .41,(M.t.) = ..It(.Ift.) . . . . . -|.-,c. As usual, we take the Higgs mixing parameter B as B(Mt.) = .4~. - r e x . All the physical parameters go from M.t do~'n to low energies governed by the r e n o r m a h z a t i o n group equattons ( R G E ) [6]. In the following we neglect all Y u k a w a couplings except for the top. This is not a bad a p p r o x i m a t i o n as long as M:(Mx)
M~(I) = ~h(t)--
(141
After solving all the other R G E for the physical parameters, all ph.~ sics at weak scale r n z are d e t e r m i n e d b.~ the six parameters (mo~..4,,, M : , , ~, t a n / / , m,). There are. moreover, two c o n d i t i o n s imposed on the parameters to have the correct scale of SU (2) × U ( 1 ) breaking. So we can reduce the n u m b e r of the independent parameters to four out of the six. Here we take the four i n d e p e n d e n t input parameters as ( M , . . g, t a n / / , m r ) . As we have discussed earlier, furthermore, we can fix one o f the input values. 3 t 2 = 22 GeV, which corresponds to M.,: = 26.7 GeV for sin: 0w = 0.232 (see eq. (14) ). Finally, only the three parameters (g, t a n / / , m,) remain. We seek numerical solutions to give a light stop with mass m?, ( = 13 G e V ) < m.,, < 20 GeV vaD4ng the three parameters (g, tan ,8. m t ). T h e results are shown in fig. 5, which is the same parameter space as in fig. 3. 35 c)
Volume 319. number I...3 •
PHYSICS I E I'IFRS B
2 .~,LXx:cmber 1993
Table I T)~,cal parameter
..~ |. ,-.a...,..... .....,...1.............. ,...~,.,. J~.~t~..! / :'
.,
"'Z
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r,
.:',2
.,.~r"
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.,.-
• :-
~': : .,
.,
• i .... .~
¢
....
t..v.l
• 2'
• '.
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,
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mt
22 2.09 -151 135
22 1.83 -94.0 117
22 2.0 -135 130
"'v~
•
;,
1"
;
."
M.,c mx .4 .,,. #x
26.7 125.0 332.0 132.8
26.7 84.0 207.8 -78.0
26.7 111.7 293.5 -116.7
mi~
14.6 201.9 0.9] 107.0 142.8 135.9 138.4 149.9 142.6 131.9 130.2 115.7 55.4 210.9 224.8 225.5 -0.56 13.1 48.2 159.0 187.3 45.0 184.5 74.4
15.0 183.5 0.85 93.4 108.8 10(3.7 103.4 116.6 108.2 92.9 q0.6 72.0 44.4 134.9 15q.0 156.8 - 0.69 13.3 54.7 107.3 142.2 53.7 138.6 74 4
15.5 196.4 0.89 102.0 131.2 124. I 126.7 138.6 131.0 119.0 I 17.2 101.7 52.6 189.0 205.2 205.2 - 0.59 13.2 50.5 143.6 174.2 47.2 171.0 74.4
:::..'
..~'.
"':'f;1
I"x7:
-41.'*'
,
• I
~
'
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1'
(,'~
F,g. 5. Stop mass contours ,n (u. tan#~ plane for fixed m~. Each hatched area corresponds to the region m 2 < ,hi, < 20 GeV. The upper (lower) hne of each area corresponds to mit = m2~ Imi~ = 20 GeV). We also plot the mass m h contours as well as the LEP bounds. Points denoted b.,, A. B and C correspond to I)plt~dl parameter sets m the text
mi, 0", m/,~ m/,: m~ t m,'.a mdt mda
.IlL Each hatched area corresponds to the region allowing m2t < mi, < 20 G e V for a fixed m, value. T h e upper (lower) line o f each area corresponds to m~, = m2, = 13 G e V (mi, = 20 G e V ) . We also plot the mass m , c o n t o u r s o f the lighter C P - c v e n neutral H~ggs boson as well as the LEP b o u n d s from the data discussed above. R r s t we realize that there is a rather narrow, but finite range allowfng the existence o f the light stop. if the top is slightly light too, m, < 135 GcV. Second we find that the light stop solutions inevitably g~ve a hght Higgs b o s o m m~ < 60 GeV. While we have included the r a d i a u v e correction in the calculation of the Higgs mass [21 ], d e v i a t i o n s ,6m, from the tree level results are not so large. :~-o, < 2 GeV. The neutral Higgs is standard Higgs like. i.e.. s i n ( / / - , ) ~_ I, where ¢, denotes the Higgs mixing angle [221- A result from the negative searches for the M S S M Higgs at LEP could set a n o t h e r constraint on the S U S Y p a r a m e t e r space ,n fig. 5. W h d e the present h m i t on the M S S M Higgs mass is m , ;~ 5 0 G e V
(95%C.L.)
{15)
for sin(,8 - ,,) "- I [231. this is o b t a i n e d based upon the a s s u m p t i o n that the Higgs do not decay into the stop. We can find. in fact. that the neutral Higgs could have a d o m i n a n t decay m o d e h - - it/'7 with almost 100% branching ratio as we will discuss below, in this 3h()
GeV
B
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,, m21 m2:
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case energ,es o f visible jets from the Higgs production would b e c o m e softer and it can be smaller than the detection lower cuts. Therefore. if we incorporate such a decay m o d e m data analyses, the present lower b o u n d s gall be weakened significantly. Here we ass u m e a c o n s e ~ ' a h v e b o u n d mh ~ 45 GeV. Note that this is a c o m p l e t e l ) tentative assumption. The exact regaons " e x c l u d e d " are unclear, because we have to perform a detailed M o n t e Carlo analyses o f the LEP data including the exotic decay m o d e h ~ t') ~ in order to obtain the exact excluded regions. A d o p t i n g the b o u n d mh ~ 45 G e V . we can choose three typical parameter wets A, B and C. d e n o t e d in fig. 5. The set A
Volume 319. number 1.2.3
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( B )gtves the largest (smallest) scalar fermion masses and the smallest (largest) lighter chargino mass. The set C corresponds almost to the center point m the allowed range. Input and output values of the parameters o f t h e sets A. B and C are presented in table I. We find that masses and mixing parameters are severely constrained, for example, ma., ,< 55 GeV, 90 GeV < m; < 130GeV. 100GeV < m 4 < 150GeV a n d 0 . 8 5 < 0, < 0.95. Note that only the upper limits on ma, and the lower limits on m/, n:~ and 0, depend on the tentatnve assumption m~ ;~ 45 GeV.
6. Phenomenologtcal implications Now. we are in positxon to &seuss some consequence of the hght stop scenario in the M S G t l T and give strategtes to confirm or reject such a possxbility in present and future expernmcnts. Some numerical results are calculated with the t.sptcal parameter sets A, B and C. The existence of a light stop wtth mass 15-20 GeV will completely alter the decay patterns of some ordinars and St.:SY particles (sparticles). First we discuss the top decay [ 11.24 ]. In our scenario, the top can decay into final states including the stop: t ~ lrn~.t. ?~2: and t'~.~. Branching ratnos of the top for the typical parameter sets are presented in table 2. We find that the gluino mode t - - ?nob has 40-50% branching ratio and dominates over the standard mode t + b l i "÷ in almost the whole allowed parameter region. Strategies for the top search at Tcvatron would be forced to change because the leptomc branching ratios of the top would be reduced b.~ the dominance of the stopgluino mode. The decay patterns of the H~ggs parttcles will be changed too. The lighter C P . e v e n neutral Hnggs decays dominantly into the stop pair. h - t'u?~, owing Table 2 Branching ratios of top. ~X t -- in2] ';'t~." t'n.~ bll'*
0.060 0.030 0.524 0.386
B
C
0.0q6 0. I 18 0.410 0.376
0.068 0.039 0 500 0.393
23 December Iqq3
to the large Yukawa coupling of the top. In rough estimation, we obtain
I BR(h~?l~)~
i + 3 m h m j ..~n b.~2 4 -~ I.
(16)
This fact would change the experimental methods o f the Higgs searches at the present and future collider experiments. More detailed analyses of the charged [25] and neutral Higgs bosons are presented separately. Now we briefly, discuss the light stop impact on the spanicle decays. The lightest charged sparticle apart from the stop is the lighter chargino tl]. The two body stop mode It'~ - • b,~ would dominate over the convenuonal three body mode fl'~ ~ f ~ 2 n . As a consequence, it would be difficult to use the leptonic signature m the chargino march at e + e - and hadron colhders. Smce the chargino II~. the neutral Higgs h and the gluino ~,. whose dominant decay modes are respecw.'el:, fl'l -" M , . h - - ?~?T and ~ ~ ?~?~2n, are copiously produced nn the other sparticle decays, many stops would be expected m the final states of the sparticle production. For example, fL " I,l.l"t .. v ( b ? t ) .
~.,R
" q g - - q ( ~ ? ~ 2 ~ ), qt ~ q'W~ - q'(b?n) and 2,,,¢t~ ~ 2 t h ~ 2 t ( i t t [ ) . Note that the d o m m a n t
decay modes of the right-handed slcptons would be unchanged, i.e.. BR(/'R - - t 2 , ) -.- 100%. Needless to sa.,,, all experimental groups, AMY, T O P A Z and VENUS. at TRISTAN should perform a detailed data analyses to confirm or reject the exciting scenario. Furthermore. we can see that the stop and ~ts relatively light accompaniments, the gluino ~. light neutralinos 2t.:, and neutral Higgs h, should be visible at LEP. SLC, HERA and Tevatron. Espectall.~, LEP could search the allowed region presented in figs. 1 and 5 in terms of the width of Z-boson and the direct stop search. First we find from table 1. that the stop mixing angle 0, is severely limited as 0.85 < 0, ~< 0.95 in the allowed range in fig. 5. It should be noted that the lower bound depends on the tentative assumption mh > 45 GeV. A larger (smaller) lower limit on m, gives a slightly narrower (wider) range of 0,. On the other hand. the upper bound on 0t is determined by the estabi,shed limit rna., ~ 45 GeV. It is interesting that 0, _-. 0.9 is not input but output of the M S G U T calculation. As the stop search in terms o f A F / w o u l d be difficult in this case. the direct search for e +e - • tt ?; will be important [ 141. We
~61
Volume 319. number 1.2.3
PHYSI('~ I.E'i I ERS B
Table 3 Branchin8 ratios of glumo.
k _
q~2t q~ ~.., q~Tfl. ~t i:~~'.j
experimental upper limits. Note again that the light
stop and neutralino can sur'v~ve even after the negaA
B
C
0.252 0.023 0.089 0.636
0.489 0.011 0.042 0.458
0.332 0.020 0.085 0.563
find. in fact, that the stop contribution F ( Z ~ ~?~) to AFz is larger than about 0.2 MeV for O, < 0.95 and m/. < 20 GeV. Second, the whole allowed region m fig. 5 can be explored b.,, the precise measurement of B R ( Z ~ ,,'is.). In fact, the smallest value of the neutralino contribution ~ ,., F ( Z ~ ~,~..j)/F,J °t ~atgl
to B R t Z - - vis.) is 1.1 ', l0 * (I.8 × l0 -~) for mh > 45 GeV ( m , > 50 GeV). Of course, the Htggs h search at LEP with the stop signature h - - i~i;; is veD' ~mportant to set a further constraint on the allowed region. C l e a r b . the lighter ehargmo, ma., < 55 GeV. would be visible at LEPII. Furthermore, there is a possibility that some sleptons will be discovered at v~ < 200 GeV. As mentioned before. Tevatron will play a crucial role in confirming or rejecting the light stop scenario m the MSGLIT with the G U T relation. In this case the existence of relatively light glumo, m i x 75 GeV. with substantially large decay fraction ,~ -- ~:~i'r~'.~ is one of definite prediction. Values of branching ratios of the gluino for the typical parameter sets A. B and C are tabulated in table 3. The branching ratio of the direct decay mode B R ( ~ - q~..~) = 25 .,. 50% is expected in the allowed range. These values are rather large compared to those in fig. 4b. This originates from the fact that the allowed mass values o f ~ u a r k s except for the heavier stop t'., are relatively small, m4 < 150 GeV. Those squarks could be within reach of Tevatron. S~gnatures of those squarks, however, would be unusual because of their cascade decays such as qt.~ -" q g - - q(~r ~ ' ~ ) and ~. - - q ' l | ] ~ q'(I,t~ ). Anyway. there ~s a large possibility that some regions could have been excluded b.~ Tevatron data. Detailed Monte Carlo studies including the stop mode .~ - . t't t'; 2~ are required at any cost. At least we expect that the region near the point corresponding to the set B could have been excluded because BR(£, - - q ~ ) ~ould be large enough to make the ~'t s,gnal events larger than ,is 3~,2
23 December 1993
tive search for the gluino and squarks at Tevatron if we remove the G U T relation (I 2). Removal of the G U T relation corresponds to the change o f boundary conditions on the soft gaugino masses at the unificatmn scale Mx. Owing to this change the RGE solution for the stop mass is modified and in turn we will get a d~fferent allowed parameter region from fig. 5. The analyses based on such models will be presented elsewhere. The e p collider HERA could search the light stop through its pair production process e p ~ e ~ t ~ X via boson-gluon fusion [26J. The total cross section of the process is larger than about 10 pb for ml~ ~< 20 GeV, which is independent on the mixing angle 0,. That is. o ;~ I 0 pb is expected for all parameters with m h < 20 GeV in the allowed range in figs. I and 5. Detailed analyses with Monte Carlo studies including possible dominant background process e p ~ e c ? X can be found in ref. [27]. The process e p - - eil~[.~t" is useful to confirm or reject the ve~. light stop. but not too effective in determining model parameters in the MSSM such as the other sparticle masses as well as 0t. We have calculated another process.
ep
• b~b.~'.
(17)
~,hzch is expected to be useful for the latter purpose because the cross section depends on m a , . m~. O, and the mix,ng angles of Ill. The total cross sectmn is obtained as 1.4 ~ 10 -3 pb for the set A and 2.0 × 1 0 - : pb for the set B. Although these values are rather small and a high luminosity ~,ould be needed to see. sensitivity on the SUSY parameters is rather high. Here a comment on the R-pant,, breaking coupl,ngs of the stop may be in order. We have calculated not only the R-conserving process e p ~ ei~ t'~X but also the R-breaking process e p ---* ( i j ) ~ e q X in refs. [27.28]. The latter process could have a distinctive s~gnature, i.e.. a sharp peak in the Bjorken parameter x distribution. In our scenario o f a veD' light stop. however, the strength of the R-parity (and lepton number) breaking coupling of the stop d e f n e d in the superpotentlai 129]. Ii" = 2'13tLiQ3D ~,
(18)
Volume 319. number 1.2.3
f" ....
' . . . . . . . .
$:-~
PHYSICS LEFFERS B
....
~::;.."7-".~.
""
" "
tl
// , [
,
'
.,'/
"~'"
."
"' ....
""1
.¢
''r
6. Another important property is that .4L~ is independent on the mass of stop mi, as well as on the Q C D c o r r e c t t o n J O c o since ,8,), and I + JOco dlsappeared in the fractional combination of o in AiR. "I'hereforc, this method for mcasuring 0~ will be applicablc for the stop w H h any' mass satisfying mi, < ~ / 2 .
I
7.
F~g. 6. Total encrg) v'~ dependence of left-right asymmct~ for the stop productton at e + e - colhders. For comparison we also plot .4LR for the up-t)pe quark production. cannot be large enough for possible detection at HERA. This ~s because the coupling {18) with 2't~t > 10 -~ makes the R-breaking stop decay mode/'t ~ ed dominant and thts fact contradicts BR{~:t - - c 2 t ) 100% expected at TRISTAN. Polarized imtial electron beams at SLC and at any l i n e a r e * e colliders will be efficient to reveal the nature of left-right mixing m the stop sector, in other words, to measure the mixing angle o f s t o p 0t. In fig. 6 we show the ~,~ dependence of the left-right as~,mmerry. •-tL~ --
o(~.)
-
aIeR) (19)
O'(eL) + a ( e a ) "
where ale1 R) - O(e~'el'~R - - l l l ' ; I . ~hich are obtained by'
It
+
=
,,
23 l.k~zcmber 1993
+ i ( ' f ~T', .¢. a~
:"'1Re ),
(')
{I + f ~ - D I .
(20)
where ,8i, -- v / l - 4m~,is. Dz - s - ,n~ + i m z F z . v, - ( ~ + 2sin2OL¢ )/(sinZOj~ c o s : O . ) and a, = I / ( 2 s m 20w cos 2 8 w ) . In the asymmetric combination in eq. (19) the photon c o n t r i b u t i o n is cancelled out and ..h.K ,s p r o p o r t i o n a l to ('fl ( I I ). This is thc reason for senslt,ve dependence on 0, o f .4,.k in fig.
Conclusion
We have investigated the possibihty of the existence of the light stop ,m, = 15-20 GeV and the ncutralino m2, _-2 13 GeV in the M S G U T scenario taking into account of the present experimental bounds on the SUSY parameter space. We have pointed out that the existence of such a stop could change the dominant decay mode of some panicles. For example, the stop modes .~ - - i~/'; ~.~ and h - . / ' l / ' ; could dominate over respect,rely the conventional modes ~ ~ q ~ 2 , and h - - bh even for relatively light gluino and Higgs. As a consequence, present experimcntal bounds on the SUSY parameter space could be weakened considerably. It seems that there is a finite parameter region allowing the existence of such a light stop even if we consider the present experimental data. Inversely. if such a light stop is discovered at TRISTAN. masses and mixing parameters of the other SUSY partners as well as masses of the Higgs and thc top will be severely constra,ned, for example. - t i "" 75 GeV, ma, £ 55 GeV. 90 GeV ,< mt ~< 130 GeV. 100 GeV _% m# ~< 150 GeV, 0.85 < 0, < 0.95, mh ~< 60 GeV and 115 GcV < rn, < 135 GeV. Actually, the light stop and its relatively, light accompaniments, the gluino .~. the light ncutralinos ~L:. and the neutral Higgs h, should be v~s~ble in the near future at LEP. HER,-% and Tevatron. In fact, LEP and HERA could explore the whole allowed parameter region in terms of the precise measurement of the width of Z and by means o f searching for the process ep ~ eft ~.lf. respectively. There exists, moreover, special interest m a Tevatron experiment, i.e.. Tevatron could either discover or exclude the light gluino m i "" 75 GeV. If we could not discover such a gluino, this fact would indicate invalidity of the G U T relatton, tn other words, the assumption of the common gaugmo mass at Mr.. Experimental sign for violation of the G U T relat,on may be ,mportant to select a specific model out o f a great number of string model candidates. 363
Volume 319. number 1.2.3
PHYSI( ,'S LETI'I-RS B
Recently,, Altarelh et al. [30] haxe shown that a light stop mi, ~< 50 G e V and a light chargino m~. < 60 G e V could well explain the precision data at LEP. "l'he~r result seems to support our light stop scenario. In this paper we have e x e m p l i f i e d that f f w e d i s c o v e r the hght stop we wdl be able to constrain severely all the S U S Y parameters at the unification scale. We can conclude that, therefore, the discovery,' o f the stop will bring us a great physical impact. Not only will it be the first signature o f the top flavor and supersymmetr3' but it could shed a light on the physics at the unification scale as well.
Acknowledgement O n e o f the authors ~T.K. ) would like to thank Drs. R. E n o m o t o and M. Pieri for valuable i n f o r m a t i o n .
References [ I I TOPAZ Collab.. R. Enomoto et al.. KEK-prcprmt. 93107 (1993). [2] K. Hika~a and M. Kobayash~. Phys. Re" D 36 (1987) 724. 131 M. Drees and K. H~kas.a. Phys. Left. B 252 ( 1990 ) 127. 14]T. Kon. Prec. of the Workshop on TRISTAN Physi~ at High Lummosmes, ed. M. Yamaucht. KEK Preceedmgs 93-2 119931 p. 274 [51 B Barb)en, S. Ferrara and C. Savo.~. Phys. Lett. B 119 11982) 343; A. Chamseddme. R. Arnow)tt and P. Nath. Phys. Rev. Lett. 49 11982) 970. [6] I. Inouc. A. Kakuto. H. Komatsu and S. T a k e , ira, Prog. Theor. Phys. 67 (1982) 1889; 68 11982) 927; J. Elhs, J. Hagehn. D. Nanopoulos and K Tamvakls. Phys Left. B 125 11983) 275. L. Al,,arcz-Gaumc. J Polchmski and M. Wise. Nucl. Phys. B 221 11983) 495. L. Ibafiez and C. L6pez. Phys. Lett B 126 (1983) 54. [7] For reviews, see H. Ndles. Phys. Rep. II0 11984) 1; H. Haber and G. Kane. Phys. Rep. 117 11985) 75. 18] For example. H E. Haber. Note on Supcrsymmetry in Review of Particle properlles, Part II. Phys. Rev. I.) 45 (1992) IX.5 191 K. Hikasa. JLC Supers~,mmetr) Manual. unpubhs.hed. [10l J. Elhs and S. Rudaz. Phys. Lett. B 128 11983) 248.
3~',4
23 l)t'cember 1993
G. Altardh and R. Ruckl, Ph~. Lctt. B 144 (1984) 126; I. Biga and S. Rudaz, Ph)s. Left. B 153 (1985) 335. I I I ] H. Baer. M. Drees. R. Godbole. J Gunion and X. Tata. Phys. Rev. D 44 11991 ) 725. [12] L3 Collab., prepnnt, CERN-PPE/93-31 11993). [131 TOPAZ Collab., I. Adachl et al.. Phys. Left. B 218 (1989) 105; AMY Collab., Y. Sakal et al.. Phys. Lett. B 234 11990) 534. 114] R. Keranen. Proc. of the Fermdab Meeting DPF92. eds. C. Albnght et al. (World Scientific. Singapore. 1993). Vol. 2. p. 1275. [15] Y. Okada. preprmt. KEK-TH-365 11903). [161K. Hidaka. Phys. Re~,. D 44 (1991) 927. [ 17 ] H. Baer, V. Barger. D. Karatas and X. "rata. Phys. Rev. D 36 (1987)96; R. Barnet. J. Gumon and H. Haber. Phys. Re,,. D 37 (1988) 1892. H. Baer, X. Tara and J. Woodside, Ph~,s. Re,,'. Lett. 63 11989) 352. Phys. Re'. I) 41 11990) 906. D 44 (1991) 207. 1181A. Lopez-Fernandez. Prec. of the Fermilab Meelmg DPF92. eds. C. Albnght el al. (World Scientific, Singapore. 1993). Vol. 2. p. 1221. 1191CDF Collab., F. ,kbe el al., Phys. Rev. Left. 69 (1992) 3439. [201 UA2 Collab., J. Alitti et al. Phys. Lett. B 235 11990) 363. [211 J. Elhs. G. Ridolfi and F. Zw~rner. Phys. Le¿I. B 262 (1991) ,177. A. Bngnole, J. Elhs, G. Ridolfi and F. Zwirner. Phys. Lctt. B 271 )1991 ) 123. [22] J. Gumon and H. Haber. Nucl. Phys. B 272 (1986) I. 123]G. Wormser, Proc of the XXVI International Conference on High Energy Physics, ed. J.R. Sanford (MP, New York, 1993). Vol. II. p. 1309. [24] K. Hidaka. Y. Kirukuri and T. Kon, Phys. Left. B 278 11992) 155. [25]-~ Bartl. K lhdaka. Y. Kizukun. T. Kon and W. Majerotto, Ph.,,s. Left. B 11993) 360. [26] 1-. Kobayasht, T. Kon, K. Nakamura and "1. Suzuki. Mod. Phys. Lett. A 7 11992) 1209 [271T. Kon. T. Koba~,ash~. S. K~tamura. K. Nakamura and S. Adachl. preprmt. ITP-SU-93/03 (1993), to be pubhshed m Z. Ph)s. C. [281T. Kon and T. Koba~,ash). Ph~,,s. Lett. B 270 (1991) 81. [29] V. Bargcr, G.F. Giudicc and T. Han, Ph)s. Re'. D 40 (1989) 2987 [301G. Altarelh. R. Barbieri and F. Cara~,aghos. prcpnnt, CERN-TH.6902/93 11993).
PHYSICS LETTERS B
Can stop be light enough? T a d a s h i K o n a.t a n d T o s h i h i k o N o n a k a b.? Pacult.r ofEng+neermg. Setket Umverstty. Tokyo 180. Japan u Department ofPhystcs. Rddc)'o I.'mverstt.r. Tokyo 171. Japan
•
Received 23 September 1993 Ed,tor L. Montanet
We examme a possibthty for the extstence of a hght supers)mmctric partner of the top quark (slop) walh mass 15-20 GcV m the framework of the minimal supcrgravtty GUT model. Such light stop could explain the slight excess of the htgh PT cross section of the D "~-meson production m the two-photon process at TRISTAN. We point out that the extstence of such a stop could change the dominant decay mode of some panicles and could weaken substantially present experimental bounds on the supersymmelric parameter space. It seems that lherc is a finite parametcr region allowing the existence of the hght stop even ff we consider the present experimental data. Inversely, tf the light stop was dtscovered at TRISTAN. masses and mixing parameters of the other SUSY partners as well as masses of the Higgs and the top wdl be severely constrained, for example, rn k " 75 CrcV, ma < 55 GeV. 90 GeV < ml < 130 GcV, 100 GeV < m~ < 150 GeV, m h < 60 GeV and 115 GeV < mf < 135 ~,cV. Some phcnomenologtcal implications on the present and future experiments arc also discussed.
!. Introduction Reccntly, Enomoto et al. in the T O P A Z group at TRISTAN have reported a slight excess of the high Pt cross section of D ' ± - m e s o n production in a twophoton process [ I ]. While the d~sagrcement between the measured value and the standard model prediction is at I.Sa level, there is a exciting way to interpret this enhancement. It is the pair production of the supers.vmmetnc {SUSY) p a n n e r of the top quark {stop) at e + e - collision, e * e - - - t', t'[ [ 2-4 I. Since the stop wdl decay into the charm quark plus the hghtest neutralino [ 2 ]. which can be regarded as the lightest SUSY particle (LSP). the signature of events will be the charm quark pa~r plus large missing momentum. This signature would resemble the charmed-hadron production in the two-photon process at e * e - colhders. Enomoto et al. have pointed out that the stop with mass about 15 GeV and the neutralino with mass about 13 GeV could well explain the experimental data.
I -'
E-mad address: d34477~jpnac.bimet. mtsk ~jpnkektr b=tnet. E-mail address: rra0OIc~.jpnrky00.btmct.
Else,,tcr Science Pubhsher~ B.V. .KSD!0370-2ht,~3( 93 IF 1405.M
It is natural to ask: "Have not such a light stop and neutralino already been excluded by LEP or Tevatron experiments?" and "Could such a hght stop be favored theoretically?" in this paper we examine the possibilit) for the existence of the light stop and the neutralino in the minimal supcrgravity G U T ( M S G U T ) scenario [ 5,6 ] taking into account the present experimental bounds on the SUSY parameter space. Here we consider onl) the bounds from collider data and do not conmder rather model dependent bounds from the proton decay' experiments and the dark matter searches.
2. Light stop: its theoredcal bases In the framework of the MSSM [ 7 ]. the stop mass matrix in the {IL. l'R ) basis is expressed by .~p
=
(
,,,+; \ a,m,
,~,m,
nil=
)
.
(i)
where m, is the top mass. The SUSY mass parameters m~m, and a, arc paramctrized in the following way [8l:
355
Volume 319. number 1.2.3 •
~
•
,,,'~ = .,~,,
•
PIIYSIC'S LI: I-rFR.',;B
23 Lk~cmber 19~3
•
+ .z:, cos 2,8 ( ! - i' sin"' O, ) + m;.
(2)
m,~ = mb~ + inC, cos2,gsin:O~ + roT.
(3)
a, = ..1~ + ~cot,8.
(4)
where tan,8.1~ and ..I, denote the ratio of t~,o Higgs vacuum expectation values ( = v:/t,~ ). the SUSY Higgs mass parameter and the trilinear coupling constant, respectively. The soft breaking masses of the th,rd generation doublet ~¢~ and the up-type singlet ~ht.~ squarks are related to those o f the first (and second) generation squarks as
and the corresponding mass eigenstates are expressed by
)
sinO, + .7~ cosO, ~ '
(9)
where 0, denotes the mixing angle of stops: tan Ot =
at mt
,n~,
- mi, "
(105
We see that ff the SUSY mass parameters and the top mass are of the same order o f magnitude, small m h is possible owing to the cancellation in the expressmn (8) [2,101
(s)
=
~,~., = ,~.,
-
16)
2t,
where I is a function proportional to the top quark Yukawa coupling ¢,, and is determined by the renorrealization group equations in the MSGUT. Throughout this paper we adopt the notation of ref. [9]. There are two origins for lightness of the stop compared to the other squarks and slcptons. ( t 5 smallness of the diagonal soft masses m,~ and nh~ and (ii) the left-right stop mixing. Both effects originate from the large Yukawa interaction of the top. The origin (i) can be easib seen from eqs. ( 2 ) - ( 6 5 . The diagonal mass parameters m,;t and m~ in eq. ( I ) h a v c possibly small values owing to the negati~ e large contributions o f / p r o p o r t i o n a l to ,~t in eqs. (51 and (6)• It should be noted that this c o n t n b u t m n is also important in the radmtive SU(2)~, LI(I ) breaking ,n the MSGUT. The Higgs mass squared has an expression simdar to eqs. 15) and (6). mh: = m~_, - 31.
(75
where rh~., denotes the soft breaking mass of first generation doublet slepton. The large contribution of I enables n~l, to become negative at an appropriate weak energy scale. In order to see another origin (n) we should diagnnalize the mass matrix { 15. The mass eigenvalues are obtained by --
+
i,
' .t50
+ ( 2 a : m , ) ' ] I -'}.
(8)
After the mass diagonahzatmn we can obtain the interactmn Lagrangian in terms of the mass eigenstate t'~. We note. m particular, that the stop coupling to the Z-boson (tli'~Z) depends sensitively on the mixing angle 0,. More specifically, it is proportional to
C'i, - i sm" 0u - .~cos" 0,.
(I I )
Note that for the s p e o a l value of 0r -,, 0.98. the Z boson couphng completely vanishes [ 3 ].
3. Present bounds on stop mass
Before a d,scusston of experimental bounds on the stop mass mi,, we examine the decay modes o f the stop. In the MSSM. the stop lighter than the other squarks and gluino can decay into the various final states t'l - - t 2 1 (a). bll'l ( b ) . b f b ( c ) . b v [ ( d ) , b W 2 1 (el. t , f f ' 2 t (f), c2t (g). where 21, fli, b and t'. respectively, denote the hghtest neutralino, the lighter chargmo, the sneutrino and the charged slepton. If we consider the hght stop with mass smaller than 20 GeV. the first five decay modes (a) to (e) are kinemat~cally forbidden due to the model independent lower mass bounds for the respective particles: rn, ;~ 90 GeV, mD~, ;~ 4 5 G e V . mi ;~ 4 5 G c V a n d m , ~ > 4 0 G e V . So If) and (g) are left. Hikasa and Kobayashi [2] have shown that the one-loop mode t'l ~ c~..t (g) dominates over the f o u r - M y mode ,;~ ~ b.f.f'2~ (f). This is absolutel.~ true in the case considered here. because the mode (f) is negligible b) the kinematical suppressmn, m 6 ",- m2, + m~,. So we can conclude that such a light stop will decay into the charm quark jet plus the missing momentum taken awa.~ by the
Volume 319. number 1.2.3
PHYSICS LEI'I-F.RS B
bounds, however, are invalidated if mo - m~.~ < 8 GeV. in addition, the mass bound mi~ ~ 37 GeV from the direct stop search by the DELPHI group at LEP is valid only for mi, - m2, > i 7 GeV [ 14 ]. Recentb Okada [i 5] has investigated possible bounds on masses of the stop and the neutralino from the exIxrimental data of the b ~ s7 decay. He has shown that the light stop with mass m h < 20 GeV has not been excluded by the data. After all. we can conclude that there ~s no bound on the stop mass for m,~, 10 GeV and 0, ;~ 0.6 ifm~, - m,~, < 8 GeV.
i .i
i
._,,
23 December 1993
. [El'
1 + ,
..,
. , ,
. . . . . .
°
Ftg. I. Excluded region in (Or. mi.) plane by LEP ~ath A/~ < 35.1 MeV.
neutralino with almost 100% branching ratio. Note that the width of stop in this cave is xer3' small, i.e., of the order of magnitude of eV. Naively. it will be expected that Tevatron a n d / o r LEP can set severe bounds on the stop mass through the processes .gg - - tt t; . c'72, 21 (Tevatron) a n d / o r Z --/'j/'~
4. Present bounds on gaugino parameters
In the MSSM. masses and mixing parameters of the gaugino-higgsino sector are determined b~ three parameters, ~. tan ,8 and M:, where M,, denotes the soft breaking S U ( 2 ) gaugino mass. Some regions in 1/,, tan ,8..*,!2) parameter space have already excluded by the negative searches for the SUSY particle's at some collider experiments. First, we consider the experimental data at LEP: (i) lower bound on the mass of lighter chargino, mih ;~ 45 GeV, (ii) upper bound on the branching ratio of the visible neutralino modes of the Z. B R ( Z - - vis.) - ~ ,., F ( Z - - 2 , 2 j ) / 1 " , , ~ i~/vI
< 5 × l0 -~ [18]. and (iii) upper bound on the invisible width of the Z . F { Z ~ 2,21) < 16.2 MeV [I 2]. In fig. 2 we show the region excluded by the experimental data ( i ) - { i i i ) in the (#. M 2 ) plane for tan,8 = 2. We also plot a contour of m,~, = 13 GeV which can explain the TRISTAN data as mentioned above. First we realize that the neutralino with mass 13 GcV can be allowed in the range - 1 6 0 GeV £ - I I 0 GeV for tan ,8 = 2. Note that the contour of m~, = 13 GeV lies in the excluded region for/~ > 0. If we take larger {smaller) values of tan ,8, the allowed region becomes narrower {wider). We find that the allowed region disappears for tan ,8 ;~ 2.3. Second ~e see that oh,: = 13 GeV corresponds to M , ~- 22 GeV in the allowed region and we can find that this correspondence is independent of the values of tan ,8. Con,~quently, we can take M: = 22 GeV as an input value in the follovdng calculation. The allowed region in the (1~, tan ,8) plane fixed by M: = 22 GeV is shown in fig. 3. Additional bounds on the (,u. tan,8) parameter space from the negative search for the neu357
Volume 319. number 1.2.3
PHYSI( .'S I.E VIERS B
23 rx"gx-mbcr1993
m i = .ll~ = "...! sm'OwAI2. _.
.~
.,
.
-
.
:
I
! ','"
i
[ 7 F-
in the M S G U T . the gluino mass m i bounds from the hadron collidcrs could be converted into the bounds on M : [ 16 ]. The gluino mass bound at C D F taken into account of the cascade decays ,~ ~ q~2:.~., and ~? -- udll].2 [17] as well as the direct deca) ,~ q ~ 2 f has been reported as [191
:
-,.
,
m i ~ 95GeV
.',
I •
!
].1 '( i~\'. Fig. 2. Contour of m 2. = 13 G e V m the ( p . M2 ) plane for tan B = 2. The excluded rcgaon b) LEP ns also depicted.
-.
"
I
Xl -22(;.\
• -.
"-"'~.':t't,i
. . . . . n,
rl't"x,.
.
.
.... .
.
~T . . . . .
:
vt~V----,r--~,
(90%C.L.)
t.
.
Fig. 3. Allowed revon nn the (/a. tanB) plane for . t / : = 22 GeV. The dashed Inneand the dotted hne correspond to the contourofBR(Z ~ vis.) = 5 x 10 -5 and that o f m ~ L = 45 GeV, respecllveb. tral Higgs boson at LEP will be discussed below. It us worth mentioning that the lightest neutralino 2, is almost the photino ~'. in the allowed parameter range in fig. 3. In fact, the photmo component of the neutralino is larger than 99% in the range. Next we should discuss bounds on the gauglno parameters from the hadron collider experiments. If we assume the G~'I" relation,
(13)
for p = -250 GeV and tanB = 2. This bound can easily be converted into the bound on M: by eq. ( ! 2 ) as M: ;~ 28 GeV. which rejects the above fixed value. M: = 22 GeV. (Note that the G U T relation (121 depends sensitively on sin: 0,. and ,,,. Here we take s i n : 0 w = 0.232 and n, = 0.113. ) We must consider, however, the fact that the bound 113) is obtained based on the assumption that m h > m i and the 81uino cannot decay into the stop. This is not the case we consider here. In fact• the gluino can decay into the stop pair. ~ - - ?~?~2t. which becomes another seed for the cascade decay. In fig. 4 we show the m i dependence of the branching ratio of 81uino. where we include the mode ~ - and sum up quark flavors q . q ' = u . d . c , s . W e t a k e t a n f l = 2,,u = - 1 5 0 G e V . mr, = 15 GeV. 0, = 0.7. m, = 135 GeV and .it: = 22 GcV. and take m i as a free parameter. The squark masses are taken as m# = 2 m i Ca) and m# = 3ink (b),where m # - m..LR = mdt., = m 6 . j = m h ~ . The arrow in the figure denotes the rni value determined by the G U T relation. The branching ratio of the direct decay mode .~ - - q ~ , . which is important in the search in terms of large ~'~ signature, is reduced substantially as BR(~ ~ q~ZT, ) < 50% (15%). even for the hght gluino w,th mass rni ;~ 60 GeV for rn~ = 2m i (m~ = 3 m i ) . Therefore. we should reconsider the UA2 bound n q ;~ 79 GeV [20] obtained under the assumption BR(,~ ~ qq.~,) .-- 100% as well as the CDF bound (13). For the v a l u e m i = 74 GeV determined by the GLIT relation. BR(~, ~ q ~ 2 ~ ) ,~ 20% ( 4 % ) f o r m 4 = 2 m i (mo = 3 m i ) . w h i c h should be compared with BR(,~ ~ q ~ ) -,- 70% obtained when there is no stop mode. We can find that if we take larger values of mo. BR(~ ~ q~2.~ ) is reduced rapidly. In this case the Tevatron bound (13) would Ix" d~minished s,gnificantly. This ,s because the width of the stop mode F ( ~ ~ ?~?72~ ) does not depend on
~,?~2,
. r.I
:.
358
(12)
.
.!
M 't ic\
. . . .
Volume 319. number 1.2.~
PHYSICS LETTERS B
23 December 1993 m;-m~M.)
mf-m~M:, I F ........ [ ......
"t t~
'
1 ............., '
'i
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L. . . . /
, L,-,-I~., !~.~..t-,.:t.;':'z.::~:.~:.;.~.,...~-*--.~,~
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q q ' ~ ' _. ~.:: .....................
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m~ IGcV I
Ftg. 4. m i dependence of the branchmg ratios of the glumo. The sum over quark flavors q . q ' = u . d , c . s Is taken. Input Darametcrs are tan// = 2. t~ = -150 GeV. m h = 15 GcV. 0t = 07. mt = 135 GeV..it'_, = 22 GcV and m# = 2rn i la) and m d = 3m k (b} The arro~ tn the figure denotes the m i value determined by the GUT relation. m# but all the other widths become smaller for larger values of rod. While all squark masses are independent parameters in the MSSM. they are d e t e r m i n e d by small n u m b e r s of input parameters in the M S G U T . Hereafter we adopt the G U T relation a n d will reconsider the T e v a t r o n b o u n d after presenting the results of the M S G U T analyses. Note that if we remove the G U T relation, the gluino can be hear,, with no relation with 312 and m 2 , a n d BR(,~ - - q~2.t) can be small.
t a n / / is not too large (<< m , / m ~ ) , which is the case we consider here, tan # < 2.3. As for the e v o l u t i o n o f t h e gauge couplings ¢,, (t) a n d the gauglno masses M , ( t ) . we take the input values , - I ( m , , ) = 128.8 a n d s i n ' 0 , . = 0.232. A s s u m i n g that the SUSY scale is not too different from r n z . we may use the SUSY beta function at all scales above m z for simplification. T h e n one finds M,. = 2.1 x 10 .6 GeV. ,~.l 1= a~ l ( M x ) = ~ T l ( M ~ .) = a ~ - I ( M ¢ ) ) = 24.6 and n 3 l m z ) = 0.113. Moreover. the R G E for gaugino masses are easily solved as M:,.
5. M S G U - r analysis Before presenting our results for analysis, we wtll s u m m a r i z e briefly the calculational scheme in the M S G U T [9]. In this scheme the i n d e p e n d e n t parameters, besides the gauge a n d Yukawa couplings, at G U T scale M r are the SUSY Higgs mass p a r a m e t e r u ( M r ) = l l x and three soft breaking mass parameters: the c o m m o n scalar mass th} ( M r ) = rh]h (.tit') =
m~.. the c o m m o n gaugino mass A t 3 ( M t . ) = = M l i A t . r ) = M.~ a n d the t r i h n e a r coupling A , ( . l t t . ) = .41,(M.t.) = ..It(.Ift.) . . . . . -|.-,c. As usual, we take the Higgs mixing parameter B as B(Mt.) = .4~. - r e x . All the physical parameters go from M.t do~'n to low energies governed by the r e n o r m a h z a t i o n group equattons ( R G E ) [6]. In the following we neglect all Y u k a w a couplings except for the top. This is not a bad a p p r o x i m a t i o n as long as M:(Mx)
M~(I) = ~h(t)--
(141
After solving all the other R G E for the physical parameters, all ph.~ sics at weak scale r n z are d e t e r m i n e d b.~ the six parameters (mo~..4,,, M : , , ~, t a n / / , m,). There are. moreover, two c o n d i t i o n s imposed on the parameters to have the correct scale of SU (2) × U ( 1 ) breaking. So we can reduce the n u m b e r of the independent parameters to four out of the six. Here we take the four i n d e p e n d e n t input parameters as ( M , . . g, t a n / / , m r ) . As we have discussed earlier, furthermore, we can fix one o f the input values. 3 t 2 = 22 GeV, which corresponds to M.,: = 26.7 GeV for sin: 0w = 0.232 (see eq. (14) ). Finally, only the three parameters (g, t a n / / , m,) remain. We seek numerical solutions to give a light stop with mass m?, ( = 13 G e V ) < m.,, < 20 GeV vaD4ng the three parameters (g, tan ,8. m t ). T h e results are shown in fig. 5, which is the same parameter space as in fig. 3. 35 c)
Volume 319. number I...3 •
PHYSICS I E I'IFRS B
2 .~,LXx:cmber 1993
Table I T)~,cal parameter
..~ |. ,-.a...,..... .....,...1.............. ,...~,.,. J~.~t~..! / :'
.,
"'Z
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r,
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.,
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¢
....
t..v.l
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,
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mt
22 2.09 -151 135
22 1.83 -94.0 117
22 2.0 -135 130
"'v~
•
;,
1"
;
."
M.,c mx .4 .,,. #x
26.7 125.0 332.0 132.8
26.7 84.0 207.8 -78.0
26.7 111.7 293.5 -116.7
mi~
14.6 201.9 0.9] 107.0 142.8 135.9 138.4 149.9 142.6 131.9 130.2 115.7 55.4 210.9 224.8 225.5 -0.56 13.1 48.2 159.0 187.3 45.0 184.5 74.4
15.0 183.5 0.85 93.4 108.8 10(3.7 103.4 116.6 108.2 92.9 q0.6 72.0 44.4 134.9 15q.0 156.8 - 0.69 13.3 54.7 107.3 142.2 53.7 138.6 74 4
15.5 196.4 0.89 102.0 131.2 124. I 126.7 138.6 131.0 119.0 I 17.2 101.7 52.6 189.0 205.2 205.2 - 0.59 13.2 50.5 143.6 174.2 47.2 171.0 74.4
:::..'
..~'.
"':'f;1
I"x7:
-41.'*'
,
• I
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F,g. 5. Stop mass contours ,n (u. tan#~ plane for fixed m~. Each hatched area corresponds to the region m 2 < ,hi, < 20 GeV. The upper (lower) hne of each area corresponds to mit = m2~ Imi~ = 20 GeV). We also plot the mass m h contours as well as the LEP bounds. Points denoted b.,, A. B and C correspond to I)plt~dl parameter sets m the text
mi, 0", m/,~ m/,: m~ t m,'.a mdt mda
.IlL Each hatched area corresponds to the region allowing m2t < mi, < 20 G e V for a fixed m, value. T h e upper (lower) line o f each area corresponds to m~, = m2, = 13 G e V (mi, = 20 G e V ) . We also plot the mass m , c o n t o u r s o f the lighter C P - c v e n neutral H~ggs boson as well as the LEP b o u n d s from the data discussed above. R r s t we realize that there is a rather narrow, but finite range allowfng the existence o f the light stop. if the top is slightly light too, m, < 135 GcV. Second we find that the light stop solutions inevitably g~ve a hght Higgs b o s o m m~ < 60 GeV. While we have included the r a d i a u v e correction in the calculation of the Higgs mass [21 ], d e v i a t i o n s ,6m, from the tree level results are not so large. :~-o, < 2 GeV. The neutral Higgs is standard Higgs like. i.e.. s i n ( / / - , ) ~_ I, where ¢, denotes the Higgs mixing angle [221- A result from the negative searches for the M S S M Higgs at LEP could set a n o t h e r constraint on the S U S Y p a r a m e t e r space ,n fig. 5. W h d e the present h m i t on the M S S M Higgs mass is m , ;~ 5 0 G e V
(95%C.L.)
{15)
for sin(,8 - ,,) "- I [231. this is o b t a i n e d based upon the a s s u m p t i o n that the Higgs do not decay into the stop. We can find. in fact. that the neutral Higgs could have a d o m i n a n t decay m o d e h - - it/'7 with almost 100% branching ratio as we will discuss below, in this 3h()
GeV
B
.W: tan B
-
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, Q'.)"
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sets.
ml m
m; m~ m.4 rnt/ m/t.
,, m21 m2:
m/~ nz2,
rn~l, ma: mk
case energ,es o f visible jets from the Higgs production would b e c o m e softer and it can be smaller than the detection lower cuts. Therefore. if we incorporate such a decay m o d e m data analyses, the present lower b o u n d s gall be weakened significantly. Here we ass u m e a c o n s e ~ ' a h v e b o u n d mh ~ 45 GeV. Note that this is a c o m p l e t e l ) tentative assumption. The exact regaons " e x c l u d e d " are unclear, because we have to perform a detailed M o n t e Carlo analyses o f the LEP data including the exotic decay m o d e h ~ t') ~ in order to obtain the exact excluded regions. A d o p t i n g the b o u n d mh ~ 45 G e V . we can choose three typical parameter wets A, B and C. d e n o t e d in fig. 5. The set A
Volume 319. number 1.2.3
PH~ SICS I.EIITRS B
( B )gtves the largest (smallest) scalar fermion masses and the smallest (largest) lighter chargino mass. The set C corresponds almost to the center point m the allowed range. Input and output values of the parameters o f t h e sets A. B and C are presented in table I. We find that masses and mixing parameters are severely constrained, for example, ma., ,< 55 GeV, 90 GeV < m; < 130GeV. 100GeV < m 4 < 150GeV a n d 0 . 8 5 < 0, < 0.95. Note that only the upper limits on ma, and the lower limits on m/, n:~ and 0, depend on the tentatnve assumption m~ ;~ 45 GeV.
6. Phenomenologtcal implications Now. we are in positxon to &seuss some consequence of the hght stop scenario in the M S G t l T and give strategtes to confirm or reject such a possxbility in present and future expernmcnts. Some numerical results are calculated with the t.sptcal parameter sets A, B and C. The existence of a light stop wtth mass 15-20 GeV will completely alter the decay patterns of some ordinars and St.:SY particles (sparticles). First we discuss the top decay [ 11.24 ]. In our scenario, the top can decay into final states including the stop: t ~ lrn~.t. ?~2: and t'~.~. Branching ratnos of the top for the typical parameter sets are presented in table 2. We find that the gluino mode t - - ?nob has 40-50% branching ratio and dominates over the standard mode t + b l i "÷ in almost the whole allowed parameter region. Strategies for the top search at Tcvatron would be forced to change because the leptomc branching ratios of the top would be reduced b.~ the dominance of the stopgluino mode. The decay patterns of the H~ggs parttcles will be changed too. The lighter C P . e v e n neutral Hnggs decays dominantly into the stop pair. h - t'u?~, owing Table 2 Branching ratios of top. ~X t -- in2] ';'t~." t'n.~ bll'*
0.060 0.030 0.524 0.386
B
C
0.0q6 0. I 18 0.410 0.376
0.068 0.039 0 500 0.393
23 December Iqq3
to the large Yukawa coupling of the top. In rough estimation, we obtain
I BR(h~?l~)~
i + 3 m h m j ..~n b.~2 4 -~ I.
(16)
This fact would change the experimental methods o f the Higgs searches at the present and future collider experiments. More detailed analyses of the charged [25] and neutral Higgs bosons are presented separately. Now we briefly, discuss the light stop impact on the spanicle decays. The lightest charged sparticle apart from the stop is the lighter chargino tl]. The two body stop mode It'~ - • b,~ would dominate over the convenuonal three body mode fl'~ ~ f ~ 2 n . As a consequence, it would be difficult to use the leptonic signature m the chargino march at e + e - and hadron colhders. Smce the chargino II~. the neutral Higgs h and the gluino ~,. whose dominant decay modes are respecw.'el:, fl'l -" M , . h - - ?~?T and ~ ~ ?~?~2n, are copiously produced nn the other sparticle decays, many stops would be expected m the final states of the sparticle production. For example, fL " I,l.l"t .. v ( b ? t ) .
~.,R
" q g - - q ( ~ ? ~ 2 ~ ), qt ~ q'W~ - q'(b?n) and 2,,,¢t~ ~ 2 t h ~ 2 t ( i t t [ ) . Note that the d o m m a n t
decay modes of the right-handed slcptons would be unchanged, i.e.. BR(/'R - - t 2 , ) -.- 100%. Needless to sa.,,, all experimental groups, AMY, T O P A Z and VENUS. at TRISTAN should perform a detailed data analyses to confirm or reject the exciting scenario. Furthermore. we can see that the stop and ~ts relatively light accompaniments, the gluino ~. light neutralinos 2t.:, and neutral Higgs h, should be visible at LEP. SLC, HERA and Tevatron. Espectall.~, LEP could search the allowed region presented in figs. 1 and 5 in terms of the width of Z-boson and the direct stop search. First we find from table 1. that the stop mixing angle 0, is severely limited as 0.85 < 0, ~< 0.95 in the allowed range in fig. 5. It should be noted that the lower bound depends on the tentative assumption mh > 45 GeV. A larger (smaller) lower limit on m, gives a slightly narrower (wider) range of 0,. On the other hand. the upper bound on 0t is determined by the estabi,shed limit rna., ~ 45 GeV. It is interesting that 0, _-. 0.9 is not input but output of the M S G U T calculation. As the stop search in terms o f A F / w o u l d be difficult in this case. the direct search for e +e - • tt ?; will be important [ 141. We
~61
Volume 319. number 1.2.3
PHYSI('~ I.E'i I ERS B
Table 3 Branchin8 ratios of glumo.
k _
q~2t q~ ~.., q~Tfl. ~t i:~~'.j
experimental upper limits. Note again that the light
stop and neutralino can sur'v~ve even after the negaA
B
C
0.252 0.023 0.089 0.636
0.489 0.011 0.042 0.458
0.332 0.020 0.085 0.563
find. in fact, that the stop contribution F ( Z ~ ~?~) to AFz is larger than about 0.2 MeV for O, < 0.95 and m/. < 20 GeV. Second, the whole allowed region m fig. 5 can be explored b.,, the precise measurement of B R ( Z ~ ,,'is.). In fact, the smallest value of the neutralino contribution ~ ,., F ( Z ~ ~,~..j)/F,J °t ~atgl
to B R t Z - - vis.) is 1.1 ', l0 * (I.8 × l0 -~) for mh > 45 GeV ( m , > 50 GeV). Of course, the Htggs h search at LEP with the stop signature h - - i~i;; is veD' ~mportant to set a further constraint on the allowed region. C l e a r b . the lighter ehargmo, ma., < 55 GeV. would be visible at LEPII. Furthermore, there is a possibility that some sleptons will be discovered at v~ < 200 GeV. As mentioned before. Tevatron will play a crucial role in confirming or rejecting the light stop scenario m the MSGLIT with the G U T relation. In this case the existence of relatively light glumo, m i x 75 GeV. with substantially large decay fraction ,~ -- ~:~i'r~'.~ is one of definite prediction. Values of branching ratios of the gluino for the typical parameter sets A. B and C are tabulated in table 3. The branching ratio of the direct decay mode B R ( ~ - q~..~) = 25 .,. 50% is expected in the allowed range. These values are rather large compared to those in fig. 4b. This originates from the fact that the allowed mass values o f ~ u a r k s except for the heavier stop t'., are relatively small, m4 < 150 GeV. Those squarks could be within reach of Tevatron. S~gnatures of those squarks, however, would be unusual because of their cascade decays such as qt.~ -" q g - - q(~r ~ ' ~ ) and ~. - - q ' l | ] ~ q'(I,t~ ). Anyway. there ~s a large possibility that some regions could have been excluded b.~ Tevatron data. Detailed Monte Carlo studies including the stop mode .~ - . t't t'; 2~ are required at any cost. At least we expect that the region near the point corresponding to the set B could have been excluded because BR(£, - - q ~ ) ~ould be large enough to make the ~'t s,gnal events larger than ,is 3~,2
23 December 1993
tive search for the gluino and squarks at Tevatron if we remove the G U T relation (I 2). Removal of the G U T relation corresponds to the change o f boundary conditions on the soft gaugino masses at the unificatmn scale Mx. Owing to this change the RGE solution for the stop mass is modified and in turn we will get a d~fferent allowed parameter region from fig. 5. The analyses based on such models will be presented elsewhere. The e p collider HERA could search the light stop through its pair production process e p ~ e ~ t ~ X via boson-gluon fusion [26J. The total cross section of the process is larger than about 10 pb for ml~ ~< 20 GeV, which is independent on the mixing angle 0,. That is. o ;~ I 0 pb is expected for all parameters with m h < 20 GeV in the allowed range in figs. I and 5. Detailed analyses with Monte Carlo studies including possible dominant background process e p ~ e c ? X can be found in ref. [27]. The process e p - - eil~[.~t" is useful to confirm or reject the ve~. light stop. but not too effective in determining model parameters in the MSSM such as the other sparticle masses as well as 0t. We have calculated another process.
ep
• b~b.~'.
(17)
~,hzch is expected to be useful for the latter purpose because the cross section depends on m a , . m~. O, and the mix,ng angles of Ill. The total cross sectmn is obtained as 1.4 ~ 10 -3 pb for the set A and 2.0 × 1 0 - : pb for the set B. Although these values are rather small and a high luminosity ~,ould be needed to see. sensitivity on the SUSY parameters is rather high. Here a comment on the R-pant,, breaking coupl,ngs of the stop may be in order. We have calculated not only the R-conserving process e p ~ ei~ t'~X but also the R-breaking process e p ---* ( i j ) ~ e q X in refs. [27.28]. The latter process could have a distinctive s~gnature, i.e.. a sharp peak in the Bjorken parameter x distribution. In our scenario o f a veD' light stop. however, the strength of the R-parity (and lepton number) breaking coupling of the stop d e f n e d in the superpotentlai 129]. Ii" = 2'13tLiQ3D ~,
(18)
Volume 319. number 1.2.3
f" ....
' . . . . . . . .
$:-~
PHYSICS LEFFERS B
....
~::;.."7-".~.
""
" "
tl
// , [
,
'
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."
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""1
.¢
''r
6. Another important property is that .4L~ is independent on the mass of stop mi, as well as on the Q C D c o r r e c t t o n J O c o since ,8,), and I + JOco dlsappeared in the fractional combination of o in AiR. "I'hereforc, this method for mcasuring 0~ will be applicablc for the stop w H h any' mass satisfying mi, < ~ / 2 .
I
7.
F~g. 6. Total encrg) v'~ dependence of left-right asymmct~ for the stop productton at e + e - colhders. For comparison we also plot .4LR for the up-t)pe quark production. cannot be large enough for possible detection at HERA. This ~s because the coupling {18) with 2't~t > 10 -~ makes the R-breaking stop decay mode/'t ~ ed dominant and thts fact contradicts BR{~:t - - c 2 t ) 100% expected at TRISTAN. Polarized imtial electron beams at SLC and at any l i n e a r e * e colliders will be efficient to reveal the nature of left-right mixing m the stop sector, in other words, to measure the mixing angle o f s t o p 0t. In fig. 6 we show the ~,~ dependence of the left-right as~,mmerry. •-tL~ --
o(~.)
-
aIeR) (19)
O'(eL) + a ( e a ) "
where ale1 R) - O(e~'el'~R - - l l l ' ; I . ~hich are obtained by'
It
+
=
,,
23 l.k~zcmber 1993
+ i ( ' f ~T', .¢. a~
:"'1Re ),
(')
{I + f ~ - D I .
(20)
where ,8i, -- v / l - 4m~,is. Dz - s - ,n~ + i m z F z . v, - ( ~ + 2sin2OL¢ )/(sinZOj~ c o s : O . ) and a, = I / ( 2 s m 20w cos 2 8 w ) . In the asymmetric combination in eq. (19) the photon c o n t r i b u t i o n is cancelled out and ..h.K ,s p r o p o r t i o n a l to ('fl ( I I ). This is thc reason for senslt,ve dependence on 0, o f .4,.k in fig.
Conclusion
We have investigated the possibihty of the existence of the light stop ,m, = 15-20 GeV and the ncutralino m2, _-2 13 GeV in the M S G U T scenario taking into account of the present experimental bounds on the SUSY parameter space. We have pointed out that the existence of such a stop could change the dominant decay mode of some panicles. For example, the stop modes .~ - - i~/'; ~.~ and h - . / ' l / ' ; could dominate over respect,rely the conventional modes ~ ~ q ~ 2 , and h - - bh even for relatively light gluino and Higgs. As a consequence, present experimcntal bounds on the SUSY parameter space could be weakened considerably. It seems that there is a finite parameter region allowing the existence of such a light stop even if we consider the present experimental data. Inversely. if such a light stop is discovered at TRISTAN. masses and mixing parameters of the other SUSY partners as well as masses of the Higgs and thc top will be severely constra,ned, for example. - t i "" 75 GeV, ma, £ 55 GeV. 90 GeV ,< mt ~< 130 GeV. 100 GeV _% m# ~< 150 GeV, 0.85 < 0, < 0.95, mh ~< 60 GeV and 115 GcV < rn, < 135 GeV. Actually, the light stop and its relatively, light accompaniments, the gluino .~. the light ncutralinos ~L:. and the neutral Higgs h, should be v~s~ble in the near future at LEP. HER,-% and Tevatron. In fact, LEP and HERA could explore the whole allowed parameter region in terms of the precise measurement of the width of Z and by means o f searching for the process ep ~ eft ~.lf. respectively. There exists, moreover, special interest m a Tevatron experiment, i.e.. Tevatron could either discover or exclude the light gluino m i "" 75 GeV. If we could not discover such a gluino, this fact would indicate invalidity of the G U T relatton, tn other words, the assumption of the common gaugmo mass at Mr.. Experimental sign for violation of the G U T relat,on may be ,mportant to select a specific model out o f a great number of string model candidates. 363
Volume 319. number 1.2.3
PHYSI( ,'S LETI'I-RS B
Recently,, Altarelh et al. [30] haxe shown that a light stop mi, ~< 50 G e V and a light chargino m~. < 60 G e V could well explain the precision data at LEP. "l'he~r result seems to support our light stop scenario. In this paper we have e x e m p l i f i e d that f f w e d i s c o v e r the hght stop we wdl be able to constrain severely all the S U S Y parameters at the unification scale. We can conclude that, therefore, the discovery,' o f the stop will bring us a great physical impact. Not only will it be the first signature o f the top flavor and supersymmetr3' but it could shed a light on the physics at the unification scale as well.
Acknowledgement O n e o f the authors ~T.K. ) would like to thank Drs. R. E n o m o t o and M. Pieri for valuable i n f o r m a t i o n .
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