- Email: [email protected]
Discovery limit of the charged Higgs boson via top quark decay at future hadron colliders
Physics Letters B 283 (1992) 403-410 Non.h-Holland
P H Y S I C S LETTERS B
Discovery limit of the charged Higgs boson via top quark decay at future hadron colliders D.P. R o y J Theoretical Phvsws Division, ('ERN, Ctl- 1211 Geneva 23. Switzerland Received 8 November 1991
We study the kinematic cuts which can be used to enhance the charged Higgs signal over the W boson background, for mH- > row, in the decay of a heavy top quark at LHC energy. With suitable cuts it is possible to ensure a sizeable signal and a signal-tobackground ratio > 1 up to mH_. -~ nt~- 20 GeV, which hold throughout the allowed coupling parameter (tan 1~) space in the minimal SUSY model. Thus one should be able to search for the charged Higgs boson to within 20 GcV of the parent top quark mass at the LHC/SSC collidcrs, i.e., up to 130 GeV tbr m~ -~ 150 GeV. going up to 180 GeV for m, -~ 200 GeV.
The results of the top search experiment at the Tevatron 10p collider [ 1 ] as well as the Bo-13d mixing data [ 2 ] suggest a heavy top quark of mass mt > 80 GeV. Moreover, the radiative correction to the W, Z masses suggests a central value of top quark mass mt_~ 150 GcV with an upper bound of about 200 GeV [ 3 ]. A top quark in this mass range is expected to be seen at the Tevatron upgrade and produced more copiously at the LHC/SSC colliders [4]. Besides providing direct evidence for top, this will enable one to search for new particles in the top quark decay; the large top quark mass offers the possibility of carrying on the search to a hitherto unexplored mass range. There has been a great deal of recent interest in the search for one such new particle, i.e., the charged Higgs boson [5,6] of the two-Higgs-doublet version of the standard model [7]. In particular it was shown in ref. [6] that for m~-~ 150 GeV a systematic comparison of the top signal in different decay channels provides an effective signature for charged Higgs bosons up to a mass of mH = 100 GeV at the Tcvatron upgrade. For the theoretically most attractive two-Higgs-doublet model of MSSM (minimal supersymmetric standard model) one expects an observable signal throughout the allowed coupling parameter space. Thus one can probe the charged Higgs mass up to about 100 GcV On sabbatical leave from the Tata Institute of Fundamental Research, Bombay 400005, India.
unambiguously for this model. This is already larger than the charged Higgs discovery limit of 80-90 GeV at LEP-II [8,9]. However, it is not large enough considering the theoretical expectation of mt~ > m w in MSSM [ 7 ]. It should be mentioned here that, unlike the neutral Higgs mass, the charged Higgs mass has little sensitivity to the radiative correction from the heavy top quark, so that this tree-level bound remains valid for most of the parameter space [9]. In view of the above discussion it is important to devise means of extending the charged Higgs probe beyond 100 GeV without restricting ourselves to specific corners of the coupling parameter space. This is of course not possible at the Tevatron upgrade, where both the signal size and the signal/background ratio were seen to become marginal in the region of the coupling parameter tan flu \,/mt/m, [6]. However, one expects a much larger size of the signal at LHC/ SSC due to the larger tt cross-section and luminosity. For m . > 100 GeV. the increasing gap between the charged Higgs and W boson masses offers the possibility of enhancing the signal/background ratio by suitable kinematic cuts. As we shall see in this note, it is possible to exploit the above two features to devise a viable charged Higgs signature which holds up to m H = m , - 2 0 GeV and throughout the allowed coupling parameter space of MSSM. Thus it seems possible to probe for the charged Higgs mass to within 20 GeV of the top quark mass at these future hadron
0370-2693/92/$ 05.00 (C) 1992 Elsevier Science Publishers B.V. All rights reserved.
403
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colliders, i.e., up to 130 GeV for m, -~ 150 GeV. going up to 180 GeV for m, -- 200 GeV. This represents an important discovery, limit, as it seems impossible to probe the region m u > m ~ + m b at hadron colliders [10]. The essential features of the two-Higgs-doublet model are as follows. It contains two SU (2) doublets of complex scalar fields
OcJko°J" with vacuum expectation values (VEVs) < ¢;? > = v~ Iv,'2,
( 0 2<,)
=v,/\./2~
(1)
which satisfy the W mass constraint v{+v~=v 2
(v=246GeV).
(2)
This leaves one free parameter, i.e., the ratio of the two VEVS tan,8= v2/v..
(3)
After absorbing the three Goldstone bosons one is left with five physical states - the neutral scalars h °, H ° and pseudoscalar A ° along with the charged states H We shall be concerned only with the charged states, i.e., H -~= ¢ ~ c0s,8-0¢- sin ft.
(4)
The two-Higgs-doublet model represents a minimal extension of the standard model which automatically satisfies the constraint of p= I at the tree level. Furthermore, the absence of flavour changing neutral current at the tree level can be naturally ensured via the Glasgow-Weinberg theorem [ 11 ], which states that the tree-level FCNC mediated by Higgs bosons will be absent if all the fermions of the same electric charge have Yukawa couplings to only one Higgs doublet. A very important model automatically satisfying this constraint is the minimal supersymmetric extension of the standard model (MSSM), where the up-type quarks have Yukawa couplings to one Higgs doublet (¢~2, say) while the down-type quarks and charged leptons couple to the other. This model has received wide attention as it provides the most economical solution to the hierarchy problem of the standard model. Moreover, it offers the possibility of explaining the observed quark mass hierarchy rnc >> m~ and m, >> mb in terms of that of the VEVs 404
11 June 1992
v2 >> v~. In this model, the Yukawa couplings of the physical charged Higgs field of eq. (4) to fermions are given by S=
g
H + (cotfl
\ '2 iV/w
v,/nu, a,d~L
+ tan B ~,j m,~tzi,6. + tan [3 rn~,~j R ) +h.c.,
(5)
where I~, are the KM matrix elements. One has identical charged Higgs couplings to the fermions in the E0 superstring-inspired model [12] as well; but this model gives a less restrictive mass bound (ran> 53 GeV) than the MSSM. We shall concentrate on the above coupling scheme ofeq. (5) in view ofthe wide theoretical interest behind the underlying models. Besides, as shown in ref. [6], it is only for this coupling scheme that one can ensure an observable charged Higgs signal throughout the allowed range of the coupling parameter tan ft. This range is summarized below [ 13 ]. The validity of perturbation theory implies upper bounds on the charged Higgs-fermion couplings appearing in eq. (5). Requiring the tbH ÷ coupling in the first term to be bounded by the strong coupling constant 4na~( -- 1.5 ) gives a lower bound on tan/3, i.e,, tan/3> m,/600 GeV ( -,- ] ).
(6)
The size of this coupling can also be constrained by the charged Higgs exchange contributions to Bd--f3d mixing, b--*sv decay and CP violation in K decay [ 13 ]. They give a slightly better bound tan J3> 0.4
(7)
for m, ~ 150 GeV and mu ~ 100 GeV. The perturbative limit on the tbH ÷ coupling appearing in the second term ofeq. (5) gives the upper bound tan ,8<600 GeV/m~,( -~ 120) .
(8)
Thus the region of interest in the coupling parameter space is 0 . 4 < t a n / 3 < 120.
(9)
While the lower hound holds for any two-Higgs-douhlet model, the upper hound is specific to those where the up- and down-type quarks have Yukawa cou-
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plings to separate Higgs doublets like the MSSM ~ It should be remarked here that we have adopted the most general definition of MSSM implying only the minimal particle content [7]. The most predictive form of this model, characterized by minimal set of SUSY breaking parameters at the grand unification point, leads to a more restrictive range of the coupling parameter [ 15 ] 1
(10)
However, we shall consider the more general range of the coupling parameter space given by eq. (9) above. In any case the most unfavourable region of this parameter space for the charged Higgs signal (tan fl~ v"mJmb) occurs in the middle of the range (10), as we shall see below. The size of the charged Higgs signal versus the W boson background in top quark decay is controlled by the relative decay widths of t - , b H + and t--+bW +. In the diagonal KM matrix approximation one gets, from eq. ( 5 ),
g2 ?j 64nm~,m 2 I/2 ( 1 rn-{'m~" m H
Ft .bil,
× [(m~ cot-'fl+ mb tan2/3) (m~ +rap, --m~.) +4m~m~,l ,
(11)
and the corresponding decay width into the W boson is F~ .t,w+
--
g-+
, 64rem~.,m,
2 ~/2
(
1,
,nb ,n~,,']
m,v , m~ ]
X[m~.,(mp +m~,)+(mp-m~)'--2m~.,].
(12)
Thus one gets the branching fraction B(t--+bH+ ) = G .b.+ / (Ft-b.+ +Ft ,bW+ ) .
(13)
From eq. (5) one can also calculate the two significant charged Higgs decay widths, i.e., m~ tan~+/3, ~g-mH + , 32re'n+,,
/~H+
+,~,
F.+
.,.,- 32trm~,,
,+, - -
3g'-m. (m~.cot'-fl+m~" tan:fl)
(14)
'
(15)
and the branching fraction ~k Thereare no more constraints on this parameter from the LEP data once the radiativecorrectionsare taken into account [ 14].
1I June 1992
B ( H + - , T + v ) = m ~ tan2fl/3(m~ cot-'fl+ms tan-+fl) + m ~ tan2fl.
(16)
The effect of the QCD correction has been analyzed in detail by Drces and Roy [ 6 ] following the formalism of ref. [ 16 ]. The most significant effect comes from the H + -+cg decay width. In the leading log approximation the QCD correction can be simply implemented by replacing the quark mass terms appearing in the width of eq. (15), or equivalently in the Yukawa couplings ofeq. (5), by the running mass
( l n ( 2 m d A ) ~l+-,,( ~3- 2,.,, ~q(mH) =mq \ In(re.~,! ) ]
(17)
where one has assumed the standard initial condition [16]
p~q(2mq) = m,~ .
( 18 )
The initial values are chosen to be m,.= 1.5 GeV and ms= 0.2 GeV. The quantity of phenomenological interest is of course the resulting branching fraction of eq. ( 16 ), which is clearly insensitive to m,. The corresponding branching fractions for W decay are of course given by the universality of W coupling to leptons and quarks, i.e., 10% into each lepton pair and 70% into hadrons (including the small QCD enhancement of hadronic width by ~ 4%). The striking difference between the two sets of branching fractions makes it possible to separate the charged Higgs and W contributions by comparing the relative size of the ti signal in different decay channels [6]. Like W, the charged Higgs has also to be identified through its leptonic (i.e., t) decay to avoid the large QCD background. Thus it is the product of the two branching fractions (13) and ( 16 ) that controls the size of the charged Higgs signal. These two branching fractions are shown in fig. 1 against the coupling parameter tan ft. The branching fraction for charged Higgs production t--+bH is shown for m~ = 150 GeV (mH = 110, 130 GeV) and m~ = 200 GeV ( m . = 160, 180 GeV), while the H - , w decay branching fraction is practically independent of m , . The t--+bH branching fraction becomes veD' small around t a n f l - (mt/mb)~/2~6 where eq. (11) has a minimum. This partly compensated by the maximal 405
Volume 283. number 3.4 10
.
PHYSICS LETTERS B
.
.
.
.
.
!
" ""
- -
B(I
,bH),mt=150,
.....
B(t--~bH),m t=200'm
production through gluon-gluon or q u a r k - a n t i q u a r k fusion followed by their decay into charged Higgs or W boson channels ( t - , b H , b W ) , i.e.,
11
m H = 110,130 H = 160,180
......... B ( H ~ Iv) 1 •
ggorqCl-*t[--*bb(H÷H - H'W',W+W
.."
0.1
- ).
(19)
Here the first two terms in the parentheses represent the charged Higgs signal and the third one the W background. This is followed by the charged boson decays
",
/
H ,zv,
"
"
"
H--,c~,,
(20a,b)
with the branching fractions o f e q . (16), and
//
0.01
1I June 1992
W J L ev, p_v, zv,
"
W _~o~ q?t' •
(21a,b)
Finally, the z is to be observed in its muonic or hadtonic decay channel I 8%
1
0.1
1
10
100
Tan I~ Fig. I. Branching fractions for t .bH for m,= 150 GeV with m,=ll0 and 130 GeV (solid upper and lower lines), and m,=200 GeV with mR= 160 and 180 GcV (dashed upper and lower lines ). The branching fraction of charged Higgs deca.~ into ~ lepton is shown b.', the dotted line. The allowed range of tan f l ( ~ 0 . 4 ) is indicated by the hatched ]inc.
value o f the H -.zv branching fraction in this region. As remarked in ref. [6 ], this c o m p e n s a t i o n mechanism is typical o f the coupling scheme o f e q . ( 5 ) and ensures a viable charged Higgs signal throughout the allowed tan fl space in this scheme for m . ~ m w . However, the c o m p e n s a t i o n is no longer adequate as nh~ *m~. For instance, in the extreme case of m~ = 200 GeV ( m n = 180 GeV ) one sees that the s i g n a l / b a c k ground ratio for the z channel is only ~ 2% a r o u n d tan fl-~ 6. For the 2~ channel, corresponding to ~-decay of both t and t. one gains a c o m b i n a t o r i a l factor o f 2 raising this ratio to ~ 4%. Thus one needs a background rejection factor o f ~ 25 from kinematic cuts to have a viable charged Higgs signal in this region. We shall see below that it is indeed possible to devise such kinematic cuts and ensure a s i g n a l / b a c k g r o u n d ratio > I as well as a sizeable signal throughout the allowed tan fl space. The charged Higgs signal and the W boson background are estimated using a parton level event generator program. The basic process o f interest is tt 406
"c--.v,v,p.
64%
z--,v,q~l',
(22a,b)
as a soft muon or a narrow jet (r-jet), a c c o m p a n i e d by a significant amount o f missingpw. We shall largely concentrate on the hadronic decay channel o f "r and refer to it simply as the r-channel. The t[ signal in the hard dilepton channel t[--,bbW+W--,bl~+';,~ v
(~=e,~)
(23)
(with p ~ > 2 0 GeV, say) can be used to normalize the W ~ W - contribution since the charged Higgs does not contribute to this channel. Then the W + W background in any other channel is predicted by universality [cqs. (21), ( 2 2 ) ] . A sizeable excess over this prediction will constitute a charged Higgs signal. whose magnitude is also predicted by eqs. ( 13 ) and (14). Thus the uncertainties associated with the tt production are effectively factored out. One can scc from fig. 1 that the predicted W + W - contribution to an,,' channel would d e p e n d on mH and tan [3: the maximal value obtained at tan/3~ 6 corresponds to the standard model prediction (see figs. 3 and 4). However, this dependence drops out when normalized with respect to the hard dilepton channel "-' The results presented below are obtained using the '-" The obser',ation of a ti signal in the hard dilepton channel below the level of standard model prediction is in principle indicative of a charged Higgs boson. But it cannot be used in practice because of the uncerlaint.~ in the production crosssection.
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structure functions and c~,of refl [ 17 ]. We have also cross-checked them by using the corresponding Q C D parameters ofref. [ 18] "3. There is essentially no difference apart from a drop of overall normalization by a factor of ~ 2, mainly due to a,. The normalization has of course no effect on the relative size of the signal in different channels as m e n t i o n e d above. For the same reason one expects the result to bc insensitive to higher-order Q C D corrections. We concentrate below on the most viable channels for the charged Higgs signal and the LHC energy of,v"s= 16 TeV. 2r channel. It corresponds to "c decay of both the charged bosons of (19) followed by hadronic decay o f t (22b). We have chosen a m i n i m a l set of cuts T p,_,,.~ > 10 GeV,
[.V~_j~.,I < 3 ,
1 Pmtss > 20 GeV,
(24)
which come by default. Similarly we have chosen a m i n i m a l isolation cut of a c c o m p a n y i n g Pr < 5 GeV within 0.4 rad of the x direction. They can be increased significantly without a drastic reduction in cross-section. For m, = 150 GeV, mH = 130 GeV one has a 30% reduction in the signal cross-section from increasing each p~.,~., cut to 30 GeV and a similar reduction from increasing the missingp T cut to 50 GeV. For ,n, = 200 GeV. mH = 180 GeV the corresponding reductions are ~ 20% each. In each case of course the reduction to the background is larger. Thus increasing the z-jet and m i s s i n g p r cuts to more realistic values would improve the signal/background ratio at the cost of a moderate loss to the signal size '4. This channel offers the best s i g n a l / b a c k g r o u n d ratio because (i) the signal gets c o n t r i b u t i o n s from both HH and HW terms and (ii) the latter is enhanced by a combinatorial factor of 2. The disadvantage is that it is not possible to reconstruct the charged boson masses because of the large n u m b e r of neutrinos. Nonetheless one can separate the signal from the background by exploiting the fact that as mH-~m, the accompa,3 This set of structure functions was accessed via The structure function packagc [19]. ,,s The 2x background from Drcll-Yan and Z alcoa', can be readily distinguished by its azimuthally back-to-back configuration. no missingp-r normal to this 2x axis and a relatively low invariant mass of the "tpair. Similarly the 2"t background from the bb decay can bc effectivelysuppressed by the p~ and isolation cuts.
I I June 1992
nying b-jet becomes soft. Thus the W W background of (19) has two hard accompanying jets while the signal has at least one soft jet. Fig. 2a shows the pT distribution of the hardest acc o m p a n y i n g jet for the signal and background events for the most unfavourable coupling parameter tan fl=6. For this choice the signal is d o m i n a t e d by the HW term and consequently the peak value of the accompanyingp]i is not very different from the W W background. Note, however, that, in the region p f < 30 GeV, the background is doubly suppressed by the probability of each accompanying jet becoming soft, while the signal is suppressed singly. Thus one can get a signal/background ratio ~_ 1 by ensuring that there is no accompanying b-jet with pV> 30 GeV "~. Fig. 3a shows the resulting signal and background over the allowed range of tan ,8 at the LHC energy. It shows a viable signal up to mH-~ m ~ - 2 0 GeV with a signal/ background ratio > 1 and a signal size > 10 lb. The latter corresponds to a m i n i m u m of 100(1000) events us Identification of the b-jet is not necessary, since one expects only a modest fraction of ti events to be accompanied by a QCD jet ofpT>30 GeV [201. Thus it is sufficient to ensure that there are no accompanyingjets ofp~> 30 GeV. 100
mt
/
".
• 50 ,~f----....
a)
"-.
ill Y
-q "
~"~
".,
-~//'-"
b)
:.
"',
°-r \
V
\ •/
....
WW
001 . . . . . . . . t 0 50
Bg
.......... 100 P/T,(GeV)
1 . . . . ,._ . 0 50 p;',GeV',
Fig. 2. The distribution of 2~ events in the transverse momentum of the accompanyingb-jets: (a) hardest jet and (b) second hardest jet. The normalizationsof the charged Higgssignal (solidlines) and the WW background (dashed lines) correspond to the most unfavourable value of tan fl ( =6 ). The upper and lower sets of curves correspond to m~= 150 GeV (mt~= 110. 130 GeV). and m, = 200 GeV ( mH= 160, 180 GeV ) respectivelyin this and the followingfigures. The energy is the LHC energyof x s= 16 TeV. 407
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105
.I
PHYSI('S LETTERS B
a) 2 t c h . ( p T < 3 0
T
n'ttl,n,,
i
b) 2 r c h . pT<20
pr
//
//
"
-'.
1
0.1
1
10
Tar~ ',~,
100
1
10
~00
Tan 3
Fig. 3. (a) The charged Higgs signal (solid line) and WW background (dolled line) for the 2t channel with a p T < 3 0 GeV cut on the hardest accompanyingjet. In each set of curves the lower solid ( u p p e r dashed) lines correspond to the higher Higgs mass. ( b ) Same as above with a p r < 20 (.ieV cut on lhc second hardest jet ( I0 < P]i < 20 G e V f o r the lower set o f curves ).
for an annual luminosity of 10(100) ~ - ~ , expected from the low (high) luminosity option o f LHC. Fig. 2b shows the pT distribution of the second hardest b-jet for the signal and background for tan if,=6. Although the background peaks at a significantly higher value o f pl r compared to the signal, there is a residual background left in the pjL = 0 region. This is due to the .jet folding algorithm which merges the b-jets emerging within an opening angle of ~ radian into one. This limits the background suppression potential of a low p~ cut. Fig. 3b shows the signal and background over the allowed tan fl range with p,L < 20 GeV. The lower set of curves is evaluated with 10
> 10 GeV.
r >20GeV. p .....
p~>20GeV,
[.l',.~_j~., I < 3 ,
:.-
]0
1 I June 1992
( 25 )
which have little effect on the cross-section. Supplementing this with the p , ~ < 3 0 GeV cut. we get the signal and background curves shown in fig. 4a. While the signal size remains viable throughout the allowed tan/? range, the signal/background ratio fails significantly below 1 in the neighbourhood of tan//-~6. Nonetheless the signal cross-section remains >/200 fb against a background of 800 Po for m, = 150 GeV. and i> 8 fb against a background ot"25 fb for m, = 200 GeV. The resulting numbers of signal and background events for an integrated luminosity of 10 fb ~ correspond to a figure of merit (N,.g/,,, "N~g ) of >/22 and 5 respectively. Thus it remains a viable channel for charged Higgs search up to m u = m , - 2 0 GeV. This is worth emphasizing, because the r plus hard u channel is by far the easiest to identify using the hard muon as a trigger. Besides it is free from the Drell-Yan and Z decay backgrounds. r + .sqti p chamwl. It corresponds to "[decay of both the charged bosons of (19) followed by the muonic decay of one ~ (22a). The smaller muonic branching fraction of r results in a smaller signal size compared to the 2r channel. Besides one has to include the soft 105
i
:
"
i
a) ': • hard p 104
rnt (rr'H)
. . . . . . . ' b) "[ • soft p
i
"
/1
~ 102
lo2!
10
1
v
0 1
.
1
.
10 Tan [:~
Fig. 4. The charged ground (dotted line) and (b) z+soft p(pr a p r < 30 GeV cut on
l
.
.
.
100
10
!00
Tan p,
Higgs signal (solid line) and WW backfor (a) 't+ hard p(pi > 20 GeV) channel =5-20 OeV) channel. In each case there is the hardest accompanying jet.
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la tail from the direct W - . p decay, which makes the s i g n a l / b a c k g r o u n d ratio somewhat smaller as well. The cuts used are pr,~, > 10 GeV.
104 ;.
103
n, >/2,
-
....
150 .........
:
,
.....
.....
200
.
~
V ~
......
T
,-
,-
Bg
~. t + multi.jet ch HW Sig j
"-, \
(26)
where the p [, cut is o p t i m i z e d to retain most the rdecay muons ( ~ 50%) while m i n i m i z i n g contamination from direct W decay ( ~ 10%). Supplementing this with the p~ < 30 GeV cut, we get the signal and background shown in fig. 4b. C o m p a r e d to the 2r channel o f fig. 3a, one sees a smaller signal size and signal-to-background ratio. Nonetheless it could be viable for charged Higgs search up to m , = m , - 20 GeV with the high luminosity option of L H C ( = 100 fb-'). r+ mult~jet channel. It corresponds to t decay of the charged bosons o f (19) and hadronic decay of the other. For t a n / / > 1, the s i g n a l / b a c k g r o u n d ratio is identical to the x + hard la channel, while the signal size is a factor o f 7 higher [eq. ( 2 1 ) ] . The m i n i m a l cuts are pr,~., > 10 GeV,
,
rot
i
p v...... > 20 GeV,
p~ = 5-20 G e V ,
11 June 1992
102 t-:.
~~
mt (mH)
'~
F'10 :
'
"~0
1 ~ _, ' ~_ ~. . . .' . . . . . 0
(160)
~
50
.
~ 100 Mtr (GeV)
_200(180) 150
200
Fig. 5. The distribution of the x+ multijet events in the transverse mass of the x-jet and the missing Pl system. The normalization of the charged Higgs signal (solid lines) and the WW background (dashed lines) shown corresponds to the most unfavourable value of tan ,b'=6.
i > 20 G e V , p .....
pll~._,> 40 GeV .
( 27 )
The d i s a d v a n t a g e of this channel, unlike the previous ones, is a significant background from W + Q C D jets even after the large p~r._, cut. The advantage is the absence o f neutrinos in the decay o f one of the two charged bosons. Thus one can reconstruct the W ( H ) mass from, e.g., the transverse mass o f the t-jet and missing-p-r system. Fig. 5 shows this transverse mass distribution o f the W H signal and the W W background for the most unfavourable value o f tan f l = 6 . The background gets kinematically cut off at the W boson mass. Although the effect o f resolution smearing is not shown, one can check that with a ~m,~= 10 GeV, less than 1% of thc b a c k g r o u n d spills over to the ,'v/~> 100 GeV region. This would ensure a sign a l / b a c k g r o u n d ratio > 1. With good b-jet identification one could also use the p r < 30 GcV cut on the b-jets for suppressing the W W background. On the other hand one may need an identified large Pl b-jet to control the background from W + Q C D jets. Therefore, we have not explored this possibility furthor. It is clear from fig. 5, however, that the t + multijet channel can give significant clues about the
charged Higgs mass from the tail o f the M,r distribution. It is therefore an i m p o r t a n t channel for the charged Higgs search, p r o v i d e d one can identify "t in a multijet environment. It is evident from the above analysis that good x-jet identification is crucial to charged Higgs search via top quark decay at hadron colliders. We have not assumed, however, measuremcnt of x charge or polarization. If polarization measurement is available, then one can also use the correlation between the "~charge and polarization to separate the charged Higgs signal from the W boson background as recently discussed in rcf. [21 ], since one expects xC ( ~ ) from W - , ' t v and zff. ( z ~ ) from H - , z v . O f course the polarization measurement may not reach the 2% accuracy required to probe through the full p a r a m e t e r space by itself. However, once the sample o f t events have been cnriched by, e.g., the p r < 30 GeV cut, one needs no more than 20% accuracy in the polarization measurement to confirm the charged Higgs signal. A quantitative analysis of this polarization effect is given in ref. [22]. In s u m m a r y , we have tried to explore the prospect o f charged Higgs search via top quark decay at L H C / 409
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S S C a n d i d e n t i f y t h e m o s t f a v o u r a b l e c h a n n e l a n d kin e m a t i c cut for t h i s p u r p o s e . T h e y are t h e 2"~ c h a n n e l ( f o l l o w e d by t h e "qa) a n d a p~ cut o n t h e a c c o m p a n y i n g b - q u a r k jets. t h e y p r o v i d e a s i z e a b l e c h a r g e d Higgs signal a n d a s i g n a l / b a c k g r o u n d r a t i o > 1 u p to m)~ --- m, - 20 G e V , w h i c h h o l d t h r o u g h o u t t h e all o w e d r a n g e o f c o u p l i n g p a r a m e t e r s in t h e M S S M . T h e c a l c u l a t i o n s are d o n e for L H C energy; b u t o f c o u r s e w h a t is t r u e for L H C is e v e n m o r e t r u e for SSC. T h u s for t h e M S S M t h e c h a r g e d Higgs m a s s c a n b e u n a m b i g u o u s l y e x p l o r e d to w i t h i n 20 G e V o f t h e t o p q u a r k m a s s - i.e., u p to 130 G e V for m,-~ 150 G e V , g o i n g u p to 180 G e V for m,--- 2 0 0 G e V . T h i s m e a n s t h a t a r e l a t i v e l y h e a v y t o p m a y b e b a d n e w s for t h e t o p q u a r k s e a r c h b u t a g o o d o n e for the c h a r g e d Higgs boson. It is a p l e a s u r e to t h a n k Dr. G, Altarelli, Dr. H. H a b e r , Dr. B. G r z a d k o w s k i , Dr. Z. K u n s z t , Dr. F. P a u s s a n d Dr. F. Z w i r n e r for d i s c u s s i o n s a n d R . M . G o d b o l e for d r a w i n g m y a t t e n t i o n to ref. [ 2 0 ].
References [1 ] CDF Collab., F. Abe et al.. Phys. Re','. lett. 64 (1990) 142; A. Barbaro-Galtieri. Fermilab Conf-91/66-E, in: Proc. 1990 Summer Study on High energy physics (Snowmass, CO), to be published. [2] G. Altarelli and P. Franzini, Z. Phys. C 39 (1988) 271: P. Franzini, Phys. Rep. 173 ( 1989 ) I, and references therein. [ 3 ] See, e.g., J. Ellis and G.L. Fogli, Phys. Left. B 232 (1989) 139, P. Langacker, Phys. Rev. Lett. 63 ( 1989 ) 1920: J. Steinberg, Phys. Rep. 203 ( 1991 ) 345. [ 4 ] S. Gupta and D.P. Roy, Z. Phys. C 39 ( 1988 ) 417; H. Baer, V. Barger and R.J,N. Phillips, Phys. Rev. D 39 11989) 3310; F. ('avanna, D. Denegri and T. Rodrigo. Proc. ECFA-LHC Workshop, Vol. It, CERN reporl CERN 90-10 (1990) p. 329. [5] V. Barger and R.J.N. Phillips, Phys. Re,,. [)41 (1990) 884: A.C. Bawa. C.S. Kim and A.D. Martin, Z. Phys. C 47 ( 1990 ) 75: M. Felcini, Proc. ECFA-LHC Workshop. Vol. It, CERN reporl CERN 90-10 (1990) p. 414:
410
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R.M. Barnett et al., Proc. 1990 Summer Study on High energy physics (Snowmass, CO), to be published. [ 6 ] R.M. Godtx)le and DP. Roy, Phys. Rev. I) 43 ( 1991 ) 3640: M. Drees and D.P. Roy, Phys. Lett. B 269 ( 1991 ) 155. [7] For a review of Higgs physics, see e.g., J.F. Gun;on, H.E. Haber. G. Kane and S. Dawson, the Higgs hunters' guide (Addison Wesle,,, Reading, MA, 1990 ): H.E. Haber, in: Phenomenology of the standard model and beyond, eds. D.P. Roy and P. Roy (World Scientific, Singapore, 1990), p. 197. [8] S. Komamiya, Phys. Rev. D 38 11988) 2158. [glA. Brignole, J. Ellis, G. Ridolfi and F. Zwirner. CERN prcprint ('ERN-TH. 6151/91 (1991). [10]J.F. Gun;on ct al., Proc. 1987 Berkeley Workshop on Experiments. detectors and experimental areas of the supercollider, eds. P. Donaldson and M. Gilchriese (World Scientific, Singapore, 1988 ). p. I 10. [ l 1 J S. Glashow and S. Weinberg, Phys. Rev. D 15 ( 1977 ) 1958: E.A. Paschos, Phys. Rev. D 15 (1977) 1966: K. Kang and J. Kim. Phys. Left. B 64 (1976) 93. [ 12] J.L. Hewett and T.L. Rizzo, Phys. Rep. 183 (1989) 193. [ 13 ] V. Barger et al., Phys. Re',. D 41 ( 1990 ) 3421 : A. Buras et al., Nucl. Phys. B 337 (1990) 284: J.F. Gun;on and B. Grzadkowski. Phys. Left. B 243 (1990) 301. [ 14 ] J. Ellxs, G. Ridolfi and F. Zwirner. Phys. Left. B 257 ( 1991 ) 83: H.E. Haber and R. Hempfling, Phys. Rev. Left. 66 ( 1991 ) 1815ALEPH Collab., D. Decamp el al., Phys. Left. B 165 ( 1991 ) 475. [15] G. Ridolfi, G.G. Ross and F. Zwirner, Proc. ECFA-LHC Workshop. Vol. 11. CERN report CERN 90-10 119911) p. 608. [ 16] A. Mendez and A. Pomarol, Phys. Lett. B 252 (1990) 461; C.S. Li and R.J. Oakes, Phys. Rev. D 43 ( 1991 ) 855. [ 17 ] M. (;luck, F. Hoffman and E Reya, Z. Phys. C 13 ( 1982 ) 119. [ 18 ] J. Kwiecinski, A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Re'.'. D 42 (1990) 3645. [ 19] H. Plothow-Besch, I-'roc. third Workshop on Detector and event simulation in high energy physics (Amsterdam. April 1991 ). [20] M.L. Mangano, P. Nason and G. Ridolfi. Pisa preprint UPRF/91/308 (1991). [21]B.K. Bullock. K. ttagiwara and A.D. Martin. Durham preprint DTP/91/42 ( 1991 ). [22] D.P. Roy. ('ERN preprint CERN-TH6274/91 ( 1991 ).
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Discovery limit of the charged Higgs boson via top quark decay at future hadron colliders D.P. R o y J Theoretical Phvsws Division, ('ERN, Ctl- 1211 Geneva 23. Switzerland Received 8 November 1991
We study the kinematic cuts which can be used to enhance the charged Higgs signal over the W boson background, for mH- > row, in the decay of a heavy top quark at LHC energy. With suitable cuts it is possible to ensure a sizeable signal and a signal-tobackground ratio > 1 up to mH_. -~ nt~- 20 GeV, which hold throughout the allowed coupling parameter (tan 1~) space in the minimal SUSY model. Thus one should be able to search for the charged Higgs boson to within 20 GcV of the parent top quark mass at the LHC/SSC collidcrs, i.e., up to 130 GeV tbr m~ -~ 150 GeV. going up to 180 GeV for m, -~ 200 GeV.
The results of the top search experiment at the Tevatron 10p collider [ 1 ] as well as the Bo-13d mixing data [ 2 ] suggest a heavy top quark of mass mt > 80 GeV. Moreover, the radiative correction to the W, Z masses suggests a central value of top quark mass mt_~ 150 GcV with an upper bound of about 200 GeV [ 3 ]. A top quark in this mass range is expected to be seen at the Tevatron upgrade and produced more copiously at the LHC/SSC colliders [4]. Besides providing direct evidence for top, this will enable one to search for new particles in the top quark decay; the large top quark mass offers the possibility of carrying on the search to a hitherto unexplored mass range. There has been a great deal of recent interest in the search for one such new particle, i.e., the charged Higgs boson [5,6] of the two-Higgs-doublet version of the standard model [7]. In particular it was shown in ref. [6] that for m~-~ 150 GeV a systematic comparison of the top signal in different decay channels provides an effective signature for charged Higgs bosons up to a mass of mH = 100 GeV at the Tcvatron upgrade. For the theoretically most attractive two-Higgs-doublet model of MSSM (minimal supersymmetric standard model) one expects an observable signal throughout the allowed coupling parameter space. Thus one can probe the charged Higgs mass up to about 100 GcV On sabbatical leave from the Tata Institute of Fundamental Research, Bombay 400005, India.
unambiguously for this model. This is already larger than the charged Higgs discovery limit of 80-90 GeV at LEP-II [8,9]. However, it is not large enough considering the theoretical expectation of mt~ > m w in MSSM [ 7 ]. It should be mentioned here that, unlike the neutral Higgs mass, the charged Higgs mass has little sensitivity to the radiative correction from the heavy top quark, so that this tree-level bound remains valid for most of the parameter space [9]. In view of the above discussion it is important to devise means of extending the charged Higgs probe beyond 100 GeV without restricting ourselves to specific corners of the coupling parameter space. This is of course not possible at the Tevatron upgrade, where both the signal size and the signal/background ratio were seen to become marginal in the region of the coupling parameter tan flu \,/mt/m, [6]. However, one expects a much larger size of the signal at LHC/ SSC due to the larger tt cross-section and luminosity. For m . > 100 GeV. the increasing gap between the charged Higgs and W boson masses offers the possibility of enhancing the signal/background ratio by suitable kinematic cuts. As we shall see in this note, it is possible to exploit the above two features to devise a viable charged Higgs signature which holds up to m H = m , - 2 0 GeV and throughout the allowed coupling parameter space of MSSM. Thus it seems possible to probe for the charged Higgs mass to within 20 GeV of the top quark mass at these future hadron
0370-2693/92/$ 05.00 (C) 1992 Elsevier Science Publishers B.V. All rights reserved.
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colliders, i.e., up to 130 GeV for m, -~ 150 GeV. going up to 180 GeV for m, -- 200 GeV. This represents an important discovery, limit, as it seems impossible to probe the region m u > m ~ + m b at hadron colliders [10]. The essential features of the two-Higgs-doublet model are as follows. It contains two SU (2) doublets of complex scalar fields
OcJko°J" with vacuum expectation values (VEVs) < ¢;? > = v~ Iv,'2,
( 0 2<,)
=v,/\./2~
(1)
which satisfy the W mass constraint v{+v~=v 2
(v=246GeV).
(2)
This leaves one free parameter, i.e., the ratio of the two VEVS tan,8= v2/v..
(3)
After absorbing the three Goldstone bosons one is left with five physical states - the neutral scalars h °, H ° and pseudoscalar A ° along with the charged states H We shall be concerned only with the charged states, i.e., H -~= ¢ ~ c0s,8-0¢- sin ft.
(4)
The two-Higgs-doublet model represents a minimal extension of the standard model which automatically satisfies the constraint of p= I at the tree level. Furthermore, the absence of flavour changing neutral current at the tree level can be naturally ensured via the Glasgow-Weinberg theorem [ 11 ], which states that the tree-level FCNC mediated by Higgs bosons will be absent if all the fermions of the same electric charge have Yukawa couplings to only one Higgs doublet. A very important model automatically satisfying this constraint is the minimal supersymmetric extension of the standard model (MSSM), where the up-type quarks have Yukawa couplings to one Higgs doublet (¢~2, say) while the down-type quarks and charged leptons couple to the other. This model has received wide attention as it provides the most economical solution to the hierarchy problem of the standard model. Moreover, it offers the possibility of explaining the observed quark mass hierarchy rnc >> m~ and m, >> mb in terms of that of the VEVs 404
11 June 1992
v2 >> v~. In this model, the Yukawa couplings of the physical charged Higgs field of eq. (4) to fermions are given by S=
g
H + (cotfl
\ '2 iV/w
v,/nu, a,d~L
+ tan B ~,j m,~tzi,6. + tan [3 rn~,~j R ) +h.c.,
(5)
where I~, are the KM matrix elements. One has identical charged Higgs couplings to the fermions in the E0 superstring-inspired model [12] as well; but this model gives a less restrictive mass bound (ran> 53 GeV) than the MSSM. We shall concentrate on the above coupling scheme ofeq. (5) in view ofthe wide theoretical interest behind the underlying models. Besides, as shown in ref. [6], it is only for this coupling scheme that one can ensure an observable charged Higgs signal throughout the allowed range of the coupling parameter tan ft. This range is summarized below [ 13 ]. The validity of perturbation theory implies upper bounds on the charged Higgs-fermion couplings appearing in eq. (5). Requiring the tbH ÷ coupling in the first term to be bounded by the strong coupling constant 4na~( -- 1.5 ) gives a lower bound on tan/3, i.e,, tan/3> m,/600 GeV ( -,- ] ).
(6)
The size of this coupling can also be constrained by the charged Higgs exchange contributions to Bd--f3d mixing, b--*sv decay and CP violation in K decay [ 13 ]. They give a slightly better bound tan J3> 0.4
(7)
for m, ~ 150 GeV and mu ~ 100 GeV. The perturbative limit on the tbH ÷ coupling appearing in the second term ofeq. (5) gives the upper bound tan ,8<600 GeV/m~,( -~ 120) .
(8)
Thus the region of interest in the coupling parameter space is 0 . 4 < t a n / 3 < 120.
(9)
While the lower hound holds for any two-Higgs-douhlet model, the upper hound is specific to those where the up- and down-type quarks have Yukawa cou-
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plings to separate Higgs doublets like the MSSM ~ It should be remarked here that we have adopted the most general definition of MSSM implying only the minimal particle content [7]. The most predictive form of this model, characterized by minimal set of SUSY breaking parameters at the grand unification point, leads to a more restrictive range of the coupling parameter [ 15 ] 1
(10)
However, we shall consider the more general range of the coupling parameter space given by eq. (9) above. In any case the most unfavourable region of this parameter space for the charged Higgs signal (tan fl~ v"mJmb) occurs in the middle of the range (10), as we shall see below. The size of the charged Higgs signal versus the W boson background in top quark decay is controlled by the relative decay widths of t - , b H + and t--+bW +. In the diagonal KM matrix approximation one gets, from eq. ( 5 ),
g2 ?j 64nm~,m 2 I/2 ( 1 rn-{'m~" m H
Ft .bil,
× [(m~ cot-'fl+ mb tan2/3) (m~ +rap, --m~.) +4m~m~,l ,
(11)
and the corresponding decay width into the W boson is F~ .t,w+
--
g-+
, 64rem~.,m,
2 ~/2
(
1,
,nb ,n~,,']
m,v , m~ ]
X[m~.,(mp +m~,)+(mp-m~)'--2m~.,].
(12)
Thus one gets the branching fraction B(t--+bH+ ) = G .b.+ / (Ft-b.+ +Ft ,bW+ ) .
(13)
From eq. (5) one can also calculate the two significant charged Higgs decay widths, i.e., m~ tan~+/3, ~g-mH + , 32re'n+,,
/~H+
+,~,
F.+
.,.,- 32trm~,,
,+, - -
3g'-m. (m~.cot'-fl+m~" tan:fl)
(14)
'
(15)
and the branching fraction ~k Thereare no more constraints on this parameter from the LEP data once the radiativecorrectionsare taken into account [ 14].
1I June 1992
B ( H + - , T + v ) = m ~ tan2fl/3(m~ cot-'fl+ms tan-+fl) + m ~ tan2fl.
(16)
The effect of the QCD correction has been analyzed in detail by Drces and Roy [ 6 ] following the formalism of ref. [ 16 ]. The most significant effect comes from the H + -+cg decay width. In the leading log approximation the QCD correction can be simply implemented by replacing the quark mass terms appearing in the width of eq. (15), or equivalently in the Yukawa couplings ofeq. (5), by the running mass
( l n ( 2 m d A ) ~l+-,,( ~3- 2,.,, ~q(mH) =mq \ In(re.~,! ) ]
(17)
where one has assumed the standard initial condition [16]
p~q(2mq) = m,~ .
( 18 )
The initial values are chosen to be m,.= 1.5 GeV and ms= 0.2 GeV. The quantity of phenomenological interest is of course the resulting branching fraction of eq. ( 16 ), which is clearly insensitive to m,. The corresponding branching fractions for W decay are of course given by the universality of W coupling to leptons and quarks, i.e., 10% into each lepton pair and 70% into hadrons (including the small QCD enhancement of hadronic width by ~ 4%). The striking difference between the two sets of branching fractions makes it possible to separate the charged Higgs and W contributions by comparing the relative size of the ti signal in different decay channels [6]. Like W, the charged Higgs has also to be identified through its leptonic (i.e., t) decay to avoid the large QCD background. Thus it is the product of the two branching fractions (13) and ( 16 ) that controls the size of the charged Higgs signal. These two branching fractions are shown in fig. 1 against the coupling parameter tan ft. The branching fraction for charged Higgs production t--+bH is shown for m~ = 150 GeV (mH = 110, 130 GeV) and m~ = 200 GeV ( m . = 160, 180 GeV), while the H - , w decay branching fraction is practically independent of m , . The t--+bH branching fraction becomes veD' small around t a n f l - (mt/mb)~/2~6 where eq. (11) has a minimum. This partly compensated by the maximal 405
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.
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.
.
.
.
.
!
" ""
- -
B(I
,bH),mt=150,
.....
B(t--~bH),m t=200'm
production through gluon-gluon or q u a r k - a n t i q u a r k fusion followed by their decay into charged Higgs or W boson channels ( t - , b H , b W ) , i.e.,
11
m H = 110,130 H = 160,180
......... B ( H ~ Iv) 1 •
ggorqCl-*t[--*bb(H÷H - H'W',W+W
.."
0.1
- ).
(19)
Here the first two terms in the parentheses represent the charged Higgs signal and the third one the W background. This is followed by the charged boson decays
",
/
H ,zv,
"
"
"
H--,c~,,
(20a,b)
with the branching fractions o f e q . (16), and
//
0.01
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W J L ev, p_v, zv,
"
W _~o~ q?t' •
(21a,b)
Finally, the z is to be observed in its muonic or hadtonic decay channel I 8%
1
0.1
1
10
100
Tan I~ Fig. I. Branching fractions for t .bH for m,= 150 GeV with m,=ll0 and 130 GeV (solid upper and lower lines), and m,=200 GeV with mR= 160 and 180 GcV (dashed upper and lower lines ). The branching fraction of charged Higgs deca.~ into ~ lepton is shown b.', the dotted line. The allowed range of tan f l ( ~ 0 . 4 ) is indicated by the hatched ]inc.
value o f the H -.zv branching fraction in this region. As remarked in ref. [6 ], this c o m p e n s a t i o n mechanism is typical o f the coupling scheme o f e q . ( 5 ) and ensures a viable charged Higgs signal throughout the allowed tan fl space in this scheme for m . ~ m w . However, the c o m p e n s a t i o n is no longer adequate as nh~ *m~. For instance, in the extreme case of m~ = 200 GeV ( m n = 180 GeV ) one sees that the s i g n a l / b a c k ground ratio for the z channel is only ~ 2% a r o u n d tan fl-~ 6. For the 2~ channel, corresponding to ~-decay of both t and t. one gains a c o m b i n a t o r i a l factor o f 2 raising this ratio to ~ 4%. Thus one needs a background rejection factor o f ~ 25 from kinematic cuts to have a viable charged Higgs signal in this region. We shall see below that it is indeed possible to devise such kinematic cuts and ensure a s i g n a l / b a c k g r o u n d ratio > I as well as a sizeable signal throughout the allowed tan fl space. The charged Higgs signal and the W boson background are estimated using a parton level event generator program. The basic process o f interest is tt 406
"c--.v,v,p.
64%
z--,v,q~l',
(22a,b)
as a soft muon or a narrow jet (r-jet), a c c o m p a n i e d by a significant amount o f missingpw. We shall largely concentrate on the hadronic decay channel o f "r and refer to it simply as the r-channel. The t[ signal in the hard dilepton channel t[--,bbW+W--,bl~+';,~ v
(~=e,~)
(23)
(with p ~ > 2 0 GeV, say) can be used to normalize the W ~ W - contribution since the charged Higgs does not contribute to this channel. Then the W + W background in any other channel is predicted by universality [cqs. (21), ( 2 2 ) ] . A sizeable excess over this prediction will constitute a charged Higgs signal. whose magnitude is also predicted by eqs. ( 13 ) and (14). Thus the uncertainties associated with the tt production are effectively factored out. One can scc from fig. 1 that the predicted W + W - contribution to an,,' channel would d e p e n d on mH and tan [3: the maximal value obtained at tan/3~ 6 corresponds to the standard model prediction (see figs. 3 and 4). However, this dependence drops out when normalized with respect to the hard dilepton channel "-' The results presented below are obtained using the '-" The obser',ation of a ti signal in the hard dilepton channel below the level of standard model prediction is in principle indicative of a charged Higgs boson. But it cannot be used in practice because of the uncerlaint.~ in the production crosssection.
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structure functions and c~,of refl [ 17 ]. We have also cross-checked them by using the corresponding Q C D parameters ofref. [ 18] "3. There is essentially no difference apart from a drop of overall normalization by a factor of ~ 2, mainly due to a,. The normalization has of course no effect on the relative size of the signal in different channels as m e n t i o n e d above. For the same reason one expects the result to bc insensitive to higher-order Q C D corrections. We concentrate below on the most viable channels for the charged Higgs signal and the LHC energy of,v"s= 16 TeV. 2r channel. It corresponds to "c decay of both the charged bosons of (19) followed by hadronic decay o f t (22b). We have chosen a m i n i m a l set of cuts T p,_,,.~ > 10 GeV,
[.V~_j~.,I < 3 ,
1 Pmtss > 20 GeV,
(24)
which come by default. Similarly we have chosen a m i n i m a l isolation cut of a c c o m p a n y i n g Pr < 5 GeV within 0.4 rad of the x direction. They can be increased significantly without a drastic reduction in cross-section. For m, = 150 GeV, mH = 130 GeV one has a 30% reduction in the signal cross-section from increasing each p~.,~., cut to 30 GeV and a similar reduction from increasing the missingp T cut to 50 GeV. For ,n, = 200 GeV. mH = 180 GeV the corresponding reductions are ~ 20% each. In each case of course the reduction to the background is larger. Thus increasing the z-jet and m i s s i n g p r cuts to more realistic values would improve the signal/background ratio at the cost of a moderate loss to the signal size '4. This channel offers the best s i g n a l / b a c k g r o u n d ratio because (i) the signal gets c o n t r i b u t i o n s from both HH and HW terms and (ii) the latter is enhanced by a combinatorial factor of 2. The disadvantage is that it is not possible to reconstruct the charged boson masses because of the large n u m b e r of neutrinos. Nonetheless one can separate the signal from the background by exploiting the fact that as mH-~m, the accompa,3 This set of structure functions was accessed via The structure function packagc [19]. ,,s The 2x background from Drcll-Yan and Z alcoa', can be readily distinguished by its azimuthally back-to-back configuration. no missingp-r normal to this 2x axis and a relatively low invariant mass of the "tpair. Similarly the 2"t background from the bb decay can bc effectivelysuppressed by the p~ and isolation cuts.
I I June 1992
nying b-jet becomes soft. Thus the W W background of (19) has two hard accompanying jets while the signal has at least one soft jet. Fig. 2a shows the pT distribution of the hardest acc o m p a n y i n g jet for the signal and background events for the most unfavourable coupling parameter tan fl=6. For this choice the signal is d o m i n a t e d by the HW term and consequently the peak value of the accompanyingp]i is not very different from the W W background. Note, however, that, in the region p f < 30 GeV, the background is doubly suppressed by the probability of each accompanying jet becoming soft, while the signal is suppressed singly. Thus one can get a signal/background ratio ~_ 1 by ensuring that there is no accompanying b-jet with pV> 30 GeV "~. Fig. 3a shows the resulting signal and background over the allowed range of tan ,8 at the LHC energy. It shows a viable signal up to mH-~ m ~ - 2 0 GeV with a signal/ background ratio > 1 and a signal size > 10 lb. The latter corresponds to a m i n i m u m of 100(1000) events us Identification of the b-jet is not necessary, since one expects only a modest fraction of ti events to be accompanied by a QCD jet ofpT>30 GeV [201. Thus it is sufficient to ensure that there are no accompanyingjets ofp~> 30 GeV. 100
mt
/
".
• 50 ,~f----....
a)
"-.
ill Y
-q "
~"~
".,
-~//'-"
b)
:.
"',
°-r \
V
\ •/
....
WW
001 . . . . . . . . t 0 50
Bg
.......... 100 P/T,(GeV)
1 . . . . ,._ . 0 50 p;',GeV',
Fig. 2. The distribution of 2~ events in the transverse momentum of the accompanyingb-jets: (a) hardest jet and (b) second hardest jet. The normalizationsof the charged Higgssignal (solidlines) and the WW background (dashed lines) correspond to the most unfavourable value of tan fl ( =6 ). The upper and lower sets of curves correspond to m~= 150 GeV (mt~= 110. 130 GeV). and m, = 200 GeV ( mH= 160, 180 GeV ) respectivelyin this and the followingfigures. The energy is the LHC energyof x s= 16 TeV. 407
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PHYSI('S LETTERS B
a) 2 t c h . ( p T < 3 0
T
n'ttl,n,,
i
b) 2 r c h . pT<20
pr
//
//
"
-'.
1
0.1
1
10
Tar~ ',~,
100
1
10
~00
Tan 3
Fig. 3. (a) The charged Higgs signal (solid line) and WW background (dolled line) for the 2t channel with a p T < 3 0 GeV cut on the hardest accompanyingjet. In each set of curves the lower solid ( u p p e r dashed) lines correspond to the higher Higgs mass. ( b ) Same as above with a p r < 20 (.ieV cut on lhc second hardest jet ( I0 < P]i < 20 G e V f o r the lower set o f curves ).
for an annual luminosity of 10(100) ~ - ~ , expected from the low (high) luminosity option o f LHC. Fig. 2b shows the pT distribution of the second hardest b-jet for the signal and background for tan if,=6. Although the background peaks at a significantly higher value o f pl r compared to the signal, there is a residual background left in the pjL = 0 region. This is due to the .jet folding algorithm which merges the b-jets emerging within an opening angle of ~ radian into one. This limits the background suppression potential of a low p~ cut. Fig. 3b shows the signal and background over the allowed tan fl range with p,L < 20 GeV. The lower set of curves is evaluated with 10
> 10 GeV.
r >20GeV. p .....
p~>20GeV,
[.l',.~_j~., I < 3 ,
:.-
]0
1 I June 1992
( 25 )
which have little effect on the cross-section. Supplementing this with the p , ~ < 3 0 GeV cut. we get the signal and background curves shown in fig. 4a. While the signal size remains viable throughout the allowed tan/? range, the signal/background ratio fails significantly below 1 in the neighbourhood of tan//-~6. Nonetheless the signal cross-section remains >/200 fb against a background of 800 Po for m, = 150 GeV. and i> 8 fb against a background ot"25 fb for m, = 200 GeV. The resulting numbers of signal and background events for an integrated luminosity of 10 fb ~ correspond to a figure of merit (N,.g/,,, "N~g ) of >/22 and 5 respectively. Thus it remains a viable channel for charged Higgs search up to m u = m , - 2 0 GeV. This is worth emphasizing, because the r plus hard u channel is by far the easiest to identify using the hard muon as a trigger. Besides it is free from the Drell-Yan and Z decay backgrounds. r + .sqti p chamwl. It corresponds to "[decay of both the charged bosons of (19) followed by the muonic decay of one ~ (22a). The smaller muonic branching fraction of r results in a smaller signal size compared to the 2r channel. Besides one has to include the soft 105
i
:
"
i
a) ': • hard p 104
rnt (rr'H)
. . . . . . . ' b) "[ • soft p
i
"
/1
~ 102
lo2!
10
1
v
0 1
.
1
.
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Fig. 4. The charged ground (dotted line) and (b) z+soft p(pr a p r < 30 GeV cut on
l
.
.
.
100
10
!00
Tan p,
Higgs signal (solid line) and WW backfor (a) 't+ hard p(pi > 20 GeV) channel =5-20 OeV) channel. In each case there is the hardest accompanying jet.
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la tail from the direct W - . p decay, which makes the s i g n a l / b a c k g r o u n d ratio somewhat smaller as well. The cuts used are pr,~, > 10 GeV.
104 ;.
103
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-
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150 .........
:
,
.....
.....
200
.
~
V ~
......
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,-
,-
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(26)
where the p [, cut is o p t i m i z e d to retain most the rdecay muons ( ~ 50%) while m i n i m i z i n g contamination from direct W decay ( ~ 10%). Supplementing this with the p~ < 30 GeV cut, we get the signal and background shown in fig. 4b. C o m p a r e d to the 2r channel o f fig. 3a, one sees a smaller signal size and signal-to-background ratio. Nonetheless it could be viable for charged Higgs search up to m , = m , - 20 GeV with the high luminosity option of L H C ( = 100 fb-'). r+ mult~jet channel. It corresponds to t decay of the charged bosons o f (19) and hadronic decay of the other. For t a n / / > 1, the s i g n a l / b a c k g r o u n d ratio is identical to the x + hard la channel, while the signal size is a factor o f 7 higher [eq. ( 2 1 ) ] . The m i n i m a l cuts are pr,~., > 10 GeV,
,
rot
i
p v...... > 20 GeV,
p~ = 5-20 G e V ,
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102 t-:.
~~
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~
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.
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200
Fig. 5. The distribution of the x+ multijet events in the transverse mass of the x-jet and the missing Pl system. The normalization of the charged Higgs signal (solid lines) and the WW background (dashed lines) shown corresponds to the most unfavourable value of tan ,b'=6.
i > 20 G e V , p .....
pll~._,> 40 GeV .
( 27 )
The d i s a d v a n t a g e of this channel, unlike the previous ones, is a significant background from W + Q C D jets even after the large p~r._, cut. The advantage is the absence o f neutrinos in the decay o f one of the two charged bosons. Thus one can reconstruct the W ( H ) mass from, e.g., the transverse mass o f the t-jet and missing-p-r system. Fig. 5 shows this transverse mass distribution o f the W H signal and the W W background for the most unfavourable value o f tan f l = 6 . The background gets kinematically cut off at the W boson mass. Although the effect o f resolution smearing is not shown, one can check that with a ~m,~= 10 GeV, less than 1% of thc b a c k g r o u n d spills over to the ,'v/~> 100 GeV region. This would ensure a sign a l / b a c k g r o u n d ratio > 1. With good b-jet identification one could also use the p r < 30 GcV cut on the b-jets for suppressing the W W background. On the other hand one may need an identified large Pl b-jet to control the background from W + Q C D jets. Therefore, we have not explored this possibility furthor. It is clear from fig. 5, however, that the t + multijet channel can give significant clues about the
charged Higgs mass from the tail o f the M,r distribution. It is therefore an i m p o r t a n t channel for the charged Higgs search, p r o v i d e d one can identify "t in a multijet environment. It is evident from the above analysis that good x-jet identification is crucial to charged Higgs search via top quark decay at hadron colliders. We have not assumed, however, measuremcnt of x charge or polarization. If polarization measurement is available, then one can also use the correlation between the "~charge and polarization to separate the charged Higgs signal from the W boson background as recently discussed in rcf. [21 ], since one expects xC ( ~ ) from W - , ' t v and zff. ( z ~ ) from H - , z v . O f course the polarization measurement may not reach the 2% accuracy required to probe through the full p a r a m e t e r space by itself. However, once the sample o f t events have been cnriched by, e.g., the p r < 30 GeV cut, one needs no more than 20% accuracy in the polarization measurement to confirm the charged Higgs signal. A quantitative analysis of this polarization effect is given in ref. [22]. In s u m m a r y , we have tried to explore the prospect o f charged Higgs search via top quark decay at L H C / 409
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S S C a n d i d e n t i f y t h e m o s t f a v o u r a b l e c h a n n e l a n d kin e m a t i c cut for t h i s p u r p o s e . T h e y are t h e 2"~ c h a n n e l ( f o l l o w e d by t h e "qa) a n d a p~ cut o n t h e a c c o m p a n y i n g b - q u a r k jets. t h e y p r o v i d e a s i z e a b l e c h a r g e d Higgs signal a n d a s i g n a l / b a c k g r o u n d r a t i o > 1 u p to m)~ --- m, - 20 G e V , w h i c h h o l d t h r o u g h o u t t h e all o w e d r a n g e o f c o u p l i n g p a r a m e t e r s in t h e M S S M . T h e c a l c u l a t i o n s are d o n e for L H C energy; b u t o f c o u r s e w h a t is t r u e for L H C is e v e n m o r e t r u e for SSC. T h u s for t h e M S S M t h e c h a r g e d Higgs m a s s c a n b e u n a m b i g u o u s l y e x p l o r e d to w i t h i n 20 G e V o f t h e t o p q u a r k m a s s - i.e., u p to 130 G e V for m,-~ 150 G e V , g o i n g u p to 180 G e V for m,--- 2 0 0 G e V . T h i s m e a n s t h a t a r e l a t i v e l y h e a v y t o p m a y b e b a d n e w s for t h e t o p q u a r k s e a r c h b u t a g o o d o n e for the c h a r g e d Higgs boson. It is a p l e a s u r e to t h a n k Dr. G, Altarelli, Dr. H. H a b e r , Dr. B. G r z a d k o w s k i , Dr. Z. K u n s z t , Dr. F. P a u s s a n d Dr. F. Z w i r n e r for d i s c u s s i o n s a n d R . M . G o d b o l e for d r a w i n g m y a t t e n t i o n to ref. [ 2 0 ].
References [1 ] CDF Collab., F. Abe et al.. Phys. Re','. lett. 64 (1990) 142; A. Barbaro-Galtieri. Fermilab Conf-91/66-E, in: Proc. 1990 Summer Study on High energy physics (Snowmass, CO), to be published. [2] G. Altarelli and P. Franzini, Z. Phys. C 39 (1988) 271: P. Franzini, Phys. Rep. 173 ( 1989 ) I, and references therein. [ 3 ] See, e.g., J. Ellis and G.L. Fogli, Phys. Left. B 232 (1989) 139, P. Langacker, Phys. Rev. Lett. 63 ( 1989 ) 1920: J. Steinberg, Phys. Rep. 203 ( 1991 ) 345. [ 4 ] S. Gupta and D.P. Roy, Z. Phys. C 39 ( 1988 ) 417; H. Baer, V. Barger and R.J,N. Phillips, Phys. Rev. D 39 11989) 3310; F. ('avanna, D. Denegri and T. Rodrigo. Proc. ECFA-LHC Workshop, Vol. It, CERN reporl CERN 90-10 (1990) p. 329. [5] V. Barger and R.J.N. Phillips, Phys. Re,,. [)41 (1990) 884: A.C. Bawa. C.S. Kim and A.D. Martin, Z. Phys. C 47 ( 1990 ) 75: M. Felcini, Proc. ECFA-LHC Workshop. Vol. It, CERN reporl CERN 90-10 (1990) p. 414:
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R.M. Barnett et al., Proc. 1990 Summer Study on High energy physics (Snowmass, CO), to be published. [ 6 ] R.M. Godtx)le and DP. Roy, Phys. Rev. I) 43 ( 1991 ) 3640: M. Drees and D.P. Roy, Phys. Lett. B 269 ( 1991 ) 155. [7] For a review of Higgs physics, see e.g., J.F. Gun;on, H.E. Haber. G. Kane and S. Dawson, the Higgs hunters' guide (Addison Wesle,,, Reading, MA, 1990 ): H.E. Haber, in: Phenomenology of the standard model and beyond, eds. D.P. Roy and P. Roy (World Scientific, Singapore, 1990), p. 197. [8] S. Komamiya, Phys. Rev. D 38 11988) 2158. [glA. Brignole, J. Ellis, G. Ridolfi and F. Zwirner. CERN prcprint ('ERN-TH. 6151/91 (1991). [10]J.F. Gun;on ct al., Proc. 1987 Berkeley Workshop on Experiments. detectors and experimental areas of the supercollider, eds. P. Donaldson and M. Gilchriese (World Scientific, Singapore, 1988 ). p. I 10. [ l 1 J S. Glashow and S. Weinberg, Phys. Rev. D 15 ( 1977 ) 1958: E.A. Paschos, Phys. Rev. D 15 (1977) 1966: K. Kang and J. Kim. Phys. Left. B 64 (1976) 93. [ 12] J.L. Hewett and T.L. Rizzo, Phys. Rep. 183 (1989) 193. [ 13 ] V. Barger et al., Phys. Re',. D 41 ( 1990 ) 3421 : A. Buras et al., Nucl. Phys. B 337 (1990) 284: J.F. Gun;on and B. Grzadkowski. Phys. Left. B 243 (1990) 301. [ 14 ] J. Ellxs, G. Ridolfi and F. Zwirner. Phys. Left. B 257 ( 1991 ) 83: H.E. Haber and R. Hempfling, Phys. Rev. Left. 66 ( 1991 ) 1815ALEPH Collab., D. Decamp el al., Phys. Left. B 165 ( 1991 ) 475. [15] G. Ridolfi, G.G. Ross and F. Zwirner, Proc. ECFA-LHC Workshop. Vol. 11. CERN report CERN 90-10 119911) p. 608. [ 16] A. Mendez and A. Pomarol, Phys. Lett. B 252 (1990) 461; C.S. Li and R.J. Oakes, Phys. Rev. D 43 ( 1991 ) 855. [ 17 ] M. (;luck, F. Hoffman and E Reya, Z. Phys. C 13 ( 1982 ) 119. [ 18 ] J. Kwiecinski, A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Re'.'. D 42 (1990) 3645. [ 19] H. Plothow-Besch, I-'roc. third Workshop on Detector and event simulation in high energy physics (Amsterdam. April 1991 ). [20] M.L. Mangano, P. Nason and G. Ridolfi. Pisa preprint UPRF/91/308 (1991). [21]B.K. Bullock. K. ttagiwara and A.D. Martin. Durham preprint DTP/91/42 ( 1991 ). [22] D.P. Roy. ('ERN preprint CERN-TH6274/91 ( 1991 ).