- Email: [email protected]
Search for flavor lepton number violation in slepton decays at LEP2 and NLC
.__ i!!B
a
28 November 1996
d
__
PHYSICS
ELSEVIER
LETTERS B
Physics Letters B 388 (1996) 783-787
Search for flavor lepton number violation in slepton decays at T UEP2 and NLC N.V. Krasnikov Institute for Nuclear Research, Moscow 117312, Russia
Received 1 December 1995; revised manuscript received 16 August 1996 Editor: R. Gatto
Abstract We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking mass terms there could be detectable flavor lepton number violation in slepton decays. We propose to look for flavor lepton number violation in right-handed slepton decays. We estimate LEP2 and NIX discovery potentials of the lepton flavor
number violation in slepton decays.
Supersymmetric electroweak models offer the simplest solution of the gauge hierarchy problem [ l-41. In real life supersymmetry has to be broken and the masses of superparticles have to be lighter than O( 1) TeV [4], Supergravity gives a natural explanation of the supersymmetry breaking, namely, taking into account that the supergravity breaking in hidden sector leads to soft supersymmetry breaking in observable sector [4]. For the supersymmetric extension of the Weinberg-Salam model soft supersymmetry breaking terms usually consist of the gaugino mass terms, squark and slepton mass terms with the same mass at Planck scale and trilinear soft scalar terms proportional to the superpotential [4]. For such “standard’ supersymmetry breaking terms the lepton flavor number is conserved in supersymmetric extension of WeinbergSalam model. However, in general, squark and slepton soft supersymmetry breaking mass terms are not diagonal due to many reasons [ 5-151 (an account of stringlike or GUT interactions, nontrivial hidden sector, ...) and flavor lepton number is explicitly broken due to nondiagonal structure of slepton soft supersym-
metry breaking mass terms. As a consequence such models predict flavor lepton number violation in pand r-decays [5-131. In our previous note [ 161 we proposed to look for flavor lepton number violation at LEP2 in right-handed slepton decays. In this paper we investigate the “discovery potential” of LEP2 and NLC (next linear collider) of flavor lepton number violation in slepton decays. We find that at LEP2 there is nonzero chance to detect flavor lepton number violation in slepton decays for slepton masses up to 75 GeV provided the mixing is not small. We also discuss the perspectives of NLC for the discovery of lepton flavor number violation in slepton decays. In supersymmetric extensions of the WeinbergSalam model supersymmetry is softly broken at some high energy scale Mour by generic soft terms
0370-2693/96/$12.00 Copyright 0 1996 Published by Elsevier Science B.V. All rights reserved. PZI SO370-2693(96)01213-O
N.V. Krasnikov/Physics
784
+ (mi)ijZk(Z$)+ + (Bm$H,,Hd
+ miHuH,f + m;HdHz + $m,(AA)a
+ h.c.) ,
(1)
where i, j, a are summed over 1, 2, 3 and &,, iiR, 2~ denote the left- (right-) handed squarks, IL, e”Rthe left(right-)handed sleptons and H,, Hd the two Higgs doublets; m, are the three gaugino masses of SU( 3), SU(2) and U( 1) respectively. In most analysis the mass terms are supposed to be diagonal at Mour scale and gaugino and trilinear mass terms are also assumed universal at Mom Scale. The renormalization group equations for soft parameters [ 171 allows one to connect high energy scale with observable electroweak scale. The standard consequence of such an analysis is that right-handed sleptons e”R, ,&R and ?R are the lightest sparticles among squarks and sleptons. In the approximation when we neglect lepton Yukawa coupling constants they are degenerate in masses. An account of the electroweak symmetry breaking gives additional contribution to right-handed slepton square mass equal to the square mass of the corresponding lepton and besides an account of lepton Yukawa coupling constants in the superpotential leads to the additional contribution to right-handed slepton masses
(2)
Letters B 388 (1996) 783-787
tion [ 181. As it has been discussed in many papers [5-151 in general we can expect nonzero nondiagonal soft supersymmetry breaking terms in Lagrangian (1) that leads to additional contributions for flavor changing neutral currents and to flavor lepton number violation. From the nonobservation of ,X --+ e + y decay (Br(p -+ e +y) i 5. lo-” [20]) one can find that [ 5-191
(5) For mzR = 70 GeV we find that (a,,) RR 5 5 . 10e3. Analogous bounds resulting from the nonobservation of r -+ ey and r + ,uy decays are not very stringent [5-191. The mass term for right-handed e”Rand ,& sleptons has the form
(6) After the diagonalization of the mass term (6) we find that the eigenstates of the mass term (6) are ci =e”Rcos(+) ,& = ,&cos(~$)
Here hl is the lepton Yukawa coupling constant and M, is the average mass of sparticles. These effects lead to a splitting between the right-handed slepton masses of the order of
- e”Lsin(C$),
(7) (8)
with the masses M~,2=~[(m~+m~)+((m~-m~)2+4(m~2)2)1~2] (9)
- 0( lo-s)
)
4R Cm& -d,>
+,&sin(#),
- O( lo-‘)
which practically coincide for small values of rnf - rn$ and my2. Here the mixing angle 4 is determined by the formula
m& For nonzero values of the trilinear parameter A after electroweak symmetry breaking we have nonzero mixing between right-handed and left-handed sleptons, however the lefthanded and right-handed sleptons differ in masses (lefthanded sleptons are slightly heavier), so the mixing between right-handed and Iefthanded sleptons (for 2~ and @R) is small and we shall neglect it. In our analysis we assume that the lightest stable particle is gaugino corresponding to U( 1) gauge group that is now more or less standard assump-
tan(24)
= 2mf2(mt
- rni)-’
(10)
The crucial point is that even for a small mixing parameter my2 due to the smallness of the difference rn: - rn: the mixing angle 4 is in general not small (at present state of the art it is impossible to calculate the mixing angle # reliably). For the most probable case when the lightest stable superparticle is the superpartner of the lJ( 1) gauge boson plus some small mixing with other gaugino and higgsino, the sleptons jiR, .!?Rdecay mainly into leptons p,R and eR plus U( 1)
N.V. Krasnikou / Physics Le&m B 388 (1996) 783-787
gaugino A. The corresponding term in the Lagrangian responsible for slepton decays is
785
At LEP2 and NLC in the neglection of slepton mixing ,& and ?R sleptons pair production occurs [ 2 11 via annihilation graphs involving the photon and the Z” boson and leads to the production of jiipi and ?i?R pairs. For the production of right-handed selectrons in addition to the annihilation graphs we also have contributions from the t-channel exchange of the neutralino [ 211. In the absence of mixing the cross sections can be represented in the form
the detection of sleptons at LEP2 have been discussed in Refs. [ 2 1,221 in the assumption of flavor lepton number conservation. The main background at LEP2 energy comes from the W-boson decays into charged lepton and neutrino [ 2 1] . For fi = 190 GeV the cross section of the W+ W- production is aw( W+W-) M 26 pb. [ 221. For selectrons at fi = 190 GeV, selecting events with electron pairs with pztis 2 10 GeV and the acoplanarity angle 19,~2 34” [ 211, the only background effects left are from W 4 evev and evrv where r + evy. For instance, for M% = 85 GeV and Mur = 30 GeV one can find that the accepted cross section is sac = 0.17 pb whereas the background cross . . sectron is Dba&sr = 0.17 pb that allow to detect righthanded selectrons at the level of 5~ for the luminosity 150 pb-’ and at the level of lla for the luminosity 500 pb-‘. For the detection of right-handed smuons we have to look for events with two acoplanar muons however the cross section will be (4-l .5) smaller than in the selectron case due to absence of the t-channel diagram and the imposition of the cuts analogous to the cuts for selectron case allows to detect smuons for masses up to 80 GeV Again here the main background comes from the W decays into muons and neutrino. The imposition of more elaborated cuts allows one to increase the LEP2 right-handed smuon discovery potential up to 85 GeV on smuon mass [ 21,221. Consider now the case of nonzero mixing sin 4 Z 0 between selectrons and smuons. In this case an account of the t-exchange diagram leads to the following cross sections for the slepton pair production (compare to the formulae (15), (16)):
a(e+e-
-+ Jiifi;)
(15)
a(e’e-
-+ jiiF;>
a(e+e-
-+ Zie”;)
(16)
c+(e+e-
--+ $zi)
u(e+e-
-+ Z:jiz)
L1 = @ ( Z_RALZR+ ji~h~fi~ dz
+ h.c.) ,
(11)
where gy M 0.13. For the case when mixing is absent the decay width of the slepton into lepton and LSP is given by the formula
(12) Af=(LMZ)
@SP
2
,
(13)
Sl
where M,r and M~sp are the masses of slepton and the lightest superparticle (U( 1) -gaugino) respectively. For the case of nonzero mixing we find that the Lagrangian ( 11) in terms of slepton eigenstates reads
+,%&(,&Cos(#
+zXsin(4))
= kA2, = k(A + B>2,
+h.c.]
(14)
where A is the amplitude of the s-exchange, B is the amplitude of the t-exchange and k is the normalization factor. The corresponding expressions for A, B and k are contained in [ 2 11. The amplitude B is determined mainly by the exchange of the lightest gaugino and taking this into account leads to an increase of the selectron cross section by factor kin = (4-1.5). As it has been mentioned before we assume that righthanded sleptons are the lightest visible superparticles. So sleptons decay with 100 percent probability into leptons and LSP that leads to acoplanar events with missing transverse momentum. The perspectives for
= k(A+ = k(A+
Bsin2(@))2,
(17)
Bcos2(q5))2,
(18)
= kB2cos2(4)
sin2(4)
(19)
Due to slepton mixing we have also lepton flavor number violation in slepton decays, namely: l-(&R ---) ,.&+ LSP) = Icos2(& I&
-+ e +LSP)
r(z, -+e + LSP) r(zR+ p + LSP)
,
=Isin2(4), =
r c0s2($) ,
= Isin2(4)
Taking into account formulae
(20)
(21) (22) (23)
(20) - (23) we find that
N.V. Krasnikov / Physics Letters B 388 (1996) 783-787
786
a( e+e- -+ e+e-
= k[ (A + Bcos~(@)~ + (A+
To be concrete consider the case of maximal selectron smuon mixing (ml = m2 in formula (6)). For this case bound (5) resulting from the absence of the
+ LSP + LSP) cos4(&
Bsin2(4))2sin4(4)
+ B2sin4(24)/S],
decay ,U --+ ey reads * (24)
a(e+e-
+ p+p”-
+ LSP + LSP)
= k[ (A + Bcos~(~~))~
sin4(@)
+ (A + Bsin2(4))2cos4(4)
+ B2sin4(24)/8]
,
5 5 . low4 (m,-= 70 GeV) ;
2.25~10~~ (m,-= 150 GeV); 4.10W3 (mz = 200 GeV, 5. 10e3 (m,-= 225 GeV) . From the requirement (27) of the absence of destructive interference for the cross section with flavor lepton number violation we find that
(25) a(e+e-
42 m:
--+ p& + eT + LSP + LSP)
ksind24) [(A +Bcos~(+))~
=
+ (A + Bsin2(4))2
+ B2(cas4(+>
+sin4(+))l (26)
It should be noted that formulae (24) -(26) are valid only in the approximation of narrow decay width of sleptons 5 lrn2, - rni,1
2l%,-,
(27)
For the case when the inequality (27) does not hold the effects due to the finite decay width are important and decrease the cross section with violation of flavor lepton number. To be concrete consider the case of maximal slepton mixing. The cross section of the process e+e- ---f e+p- + LSP + LSP is proportional to uN
J -
lD(pl,m,-,r)D(p2,ma,r)
(28) D(p2,m~,r)D(pz,m~,r)12dp:dp~7
where 1 D(p,m,r)
=
p2-m2-irm
(29)
(24)-( 26) and r? M rp = r. The approximation corresponds to the neglection of the interference terms in (28) and it is valid if the inequality (27) takes place. For smaller slepton mass difference an account of the interference terms in (28) is very important. For instance, for Im,- = 5 . 10-3mz we have found numerically that an account of the interference effects leads to the decrease of the cross section (26) by factors 0.99, 0.82, 0.52, 0.15 for Irni - rnil= 2rm,-, 1.5r,-, rm,-, 0.5FmZ respectively.
> 5. 10-3Af
(30)
So we see that for LEP2 energies it is possible to improve p -+ ey bound only for the case when LSP masses closed to slepton mass. For instance, for mr.sP = 0.95m,-,0.9mz,0.8m,-,0.7m,-,0.6mz,0.5mz Af is equal to 0.01, 0.036, 0.13, 0.26, 0.41, 0.56 respectively. For m,-= 70 GeV it is possible to improve ,u -+ ey bound (5) only for rnLsp2 0.9mLsp.However as it has been mentioned in Ref. [ 231 due to the big background the detection of sleptons can become problematic when the mass difference between slepton and neutralino becomes smaller than 10 GeV so the detection of possible selectron-smuon mixing at LEP2 becomes also very problematic. For the Next Linear Collider energies and for mE 5 150 GeV the p --+ ey bound (5) is not so stringent and it is possible to improve it even for the case of relatively small LSP masses when A, M 1. The perspectives for the detection of sleptons at NLC (for the case of zero slepton mixing) have been discussed in Ref. [ 231. The standard assumption of Ref. [ 241 is that sleptons are the LSP, therefore the only possible decay mode is 7 -+ I+ LSP. One possible set of selection criteria is the following: 1. t&or, 2 65”. 2. p~,ti~ 2 25 GeV. 3. The polar angle of one of the leptons should be larger than 44’, the other 26’. 4. (rnll -rn~)~ 2 100GeV2. 5. El* 2 150 GeV. For fi = 500 GeV and for integrated luminosity 20 fb-‘, a 5g signal can be found up to 225 GeV provided the difference between lepton and LSP is greater than 25 GeV [ 241. Following Ref. [ 241 we have analyzed the perspective for the detection of nonzero slepton mixing at NLC. In short, we have found that for
N.V. Krasnikov / Physics Letters B 388 (1996) 783-787
M~sp = 100 GeV it is possible to discover selectronsmuon mixing at the 5a level for M,r = 150 GeV provided that sin2# _> 0.28. For MS1 = 200 GeV it is possible to detect mixing for sin 24 > 0.44 and M,r = 225 GeV corresponds to the limiting case of maximal mixing (sin 24 = 1) discovery. It should be noted that up to now we restricted ourselves to the case of smuon selectron mixing and have neglected stau mixing with selectron and smuon. Moreover for the case of stau smuon or stau selectron mixings bounds from the absence of r + py and 7 -+ ey decays for rn?2 70 GeV are not stringent [5-191 and it is not necessary to have neutralino mass closed to slepton mass as in the case of selectron-smuon mixing. For instance, for the case of stau-smuon mixing in formulae (24) - (26) we have to put B = 0 (only sexchange graphs contribute to the cross sections) and in final states we expect as a result of mixing rfpr acoplanar pairs. The best way to detect 7 lepton is through hadronic final states, since Br( 7 -+ hadrons+ v,) = 0.74. Again, in this case the main background comes from W-decays into (r)*(p) r + v + v in the reaction e+e- -+ W+W-. The imposition of some cuts [ 2 1,221 decreases W-background to 0.07 pb that allows to detect stau-smuon mixing for slepton masses up to 70 GeV. We have found that for m,l = 50 GeV and rnLSp = 25 GeV it would be possible to detect mixing angle sin( 24,) bigger than 0.70. Another detectable consequence of big stau-smuon mixing is the decrease of acoplanar fiWfpCL-events compared to the case of zero mixing. For instance, for the case of maximal mixing sin( 2#++) = 1 the suppression factor is 2. In general we cannot exclude big mixing between all three right-handed sleptons and as a typical consequence of such mixing we expect the excess of nondiagonal acoplanar lepton pairs. Let us formulate the main result of this paper: in a supersymmetric extension of the standard WeinbergSalam model there could be soft supersymmetry breaking terms responsible for flavor lepton number violation and slepton mixing. If sleptons are relatively light and stau-smuon and stau-selectron mixings are not small it would be possible to discover both sleptons and lepton flavor number violation in slepton decays at LEP2. The search for selectron-smuon mixing at LEP2 is rather problematic. At NLC it would be possible to look for not only stau-smuon and stauselectron mixings but also selectron-smuon mixing.
787
I thank CERN TH Department for the hospitality during my stay at CERN where this paper has been started. I am indebted to the collaborators of the INR theoretical department for discussions and critical comments. I am indebted to a referee for pointing out to me an error in the original version of this paper.
References [ 11 S. Dimopoulosand S. Raby, Nucl. Phys. B 192 (1981) 353. [2] E. Witten, Nucl. Phys. B 185 (1981) 513. [3] S. Diiopoulos, S. Raby and F. Wrlczek, Phys. Rev. D 24 (1981) 1681. [4] For reviews and references, see HP Nilles, Phys. Rep. 110 (1984) 3. [5 ] E Gabbiani and A. Masiero, Nucl. Phys. B 322 (I 989) 235. [6] J. Hagelin, S. Kelley and T. Tanaka, Nucl. Phys. B 415 (1994) 293. [7] E Barzumanti and A. Masiero, Phys. Rev. Lett. 57 (1986) 961. [S] G.K. Leontaris, K. Tamvakis and J.D. Vergados, Phys. Lett. B 171 (1986) 412. [9] I. Antoniadis, J. Ellis, J.S. Hagelin and D.V. Nanopoulos, Phys. Lett. B 231 (1989) 65. [lo] S. Kelley, J.L. Lopez, D.V. Nanopoulos and H. Pois, Nucl. Phys. B 358 (1991) 27. [ 1l] L. Ibanez and D. Lust, Nucl. Phys. B 382 (1992) 305. [ 121 V. Kaplunovsky and J. Louis, Phys. Lett. B 306 (1993) 269. [ 131 R. Barbieri and L.J. Hall, Phys. Lett. B 338 (1995) 212. [ 141 D. Choudhury et al., Phys. Lett. B 342 (1995) 180. [ 151 N.V. Krasnikov, Mod. Phys. Lett. A 9 (1994) 2825. [ 161 N.V. Krasnikov, Mod. Phys. Lett. A 9 (1994) 791. [ 171 L.E. Ibanez and C. Lopez, Nucl. Phys. B 233 (1984) 511. [18] For reviews, see HP Nilles, Phys. Rep. 110 (1984) 1; G.G. Ross, Grand Unified Theories (Benjamin, New York 1984); R.N. Mohapatra, Unification and Supersymmetry (Springer, New York 1992). [ 191 Y. Nii and N. Seiberg, Phys. Lett. B 309 (1993) 340. [20] Particle Data Group, Review of particle properties, Phys. Rev. D 50 ( 1994). [21] M. Chen, C. Dionisi, M. Martinez and X. Tata, Phys. Rep. 159 (1988) 201. 1221 H. Baer et al., Low Energy Supersymmetry Phenomenology, CERN-PREj94-45. [23] Report on Searches for New Physics at LEP2, hepphi9602207. [24] R. Becker and C. Van der Velde, in: Proceedings of European Meeting of the Working Groups on Physics and Experiments at linear e+e- Colliders, ed. PM. aNas, DESY-93-123C.
a
28 November 1996
d
__
PHYSICS
ELSEVIER
LETTERS B
Physics Letters B 388 (1996) 783-787
Search for flavor lepton number violation in slepton decays at T UEP2 and NLC N.V. Krasnikov Institute for Nuclear Research, Moscow 117312, Russia
Received 1 December 1995; revised manuscript received 16 August 1996 Editor: R. Gatto
Abstract We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking mass terms there could be detectable flavor lepton number violation in slepton decays. We propose to look for flavor lepton number violation in right-handed slepton decays. We estimate LEP2 and NIX discovery potentials of the lepton flavor
number violation in slepton decays.
Supersymmetric electroweak models offer the simplest solution of the gauge hierarchy problem [ l-41. In real life supersymmetry has to be broken and the masses of superparticles have to be lighter than O( 1) TeV [4], Supergravity gives a natural explanation of the supersymmetry breaking, namely, taking into account that the supergravity breaking in hidden sector leads to soft supersymmetry breaking in observable sector [4]. For the supersymmetric extension of the Weinberg-Salam model soft supersymmetry breaking terms usually consist of the gaugino mass terms, squark and slepton mass terms with the same mass at Planck scale and trilinear soft scalar terms proportional to the superpotential [4]. For such “standard’ supersymmetry breaking terms the lepton flavor number is conserved in supersymmetric extension of WeinbergSalam model. However, in general, squark and slepton soft supersymmetry breaking mass terms are not diagonal due to many reasons [ 5-151 (an account of stringlike or GUT interactions, nontrivial hidden sector, ...) and flavor lepton number is explicitly broken due to nondiagonal structure of slepton soft supersym-
metry breaking mass terms. As a consequence such models predict flavor lepton number violation in pand r-decays [5-131. In our previous note [ 161 we proposed to look for flavor lepton number violation at LEP2 in right-handed slepton decays. In this paper we investigate the “discovery potential” of LEP2 and NLC (next linear collider) of flavor lepton number violation in slepton decays. We find that at LEP2 there is nonzero chance to detect flavor lepton number violation in slepton decays for slepton masses up to 75 GeV provided the mixing is not small. We also discuss the perspectives of NLC for the discovery of lepton flavor number violation in slepton decays. In supersymmetric extensions of the WeinbergSalam model supersymmetry is softly broken at some high energy scale Mour by generic soft terms
0370-2693/96/$12.00 Copyright 0 1996 Published by Elsevier Science B.V. All rights reserved. PZI SO370-2693(96)01213-O
N.V. Krasnikov/Physics
784
+ (mi)ijZk(Z$)+ + (Bm$H,,Hd
+ miHuH,f + m;HdHz + $m,(AA)a
+ h.c.) ,
(1)
where i, j, a are summed over 1, 2, 3 and &,, iiR, 2~ denote the left- (right-) handed squarks, IL, e”Rthe left(right-)handed sleptons and H,, Hd the two Higgs doublets; m, are the three gaugino masses of SU( 3), SU(2) and U( 1) respectively. In most analysis the mass terms are supposed to be diagonal at Mour scale and gaugino and trilinear mass terms are also assumed universal at Mom Scale. The renormalization group equations for soft parameters [ 171 allows one to connect high energy scale with observable electroweak scale. The standard consequence of such an analysis is that right-handed sleptons e”R, ,&R and ?R are the lightest sparticles among squarks and sleptons. In the approximation when we neglect lepton Yukawa coupling constants they are degenerate in masses. An account of the electroweak symmetry breaking gives additional contribution to right-handed slepton square mass equal to the square mass of the corresponding lepton and besides an account of lepton Yukawa coupling constants in the superpotential leads to the additional contribution to right-handed slepton masses
(2)
Letters B 388 (1996) 783-787
tion [ 181. As it has been discussed in many papers [5-151 in general we can expect nonzero nondiagonal soft supersymmetry breaking terms in Lagrangian (1) that leads to additional contributions for flavor changing neutral currents and to flavor lepton number violation. From the nonobservation of ,X --+ e + y decay (Br(p -+ e +y) i 5. lo-” [20]) one can find that [ 5-191
(5) For mzR = 70 GeV we find that (a,,) RR 5 5 . 10e3. Analogous bounds resulting from the nonobservation of r -+ ey and r + ,uy decays are not very stringent [5-191. The mass term for right-handed e”Rand ,& sleptons has the form
(6) After the diagonalization of the mass term (6) we find that the eigenstates of the mass term (6) are ci =e”Rcos(+) ,& = ,&cos(~$)
Here hl is the lepton Yukawa coupling constant and M, is the average mass of sparticles. These effects lead to a splitting between the right-handed slepton masses of the order of
- e”Lsin(C$),
(7) (8)
with the masses M~,2=~[(m~+m~)+((m~-m~)2+4(m~2)2)1~2] (9)
- 0( lo-s)
)
4R Cm& -d,>
+,&sin(#),
- O( lo-‘)
which practically coincide for small values of rnf - rn$ and my2. Here the mixing angle 4 is determined by the formula
m& For nonzero values of the trilinear parameter A after electroweak symmetry breaking we have nonzero mixing between right-handed and left-handed sleptons, however the lefthanded and right-handed sleptons differ in masses (lefthanded sleptons are slightly heavier), so the mixing between right-handed and Iefthanded sleptons (for 2~ and @R) is small and we shall neglect it. In our analysis we assume that the lightest stable particle is gaugino corresponding to U( 1) gauge group that is now more or less standard assump-
tan(24)
= 2mf2(mt
- rni)-’
(10)
The crucial point is that even for a small mixing parameter my2 due to the smallness of the difference rn: - rn: the mixing angle 4 is in general not small (at present state of the art it is impossible to calculate the mixing angle # reliably). For the most probable case when the lightest stable superparticle is the superpartner of the lJ( 1) gauge boson plus some small mixing with other gaugino and higgsino, the sleptons jiR, .!?Rdecay mainly into leptons p,R and eR plus U( 1)
N.V. Krasnikou / Physics Le&m B 388 (1996) 783-787
gaugino A. The corresponding term in the Lagrangian responsible for slepton decays is
785
At LEP2 and NLC in the neglection of slepton mixing ,& and ?R sleptons pair production occurs [ 2 11 via annihilation graphs involving the photon and the Z” boson and leads to the production of jiipi and ?i?R pairs. For the production of right-handed selectrons in addition to the annihilation graphs we also have contributions from the t-channel exchange of the neutralino [ 211. In the absence of mixing the cross sections can be represented in the form
the detection of sleptons at LEP2 have been discussed in Refs. [ 2 1,221 in the assumption of flavor lepton number conservation. The main background at LEP2 energy comes from the W-boson decays into charged lepton and neutrino [ 2 1] . For fi = 190 GeV the cross section of the W+ W- production is aw( W+W-) M 26 pb. [ 221. For selectrons at fi = 190 GeV, selecting events with electron pairs with pztis 2 10 GeV and the acoplanarity angle 19,~2 34” [ 211, the only background effects left are from W 4 evev and evrv where r + evy. For instance, for M% = 85 GeV and Mur = 30 GeV one can find that the accepted cross section is sac = 0.17 pb whereas the background cross . . sectron is Dba&sr = 0.17 pb that allow to detect righthanded selectrons at the level of 5~ for the luminosity 150 pb-’ and at the level of lla for the luminosity 500 pb-‘. For the detection of right-handed smuons we have to look for events with two acoplanar muons however the cross section will be (4-l .5) smaller than in the selectron case due to absence of the t-channel diagram and the imposition of the cuts analogous to the cuts for selectron case allows to detect smuons for masses up to 80 GeV Again here the main background comes from the W decays into muons and neutrino. The imposition of more elaborated cuts allows one to increase the LEP2 right-handed smuon discovery potential up to 85 GeV on smuon mass [ 21,221. Consider now the case of nonzero mixing sin 4 Z 0 between selectrons and smuons. In this case an account of the t-exchange diagram leads to the following cross sections for the slepton pair production (compare to the formulae (15), (16)):
a(e+e-
-+ Jiifi;)
(15)
a(e’e-
-+ jiiF;>
a(e+e-
-+ Zie”;)
(16)
c+(e+e-
--+ $zi)
u(e+e-
-+ Z:jiz)
L1 = @ ( Z_RALZR+ ji~h~fi~ dz
+ h.c.) ,
(11)
where gy M 0.13. For the case when mixing is absent the decay width of the slepton into lepton and LSP is given by the formula
(12) Af=(LMZ)
@SP
2
,
(13)
Sl
where M,r and M~sp are the masses of slepton and the lightest superparticle (U( 1) -gaugino) respectively. For the case of nonzero mixing we find that the Lagrangian ( 11) in terms of slepton eigenstates reads
+,%&(,&Cos(#
+zXsin(4))
= kA2, = k(A + B>2,
+h.c.]
(14)
where A is the amplitude of the s-exchange, B is the amplitude of the t-exchange and k is the normalization factor. The corresponding expressions for A, B and k are contained in [ 2 11. The amplitude B is determined mainly by the exchange of the lightest gaugino and taking this into account leads to an increase of the selectron cross section by factor kin = (4-1.5). As it has been mentioned before we assume that righthanded sleptons are the lightest visible superparticles. So sleptons decay with 100 percent probability into leptons and LSP that leads to acoplanar events with missing transverse momentum. The perspectives for
= k(A+ = k(A+
Bsin2(@))2,
(17)
Bcos2(q5))2,
(18)
= kB2cos2(4)
sin2(4)
(19)
Due to slepton mixing we have also lepton flavor number violation in slepton decays, namely: l-(&R ---) ,.&+ LSP) = Icos2(& I&
-+ e +LSP)
r(z, -+e + LSP) r(zR+ p + LSP)
,
=Isin2(4), =
r c0s2($) ,
= Isin2(4)
Taking into account formulae
(20)
(21) (22) (23)
(20) - (23) we find that
N.V. Krasnikov / Physics Letters B 388 (1996) 783-787
786
a( e+e- -+ e+e-
= k[ (A + Bcos~(@)~ + (A+
To be concrete consider the case of maximal selectron smuon mixing (ml = m2 in formula (6)). For this case bound (5) resulting from the absence of the
+ LSP + LSP) cos4(&
Bsin2(4))2sin4(4)
+ B2sin4(24)/S],
decay ,U --+ ey reads * (24)
a(e+e-
+ p+p”-
+ LSP + LSP)
= k[ (A + Bcos~(~~))~
sin4(@)
+ (A + Bsin2(4))2cos4(4)
+ B2sin4(24)/8]
,
5 5 . low4 (m,-= 70 GeV) ;
2.25~10~~ (m,-= 150 GeV); 4.10W3 (mz = 200 GeV, 5. 10e3 (m,-= 225 GeV) . From the requirement (27) of the absence of destructive interference for the cross section with flavor lepton number violation we find that
(25) a(e+e-
42 m:
--+ p& + eT + LSP + LSP)
ksind24) [(A +Bcos~(+))~
=
+ (A + Bsin2(4))2
+ B2(cas4(+>
+sin4(+))l (26)
It should be noted that formulae (24) -(26) are valid only in the approximation of narrow decay width of sleptons 5 lrn2, - rni,1
2l%,-,
(27)
For the case when the inequality (27) does not hold the effects due to the finite decay width are important and decrease the cross section with violation of flavor lepton number. To be concrete consider the case of maximal slepton mixing. The cross section of the process e+e- ---f e+p- + LSP + LSP is proportional to uN
J -
lD(pl,m,-,r)D(p2,ma,r)
(28) D(p2,m~,r)D(pz,m~,r)12dp:dp~7
where 1 D(p,m,r)
=
p2-m2-irm
(29)
(24)-( 26) and r? M rp = r. The approximation corresponds to the neglection of the interference terms in (28) and it is valid if the inequality (27) takes place. For smaller slepton mass difference an account of the interference terms in (28) is very important. For instance, for Im,- = 5 . 10-3mz we have found numerically that an account of the interference effects leads to the decrease of the cross section (26) by factors 0.99, 0.82, 0.52, 0.15 for Irni - rnil= 2rm,-, 1.5r,-, rm,-, 0.5FmZ respectively.
> 5. 10-3Af
(30)
So we see that for LEP2 energies it is possible to improve p -+ ey bound only for the case when LSP masses closed to slepton mass. For instance, for mr.sP = 0.95m,-,0.9mz,0.8m,-,0.7m,-,0.6mz,0.5mz Af is equal to 0.01, 0.036, 0.13, 0.26, 0.41, 0.56 respectively. For m,-= 70 GeV it is possible to improve ,u -+ ey bound (5) only for rnLsp2 0.9mLsp.However as it has been mentioned in Ref. [ 231 due to the big background the detection of sleptons can become problematic when the mass difference between slepton and neutralino becomes smaller than 10 GeV so the detection of possible selectron-smuon mixing at LEP2 becomes also very problematic. For the Next Linear Collider energies and for mE 5 150 GeV the p --+ ey bound (5) is not so stringent and it is possible to improve it even for the case of relatively small LSP masses when A, M 1. The perspectives for the detection of sleptons at NLC (for the case of zero slepton mixing) have been discussed in Ref. [ 231. The standard assumption of Ref. [ 241 is that sleptons are the LSP, therefore the only possible decay mode is 7 -+ I+ LSP. One possible set of selection criteria is the following: 1. t&or, 2 65”. 2. p~,ti~ 2 25 GeV. 3. The polar angle of one of the leptons should be larger than 44’, the other 26’. 4. (rnll -rn~)~ 2 100GeV2. 5. El* 2 150 GeV. For fi = 500 GeV and for integrated luminosity 20 fb-‘, a 5g signal can be found up to 225 GeV provided the difference between lepton and LSP is greater than 25 GeV [ 241. Following Ref. [ 241 we have analyzed the perspective for the detection of nonzero slepton mixing at NLC. In short, we have found that for
N.V. Krasnikov / Physics Letters B 388 (1996) 783-787
M~sp = 100 GeV it is possible to discover selectronsmuon mixing at the 5a level for M,r = 150 GeV provided that sin2# _> 0.28. For MS1 = 200 GeV it is possible to detect mixing for sin 24 > 0.44 and M,r = 225 GeV corresponds to the limiting case of maximal mixing (sin 24 = 1) discovery. It should be noted that up to now we restricted ourselves to the case of smuon selectron mixing and have neglected stau mixing with selectron and smuon. Moreover for the case of stau smuon or stau selectron mixings bounds from the absence of r + py and 7 -+ ey decays for rn?2 70 GeV are not stringent [5-191 and it is not necessary to have neutralino mass closed to slepton mass as in the case of selectron-smuon mixing. For instance, for the case of stau-smuon mixing in formulae (24) - (26) we have to put B = 0 (only sexchange graphs contribute to the cross sections) and in final states we expect as a result of mixing rfpr acoplanar pairs. The best way to detect 7 lepton is through hadronic final states, since Br( 7 -+ hadrons+ v,) = 0.74. Again, in this case the main background comes from W-decays into (r)*(p) r + v + v in the reaction e+e- -+ W+W-. The imposition of some cuts [ 2 1,221 decreases W-background to 0.07 pb that allows to detect stau-smuon mixing for slepton masses up to 70 GeV. We have found that for m,l = 50 GeV and rnLSp = 25 GeV it would be possible to detect mixing angle sin( 24,) bigger than 0.70. Another detectable consequence of big stau-smuon mixing is the decrease of acoplanar fiWfpCL-events compared to the case of zero mixing. For instance, for the case of maximal mixing sin( 2#++) = 1 the suppression factor is 2. In general we cannot exclude big mixing between all three right-handed sleptons and as a typical consequence of such mixing we expect the excess of nondiagonal acoplanar lepton pairs. Let us formulate the main result of this paper: in a supersymmetric extension of the standard WeinbergSalam model there could be soft supersymmetry breaking terms responsible for flavor lepton number violation and slepton mixing. If sleptons are relatively light and stau-smuon and stau-selectron mixings are not small it would be possible to discover both sleptons and lepton flavor number violation in slepton decays at LEP2. The search for selectron-smuon mixing at LEP2 is rather problematic. At NLC it would be possible to look for not only stau-smuon and stauselectron mixings but also selectron-smuon mixing.
787
I thank CERN TH Department for the hospitality during my stay at CERN where this paper has been started. I am indebted to the collaborators of the INR theoretical department for discussions and critical comments. I am indebted to a referee for pointing out to me an error in the original version of this paper.
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