SUSY at TeV energy scale

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1 SUSY at TeV energy scale Masato JlMBO Theoretical Physics Laboratory, School of Health Science, Fujita Health University, Toyoake, Aichi , Japan ABSTRACT A guide to prospective studies for SUSY particle search is given within the minimal supersymmetric standard model. 1. INTRODUCTION The hypothesis that supersymmetry (SUSY) is a symmetry of a more fundamental theory than the standard model has fasinated many physicists [1, 2, 3]. As a consequence of SUSY theory, new particles called SUSY particles emarge with spin differing from the corresponding usual particles by half a unit. The search for SUSY particles is a crucial part of the present high-energy physics [4, 5, 6]. Such particles, however, have not yet been discovered. Thus we hope wc will get a glance at the SUSY world at TeV e + e~ colliders such as CLIC, NLC and JLC [7]. In this talk we shall discuss the methodology on the SUSY particle search within the minimal supersymmetric standard model (MSSM). In section 2 we briefly review the theoretical feature of MSSM. In section 3 and 4 experimental lower bounds and theoretical upper bounds on masses of SUSY particles are summarized. We give the way to search for SUSY particles through pair production and associated production in section 5 and 6. Finally we discuss various possibilities at TeV energy scale in section

2 2. MSSM A SUSY standard model with soft global SUSY-breaking terms is obtained from a SUSY GUT coupled with N = 1 supergravity which is broken in the hidden sector [1]. It has important properties as follows. i) Gauge couplings and Yukawa couplings are fixed to those of the standard model. ii) Masses and mixings of the SUSY particles are quite arbitrary. To specify MSSM we adopt the following assumptions here: 1) Minimal particle contents J The gauge group is SU(Z) C x SU(2) L x U(l) Y - [ The "matters" are quarks, leptons and two Higgs doublets. 2) Universality A universal mass exists for all the scalars ^1 > at GUT energy scale. A universal mass exists for all the gauginos J 3) R-parity unbroken R usual) = + usual) R SUSY) = - SUSY) i.e., the lightest SUSY particle (LSP) is stable. The mass terms in the lagrangian for gaugino-higgsino fields are L m = - l -M 3 \\ a - l -xm (0) X ~ (?M< C >V + h.c.), where A, \ a n d 4> denote gluino, neutralino and chargino fields, respectively. We are concerned with the last two because we have interest in e + e~ collisions mainly. Their expressions are as follows: f X l\ 1 'w+ + (w-) c h+ + (h-) c -186-

3 and AfW I M\ 0 -Mzc/?sin0w Mzs/?sin0 w \ 0 Mi Mzc/3cos9yv -Mzsflcosdyj -MzcfismByj Mzcj3cos8w 0 /J.R \ Mzsf3sh\9w Mzs(3cos6w MR 0 / M { c )_( * Ww0) \s/2m w cp fi K J where cf3 and sf3 mean cos0 and sin/?,.respectively. The gaugino masses Mi's are related to the universal mass M at GUT energy Mx as ai(mx) The renormalized mass parameter fir is in the coupling between the two Higgs fields, and related to the top quark mass M t or the Yukawa coupling constant h t [2] as MR = Znn,. C{l-2KM l iyi* yjlhtjgmw The parameter j3 is related to the vacuum expectation values of the two Higgs fields as (#2 ) "2 tan 3 = j - ^ - =. The physical masses of gauginos and higgsinos are determined by the diagonali?,ation of the mass matrices above. Those are obtained numerically, and expressed by contour plots on the (M, pi) plane as in Ref. [3] (hereafter we use the symbol H instead of /*R). We assume that the lightest neutralino is LSP

4 3. EXPERIMENTAL LOWER BOUNDS The search for SUSY particles is now in process on the Z pole in e + e~ collisions at LEP [4, 5, 6]. There has not been any signal confirmed, but exist excluded regions for several processes of SUSY particle production. For example, excluded regions obtained from neutralino search [5] are shown in Fig. 1. MM,mm ±~] Fig. 1. Excluded regions in the (M,/i) plane (from Ref. [5]). The region A and B is excluded by search for Z * xlxh a n c ' ^ ~* X2X2 (,\ : the lightest neutralino; x : ^e next-to-lightest neutralino), respectively. The region C is not examined because the lighter chargino xf ' s lighter than X there. The doted contour and the dashed one denote the boundary of the domain kinematically accessible in Z decays into neutralinos with and without the invisible mode Z» X?X?i respectively. The mass limits obtained for selectron search and chargino search [6] are shown in Fig. 2 and Fig. 3, respectively. The domain above the diagonal correspond to the stable case. The former limits are derived with two assumptions, Mj = Mj or Mj -C Mj. At TeV energy scale, however, the magnitude of the mass diference between /L and /^ becomes important. The latter limits are derived for pure higgsino and pure wino. For general charginos, the excluded regions in the (M, ft) plane are obtained by search for xf [6]

5 MJ*(GeV/c 2 ) Fig. 3. Mass limits for pure higgsino and pure wino (from Ref. [6]). 4. THEORETICAL UPPER BOUNDS Here we summarize an attempt to obtain upper bounds for masses of SUSY particles theoretically proposed by Barbieri and Giudice [8]. First we consider the potential along the neutral components of the Higgs fields: V(H x,h 2 ) = 9 ~^(\H l \ 2 -\H 2 \ 2? + ml\h l \ 2 +ml\h 2 \ 2 -ml(h l Hi+h.c.). o The quartic term maintains its form from high to down energy, except for the usual renormalization of the gauge coupling constants themselves. The quadratic -189-

6 terms, however, get heavily renormalized from the original ones, and acquire the form: ' m\ = -am 2 - bamm + cm 2 - da 2 m 2 + Cfi 2 < m\ = m 2 + e/«2 + f M 2, m\ = gfim + hb\im + kaftm where m, M, fi, A and B are the original parameters. The dimensionless renormalization group coefficients (a, 6, c, etc.) are functions of the gauge and of the top Yukawa couplings. The breaking of the electroweak group SU{2)\ J x U{l)y following conditions are simultaneously satisfied: takes place when the m\ + m 2 > 2\ml\ m\m\ < m\ This occurs in the direction v v (H\) 7=cos(3 = v\, (Hi) j= sin/3 = v? v2 v2 2_ S(m\ - ml tan/?) r 4A/J " -(<7»+j«)(tan l /?-l) i = (7+7 2 )J ' s i n 2 0 = _*»!_ mj + mj Considering the various conditions, ir/4 < /? < TT/2. The crucial equation is for the squared Z -mass, M 2 _ 2(ro 2 - ml tan /?) ~ (ta 2 /?-l) z This allows us to express M as a function of the five parameters, ai = (fi,m,m,a,b) (i = 1,...,5), and of the top Yukawa coupling h t, that is, Ml = Mf(a,;A,). Keeping the Z -mass fixed at its physical value, we can avoid the fine tuning

7 among a; by requiring for every a;, I a, flmf(ai;m A The upper bounds for A = 10 on the masses of SUSY particles are shown in Ref. [8]. Their applications for the discovery limits at the future colliders are shown in Ref. [3] and Ref. [9]. 5. PAIR PRODUCTION Pair production of SUSY particles in e + e~ has been considered by many authors [1], The detailed analysis, however, has been performed recently by Bear el al. with various values for mixing angles and parameters of MSSM [10] Their calculations are for pair production at vs = 2 TeV, the energy proposed for CMC at CERN [7]. Thus we would not repeat these calculations in details, but we will have to start similar calculations for JLC in the energy range between 500 GeV and 2 TeV. For the purpose above, we give a catalogue on pair production of SUSY particles. Far from the Z pole, amplitudes of annihilation processes become smaller at TeV or sub-tev energies. Thus the large cross sections are expected only for the pair production of selectron, chargino and neutralino. The signal which will be first obtained is determined by the mass hierarchy of SUSY particles. When the next-to-lightest SUSY particle (NLSP) is not so heavier than LSP, clear signals are expected due to the direct decay, NLSP > LSP + (a light usual particle). CATALOGUE OF PAIR PRODUCTION Sleptons or squarks I. Selectron - LL(RR) L(R) e L(R) + e + '" e L(R) -191-

8 n. Selectron - LR(RL),-- e l.(r) oc M^o ^e R(L) HI. Charged slepton (or squark) tim 'L(R) W Z "\ r K k(r) (*" IV. Sneutrino >/ Ch argin os Neutralinos 6. ASSOCIATED PRODUCTION Associated production of SUSY particles with a usual particle becomes important when the beam energy is less than the mass of NLSP. There are several kinds of interesting one, which are considered by our study groups [11, , 14]

9 We know that two categories of associated production exist when the direct decay is the main decay mode: Type I. Single selectron [11, 12] The event topology is quite different than that of usual particle production. Thus the signal can be easily separated. Type H. Single W + SUSY particles [13, 14] There exist the production process of usual particles with similar event topology. Thus detailed studies are necessary on various distributions of the detectable particles. In both cases we have found that polarized e 1 information on the masses of SUSY particles. beams are useful to obtain the r- My= 100 GeV a, Mg [GeV] Fig. 4. The total cross section for the single selectron production at y/s = 2 TeV. Recently, we have proposed analytical cross section formulae for the single selectron production by using the equivalent photon approximation (EPA) and -193~

10 by keeping the mass of photino [11]. In TeV energy region, the one-photon exchange diagrams dominate, so the EPA works well. Furthermore, our formulae can be easily applied to the selectron production with the general neutralino, and to several processes of associated production. We show an example calculation based on our formulae as in Fig DISCUSSION We have surveyed a field of study on the search for SUSY particle within MSSM. We, however, have not yet mentioned one of the most crucial points. As shown in Ref. [15], there is another possibility in the decay of SUSY particles than the direct decay, i.e., the cascade decay. For example, the decays ofselectron are 'X (direct decay), e and (cascade decay) The missing transverse momentum JP? of the cascade decay is lower than that of the direct decay. Thus we need more detailed studies on various distributions of the detectable particles. ACKNOWLEDGEMENTS I am grateful to Dr. S. Kawabata for provide a good opportunity for me. I thank Dr. M. Peskin for discussions at RIFP in Kyoto and at KEK in Tsukuba. Special thanks are due to Dr. A. Bartl for appriciation of a copy of transparencies used in my talk, for hospitality during visit, to Institut fiir Theoretische Physik der Universitat Wien and for acceptance of our offer for him to present a talk at the JPS meeting held March in 1991 in Tokyo

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