1
Supergravity Unification
a b cd Ali H. Chamseddine ,R.Arnowitt and Pran Nath ∗ aCenter for Advanced Mathematical Sciences (CAMS) and Physics Department, American University of Beirut, Lebanon bCenter for Theoretical Physics, Department of Physics, Texas A& M University, College Station TX 77843,-4242, USA cTheoretical Physics Division, CERN CH-1211, Geneve 23, Switzerland d Department of Physics, Northeastern University, Boston, MA 02115-5000, USA
A review is given of the historical developments of 1982 that lead to the supergravity unified model (SUGRA) with gravity mediated breaking of supersymmetry. Further developments and applications of the model in the period 1982-85 are also discussed. The supergravity unified model and its minimal version (mSUGRA) are currently among the leading candidates for physics beyond the Standard Model. A brief note on the developments from the present vantage point is included.
1. Introduction efforts to break global supersymmetry sponta- neously lead to some unpleasant features as dis- cussed below and consequently such efforts were The main advantage of supersymmetry [1] in abondoned. An alternative suggestion, advanced the context of building models of particle inter- however, was to introduce in an ad hoc fashion actions is that it offers a technical solution to the soft breaking terms consisting of dimension 2 and hierarchy problem of masses[2]. Thus, for exam- dimension 3 operators in the theory which break ple, the Higgs field is not protected from acquir- supersymmetry but nonetheless respect the ul- ing large masses though loop corrections and in traviolet behavior of the theory and respect the a grand unified theory the radiative corrections gauge hierarchy since such terms are super renor- 14 would give it a GUT size mass of O(10 )GeV. malizable[4,5]. The list of such soft terms con- However, if the scalar fields appear in a super- sists of scalar mass terms such as for squarks and multiplet then supersymmetry would require a sleptons and for the Higgs, bilinear scalar terms, cancellation of the loop corrections in the super- Majorana mass terms for the gauginos, as well as symmetric limit. When supersymmetry is bro- cubic bosonic terms involving products of scalar ken the loop corrections to the Higgs mass and fields. However, such a procedure introduces gen- to other masses will then have a dependence on erally an enormous number of free parameters in the SUSY breaking scale. So one finds that the the theory. For the so called Minimal Supersym- breaking of supersymmetry is central to getting metric Standard Model this number is around a meaningful result out of supersymmetric theo- 104. A theory such as this is not predictive. ries. Up to 1982 models in particle physics were in To understand the origin of soft breaking terms the framework of global supersymmetry[3]. How- and to derive them from the basic model one ever, this effort faced an important hurdle, i.e., needs to break supersymmetry spontaneously. it is difficult to break global supersymmetry in However, the spontaneous breaking of supersym- a phenomenologically acceptable fashion. Thus metry leads to a Goldstone fermion, or a Gold- stino and it is important to absorb this Goldstino ∗Permanent address of P.N 2 to achieve a meaningful theory which is not in couplings and on the soft parameters. The evo- contradiction with experiment. To absorb the lution of these parameters from the GUT scale Goldstino one needs a vector-spinor, i.e., a mass- down to the electro-weak scale turns the deter- less spin 3/2 field or a gravitino. The necessity minant of the Higgs mass square matrix negative to get rid of the undesirable Goldstino requires which triggers the breaking of the electro-weak that we consider an extension of supersymmetry symmetry[13]. In the framework of MSSM there to include gravity. In this extension the gravitino are two Higgs doublets in the theory, one which is the superparter of the graviton and thus one gives mass to the up quark and the other which is led to consider supergravity[6] as the starting gives mass to the down quark. These two dou- point for a phenomenologically viable breaking of blets provide a bilinear term with a mixing pa- supersymmetry. However, to build models within rameter µ in the superpotential. Although this supergravity one needs to couple N=1 supergrav- term is supersymmetric the µ parameter is of the ity with chiral multiplets and a vector multiplet size of the soft breaking terms. An important leading to the so called applied supergravity[7,8]. aspect of the radiative breaking of the electro- Remarkably the framework of applied supergrav- weak symmetry is that the spontaneous symme- ity allows one to break supersymmetry in a spon- try breaking conditions allow one to determine taneous fashion and also to build realistic mod- the µ parameter and this eliminates one of the els. One of the basic ingredients in the analysis is arbitrary parameters in the theory. that the scalar potential of the theory is not pos- The radiative breaking of the electro-weak sym- itive definite which was one of the main hurdles metry which arises in SUGRA model relates the in finding a global vacuum with broken supersym- weak scale MW with the soft SUSY breaking scale metry in the framework of global supersymmetry. which in turn depends on the Planck constant. For the case of supergravity grand unification pro- The SUGRA model in this fashion connects two posed in 1982[9] it is possible to break supersym- fundamental scales of physics, i.e., the Fermi scale metry spontaneously in a so called hidden sector and the Planck scale. Further, the fact that and arrange the vacuum energy to vanish. The MW is determined in terms of soft parameters information of supersymmetry breaking from the up to gauge and Yukawa coupling constant fac- hidden sector to the physical sector is communi- tors means that the soft parameters must lie in cated by gravity resulting in the growth of soft the TeV range, or else, one is faced with a new breaking terms in the physical sector[9,10]. For kind of a fine tuning problem. This result leads to definiteness the GUT group chosen in the 1982 the remarkable prediction in SUGRA GUTS that work was SU(5) although the main results of the one must have sparticles lying in the TeV mass effective theory are not tied to any specific GUT range. group[9,11,12]. Supergravity grand unification model proposed 2. SUGRA Unification in 1982 also resolves another problem, i.e., the puzzle of the breaking of the electro-weak We discuss now the main features of the work of SU(2)L U(1)Y symmetry. There is no natural Ref.[9]. To build models containing gravity one mechanism× for the breaking of the electro-weak needs to couple supergravity with an arbitrary symmetry in the Standard Model, and one ar- number of chiral multiples χi(x),zi(x) (where { } ranges for the breaking by the introduction of a χi(x) are left (L) Weyl spinors and zi(x) are scalar tachyonic mass term. However, the introduction fields) and a vector multiplet which belongs to of such a tachyonic mass term is rather ad hoc. the adjoint representation of the gauge group. Supergravity grand unification provides a natural Such a coupling scheme depends on three arbi- mechanisms for the generation of the tachyonic trary functions: : the superpotential g(zi), the mass term. In SUGRA unification one starts at gauge kinetic function fαβ(zi) (which enters in α µνβ the GUT scale with prescribed boundary condi- the Lagrangian as fαβFµν F with α, β = gauge tions on the gauge coupling constants, Yukawa indices) and the Kahler potential d(zi,zi†). The 3 bosonic part of the Lagrangian is given by and one has in this case that the gravitino mass is
e e a α b 2 2 LB = R + G, DαzaD z m 3 = κ = κm (7) −2κ2 κ2 b 2 e α µνβ In addition to the bosonic interactions one also fαβFµν F eV (1) −4 − has interaction structures in the theory which in- 18 volve gauge couplings of the gauginos to the chiral Here κ 1/MP` where MP lanck =2.4 10 GeV, G≡ depends on the superpotential g(z),× and multiplets and these take the form on the Kahler potential d(z,z†)sothat α α T j Lλ = igαλ¯ zi( )ij χ + h.c. (8) 2 6 − 2 κ κ 2 G = d(z,z†) ln( g )(2) − 2 − 4 | | Further, the superpotential contributes to both and V is the effective potential for the scalar com- the fermi and the bose interactions. Thus the i ponents of the chiral multiplets in the theory and Fermi interactions for the Weyl spinors χ are is given by given by[14] 1 1 G 1a b 1 α a 2 iC j V = e− (3+G− G,aG, )+ (G, aT z ) (3) Lg = (¯χ gij χ + h.c.)(9) −κ4 b 8κ4 −2 As noted in the introduction the potential is no We now elaborate on some of the further details longer positive definite because of the Planck in the construction of SUGRA GUT models. One scale corrections from supergravity. Of course, in of the immediate problems one faces in construct- the limit MP lanck one recovers the result of ing such models is that of protecting the gauge →∞ global supersymmetry. However, the terms pro- hierarchy. Since O(MP lanck) one finds ∼ portional to 1/MPLanck are essential in generat- that terms involving zizjz would develop masses ing an acceptable spontaneous breaking of super- which are size O(MP lanck) and one has to sup- symmetry. The simplest way of breaking super- press them. A very convenient way to overcome symmetry spontaneously is to introduce a term this problem is to use the separation of the hid- which is a chiral gauge singlet and enters linearly den and the physical sectors, i.e., place the chiral in the superpotential, i.e., multiplets of the physical sector in one part of
2 the superpotential (g1) and place the chiral fields gSB = m (z + B)(4)that break supersymmetry in another part of the where the constant B is chosen to absorb the superpotential in the hidden sector (g2)withno vanishing of the cosmological constant. This direct interaction between the two sectors, i.e., term generates a spontaneous breaking of su- one writes[9,12] persymmetry and gives a gravitino mass of size 2 g(zi)=g1(za)+g2(z) (10) m /MP lanck. However, it was later realized that the precise form of the superpotential that breaks where zi = za,z where za are physical sec- supersymmetry is not important, and essentially tor fields{ (squarks,} { sleptons,} higgs) and z are the what one needs is any form that breaks super- hidden sector fields whose VEVs z = (MP`) symmetry and has the property that gSB = g2(z) break supersymmetry. In this arrangementh i O of where[12] separating the superpotential into a physical sec- m2 tor and a hidden sector one finds that the gauge g = f(κz)(5) 2 κ hierarchy is maintained by the additive nature of the physical and the hidden sector terms in the so that at the minimum[12] superpotential. The actual proof of this remark- 1 m2 able theorem that the low energy theory is pro- ,<κz>O(1), (6) ∼ κ ∼ 2 ' κ tected from corrections proportional to the GUT 4 scale and the Planck scale is rather subtle and we finds that the soft SUSY breaking with the as- shall discuss this shortly. For the physical sector sumption of the flat Kahler potential generates a of the theory which involves the quarks, the lep- universal mass for the scalar fields, and also uni- tons and the higgs we take the following potential versal bilinear and trilinear couplings arise in the theory. While in the simple model with a flat gauge kinetic energy function the gauginos are 1 1 g = λ ( trΣ3 + MtrΣ2)+λ H (Σ + 3M )H massless at the tree level they do develop masses 1 1 3 2 2 0 0 x yz vw through loop corrections where the GUT fields +λ3UH0H + xyzvwH M f1M circulate in the loops with masses[15] xy +Hx0 M f2My0 (11) αi D(R) m˜ i = m 3 C (15) xy ¯ 2 Here M and Mx0 are the 10 and 5 of quarks and 4π D(A) leptons, H and H are the 5¯ and 5 of Higgs, U is a 0 where α is the gauge coupling constant associ- singlet and Σ is a 24 plet of SU(5). Minimization i ated with the sub groups SU(3), SU(2) and U(1), of the scalar potential in this case gives the result and C is the Casimir, D(R) is the dimensionality of the representation exchanged, and D(A) is the x dimensionality of the adjoint representation. One < Σy >= MDiag(2, 2, 2, 3+2, 3 2) (12) − − − can also generate tree level masses by assuming a x 2 x and = O(κm )δ ,where field dependence in the gauge kinetic energy func- x ∼ 5 2 depends on the soft SUSY parameters. Here tion fαβ. In this case one finds that the gauginos α 0 β α one finds quite remarkably that supersymmetry gain a mass at MG of (m1/2)αβλ γ λ (λ = breaking in the hidden sector induces the break- gaugino Majorana field) where ing of SU(2)L U(1)Y so that SU(2)L U(1)Y × × → 1 1 i 1 i U(1)em. One notes that the breaking of SU(2)L (m1/2)αβ = κ− G (d− )j fαβj† m3/2 (16) 2 × 4 h i U(1)Y is semi-gravitational with κm 300 GeV ∼ and can account for the W and Z mass. i 1 i Here G ∂G/∂z†,(d− ) is the matrix uni- ≡ i j As noted earlier the miraculous thing in this verse of di and f = ∂f /∂z . For the case of model is that the integration of the heavy fields j αβj αβ j the flat Kahler potential where di = δi one finds do not mix with the low energy sector of the the- j j that the gaugino masses are universal at the GUT ory. In general the presence of the large scale scale. Further, more generally one can write the M M and M introduces a new hierar- G P lanck gravitino mass so that chy∼ problem as one can expect gravitaional cor- 1 rections of sizes[9,12] m 3 = κ− exp[G/2] (17) 2 h i (κM)M, (κM)2M, .., (κM)6M,.. (13) In the above we discussed how spontaneous su- persymmetry breaking in the hidden sector in- However, the detailed analyses show that all such duces soft breaking terms in the physical sec- corrections vanish, and the low energy theory con- tor of the theory which in turn induce break- tains only terms of O(κm2). An analysis un- ing of the electro-weak symmetry. The fact that der the assumption of a flat Kahler potential the spontaneous breaking of the supersymmetry and on integration over the heavy fields shows triggers the breaking of the electro-weak symme- that the low energy theory can be parametrized try establishes for the first time a direct connec- by[9,11,12] tion between physics at the Planck scale and the physics at the electro-weak scale. The electro- 2 1 0 (3) 1 0 (2) Vsoft = m zaz†+ A W + B W +h.c. (14) 0 a 3 2 weak symmetry breaking in the model of Eq.(1) was induced at the tree level through an effec- where W (3) is the cubic part and W (2) is the tive cubic interaction. Now it turns out that quadratic part of the superpotential. Thus one one can in fact do away with the cubic term 5 and induce spontaneous breaking of the electro- vature terms sometimes appear in string models. weak symmetry via renormalization group ef- The appearance of non-flatness in the Kahler po- fects. The basic idea here is that the one uses tential generates non-universalities in the soft pa- the GUT boundary conditions on the gauge cou- rameters enlarging the number of parameters in pling constants and the Yukawa couplings, and the theory[16]. Further, the picture of supersym- the boundary conditions on the soft parame- metry breaking via chiral scalar terms in the hid- ters at the GUT scale and uses the renormaliza- den sector of the theory is an effective treatment tion group equations to evolve them down from of some more basic phenomenon in the underly- the GUT scale to the electro-weak scale. The ing fundamental theory which is still unknown. running of the renormalization group equations Several possibilities for the nature of such a phe- with at least one soft SUSY breaking parame- nomena including the possibility of condensates ter non-zero and the top quark Yukawa coupling breaking supersymmetry have been discussed[17] turn the determinant of the Higgs mass matrix in the literature. In addition, most string models 2 (and specifically the H2 running (mass) )neg- that accomodate grand unification at the GUT ative which triggers the breaking of the electro- scale reduce to a SUGRA model below MGUT , weak symmetry. The minimization conditions for and thus mSUGRA remains a bench mark for the scalar potential with respect to the Higgs testing experimental data with theory. Next we VEVs v1,2 = H1,2 at the electro-weak scale discuss the sparticle spectrum that emerges in provides the followingh i two relations[13] µ2 = such a theory at low energy. 2 2 2 2 2 2 (µ1 µ2tan β)/(tan β 1) MZ /2; and sin β The minimal SUGRA model with the soft − 2 2 2− − =( 2Bµ)(2µ + µ1 + µ2). Here tanβ = v2/v1,B SUSY parameters defined by Eq.(18) generates − B is the quadratic soft breaking parameter (Vsoft = a low energy mass spectrum for the Higgs and for BµH H ), µ = m2 +Σ,andΣ are loop cor- the sparticles which possesses identifiable proper- 1 2 i Hi i i rections. In the above all parameters are run- ties. The Higgs sector of the theory gives three ning parameters at the electroweak scale Q which neutral fields, one of which is a pseudo-scalar (A) can be taken to be Q = MZ . The first relation and the other two are scalars (h,H). The masses above determines µ while the second allows one of the scalars are related to the masses of the to eliminate B in favor of tanβ. This determina- pseudo-scalars by the relation[18] tion increases the predictivity of the model. With inclusion of the constraints of the electro-weak 1 symmetry breaking the minimal SUGRA model m2 = [M 2 + M 2 ((M 2 + M 2 )2 h,H 2 Z A ± Z A (mSUGRA) depends on four soft breaking param- 2 2 2 1 4(cos 2β) m M ) 2 ] (19) eters and one sign − Z A m0,m1/2,Ao,B0,sign(µ) (18) In addition there is a charged Higgs boson whose mass is given by Alternately one may choose m0, mg˜, At, tanβ, 2 2 2 and sign(µ) as the independent parameters. If M = MW + MA (20) one allows for complex soft parameters then af- ± ter field redefinitions there are two additional pa- The mass relations for the scalar Higgs lead to rameters which can be chosen to be the phase of the result[18] A0 and the phase of µ. The appearance of the mh MZ (21) phases brings into the theory in a natural way ≤ new sources of CP violation over and above the Of course, this is a relation at the tree level and CP violation in the CKM mass matrix. Further, there are important loop corrections to this for- the nature of physics at the Planck scale is not mula. fully understood and it is likely that the assump- One can also discuss the masses and the cou- tion of a flat Kahler potential should be relaxed plings for the sparticles that appear in the the- by the introduction of curvature terms. Such cur- ory. The superpartners in the theory consist of 6 gauginos, Higgsinos and sfermions. The gaugino- Higgsino sector involves the trilinear Higgs- 2 2 2 8 3 1 2 Higgsino-gaugino coupling which after sponta- m = m + m +˜α [ f + f + f ]m 1 u˜L 0 u G 3 2 1 neous breaking of the electro-weak symmetry gen- 3 2 30 2 erates a gaugino -Higgsino mixing term. In the 1 2 2 2 + sin θW MZ cos2β (26) charged gaugino-Higgsino sector one finds a mass 2 − 3 ˜ matrix (in the W˜ ± H± basis) of the form[19] − and foru ˜R one has 8 8 m˜ √2M sinβ 2 2 2 2 W mu˜ = m0 + mu +˜αG[ f3 + f1]m 1 R 3 15 2 Mχ± = (22) 2 2 2 √2MW cosβ µ + sin θ M cos2β (27) 3 W Z The eigen-vectors of this matrix (Winos) have the 2 Here fi(t)=(1 1/(1 + βit) )/βi (i=1,2,3) mass eigen-values 2 − 2 where t = ln(MG/Q ), βi =(bi/4π)˜αi,where bi =(33/5, 1, 3) for U(1), SU(2) and SU(3), 1 1 1 − 2 2 2 2 2 2 m˜ = [4ν++(µ m˜ 2) ] [4ν +(µ+˜m2) ] (23) andα ˜G = αG/(4π), where fi are the form fac- ± 2| − ± − | tors. Similar relations hold for the sleptons. Us- wherem ˜ = λ and λ are the eigen-values of ing the above analysis one can write the low en- the M, and± ν | are±| defined± by ergy effective Lagangian in terms of the diagonal- ± ized fields. This effective Lagrangian was given in Ref.[19,8,18]. √2ν = MW (sinβ cos β) (24) ± ± Soon after the invention of SUGRA model there was an intense activity to elucidate its ex- In the neutral gaugino - Higgsino sector one perimental implications. Since the values of m ˜ ˜ ˜ ˜ 0 finds (in the (W3, B, H1, H2) basis) the mass and m 1 were not fixed by the theory (and re- 2 matrix main still to be fixed by experiment) it was nat- ural then to assume the lowest values compatible m˜ 2 oab with experiment at that time. One of the im- portant signals for SUGRA models with R parity o m˜ cd 1 invariance that emerged was the missing energy M 0 = (25) χ signal. Thus supersymmetric decays of the W aco µ and Z were widely discussed such as W W˜ +Z˜ − ˜ ˜ → and Z W + Z as well as decays of the Wino, bd µo the neutralino→ and the sfermions, etc were widely − studied[20,21] where a = M cosθ cosβ, c = tanθ a, b = Z W W ˜ ˜ ˜ ˜ − W l +¯νl + Zi,,q1 +¯q2 + Zi,h+ Zi,.. MZ cosθW sinβ,d=-tanθW b and θW is the weak − → ˜ ˜ ¯ ˜ mixing angle. The eigen-vectors of this mass ma- Zk ± +W ∓,l+ l + Zj,.. → trix (Zinos) have a somewhat complicated analyt- ˜ ˜ ˜ f f + Z, f1 + W,.. (28) ical form since the eigen value equation here is a → quartic one. However, the structure of the matrix In all these decays the identifying signal is large reveals that there are regions where some Zinos missing energy associated with the disappearance may be mostly either gauginos or Higgsinos. of the lightest neutral particle which is abso- For the sfermions it is found that the masses lutely stable under the assumption of R parity receive contributions from the D terms and from invariance. Missing energy signals at colliders the gaugino loop corrections so that at low energy also arise, such as in sparticle (˜s) pair produc- one has, example foru ˜L[19,13], tion pp¯ s˜ +˜s + X. Each sparticle is expected → 7 to decay producing missing energy. An impor- dimension five operator depends on the nature of tant implication of the fact that the lightest su- the GUT group and there are several possibili- persymmetric particle (lsp) would be absolutely ties here such as SU(5), SO(10), E(6) etc. Much stable under R parity conservation is that such a of the early work in proton stability was in the particle is a candidate for non-baryonic cold dark framework of the minimal SU(5) model since such matter. Specifically, the lightest neutralino ap- a group also appears in the breaking of larger pears a good candidate for the LSP[22]. GUT groups. However, what is unique about pro- Another important implication of SUGRA ton decay via dimension five operators is that it model that was analysed was the supersymmetric depends on both the GUT structure which gen- correction to the muon anomalous moment gµ 2. erates the baryon and lepton number violation Thus soon after the formulation of the SUGRA− in the theory and on the soft breaking sector of models analyses of gµ 2 were carried out us- the theory which enters in the dressing of the ing the SUGRA unification− framework[23]. These dimension five operators and leads to dimension represented the first realistic and reliable analy- six operators after dressing with the chiral struc- ses of the effects of supersymmetry on the muon ture LLLL, LLRR, RRLL and RRRR for the four anomaly. Since SUGRA provided the first realis- fermi interaction that governs proton decay. Thus tic framework it was now possible to make quan- after the formulation of the SUGRA models it was titative predictions. Specifically it was pointed possible to carry out detailed analyses of proton out that the effect of the electro-weak corrections decay amplitudes using the framework of SUGRA could be as large or larger than the Standard unification in the dressing loop diagrams. This Model electro-weak correction and any experi- analysis was carried out in Refs.[25,26]. As is evi- ment which tests the SM electro-weak contribu- dent predictions of the proton lifetime depend on tion to gµ 2 would also test the supersymmetric the low energy parameters and on the GUT pa- correction.− This result played a role in the pur- rameters. If one has sufficient information on the suit to improve the experimental limits on gµ 2 low energy parameters then that would lead to a and provided another reason aside from checking− constraint on the nature of GUT physics. the Standard Model result to get a better mea- surement when the Brookhaven experiment E821 6. A View from the Present was being proposed around 1984. In the intervening period since 1982-85 -present We turn now to another aspect of SUGRA there has been considerable further activity in the models which pertains to baryon and lepton num- applications of SUGRA models. Further, there is ber violation in the model. Here on must distin- now beginning to accumulate some indirect ev- guish between two aspects to SUGRA unification, idence that generally favors SUGRA unification. the first being a specific mechanism for the spon- Recall that in Sec.2 one discussed a crucial aspect taneous breaking of supersymmetry in the hidden of SUGRA unification which is the connection be- sector and its transmittal to the visible sector and tween the soft breaking scale and the electro-weak the second being the GUT structure of the the- scale. Because of this connection one finds that ory. The first aspect of the theory, i.e., growth of the sparticle masses should be in the TeV range. soft breaking terms protects baryon and lepton This result finds an indirect support in the high number conservation under the constraint of R precision LEP data. Thus the LEP data measures parity invariance. Further, under the constraint the gauge coupling constants α1,α2 and α3 to a of R parity invariance baryon and lepton number great precision. Extrapolation of these coupling violating dimension four operators are also ab- constants to high scales shows that they do not sent which eliminates rapid proton decay. How- meet at a point using the Standard Model spec- ever, even under the constraint of R parity one trum but do meet in MSSM with the supersym- can generate dimension five operators which vi- metric particle spectrum with sparticle masses olate baryon and lepton number and lead to nu- typically in the TeV range. The crucial ingredi- cleon instability[24]. However, the nature of the ent in the unification of the gauge couplings is the 8 References fact that the SUSY particles with masses in the 6. Conclusion TeV range give just the right amount of correc- Supergravity unification proposed 19 years ago tions to the beta functions for all the three cou- remains one of the leading candidates for physics plings to meet at a point. Thus one of the predic- beyond the Standard Model. The model is consis- tions of SUGRA GUTs that sparticle masses must tent with all known data and predicts new physics lie in the TeV range finds support in the high within reach of accelerators, specifically the LHC precision LEP data. The theoretical analyses us- and also possibly within reach of RUNII of the ing SUGRA unification produce a unification of Tevatron. Deviations from the Standard Model the gauge couplings to within 2 sigma. However, are determined by the soft breaking sector of the there could be additional contributions due to theory which is governed by Planck scale physics. Planck scale corrections, which induce terms via Thus observation of deviations from the Standard corrections to the gauge kinetic energy term. model will provide information about the nature Since the early work of 1982-1985 the experi- of physics at the Planck scale and possibly about mental lower limits on the sparticles have moved the nature of the underlying string model. up eliminating many of the possible decay chan- Acknowledgemnets: This work was supported nels such as the supersymmetric decays of the W in part by NSF grant numbers PHY-0070964 and and Z. However, the off shell decay of particles PHY-9901057. ˜ ˜ such as the decay W ∗ W +Z2 l1+l1+l2+ET produces a trileptonic→ signal which→ is one of the prime signals for the discovery of Winos in the References Tevatron RUNII and at the LHC. Further, there is now a considerable body of work which anal- [1] Yu A. Golfand and E.P. Likhtman, JETP yses the signals in the SUGRA models in an ar- Lett. 13, 452 (1971); D. Volkov and V.P. ray of channels depending on the nature of the Akulov, JETP Lett. 16, 438 (1972). sparticles produced (see, eg., SUGRA Working [2] S. Weinberg, in Proc. of Gauge Theories and Group Collaboration, hep-ph/0003154). A very Modern Field Theory, edit by R. Arnowitt encouraging sign for weak scale supersymmetry and P. Nath, MIT Press (1975); E. Gildener, is the recent precise determination of the muon Phys. Rev. D14, 1667 (1976). g-2 at Brookhaven (H.N. Brown et.al., Muon (g- 2) Collaboration, hep-ex/0102017). The experi- [3] J. Wess and B. Zumino, Nucl. Phys. B78,1 ment finds a difference at the 2.6 sigma level be- (1974); S. Ferrara and B. Zumino, Nucl. Phys. B79, 413(1974); A. Salam and J. Strathdee, tween the experimental value of aµ (where aµ = Fort. der Phys. 26, 57(1978). (gµ 2)/2) and its prediction in the Standard − exp SM 10 Model so that a a = 43(16) 10− . This µ − µ × [4] S. Dimopoulos and H. Georgi, Nucl. Phys. result indicates a very significant correction to B193, 150 (1981); Sakai, Z. Phys. C11, 153 the Standard Model from new physics. Now the (1981). prime candidate for this new physics is supersym- metry and specifically we note at this point that [5] L. Giradello and M.T. Grisaru, Nucl. Phys. in the well motivated SUGRA model the super- B194, 65 (1982). symmetric electro-weak correction was predicted [6] D.Z. Freedman, P. van Nieuwenhuizen and S. to be of the size of the Standard Model electro- Ferrara, Phys. Rev. D14, 912 (1976); S. Deser weak correction or larger[23]. Further, analysis of and B. Zumino, Phys. Lett. B62, 335 (1976). this correction within mSUGRA shows that the Brookhaven result implies the existence of some [7] E. Cremmer, S. Ferrara, L.Girardello and A. low lying particles which can be produced at the van Proeyen, Phys. Lett. 116B, 231(1982); LHC and possibly in RUNII of the Tevatron. Test A.H. Chamseddine, R. Arnowitt and P. Nath, of this prediction await experiments at RUNII Phys. Rev. Lett. 29, 970 (1982); J. Bagger and at the LHC. and E. Witten, Phys. Lett. B118, 103(1982). References 9
[8] P. Nath, R. Arnowitt and A.H. Chamseddine, [19] P. Nath, R. Arnowitt and A.H. Chamsed- “Applied N =1 Supergravity” (World Scien- dine, HUTP-83/A077, NUB No. 2588 (1983). tific, Singapore, 1984). [20] S. Weinberg, Phys. Rev. Lett. 50, 387(1983). [9] A.H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 29, 970 (1982). [21] R. Arnowitt, A.H. Chamseddine and P. Nath, Phys. Rev. Lett. 50, 232(198); Phys. [10] R. Barbieri, S. Ferrara and C.A. Savoy, Phys. Lett. 129B, 445(1983); D.A. Dicus, S. Lett. B119, 343 (1982). Nandi, W.W. Repko and X.Tata, Phys. Lett. 129B, 451(1983); J. Ellis, J.S. Hagelin, D.V. [11] L. Hall, J. Lykken and S. Weinberg, Phys. Nanopoulos, and M. Srednicki, Phys. Rev. Rev. D27, 2359 (1983). Lett. 127B, 233(1983); B. Grinstein, J. Polchinski and M. Wise, Phys. Lett. B130, [12] P. Nath, R. Arnowitt and A.H. Chamsed- 285(1983); J.M. Frere and G.L. Kane, Nucl. dine, Nucl. Phys. B227, 121 (1983). Phys. B223, 33(1983); M. Gluck and E. Reya, [13] K. Inoue et al., Prog. Theor. Phys. 68, 927 Phys. Rev. Lett. 51, 867(1983); E. Reya and (12982); L. Iba˜nez and G.G. Ross, Phys. Lett. D.P. Roy, Phys. Lett.B141, 442(1984). B110, 227 (1982); L. Ibanez, Nucl Phys. [22] H. Goldberg, Phys. Rev. Lett. 50 , B218, 514(1983); J. Ellis, D.V. Nanopou- 1419(1983); J. Ellis, J.S. Hagelin, D.V. los, and K. Tamvakis, Phys. Lett. B121, Nanopoulos, K. Olive, and M. Srednicki, 123(1983); L. Alvarez-Gaum´e, J. Polchin- Nucl. Phys. B23, 453(1984). ski and M.B. Wise, Nucl. Phys. B221, 495 (1983); J. Ellis, J. Hagelin, D.V. Nanopou- [23] T. C. Yuan, R. Arnowitt, A.H. Chamseddine los and K. Tamvakis, Phys. Lett. B125, 2275 and P. Nath, Z. Phys. C26, 407(1984); D. A. (1983); L. E. Iba˜nez and C. Lopez, Phys. Kosower, L. M. Krauss, N. Sakai, Phys. Lett. Lett. B128, 54 (1983); Nucl. Phys. B233, 545 133B, 305(1983). (1984); L.E. Iba˜nez, C. Lopez and C. Mu˜noz, Nucl. Phys. B256, 218(1985). [24] S. Weinberg, Phys.Rev.D26,287(1982); N. Sakai and T. Yanagida, Nucl. Phys. B197, [14] A. Salam and J. Strathdee, Fort. der Phys. 533(1982); S. Dimopoulos, S. Raby and F. 26, 57(1978). Wilczek, Phys.Lett. 112B, 133(1982); J. Ellis, D.V. Nanopou- [15] R. Arnowitt, A.H. Chamseddine and P. los and S. Rudaz, Nucl.Phys. B202,43(1982); Nath, in Proc. of Workshop on Problems in B.A. Campbell, J. Ellis and D.V. Nanopoulos, Unification and Supergravity, La Jolla Insti- Phys.Lett.141B,299(1984); S. Chadha, G.D. tute, Jan. 1983; See also Alvarez-Gaume et.al. Coughlan, M. Daniel and G.G. Ross, Phys. in Ref.[13]. Lett.149B,47(1984). [16] S. Soni and A. Weldon, Phys. Lett. B126, [25] R.Arnowitt, A.H.Chamseddine and P.Nath, 215 (1983). Phys.Lett. 156B,215(1985). [17] H.P. Nilles, Phys. Lett. B217, 366(1983); [26] P.Nath, R.Arnowitt and A.H.Chamseddine, H.P. Nilles, M. Srednicki and D. Wyler, Phys. Phys.Rev.32D,2348(1985). Lett. B120, 346(1983).
[18] P. Nath, R. Arnowitt and A.H. Chamsed- dine, in Proceedings of the Winter School on Supersymmetry, Supergravity/Non- perturbative QCD, edited by P. Roy and V. Singh (Springer, Berlin 1984),pp. 113-185.