Lectures on Supersymmetry III

Lectures on Supersymmetry III Carlos E.M. Wagner HEP Division, Argonne National Laboratory Enrico Fermi Institute, University of Chicago Ecole de Physique de Les Houches, France, August 2 5, 2005. PASI 2006, Puerto Vallarta, Mexico, October 31, 2006 1

Why Supersymmetry? Helps to stabilize the weak scale Planck scale hierarchy Supersymmetry algebra contains the generator of space-time translations. Necessary ingredient of theory of quantum gravity. Local Supersymmetry: SuperGravity Minimal supersymmetric extension of the SM : Leads to Unification of gauge couplings Starting from positive masses at high energies, electroweak symmetry breaking is induced radiatively 3B+L+2S If discrete symmetry, P = (-1) is imposed, lightest SUSY particle neutral and stable: Excellent candidate for cold Dark Matter. 2

Minimal Supersymmetric Standard Model SM particle SUSY partner G SM (S = 1/2) (S = 0) Q = (t, b) L ( t, b) L (3,2,1/6) L = (ν, l) L ( ν, l) L (1,2,-1/2) U = ( t C) t L R ( 3,1,-2/3) D = ( b C) b L R ( 3,1,1/3) E = ( l C) l L R (1,1,1) (S = 1) (S = 1/2) B µ B (1,1,0) W µ W (1,3,0) g µ g (8,1,0) 3

Higgs Doublets Solution: Add a second doublet with opposite hypercharge. Anomalies cancel automatically, since the fermions of the second Higgs superfield act as the vector mirrors of the ones of the first one. Use the second Higgs doublet to construct masses for the down quarks and leptons. P [Φ] = h u QUH 2 + h d QDH 1 + h l LEH 1 (1) Once these two Higgs doublets are introduced, a mass term may be written δp [Φ] = µh 1 H 2 (2) µ is only renormalized by wave functions of H 1 and H 2. 4

Supersymmetry Breaking Parameters Standard Model quark, lepton and gauge boson masses are protected by chiral and gauge symmetries. Supersymmetric partners are not protected. Explanation of absence of supersymmetric particles in ordinary experience/ high-energy physics colliders: Supersymmetric particles can acquire gauge invariant masses, as the one of the SM-Higgs. Different kind of parameters: Squark and slepton masses m2 q, m2 l Gaugino (Majorana) masses M i, i = 1-3 Trilinear scalar masses ( f L f R H i ) A f, -µ (This last one comes from the scalar potential derived from the superpotential P/ A i 2. They induce mixing between left and right sfermions. Higgsino Mass µ and associated Higgs Mass Parameters µ 2 + m 2 H i (The first term may be derived from the superpotential). 6

Chargino Mass matrix Lets take, for instance, the chargino mass matrix in the basis of Winos and Higgsinos, ( W +, H + 2 ) and ( W, H 1 ), with W ± = W 1 ± i W 2. The mixing term is proportional to the weak coupling and the Higgs v.e.v. s M χ ± = M 2 g 2 v 2 g 2 v 1 µ (3) Here, M 2 is the soft breaking mass term of the Winos and µ is the Higgsino mass parameter. The eigenstates are two Dirac, charged fermions (charginos). If µ is large, the lightest chargino is a Wino, with mass M 2, and its interactions to fermion and sfermions are governed by gauge couplings. If M 2 is large, the lightest chargino is a Higgsino, with mass µ, and the interactions are governed by Yukawa couplings. 8

Neutralino Mass Matrix Similarly, for neutralinos in the basis of Binos, Winos and Higgsinos M 1 0 g 1 v 1 / 2 g 1 v 2 / 2 0 M 2 g 2 v 1 / 2 g 2 v 2 / 2 M χ 0 = g 1 v 1 / 2 g 2 v 1 / 2 0 µ g 1 v 2 / 2 g 2 v 2 / 2 µ 0 (4) The eigenstates are four Majorana particles. If the theory proceeds from a GUT, there is a relation between M 2 and M 1, M 2 α 2 (M Z )/α 1 (M Z )M 1 2M 1. So, if µ is large, the lightest neutralino is a Bino (superpartner of the hypercharge gauge boson) and its interactions are governed by g 1. This tends to be a good dark matter candidate. 9

Higgs Spectrum Five Higgs bosons: Two CP-even, one CP-odd, neutral bosons, and a charged Higgs boson (two degrees of freedom). Generically, the electroweak breaking sector (Goldstones and real Higgs) is contained in the combination of doublets h = cos βh 1 + sin βiτ 2 H 2, (m h < 135 GeV) m 2 h = M 2 Z cos 2 2β + loop effects (5) while the orthogonal combination contains the other Higgs bosons. Their masses are: m 2 H m 2 A, m 2 H ± m 2 A + M 2 W (6) These relations are preserved, in a good approximation, after loop-effects. 10

Unification of Couplings The value of gauge couplings evolve with scale according to the corresponding RG equations: 1 α i (Q) = b i 2π ln ( Q M Z ) + 1 α i (M Z ) (8) Unification of gauge couplings would occur if there is a given scale at which couplings converge. 1 α 3 (M Z ) = b 3 b 2 b 1 b 2 1 α 1 (M Z ) + b 3 b 1 b 2 b 1 1 α 2 (M Z ) (9) This leads to a relation between α 3 (M Z ) and sin 2 θ W (M Z ) = α1 SM / ( ) α1 SM + α2 SM. 13

Rules to compute the beta-functions The one-loop beta-functions for the U(1) and SU(N) gauge couplings are given by (Q = T 3 + Y ), 5 3 b 1 = 2 3 b N = 11 N 3 yf 2 1 3 f s y 2 s n f 3 n S 6 2N 3 n A (10) In the above, y f,s are the hypercharges of the charged chiral fermion and scalar fields, n f,s are the number of fermions and scalars in the fundamental representation of SU(N), n A are fermions in the adjoint representation and the factor 5/3 is just a normalization factor, so that over one generation T r [ T 3 T 3] = 3 5 T r [ yf 2 ] (11) 14

The coupling g 1 is not asymptotically free, but becomes strong at scales far above M P l, where the effective theory description breaks down anyway. A full generation contributes to the same amount to all β-functions. It does not affect the unification conditions. (βgen SM = 4/3; = 2.) β SUSY gen Only incomplete SU(5) representations affect one-loop unification. b SM 1 = 41/10, b SM 2 = 19/6, b SM 3 = 7. b SUSY 1 = 33/5, b SUSY 2 = 1, b SUSY 3 = 3. (12) [( ) ] 1 M G = M Z exp α 1 (M Z ) 1 2π α 2 (M Z ) b 2 b 1 1 α 3 (M Z ) = b 3 b 1 1 b 2 b 1 α 2 (M Z ) + b 3 b 2 1 b 1 b 2 α 1 (M Z ) (13) 15

Results b 1 = 6 3N H /5, b 2 = N H, b 3 = 3 1/α 1 (M Z ) 60 1/α 2 (M Z ) 30 In the above, N H is the number of pair of Higgs doublets. With these results we can compute the strong gauge coupling at M Z 1 α 3 (M Z ) = 15 7N H 25 + 3N H 30 (1) The result depends strongly on the number of Higgs doublets. For N H equal to zero, we get α 3 (M Z ) = 1/18 0.05. For N H = 1, instead, we get α 3 (M Z ) 0.120!! Excellent prediction! For N H = 2 we get, again, a very bad result α 3 (M Z ) 1. Finally, M G = M Z exp(30 2π (5/28)) 10 16 GeV Grand Unification scale is very close to the Planck scale, suggesting a Unified description of particle interactions. 2

SM: Couplings tend to converge at high energies, but unification is quantitatively ruled out. 60 MSSM: Unification at α GUT 0.04 and M GUT 10 16 GeV. 50! "1 1 60! "1 40 30 20 10 0! "1 3! "1 2 2 4 6 8 10 12 14 16 10 10 10 10 10 10 10 10 µ(gev) a) Standard Model! "1 50 40 30 20 10 0! "1 b) M SUSY =1 TeV 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 µ (GeV) Experimentally, α 3 (M Z ) 0.118 ± 0.004 Bardeen, Carena, Pokorski & C.W. in the MSSM: α 3 (M Z ) = 0.127 4(sin 2 θ W 0.2315) ± 0.008 Remarkable agreement between Theory and Experiment!! 16! "1 3! "1 2 1

Structure of Supersymmetry Breaking Parameters Although there are few supersymmetry breaking parameters in the gaugino and Higgsino sector, there are many in the scalar sector. For instance, there are 45 scalar states and all these scalar masses might be different. In addition, one can add complex scalar mass parameters that mix squark and sleptons of different generations: L mix = m 2 ij f i f j + h.c. In addition, one can add A-terms that also mix squarks and sleptons of different generations. In general, in the presence of such terms, if the scalar masses are of the order of the weak scale, one can induce contributions to flavor changing neutral currents by interchanging gauginos and scalars. This leads to problematic phenomenological consequences. 17

Flavor Changing Neutral Currents Two particularly constraining examples of flavor changing neutral currents induced by off-diagonal soft supersymmetry breaking parameters Contribution to the mixing in the Kaon sector, as well as to the rate of decay of a muon into an electron and a photon. While the second is in good agreement with the SM predictions, the first one has never been observed. Rate of these processes suppressed as a power of supersymmetric particle masses and they become negligible if only relevant if relevant masses masses are are heavier larger than 10 TeV 18

Solution to the Flavor Problem There are two possible solutions to the flavor problem The first one is to push the masses of the scalars, in particular to the first and second generation scalars, to very large values, larger than a or fewof TeV. the order of 10 TeV. Some people have taken the extreme attitude of pushing them to values of order of the GUT scale. This is fine, but supersymmetry is then broken in a hard way and the solution to the hierarchy problem is lost. A second possibility is to demand that the scalar mass parameters are approximately flavor diagonal in the basis in which the fermions mass matrices are diagonal. All flavor violation is induced by either CKM mixing angles, or by very small off-diagonal mass terms. This latter possibility is a most attractive one because it allows to keep SUSY particles with masses of the order of the weak scale. 19

Minimal Supergravity Model The simplest possibility is the case in which all scalar masses are universl and flavor independent at a certain scale. In the minimal supergravity model, for example, one assumes that all scalars acquire a common mass m 2 0 at the Grand Unification scale In addition, since gauginos belong to the same adjoint representation, one assumes that all gauginos acquire a common mass M 1/2 at the GUT scale These two parameters must be complemented with a value of the parameter µ at M GUT. For the Higgs sector it is assumed that m 2 i = µ 2 + m 2 H i, with m Hi = m 0. Finally, all the trilinear parameters A ijk are assume to take a common value A 0. 20

Renormalization Group Evolution One interesting thing is that the gaugino masses evolve in the same way as the gauge couplings: d(m i /α i )/dt = 0, dm i = b i α i M i /4π, dα i /dt = b i α 2 i /4π The scalar fields masses evolve in a more complicated way. 4πdm 2 i /dt = Ci a4m 2 aα a + Y ijk 2 [(m 2 i + m2 j + m2 k + A2 ijk )]/4π There is a positive contribution coming from the gaugino masses and a negative contribution proportional to the Yukawa couplings. Colored particles are affected by positive, strongly coupled corrections and tend to be the heaviest ones. Weakly interacting particles tend to be lighter, particular those affected by large Yukawas. There scalar field H 2 is both weakly interacting and couples with the top quark Yukawa. Its mass naturally becomes negative. 21

Low Energy Masses in Minimal Supergravity Model All scalars acquire a common mass m 2 0 at the Grand Unification scale All gauginos acquire a common mass M 1/2 at the GUT scale Masses evolve differently under R.G.E. At low energies, Squark Masses: m 2 Q m 2 0 + 6 M 2 1/2 Left-Slepton Masses m 2 L m 2 0 + 0.5 M 2 1/2 Right-Slepton Masses m 2 Ẽ m2 0 + 0.15 M 2 1/2 Wino Mass M 2 = 0.8 M 1/2. Gluino Mass M 3 = α 3 α 2 M 2 Bino Mass M 1 = α 1 α 2 M 2 Lightest SUSY particle tends to be a Bino. 22

Electroweak Symmetry Breaking The above relations apply to most squarks and leptons, but not to the Higgs particles and the third generation squarks. The renormalization group equations of these mass parameters include negative corrections proportional to the square of the large top Yukawa coupling. In particlular, the H 2 Higgs mass parameter m 2 2, is driven to negative values due to the influence of the top quark Yukawa coupling. Electroweak symmetry breaking is induced by the large top mass! Also the superpartners of the top quark tend to be lighter than the other squarks. This effect is more pronounced if M 1/2 is small. 23

SUSY Spectrum from Universal Boundary Conditions at MGUT Coloured, strongly interacting particles tend to be heavier than weakly interacting particles. Lightest Supersymmetric Particle is lightest Neutralino. Squarks and sleptons of first two generations are degenerate. Small splitting in the slepton sector. Third generation squarks are Typically lighter. 25

Comments The previously presented spectrum depends strongly on the condition of equality of sfermion and gaugino masses at the GUT scale. Setting, for instance, different masses for particles of different quantum numbers at the GUT scale could lead to a very different spectrum. In general, very little is known about the supersymmetry breaking parameters and one should NOT make conclusions about the Tevatron and/or LHC reach for SUSY based on strong assumptions about them. In particular, although it is clear that the LHC has a larger reach, the Tevatron one is not at all negligible, and one should be open to the possibility of a SUSY discovery before the start of the LHC! 26

The new High Energy Physics Framework High Energy Physics has provided an understanding of all data collected in low and high energy collider experiments Contrary to expectations, no signature of physics beyond the SM was observed at the LEP electron-positron collider and no large deviation is being observed at the Tevatron. However, there are two reasons to believe that there is new physics around the corner. One is related to particle physics, and the other to cosmology: Electroweak Symmetry Breaking Origin of Dark Matter The aim of high energy physics experiments is, in great part, to contribute to the understanding of these two questions.

Why the interest of HEP in Dark Matter? Although high energy physicists always care about cosmology, the recent emphasis on the search for dark matter at colliders happened due to the recent progress in observational cosmology Cosmological measurements provided precision tests of the Universe energy density composition, making the case for Dark Matter quite compelling. Today we know that Dark Matter makes most of the matter of the Universe and there are experiments looking for its direct (and indirect detection). The detection of Dark Matter may just be the tip of the Iceberg of a whole new world of additional, unstable particles! High Energy Physics experiments could provide clues toward the understanding of the nature of these particles: This will depend on their energy range and interaction strength with SM particles.

Dark Matter Annihilation Rate The main reason why we think there is a chance of observing dark matter at colliders is that, when we compute the annihilation rate, we get a cross section σ ann. (DM DM SM SM) 1 pb This is precisely σ ann. α2 W M 2 W This suggests that it is probably mediated by weakly interacting particles (A.B., K. Matchev and M. Perelstein, PRD 70:077701, 2004) Connection of Thermal Dark Matter to the weak scale and to the mechanism of electroweak symmetry breaking

Dark Matter and Colliders Imagine we assume that dark matter is indeed a weakly interacting massive particle (WIMP) with mass of the order of the weak scale. The problem is that the only additional information we have is the annihilation cross section to SM particles. But, which SM particles? If we knew, we can try to collide them and see if we can test this idea. Indeed, there is a relation between the annihilation cross section and the production cross section: DMSM SMDM DM Crossing SM Symmetry SMDM

Problems There are two problems with this idea: We cannot collide all SM particles at once Producing the DM particle will just lead to invisible energy at the collider. We need to detect it in some way One possibility is to add radiation. Say you apply this idea to electron-positron collisions. Define κ e as the model dependent fraction of DM-annihilation that goes to Birkedhal, Matchev, Perelstein 05 SM γ DM e + e SM DM

Reach at a 500 GeV Linear e + e Collider d # $e % e & ' 2 DM %() +$, dx d cos* - Here x/2 E ( 01s Universal SM factor 1%$1&x ) 2 x ) 1 sin 2 *.# $e% e & ' 2 DM ) (msugra bulk region) Main background (neutrino production) considered. No systematics added. Simplistic but promising analysis. Complementary to other channels in SUSY models.

Missing Energy Events at Hadron Colliders The Tevatron is running at Fermilab (Batavia, IL) and has a chance of going beyond the LEP BSM reach. Possible to produce the WIMPS by the decay products of other weakly interacting particles participating in the annihilation cross section (charginos, selectrons). Strongly interacting particles, if sufficiently light, will be also produced at large rates. They are not motivated by dark matter considerations, but we suspect they are there in relation to electroweak symmetry breaking.

Light Strongly Interacting Particles? This argument leads to the presence of light stops. All other squarks and the gluino may be somewhat heavy. In addition, how light is light? Unfortunately, there is no physical observable that determines this. So, let s first make the optimistic assumption that all sparticle masses are of the same order of magnitude. Example of this class of models: CMSSM or msugra. It is obtained by assuming that the scale at which SUSY is broken is large and that gaugino and sfermion masses acquire simple features at the GUT scale (RG evolved to low energies).

Preservation of R-Parity: Supersymmetry at colliders Gluino production and decay: Missing Energy Signature Supersymmetric Particles tend to be heavier if they carry color charges. 0!~1 Particles with large Yukawas tend to be lighter. Charge-less particles tend to be the lightest ones. 0!~1! Lightest supersymmetric particle = Excellent Cold dark matter candidate. 28

Trilepton Signatures at the Tevatron Trileptons are associated production of chaginos and neutralinos, with subsequent decays into leptons. The final signal is three lepons and plenty of missing energy (neutralinos and neutrinos) Main background: W and Z production. 29

Trileptons: Present and Future Now:!xBR<0.2-0.3 pb 3l-max scenario: Sleptons light Optimistic msugra Large m 0 scenario: Sleptons heavy Pessimistic msugra Current data probe optimistic scenario Future: Cross section limit 0.05-0.01 pb L=1 fb -1 : probe chargino masses up to 100-170 GeV/c 2 L=8 fb -1 : probe chargino masses up to 150-240 GeV/c 2 Preferred by precision data 18

Beyond the Tevatron Searches at the Tevatron are limited by phase space. Tevatron is a proton-antiproton collider with a center of mass energy of 2 TeV. Partons c.m.e. is smaller, and strongly interacting (weakly interacting) sparticles with masses beyond 500 (250) GeV may not be discovered. Tevatron has still a chance, and we all hope that something exciting will happen there in the near future. Searches for new physics will continue in 2008 at the LHC, a proton proton collider with c.m.e. of about 14 TeV! Strongly interacting (colored) particles, with masses up to 3 TeV may be explored!

Searches at the LHC,-./01023#4511.1 New particle searches at the LHC are induced by the cascade decay of strongly interacting particles. By studying the kinematic distributions of the decay products one can determine the masses of produced particles, including the 6 78/#9:;<=>*?#?@:;&+ABC D&@*:%>@D&+#?=9*:9%:@&*:?E# LSP. FGD>G#>%?>%<*#<*>%B H*D+A*D& *@#%AI#J!''KL

m 1/2 (GeV) How well can the LHC do? 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 msugra with tan! = 30, A 0 = 0, µ > 0 3l Baer, Balazs, Belyaev, Kropovnickas and Tata 03. 2l OS 1l Z"l + l - #4l $ 0l 2l SS m(u ~ L )=2 TeV m(g ~ )=2 TeV E T miss 0 1000 2000 3000 4000 5000 m 0 (GeV)

What is essential for discovery at the LHC? Production of colored particles, which cascade decay into the weakly interacting ones. If colored particles are not light, then searches become very difficult. Reason: SM cross sections (bottom, top, etc) are huge. SM particles tend to be produced at large rates and they may decay producing plenty of leptons and missing energy (for instance, neutrinos). Is there a particular way of cutting the background?

Ideas Trileptons signatures at the LHC are not better than at the Tevatron. Reach quite limited (Baer et al 95) Weak boson fusion of equal sign charginos! P P jet W + χ 0 W + χ + χ + Missing Energy e +, µ + jet Cho, Hagiwara, Kansaki, Plehn, Rainwater, Steltzer 06 Fermion Number Violating process. Could test the Majorana nature of the neutralino! Cross sections of order of 1 fb. Simulation must be done. Background? WW production. Bottom production, combined with B- B oscillations

Connection of collider physics and cosmology Knowledge of particle masses and charges will enable the computation of the dark matter annihilation cross section One can hence compare this result with the one needed to provide the proper dark matter relic density For the success of this program, precision measurements will be necessary, as well as the determination of all particles that interact with the dark matter candidate. The LHC will be helpful in this direction, but the ILC will be essential to obtain accurate results.

-./012134#5622/2 Searches at a 500 GeV Linear Collider #/:;<=>?#%<<#;@=;*@?>*A Lepton colliders present a cleaner environment, ideal for the detection of weakly interacting particles &*D%?>E *&F;=>&?A @*AG=<F#AE%&A One can make use of threshold scans and kinematic distributions to determine particle masses accurately. I*%D#;=<%@>J%?>=& * H =;?>=& Kinematic limitations are, of course, a problem if sparticles are heavy. Hence, the ideal situation would be to upgrade * H * H the energy up to at least 1 TeV * O * H )*&+K#-*AC>& L!''MN 5%@?S& *?#%<T#L!''UN

-./01#2.34056#2.5.-703850934 /F1#<GH*I@#=%I*#I=*&%?JKLA /11E 0/1 :78; <=>??*&@A ;B%&=C <D!'E'A 8/1;M#1KINKBK+O#4>H+?K>P Q#B*R*B#=KNP%?JIK&#KS#P?*TJ=@*T#! U*P VJ@U#KHI*?R*T#! =KINK!"#$%&#'( )*&+!,

One stop must be light! What happens if all squarks and gluinos are heavy, except for a light stop? Charginos and neutralinos are still around, providing the proper dark matter annihilation cross section. Both stops cannot be light in the MSSM. Otherwise, the physical Higgs mass would be too light. Let s then study the case of a single light stop. This case is motivated by the question of electroweak baryogenesis.

Relic Density Constraints ( Arg( M 1, 2 µ ) =! / 2) Only CP-violating phase we consider is the one relevant for! Only Light Stop and Relic Density Constraints the generation of the baryon asymmetry, namely : Arg( M 1, 2 µ )! Neutralino co-annihilation with stops efficient for stop-neutralino mass differences of order 15-20 GeV. tan! = 7

Tevatron stop searches and dark matter constraints Carena, Balazs and C.W. 04 2 fb! 1 4 fb 20 fb! 1! 1 Green: Relic density consistent with WMAP measurements. Searches for light stops difficult in stop-neutralino coannihilarion region. LHC will have equal difficulties. Searches become easier at a Linear Collider! M. Carena et al. 05

Light stops at the LHC For small values of the stop mass, the situation is worse than at the Tevatron For larger values of the stop mass, decays into charginos dominate Final decay products become similar to the top quark ones and hence there is a very large background. Detection of the charginos and neutralinos become also difficult, unless there are other light colored sparticles.

The power of the ILC Detect light stop in the whole regime compatible with DM and EWBG MC, Finch, Freitas, Milstene, Nowak, Sopczak Measurement of SUSY parameters for Dark Matter density computation -- stop mass and mixing angles -- LSP mass and composition -- Higgs properties -- other relevant light SUSY particles mlsp(gev) ~ 0 t c + ~ χ (assuming BR = 1) mstop (GeV) Fraction of Dark Matter Density ILC sensitivity to DM density WMAP WMAP ILC mstop (GeV) A particle physics understanding of cosmological questions! 2σ 1σ stop mass= (neutralino mass + 15) [GeV]

How heavy can the gluinos be? Only hint comes from Unification of Couplings α 3 (M Z ) 0.123 19 α2 3(M Z ) 28π ln ( TSUSY M Z ) T SUSY µ ( M W M g ) 3/2 T SUSY Valules of of order 1 TeV preferred. For this, gluino mass should be of the order of the weak scale! If gluinos are light, then one can look for an even lighter stop by the gluino decay into a stop and a top quark

Alternative SUSY Breaking scenario: Gauge Mediation Supersymmetry Breaking is transmitted via gauge interactions Particle Masses depend on the strength of their gauge interactions. Spectrum of supersymmetric particles very similar to the case of the Minimal Supergravity Model for large values of M 1/2 : Sparticle Masses M i M j = α i α j m q m l α 3 α i (m f α 4π F M ) Lightest SM Sparticle tends to be a Bino or a Higgsino 33

Gravitino When standard symmetries are broken spontaneously, a massless boson appears for every broken generator. If the symmetry is local, this bosons are absorved into the longitudinal components of the gauge bosons, which become massive. The same is true in supersymmetry. But now, a massless fermion appears, called the Goldstino. In the case of local supersymmetry, this Goldstino is absorved into the Gravitino, which acquires mass m G = F/M P l, with F the order parameter of SUSY breaking. The coupling of the Goldstino (gravitino) to matter is proportional to 1/ F = 1/ m GM P l, and couples particles with their superpartners. Masses of supersymmetric particles is of order F/M, where M is the scale at which SUSY is transmitted. 34

Decay Width of NLSP into Gravitino In low energy supersymmetry breaking models, the SUSY breaking scale 10TeV F 10 3 TeV. The gravitino mass is very small in this case 10 1 ev m G 10 3 ev. Since the gravitino is the lightest supersymmetric particle, then the lightest SM superpartner will decay into it. It is easy to extract the decay width on dimensional grounds Just assume that the lightest SM partner is a photino, for instance, and it decays into an almost massless gravitino and a photon. Then, Γ( γ γ G) m5 γ 16πF 2 m 5 γ 16πm 2 GM 2 P l (2) where we have used the fact that [F ] = 2. 3

Gauge-Mediated, Low-energy SUSY Breaking Scenarios Special feature LSP: light (gravitino) Goldstino: m G F M P l 10 6 10 9 GeV If R-parity conserved, heavy particles cascade to lighter ones and NLSP SM partner + G Signatures: The NLSP (Standard SUSY particle) decays ( decay length L 10 2 m cm G ) 2 ( 10 9 GeV 100GeV ) 5 M NLSP NLSP can have prompt decays: Signature of SUSY pair: 2 hard photons, (H s, Z s) + E/ T from G macroscopic decay length but within the detector: displaced photons; high ionizing track with a kink to a minimum ionizing track (smoking gun of low energy SUSY) decay well outside the detector: E/ T like SUGRA 35

Gauge-Mediated Tevatron Reach Bino-like NLSP: Signal: γγxe/ T X = l s and/or jets χ 0 1 γ G Higgsino-like NLSP: χ 0 1 (h, Z, γ) G Signal: γ b E/ T X diboson signatures (Z ll/jj; h b b)e/ T 10 2 CDF projected limits from diphotons, GMSB model 10 2 CDF projected limits from γb/e t, GMSB model Discovery reach (2fb -1 ) Discovery reach (2fb -1 ) 10 σ x BR 95% CL limit (2fb -1 ) σ x BR (fb) 10 95% CL limit (2fb -1 ) 95% CL limit (10fb -1 ) 95% CL limit (10fb -1 ) 1 95% CL limit (30fb -1 ) 1 M χ ± 200 225 250 275 300 325 350 375 400 425 M(χ ~ ± 1) (GeV) 325 GeV (exclusion) & 260 GeV (discovery) M χ ± 1 95% CL limit (30fb -1 ) 120 140 160 180 200 220 240 260 280 300 M(χ ~ ± 1) (GeV) sensitivity 200 GeV for 2 fb 1 36

Conclusions Supersymmetry is a symmetry that relates boson to fermion degrees of freedom. It provides the basis for an extension of the SM description of particle interactions. Fundamental property: No new couplings. Masses of supersymmetric particles depend on supersymmetry breaking scheme. If R-Parity is imposed and the gravitino is heavier than the lightest SM partner, then the lightest supersymmetric particle is a good dark matter candidate. Electroweak symmetry breaking is induced radiatively in a natural way, provided sparticle masses are of order 1 TeV. Unification of couplings is achieved. Signature at colliders: Missing Energy, provided by the LSP. 37