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arXiv:hep-ph/9607450v1 27 Jul 1996 by ihetsadr oe ueprnri easby decays it superpartner model standard lightest igsprymtybekn otevsbesec- visible the transmit- to possible for breaking is scale su- messenger It ting for the signal energy. that de- however known missing a well of escapes the If persymmetry it to neutral, leading stable. electrically tector is is LSP and su- the lightest (LSP) the is persymmetric superpartner model standard cl eo e 00TVti ea a aepaewti de a it within superpartner place model take standard can lightest decay the this is TeV 1000 a few a below scale oehde etri hnncsaiyo order of necessarily then in is scale 10 sector breaking hidden supersymmetry some The inter- strength gravitational actions. are supersym- breaking of messengers metry the im- that colliders assume energy plicitly su- high supersymmetry of at signals of studies persymmetric phenomenological mechanism Most and breaking. scale experimentally the address is to questions interesting Introduction 1. ion minimum a to kink a with possibly track, particle charged ofrneo uesmer SS9) olg Park, College 29,1996. May (SUSY96), MD, Supersymmetry on Conference ∗ e 95064 d CA Cruz, Santa California, of University c b a hnmnlgclIpiain fLwEeg Supersymmetr Dimopoulos, Savas Energy Low of Implications Phenomenological oe ueprnri ntbeaddcy oisprnrplu partner its to decays and unstable is superpartner model tnodLna ceeao etr tnod A94309 CA Stanford, Center, Accelerator Linear Stanford Physics, Particle for Institute Cruz Santa akpeetdb .Toa tteFut International Fourth the at Thomas S. by presented Talk hsc eatet tnodUiest,Safr,C 94309 CA Stanford, University, Stanford Department, Physics hsc eatet hoSaeUiest,Clmu,O 43210 OH Columbus, University, State Ohio Department, Physics Switzerla 23, Geneva CH-1211, CERN, Division, Physics Theoretical fntr ssprymti,oeo h most the of one supersymmetric, is nature If h xeietlsgaue o o nrysprymtyb supersymmetry energy low for signatures experimental The 11 χ 1 0 e.If GeV. → ( Z 0 h , R 0 H , prt scnevdtelightest the conserved is -parity 0 b a A , 0 ihe Dine, Michael + ) G hs eascngv iet ipae etcs Alternat vertices. displaced to rise give can decays These . c tatRaby, Stuart l ˜ → l d + ct Thomas, Scott G hscnb ena rae hnmnmmionizing minimum than greater a as seen be can This . easby decays ffcieoeaos hc,i h rsneo su- of presence the in to which, rise operators, gives sector effective messenger sectors. the breaking out Integrating supersymmetry and visible the supersymmetry scale exper- low we breaking. independent of note model signatures this the imental In of some [4]. to detector describe decaying the possibly within sleptons charged heavy or os ipae hre atceor particle charged pho- displaced displaced su- tons, scale including low breaking, for This persymmetry features distinctive detector. very a the to within to leads decay place this take TeV break- can 1000 supersymmetry Goldstino few For a below scales [3]. ing component Goldstino the the plus of partner de- its and to unstable cays is superpartner model lightest lightest standard The light- the (NLSP). to particle and next supersymmetric this the LSP, est is In the superpartner model is and standard [1,2]. gravitino scale scale the Planck electro-weak case the the above between just anywhere is tor zn track. izing h oeo h esne etri ocouple to is sector messenger the of role The Goldstino, a s etr edn ovr itntv intrs If signatures. distinctive very to leading tector, ekn r rsne.Telgts standard lightest The presented. are reaking χ 1 0 → e ∗ γ nd ae .Wells D. James + G o uesmer breaking supersymmetry a For . G n fknmtclyaccessible kinematically if and , l,i lpo sthe is slepton a if ely, e Breaking y SLAC-PUB-7236 b jtvertices, -jet 1 2 persymmetry breaking, lead to soft supersymme- try breaking in the visible sector. If the messenger Particle Mass (GeV) sector interactions are of gravitational strength, Q˜L, Q˜R 870, 835 the soft terms in the visible sector are logarithmi- t˜1, t˜2 760, 860 cally sensitive to ultraviolet physics all the way to A0,H0,H± 515-525 0 ± 0 the Planck or compactification scale. In this case χ3,χ2 ,χ4 415-440 patterns within the soft terms might give an in- l˜L 270 0 ± direct window to Planck scale physics. However, χ2,χ1 175 the soft terms could then also be sensitive to some ˜lR 140 sector below the Planck scale which is responsi- h0 105 0 ble for the flavor structure of the Yukawa interac- χ1 95 tions. This generally leads to unacceptably large G 1.5 10−9 × flavor changing neutral currents, although elab- Table 1 orate flavor symmetries can be imposed to limit Typical spectrum with gauge-mediated super- this. In contrast, if the messenger scale is well symmetry breaking for tan β = 3, and a messen- below the scale at which the Yukawa hierarchies ger scale of 80 TeV. are generated, the soft terms can be insensitive to the flavor sector, and naturally small flavor changing neutral currents can result. The lack of flavor changing neutral currents is a significant advantage of low scale supersymmetry breaking. tegrating out these messenger sector fields then In the next section the form the superpart- gives rise to masses at ner spectrum for the minimal model of gauge- one-loop, and scalar masses squared at two-loops mediated supersymmetry breaking is reviewed. [1,2,5]. The scalar and gaugino masses are then In section three the model independent experi- very generally of the same order and go roughly mental signatures of supersymmetry breaking at as their gauge couplings squared. The B-ino and a low scale are presented. right handed sleptons gain masses through U(1)Y interactions, and are therefore lightest. The W - 2. Superpartner Spectrum with Gauge- ino’s and left handed sleptons, transforming un- Mediated Supersymmetry Breaking der SU(2)L, are somewhat heavier. The strongly interacting squarks and are significantly If supersymmetry is broken at a low scale it is heavier than the electro-weak states. in fact likely that the standard model gauge inter- The dimensionful parameters within the Higgs 2 actions play some role. This is because the stan- sector, W = µHuHd and V = m12HuHd + h.c., dard model couple only through gauge do not follow from the anzatz of gauge-mediated interactions. If standard model Higgs scalars re- supersymmetry breaking, and require additional ceived soft masses from non-gauge interactions, interactions which break U(1)P Q and U(1)R−P Q the standard model gauginos would then be un- symmetries. At present there is not a good model acceptably lighter than the electro-weak scale.2 which gives rise these Higgs sector masses with- The standard model gauge interactions act as out tuning parameters. The parameters µ and 2 messengers of supersymmetry breaking if fields m12 are therefore taken as free parameters in the within the supersymmetry breaking sector trans- minimal model, and can be eliminated in favor of form under the standard model gauge group. In- tan β and mZ . Electroweak symmetry breaking results from 2The argument for light gauginos in the absence of gauge 2 the negative one-loop correction to mHu from couplings within a low scale messenger sector only applies stop-top loops due to the large top Yukawa if the gauginos are elementary degrees of freedom in the ultraviolet, and would not apply if the gauginos where coupling. Although this effect is formally three- composite or magnetic at or below the messenger scale. loops, it is larger in magnitude than the elec- 3

2 troweak contribution to mHu due to the large ticles at a high energy collider therefore takes squark masses. Upon imposing electro-weak sym- place through standard model couplings (assum- metry breaking, µ is typically found to be in the ing R-parity conservation). The produced states range µ (1 2)m˜lL (depending on tan β and cascade to pairs of NLSP’s. The quasi-stable the messenger∼ − scale). This leads to a lightest neu- NLSP’s eventually decay to their partners plus 0 tralino, χ1, which is mostly B-ino, and a lightest Goldstinos, which carry away missing energy. ± , χ1 , which is mostly W -ino. A typical The specific signatures which arise from decay to spectrum at the low scale for a messenger sector the Goldstino depend crucially on the quantum at 80 TeV transforming as 5+5¯ of SU(5) is given numbers of the NLSP, as discussed in the follow- in table 1. ing subsections. These general patterns within the spectrum Associated production of Goldstinos in particle should be considered model-dependent features collisions has been discussed in the past, but is of the minimal model of gauge-mediated super- completely irrelevant unless √F almost coincides symmetry breaking. The signatures for decay of with the electro-weak scale. the NLSP to its partner plus the Goldstino dis- cussed in the next section are however very model 3.1. Neutralino NLSP independent. It is possible that the lightest standard model 0 superpartner is a neutralino, χ1. It can decay 0 3. Detecting the Goldstino through the gaugino components by χ1 γ + 0 0 → G and χ1 Z + G, and through the The spontaneous breaking of global supersym- → 0 0 0 0 components by χ1 h + G, χ1 H + G, or metry leads to the existence of a massless Gold- 0 0 → → χ1 A + G if kinematically accessible. These stone , the Goldstino. In local super- decays→ lead to very distinctive features if prompt symmetry the Goldstino becomes the longitudi- on the scale of a detector. nal component of the gravitino. For supersymme- 0 If χ1 is mostly gaugino, as in the example given try breaking scales in the range discussed below, in the previous section, it decays predominantly the gravitino is essentially massless on the scale 0 + − by χ1 γ + G. At an e e collider the sig- of accelerator experiments. The LSP is for all nature→ would be e+e− γγ+ E. The standard practical purposes the Goldstino, and the light- model backgrounds are→ easily manageable6 for this est standard model superpartner is the NLSP. 0 signal [4,6]. Since χ1 is a Majorana particle, it The lowest order couplings of the Goldstino are can decay to both Goldstino helicities, giving an fixed by the supersymmetric Goldberger-Treiman isotropic decay in the rest frame. The lab low energy theorem to be given by [3] energy distribution is therefore flat and bounded 1 1 1 by 4 √s(1 β) Eγ 4 √s(1 + β), where β is µα 0 − ≤ ≤ = j ∂µGα + h.c. (1) the χ lab frame velocity. The end points of the L −F 1 photon spectrum give an important test that the where √F is the supersymmetry breaking scale, final state carrying the missing energy µα 1 j is the supercurrent, and Gα is the spin 2 are essentially massless. 0 0 Goldstino. Since the Goldstino acts like the su- At a collider mostly gaugino χ1χ1 pro- percharge, it transforms a superpartner into its duction is suppressed by small couplings and large 0 ± + − partner. For √F below a few 1000TeV, such a de- squark mass. Production of χ2χ1 , χ1 χ1 , and ˜+˜− cay of a superpartner to its partner plus the Gold- lRlR is however not suppressed. Cascade de- stino can take place within a detector. Since the cays then lead to the final states WZγγ+ ET + − + − 6 Goldstino couplings are suppressed compared to or Wl l + ET , WWγγ+ ET , and l l γγ+ ET , 6 6 6 m 0 electroweak and strong interactions, decay to the all at comparable rates [7]. For χ1 100 GeV Goldstino is only relevant for the lightest stan- the total cross section in all such channels≃ at the dard model superpartner (NLSP). Tevatron can be up to 70 fb, and could therefore The production of pairs of supersymmetric par- be seen in current data. The existence of two hard 4

γ’s in such events gives a distinctive signature for l˜R l + G. These decays also lead to very dis- low scale supersymmetry breaking. In addition, tinctive→ signatures. the backgrounds are much smaller than for stan- At an e+e− collider the signature for slepton dard supersymmetric signals [4,7,8], with mis- pair production with prompt decay to Goldsti- identifications probably being the largest contam- nos is e+e− l+l−+ E. The standard model 0 → 6 ination of the signal. If the χ1 decay length is backgrounds are easily manageable for this sig- long enough, timing information can also be used nal. The decay leads to a flat spectrum to isolate the signal. in the lab frame, with the end points giving an If such signatures were observed experimen- important test that the missing energy is carried tally, one of the most important challenges would by essentially massless particles. be to measure the distribution of finite path At a hadron collider pair production of NLSP 0 lengths for the decaying χ1’s, thereby giving a sleptons with prompt decay to Goldstinos also + − direct measurement of the supersymmetry break- gives final states l l + ET . This suffers from ing scale. For √F between roughly 100-1000 TeV fairly large irreducible backgrounds,6 and does not the decay length is between 100 µm and a few represent a clean signature. However, production 0 m. In the case of χ1 γ + G, future detectors of heavier states which cascade to ˜lR can give will be able resolve displaced→ γ tracks at the level clean signatures with multiple leptons. For ex- of a few cm. Alternately, the rarer decay mode ample, pair production of ˜lL˜lL followed by the 0 0 ˜± ˜+ − ± χ1 Z + G gives rise to displaced charged par- cascade decays lL lRl l (through on- or off- → 0 → ticle vertices, which can be measured down to the shell χi ) gives final states 6l+ ET . Such sig- 100 µm level. natures do not suffer contamination6 by standard 0 If χ1 is mostly Higgsino, it decays (in the de- model backgrounds. 0 0 ˜ coupling limit) predominantly by χ1 h + G. If the decay l l + G takes place on the In the mostly Higgsino region of parameter→ space scale of a detector→ very distinctive charged parti- 0 + 0 − the states χ1, χ1 , and χ2, χ1 form approximate cle tracks can arise. This is because heavy non- SU(2)L doublets with splittings much smaller relativistic sleptons are more highly ionizing than than the overall mass scale. At both e+e− ultra-relativistic charged particles. Decay over a and hadron colliders the signatures are therefore finite distance can then be seen as a greater than 0 0 0 h h X+ ET with h bb, where X repre- minimum ionizing track with a kink to minimum sents off-shell6 W ∗ and Z→∗ electro-weak cascades ionizing track. Such kinks should be measurable of the heavier Higgsino states to the lightest one. down to the 100 µm level. If the slepton decay The existence of 4 b-jets which reconstruct mh0 length is long enough, timing information can also in pairs, along with missing energy is therefore be applied to isolate such events. Measurement of also a distinctive feature of low scale supersym- the decay length distribution would give a direct metry breaking. In this case, displaced b-jet ver- measure of the supersymmetry breaking scale. tices could be measured down to the 100 µm Because of the larger Yukawa coupling, theτ ˜R m 0 ,m 0 < m 0 µ e level. Finally, if H A χ1 the decays can be lighter than ˜R and ˜R from renormaliza- 0 0 0 0 0 χ1 H + G, and χ1 A + G, with H and tion group evolution. If mτ˜R + mτ + mµ < mµ˜ 0 → → ± + − ± A undergoing standard model like decays, would the electro-weak decayµ ˜R τ˜R τ µ , through → 0 represent a gold-mine for Higgs physics. the B-ino component of off-shell χi , can com- pete with the decayµ ˜ µ + G, and likewise → 3.2. Slepton NLSP fore ˜R. It is possible then that nearly all cas- With low scale supersymmetry breaking it is cades lead toτ ˜R and that all the slepton signa- equally possible that the lightest standard model tures discussed above occur with τ’s in the final superpartner is a charged slepton. For example, state. Alternately, if mτ˜R + mτ + mµ,e > mµ,˜ e˜, a gauge-mediated messenger sector with two gen- all the right handed sleptons are stable against erations of 5 + 5¯ generally gives a right handed three body electro-weak decays at lowest order, slepton as the NLSP. In this case it decays by and the decay ˜lR l + G can dominate. In this → 5 case the above signatures occur with equal rates a slepton NLSP final states with multi-leptons for all three generations. and missing energy or heavy charged particles If the supersymmetry breaking scale is well with kinks to minimum ionizing tracks can re- above a few 1000 TeV, the decay ˜l l + G takes sult from decay to the Goldstino. A measurement place well outside the detector. At both→ e+e− and of the decay length distribution to the Goldstino hadron colliders the signature for supersymmetry would give a measurement of the supersymme- ˜+˜− would then be lRlR X, i.e. heavy charged parti- try breaking scale. Supersymmetry breaking at cle pair production without missing energy! This a low scale clearly provides many experimental very non-standard signature should not be over- challenges and opportunities. looked in the search for low scale supersymmetry We would like to thank A. Litke and A. Sei- breaking. den for useful discussions. This work was sup- ported by the Department of Energy (M.D.), 3.3. Model Independent Signatures under contract DOE-ER-01545-646 (S.R.), and As discussed above, the quantum numbers and DOE-AC03-76SF00515 (S.T. and J.W.). composition of the lightest standard model super- partner (NLSP) are model dependent. Although REFERENCES attention in the literature has been focused on the the mostly gaugino neutralino case, it is impor- 1. M. Dine, W. Fischler, and M. Srednicki, Nucl. tant to allow for all possibilities in the search for Phys. B 189 (1981) 575; S. Dimopoulos and low scale supersymmetry breaking, and decays to S. Raby, Nucl. Phys. B 192 (1981) 353; M. the Goldstino. From the above discussion, the Dine and W. Fischler, Phys. Lett. B 110 model independent signatures break up into two (1982) 227; M. Dine and M. Srednicki, Nucl. exclusive possibilities Phys. B 202 (1982) 238; L. Alvarez-Gaum´e, M. Claudson, and M. Wise, Nucl. Phys. B 1. 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