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arXiv:hep-ph/9710277v1 8 Oct 1997 a Farrar R. Glennys Scenarios Gaugino Light of Status h ujc,s illmtmsl otefollowing: on the to works myself the limit will of I all so here subject, review the would to It impossible gauginos. be light of possibility the in terest Preliminaries and Introduction 1. progress phenomenological and experimental on is emphasis eprnrsetu eebsdo oesin models on based were spectrum perpartner eateto hsc n srnm,RtesUiest,Pisca University, Rutgers Astronomy, and Physics of Department umrz eetdvomnsi uesmer scenarios in devlopments recent summarize I ic UY5teehsbe osdrbein- considerable been has there SUSY95 Since o ayyas iw bu h osbesu- possible the about views years, many For • • • • • • • • • • • arnccosscinand section cross hadronic aefo rpriso the of properties conden- from and sate mass the on Constraints light including results . pQCD order Higher spec- masses. richer gaugino a of with trum models new Attractive ietsac o decaying a for search direct A “glueballino”. decaying a for search direct A cosmology. from constraints New ii rmacmie tt rprisof properties in to states fit final hadronic combined a from Limit iisfo eomlzto ru run- group of renormalization ning from Limits edl xlie ihlgtguns but with- them. explanation out gluinos, satisfactory light eluded are have with which explained observations readily tantalizing Some light. are gluinos when limits mass Squark of LEP2. test at independent scenario all-gauginos-light model the a for Proposal α s xrce rmthe from extracted , a Rsac upre yNSF-PHY-94-2302. by supported “Research Z -decay. R η ′ τ . . R e -. + e − total vri h esnesaenurludrsome under neutral How- are messengers models. the SUGRA in if that ever like complete their is and a massive spectrum form are gauginos messengers all the multiplet GUT coupling If their to gauginos. due lep- loops to and two at masses of get tons interac- 1-loop charge. the carrying gauge from supermultiplets messenger arise with tion masses gaugino ing, large. very hnthe than hnmnnadmxn.Oecagn salways the is than lighter One mixing. Higgs the and through phenomenon masses their get ier hthairdet infiatcnrbtosof contributions loops significant some- electroweak to is the due ) heavier (a what MeV 100 lightest order the of param- mass and most has For gluino the less[2,3]. choices or typi- eter GeV are 1 order masses of gaugino cally resultant The gauge-Higgs/ino electroweak loops[1]. and predominantly stop-top are to masses due gaugino low-scale the ol es hr st aearaybe excluded. lifetime been already glueballino have to the as short Otherwise, so be would scenario. gaugino 1 nainei togyboe rnt edn to leading not, De- R- or m broken mechanism, do. strongly breaking is couplings SUSY invariance gauge the on the pending as at just group another renormalization running, of one because from at distance diverge degenerate longer and be masses distance to tree-level In gauginos short the model gravity. standard expects by of trans- one sector is models, observable such breaking the a SUSY to respect mitted and interactions symmetry fundamental GUT the which nteps year. past the in hsosraini rca otesceso h light the of success the to crucial is observation This 1 nguemdae oeso UYbreak- SUSY of models gauge-mediated In / 2 ≈ hc ev oeo l agnslgt The light. gauginos all or some leave which M Z sq aa,N 85,USA 08855, NJ taway, nti yeo cnro unless scenario, of type this in or m W 1 / n he etaio lighter neutralinos three and 2 1 ≈ 23.Cagnsadheav- and [2,3]. M M l P sq 2 ntelte case, latter the In . µ is 1 2 gauge group, those gauginos are massless at lead- of event-shape and 4-jet angular distributions by ing order. Since quarks and have both Dixon and Signer[8,9]. In addition, the 3-loop SU(2) and U(1) charges, it is enough for the mes- calculations of Rhad and Rτ and the QCD beta- sengers to have SU(2) or U(1) charges to make function have been extended to the case with light the squarks and sleptons massive. In this case, gluinos[10]. These successes give hope that the gluinos do not receive mass at 1-loop. Wino and most daunting calculation of all, the 2-loop cor- bino are massive or not, depending on the messen- rections to the 3-jet matrix elements, will also ger charges. One can also obtain models in which prove feasible. These results are necessary for all the gauginos are massless at theoretical predictions to be sufficiently accurate one loop by introducing additional gauge inter- to discriminate the theory with and without light actions under which the messengers and quarks gluinos, as discussed in sec. 2.3. and leptons are charged, but the messengers are I now turn to experimental and phenomeno- standard model singlets. Mohapatra and Nandi logical constraints on the allowed mass range of (also joined by Chacko and Dutta) and Raby have gluinos. The lightest containing a single recently given models of these types[5]. One in- gluino is expected to be the -gluino bound teresting feature of the Raby model is that for state, usually denoted R0 (glueballino). The rela- part of parameter space the is heavier tion between gluino current mass and the mass of than the gluino, as are the bino and wino, so the the R0 can only be estimated. A massless gluino gluino is the LSP and is stable. Its mass can be would imply a degenerate chiral supermultiplet adjusted over a large range, from 0 to hundreds consisting of scalar, pseudoscalar and R0, if mix- of GeV. ≈ ing with qq¯ states can be ignored. Quenched The new models were constructed to have QCD predicts a 0++ mass of 1.5-1.7 nice properties in their own right, such as GeV and good candidates are the f0(1500) and 2 solving the strong CP problem in the case of f0(1700) . Thus a massless gluino suggests an 0 1 some of the Mohapatra-Nandi models. And as R mass of about 1 2 GeV. Its lifetime should be pointed out in [6], models with sufficiently small in the 10−5 10−10 sec range, or longer if the up dimension-3 SUSY breaking automaticalloy solve and down squarks− are very heavy[3]. the SUSYCP problem. Although it appears If the R0 lifetime is less than about 10−10 possible to generate essentially arbitrary com- sec, the original missing energy[12] and beam binations of gaugino masses, I will concentrate dump[13] techniques are applicable. These here on the following different light-gaugino phe- methods have been used to establish mg˜ > 150 nomenologies: GeV[14]. Ref. [15] compiled experimental limits∼ relevant to gluinos for R0 lifetimes longer than All gauginos are nearly massless and get −10 • about 10 sec. The most important constraint masses of order 1 GeV or less from stop-top is from the CUSB experiment[16] which did not and electroweak loops. find Υ γηg˜ at the pQCD-predicted level. This result→ rules out gluinos in the mass range The gluino and the bino or wino is light. 1 1 0 • 1 2 3 2 GeV and hence R ’s between about ∼1 − The gluino is the LSP. 2 2 4 GeV, for any lifetime[15]. As noted above, • for−m(R0) below the CUSB-excluded range and The case of light wino and bino and heavy gluino in the expected mass range of 1 1 ∼ 2 − is already excluded. This will be discussed below. GeV, the R0 lifetime falls out of the range of ap- Besides these model building accomplishments, plicability of beam-dump and missing energy ex- the last two years have seen advances in extend- periments and previous limits were weak. ing perturbative QCD in phenomenologically im- If the gluino is above the CUSB limit of about 1 0 portant ways. The tour-de-force 1-loop calcula- 3 2 GeV, the R mass should exceed the gluino tion of 4-jet matrix elements in e+e− annihila- tion has been completed[7] and applied to study 2See [11] for a recent discussion and references. 3

1 mass by the constituent mass of a gluon, 2 1 ballino mass should be in the range 1.4 2.2 GeV, in analogy with heavy-light .− GeV on theoretical grounds; experiment≈ requires− 1 The spectator approximation is applicable and it to be less than about 2 2 GeV. Dark is 0 0 the R lifetime is well-approximated by the free- correct if 1.3 < r m(R ) < 1.55; r> 1.8 is ruled ≡ mγ˜ gluino lifetime. For a light photino this is: τ > −14 Msq 4 4 GeV 5 ≈1 out by cosmology unless mγ˜ 10 GeV. We now 2 10 ( ) ( ) sec. Thus mg˜ > 3 100 GeV mg˜ 2 turn to constraints from new∼ direct and indirect GeV is only viable if up and down squark masses experimental searches. are at least 700 GeV, or if R0 decay to a lighter neutralino is∼ kinematically forbidden. In the case that the gluino and lightest hadron 2.1. Direct search via decays containing it are stable, the most important con- The predominant decay mode of R0’s in this − sideration is whether any new bind to scenario is to π+π γ˜[4]. Thus it was proposed 0 to produce new stable nuclei which accu- that the current generation of KL experiments mulate near Earth. If so, limits on exotic isotopes search for evidence of R0’s in their beam, whose − give stringent limits[17–20]. In order to produce decays would result in π+π pairs with high in- an interesting density, a heavy gluino variant mass and unbalanced pt[4]. KTeV has must have a mass too large to be consistent with now completed such a study using a small fraction − properties of our galaxy[19,20]. of their total data[24]. Their cut m(π+π ) > 648 A very light gluino requires a corresponding MeV restricts them to the study of the kinematic pseudogoldstone . The η′ suits this role region m(R0)(1 1/r) > 648 MeV. However sub- − well if mg˜ = 80 140 MeV and < λλ >= ject to this constraint their limits are extremely (0.15 0.36) GeV−3[21]. This mass lies within good. For the largest r allowed by cosmology, 1.8, − − 0 > 1 the range estimated from the top-stop loop[3], they are therefore sensitive to m(R ) 1 2 GeV and this condensate is consistent with the naive and considerably improve the previous∼ limits[15]. 1 1 3 9 3 expectation (<λλ>) 4 (< qq>¯ ) [15]. Fig. 1 shows the mass-lifetime region excluded If the photino is the LSP≈ and R-parity is exact, by KTeV[24], for two values of r. Unfortunately it can provide relic dark matter. For a radiatively- the sensitivity drops rapidly for lower r and they generated photino mass, i.e., of order 1 GeV or are completely blind to the R0 mass region of less, obtaining the correct dark matter abundance primary interest, 1.4-2.2 GeV, for r 1.4. The 0 ≤ requires r m(R )/mγ˜ to be in the range 1.3 - experimental challenge will be to reduce the in- 1.55[22,23].≡ In this case, interconversion of photi- variant mass cut. nos and R0’s keeps them in equilibrium until the Another strategy to find a light gluino is to look appropriate epoch. Photinos would “overclose” in a charged beam for the Rp (uudg˜) the universe if r> 1.8 unless their mass is greater decaying to the ground state R-baryon, the S0 0 + than about 10 GeV[22,23]. It is non-trivial that (udsg˜)[4]. This weak decay, Rp S + π , − − − → − the predicted R0 lifetime range 10 5 10 10 sec, should have a lifetime 2 10 10 2 10 11 sec[4]. · − · is consistent both with the experimental− limits[15] Assuming the gluino mass is O(100 MeV), the and the lifetime as estimated from requiring the mass of the uudg˜ state is calculated to be about correct dark matter abundance[23]. 200 MeV higher than the S0[17]. The most inter- esting mass range for the R is 1.6 3.1 GeV[4]. p − 2. New Experimental Constraints The lower end of this range is motivated by the speculation that the Λ(1405) is actually a crypto- To summarize the foregoing, SUSY breaking exotic flavor singlet udsg[25]. The upper end of scenarios in which gaugino masses are mainly ra- this range is the mass above which the S0 is likely diatively generated by known and their to be strong interaction stable due to the decay superpartners are naturally consistent with the S0 R0Λ. The kinematics of the charged parti- requirements of dark matter, the η′ mass, and cles→ in this decay is different from that of decays direct experimental limits as of 1995. The glue- of known particles, so an upper limit on the pro- 4

5 M + [MeV/c2] Σ- R 4.5 2510 ] Σ+

4 CL % 90 [ Ξ- 3.5

3

2.5 Ω- 2310

 Ξ+ 2

Beam Fraction at Production 2110 1.5 1910

1 1710 -10 -9 -8 -7 -6 -5 -4 -3 10 10 10 10 10 10 10 10 Lifetime [ns]

Figure 1. KTeV limits[24]. Figure 2. E761 limits vs. τ(Rp)[26] .

duction rate of Rp’s can be obtained. by E761 at Fermilab and no evidence for anoma- Unfortunately, it is difficult to reliably estimate lous decays was found[26]. The experiment’s best the production cross section. Perturbative QCD sensitivity is at m(Rp)=1.7 GeV and τ(Rp) = cannot be used, since the constitiuents of the rel- 3 10−10 sec. There, the sensitivity is about an or- evant state are not heavy and the transverse mo- der of magnitude lower than the production level mentum is not large. However one can use the of Ξ.¯ Given the suppression factors mentioned measured D- differential cross section as a above, this is a marginal level of sensitivity for ex- benchmark for R0 production, since their masses clusion. However a more serious problem is that are comparable. The larger of the the sensitivity drops rapidly as lifetime decreases R0’s constituents probably is not relevant at low into the interesting range and as mass increases pt due to color screening. On the other hand, above about 2 GeV. no known hadron provides a good analogy for Rp Thus the E761 search must be considered a production. One would expect the Rp production first step which demonstrates the feasibility of cross section to be significantly lower than that of this technique. I particularly want to stress that − 0 + Ω or Ξ,¯ since the Rp is heavier than these, is pair the Rp S π search is complementary to the produced with another whose mass is at R0 π→+π−γ˜ search and both need to be pur- 1 → least 1 2 GeV, and in addition requires binding 4 sued. Since the former is a weak decay, the su- quanta rather than 3. Hence upper bounds on perparticle spectrum is essentially irrelevant to −4 the production fraction of order 10 or better the Rp lifetime. The lifetime is unaffected by are probably the minimum needed to hope to see whether the gluino (R0) is the LSP or whether a signal. To rule it out, much better limits would the u- and d-squarks are light. The search relies be needed. only on the mass of the gluino being low enough The Rp search described above was performed that Rp production is at an experimentally acces- 5 sible level. On the other hand, the R0 search can termination is larger than in other methods. At 0 be very sensitive to small production cross sec- the Z peak CF quote αs =0.123 0.006 and at tions because of the cleanliness and intensity of lower vales of √s the errors are very± large. There- this generation of experiments. However it fore CF also use αs obtained from the hadronic depends in three crucial ways on the superparti- width of the τ, which has a smaller statistical er- cle spectrum: i) If the u- and d-squarks are heav- ror. The perturbative contributions to Rτ are ier than 130 GeV, they must be heavier than also known to 3-loops. However the error on ∼ 600 GeV as discussed in sec. 4. In this case the αs(mτ ) which should be associated with modeling ∼ −7 −10 Mq˜ 4 lifetime, (10 10 )( 100 GeV ) sec[4], may be non-perturbative effects is controversial. CF take − 3 inaccessibly long for KTeV . ii) If the gravitino αs(mτ )=0.335 0.08, but Shifman and collab- and lightest neutralino are heavier than the R0 it orators argue that± due to finite-size singularities won’t decay at all, assuming R-parity is good. iii) in the Operator Product Expansion (e.g., instan- If the Q value of the decay is too small, because tons) the actual error may be twice as large as R0 andγ ˜ are too close in mass, it will be difficult this[29]. The need for a more conservative error to discriminate signal from background. estimate is confirmed by Jan Fischer4. Besides looking forward to improvements in the CF consider two mass regions for the gluino. 1 KTeV and E761 type searches, the next couple of For mg˜ < 1 2 GeV they do not use Rτ in the fit years may see other advances in direct searches. and obtain a 70 % cl exclusion limit. For mg˜ = T. LeCompte and collaborators have been prepar- 3(5) GeV they do include αs(mτ )=0.335 0.08 ing a parasitic search at Fermilab for states with in the fit and obtain 95(90)% cl exclusion± lim- anomalously long lifetimes, which may be rele- its. However had they used the larger error advo- vant for long-lived R-hadrons. Also Nussinov has cated in [29], these limits would also be degraded made several suggestions on how to enhance the to 70 % cl. Thus unless the theoretical uncer- 0 ≤ signal to noise in searching for long-lived R ’s[20]. tainty on αs(mτ ) can be reduced, or other sources of high-precicion, model-independent information 2.2. Running of α 2 s on αs at low Q can be found, the approach of Csikor and Fodor[28] (CF) fit the Q2 evolution using the running of αs to exclude light gluinos of αs to the 3-loop beta function prediction, with is inconclusive. and without light gluinos. The problem with pre- vious attempts in this direction has been the diffi- 2.3. Hadronic Event Shapes in Z0 Decay culty of determining αs without reliance on mod- The other new effort to exclude light gluinos is els of non-perturbative physics. For instance a due to ALEPH[31]. Their strategy is to determine model or parameterization of higher twist effects the effective number of quark flavors, nf , from is required if deep inelastic scattering is used. a combined fit to several different 4-jet angular CF employ Rhad, the hadronic total cross section distributions and D2, the differential 2-jet rate. in e+e− annihilation. This is the theoretically At leading order, adding gluinos to ordinary QCD cleanest way to determine αs, on the assumption increases nf determined via the running of αs or that we know the particle content of the theory. 4-jet angular correlations by 3 units. Since it is a total cross section it is insensitive to The differential 2-jet rate is the number of hadronization and does not require resummation events as a function of y3. The variable y3 is of large logarithms of the jet definition parameter the value of ycut for a given event at which it ycut. Since it is known to 3-loops, it is insensitive changes from being a 3-jet to a 2-jet event. D2 to the arbitrary renormalization scale, µ. is statistically powerful, since every hadronic Z The drawback to using Rhad is that it is not decay is used, but is quite sensitive to the ar- very sensitive to αs, being proportional to 1 + bitrary renormalization scale, µ, since it is only αs 2 π + O(αs) . Thus the statistical error in its de- known to 1 loop (NLO) accuracy. Furthermore, the shape of the D2 distribution is distorted in 3The reactionγπ ˜ ↔ R0π can still serve its crucial cosmo- 4 logical catalysis function due to the Rπ resonance[27]. Private communication. See also [30]. 6 comparison to the fixed order PQCD predictions due to logarithms of y3 which are large when y3 is small. These logs must be resummed, and the fi- nal prediction is dependent on the procedure used to match the resummed and fixed order formu- lae. The 4-jet angular distribution is statistically weaker and is subject to large hadronization er- rors but is insensitive to µ[8]. ALEPH’s hope was that by performing a combined fit to both distri- butions, their strengths might be complementary and their deficiencies less important. ALEPH reports nf = 4.24 0.29(stat) 1.15(syst) and concludes that they± rule out± a gluino with mass less than 6.3 GeV at 95 % cl. The precision of the ALEPH result is governed by their systematic errors, specifically the uncer- tainty in the theoretical prediction, since their statistical errors are small. Thus determining their systematic errors is the critical issue. A de- tailed discussion can be found in refs. [31,32]. Here I give a brief synopsis of the main problems. The most important contribution to the sys- tematic error is the uncertainty in the predicted D2 distribution due to truncation of the perturba- tion series. This is manifested by the sensitivity of the fit to renormalization scale, µ, and to the re- summation scheme. The conventional treatment of the uncertainty due to renormalization scale is to vary µ between √s/2 and 2√s, and treat the Figure 3. ALEPH’s n , α , and χ2 vs µ[31]. spread of results as a 1σ error. Such a procedure f s 1 ± leads to a 2 2 unit uncertainty on nf (see Fig. 3, from [31]).± With such a large uncertainty, no useful constraint on light gluinos can be obtained. similar exercise for the R-matching scheme gives 2 To reduce the uncertainty coming from scale the best fit nf = 4.88, with χ = 81.6, and the sensitivity, ALEPH assumed that there is a value range nf = 3.57 5.81 as µ’s variation raises of µ at which the resummed NLO prediction for χ2 to 83. The other− systematic errors they esti- D2 agrees with the all-orders prediction. If this mate are 0.45 from hadronization modeling and hypothesis is correct, µ should be fixed to the 0.27 for± the detector simulation. Combining er- value which gives the best fit, and the associ- rors± in quadrature and averaging the results of ated uncertainty is essentially the statistical un- the two matching schemes then gives their final certainty in finding µ. Thus the scale uncertainty result quoted above. in nf would be the range in the nf obtained by Unfortunately, the “experimental optimiza- varying µ to increase χ2 by 1 unit above its min- tion” procedure employed by ALEPH to reduce imum. their scale sensitivity is known to be invalid. Bur- Using the log R-matching scheme and varying rows[33] examined the proposition that a judi- µ to get the best fit, ALEPH finds nf = 3.68, cious choice of scale can improve the accuracy with χ2 = 78.5 for 73 dof. Increasing χ2 by of the theoretical prediction for hadronic event one unit gives the range nf = 3.09 4.08. A shape distributions. He found that none of the − 7

certainty, the conservative approach is to adopt (a) (b) the traditional procedure used by other experi- τ ments, which gives 2.5. At least this allows a ρ direct comparison between± the sensitivities of pre-

BT vious analyses employing just 4-jet angular dis-

Bw tributions and the ALEPH procedure which also O uses D2. This will be done below.

C Another problem with the ALEPH analysis is the estimation of the hadronization error. That DE 2 is in principle done by repeating the analysis us- DE0 2 ing several hadronization MC’s which perform DP 2 equally well for other purposes. A fit using Her- P0 2 D2 wig instead of Jetset gave nf = 6.21 with χ = D 2 D2 91.6, instead of nf = 4.88 and χ = 81.6 (see G Table 3 of [31]). However µ was optimized only D2 for the Jetset fit and that value was used for all EEC the different MC’s, so there is no way of know- AEEC ing what the Herwig result would have been, or JCEF how small its χ2 would have been, had the µ op- 0.100.12 0.14 0.100.12 0.14 timization been systematically applied. Because α ( 2) 2 11-95 s Mz 8083A4 the χ of this Herwig fit is enough larger than for the Jetset best fit, the ALEPH error-assignment procedure discards it entirely[31]. It is also difficult to know what error to assign Figure 4. (a) αs from various event shape dis- to the resummation matching-scheme dependence tributions using µ = MZ (solid circles) and of D2. ALEPH used the dispersion between log- experimental-optimization (open circles). (b) Us- R and R matching. But since the log-R matching ing other schemes[33]. scheme gives nf < 5 for any value of µ, we can infer it is NOT the correct matching scheme. Even adopting the ALEPH hadronization error estimate and neglecting matching scheme uncer- scale fixing schemes, including exerimental opti- tainty altogether, one can see that employing D2 mization, successfully improves perturbation the- with its strong µ sensitivity leads to a worse de- ory. His procedure was to extract αs(mZ ) from termination of nf than using the angular distri- 15 different event-shape distributions, such as D2, butions alone. If one uses the R-matching scheme thrust, etc., using various scale fixing schemes, result and takes the 1σ scale error to be given by ± such as experimental optimization, minimal sen- the 1/2 < µ/√s< 2 variation, the ALEPH result sitivity, etc. If a scheme provided a systemtic im- becomes nf =4.88 0.29(stat) 2.57(syst) which ± ± provement, this procedure would lead to a con- is considerably worse than the limits obtained by sistent set of αs values, within the errors from the other LEP groups using just the 4-jet angular other sources. What Burrows found (see Fig. 4) distributions[34]. is that the dispersion in values is essentially the same in all schemes, and comparable to the one 3. Model Independent Proposal for a found using the conventional procedure[33]. LEPII Search Thus ALEPH’s method of fixing µ and esti- mating the theoretical systematic error associ- To summarize the previous section: direct ated with the scale depedence is not valid. In searches for decaying R-hadrons have not yet ex- the absence of a better way to estimate this un- plored the interesting regions of mππ[24] or Rp 8 lifetime[26]. Indirect searches for light gluinos sis[36,27]. For the moment, the integrated lumi- 0 via αs running[28] and Z event shapes[31] are nosity is too small to extend the analysis away stymied by theoretical uncertainties. In this sec- from b = 1 and b = 0, but with the integrated tion I describe a complementary search tech- luminosity planned at 183 GeV, LEP should be nique[27] which is theoretically very clean. It is able to probe all values of b. This method should relevant to the case that the gluino and either also permit the discovery or complete elimination wino or bino is light; it relies on the high energy of models such as Mohapatra and Nandi’s [5] in and integrated luminosity of LEP2. which only m2 and m3 are small, while m1 and µ When electroweak gaugino masses are negligi- may be large. The possiblilty of putting interest- ble, the chargino and neutralino masses depend ing constraints on other combinations is presently 5 only on µ and tanβ. When m2 vanishes, one under investigation. chargino is lighter than the W ±. Its mass de- A notable feature of this search is that it is creases as µ or tanβ are increased, so large µ and theoretically very clean[27]. There is essentially tanβ are excluded by the Z0 width6. However no sensitivity to µ. The sensitivity to parame- for small µ, three neutralinos have masses below ters of the standard model such as αs and mW 0 the Z if m1 and m2 are both small. Consider- is weak and introduces an uncertainty which is ing the neutralino contribution to the Z0 width small compared to present statistical errors. Most further restricts µ and tanβ but does not exclude important, since it employs the total cross section the scenario. the details of hadronization are insignificant and 0 At energies above the Z , production of inos there is no small parameter such as ycut to intro- in e+e− collisions depends on µ and tanβ, and duce large logarithms which need resummation. m(˜νe) in the case of charginos. Varying m(˜νe) over the allowed range, one can compute the min- 4. Constraints on squarks if the gluino is imum total cross section for ino production, as a light function of Ecm, µ and tanβ. Even this lower limit is quite substantial: 2 pb at 173 GeV and Lower bounds on squark masses are much 184 GeV, summing over chargino and neutralino weaker when the gluino is light than when miss- production. ing energy is a signature. Early Z0 width mea- If the gluino is heavy, the charginos and heav- surements gave mq˜ > 50 60 GeV for degenerate ier neutralinos decay mainly into the lightest squarks[38]. If only one− flavor of squark is light ± neutralino and products of W or Z0 decay. the limit becomes 30 GeV for a L-type squark and This possibility is already completely excluded by there is practically no constraint for an R-type LEP[35,36]. However if the gluino is light as well, squark[25]. Data on the Z0 has improved enor- inos can decay via a real or virtual squark, to mously in the intervening period, inconsistencies qq¯g˜. Indeed, this is the dominant decay mode with the SM such as Rb have disappeared, and for squark masses up to msq 100 GeV[37]. higher energy data is now available. Therefore ∼ Then the sensitivity of the usual ino searches is the analysis of refs. [38] should be redone – it reduced by the factor (1 b)2, where b is the suit- would surely yield significantly better limits now. − ablly averaged branching fraction of an ino into A stop more than a little lighter than the top qq¯g˜. However when both inos decay to qq¯g˜, the would dominate top decay because of t t˜+˜g. event contributes to the hadronic cross section. This is probably excluded, but the possibility→ that The total hadronic cross section is well-enough the stop decay products can “fake” the final states measured that b = 1 is excluded for any value observed by D0 and CDF deserves investigation. of µ, tanβ, and m(˜νe) by OPAL’s recent analy- There have been a number of papers on the ef-

5 fect of associated squark-gluino production on the In this context, µ is the mass parameter in SUSY dijet invariant mass distribution in pp¯ collisions, models, not the renormalization scale! 6These statements ignore radiative corrections, which is starting with Terekov and Clavelli[39]. More re- − not strictly correct for extremely large µ[2]. cently, using the full 106pb 1 of Tevatron dijet 9 data, Hewett et al[40] and Terekov[41] have ex- 2++ sectors are within about 100 MeV or tended the analysis also to dijet angular distribu- better of good candidate states. tions. They are able to exclude the mass ranges Models such as the bag and instanton gas 150 < M(˜u) < 620 GeV and 170 < M(d˜) < • calculations corroborate the lattice result 620 GeV[41] and 130 < M < 600 GeV[40]. At that m(0−+) >> m(0++). lower squark mass, QCD background∼ swamps the SUSY dijets; at larger mass the production rate There is some evidence for a suitable glue- is too low. • ball candidate in the mass range of the lat- Choudhury[42] suggested that a monojet anal- tice prediction8. ysis might allow Tevatron data to be used to ex- Overall, accounting for the η(1410) and its strong clude all squark masses below 240 GeV. The dijet- affinity for glue is difficult within QCD. However pair analysis proposed in [25], which should be the very-light gluino scenario predicts[15] the ex- useful for lower squark masses and less model de- istance of a flavor singlet pseudoscalar not present pendent than the monojet analysis, has not yet in conventional QCD, with mass about equal to been carried out. the unmixed scalar glueball, i.e., 1.4-1.8 GeV ac- 5. Hints of a light gluino? cording to lattice . The predicted properties of the ηg˜ fit the observed η(1410) prop- There are several well-established phenomena, erties[11]. which have so far eluded satisfactory explana- 5.2. Anomalies in jet production tion within the framework of standard model Shortly after the announcement by CDF of an physics, but which are readily explained with a excess in very high E jets[43], several papers light gluino. T addressed the question of whether light gluinos 5.1. The η(1410) could account for the effect[44]. The excitement The η(1410) meson is a flavor singlet pseu- abated after CTEQ announced[45] that a slight doscalar. All nearby pseudoscalar nonets are generalization of the functional form taken for the filled, so that it must be a glueball or some other pdf’s would allow the gluon pdf to be increased 7 exotic state . The relationship between its width enough to accomodate the new high ET jet data. and production in J/ψ radiative decay are appar- While the light gluino hypothesis improved the ently inconsistent with its being a qq¯ state[11]. It overall fit, it was not essential. cannot be identified with a KK∗ ”” be- However the most problematic anomaly in pp¯ cause no corresponding spin-1 state is observed jet physics is the strong violation of scaling ob- ∗ so KK binding would have to occur only in the served by both CDF and D0 in the ratio of xT p-wave and not in the s-wave which would be un- distributions at √s = 630 GeV and √s = 1800 precedented. Its coupling to glue-rich channels is GeV. Modifications in pdf’s change the inclusive strong[11] and it would naturally be interpreted xT distribution but do not significantly affect the as a glueball, except that: ratio of the scaled xT distributions. As of the CTEQ workshop in Nov. 1996, no explanation For a 2-gluon state to have J PC =0−+ re- • for the scaling violation had been found within quires one unit of orbital angular momen- standard model physics. Clavelli and Terekov[46] −+ ++ tum. This suggests m(0 ) m(0 ) point out that the observed breakdown of scaling − 3≈ 500 600 MeV, the splitting between P may result from associated production of a light −1 and S mesons. gluino and squark, with M 100 140 GeV. q˜ ≈ − Lattice gauge calculations predict the mass 5.3. Ultra High Energy Cosmic Rays • − of the lightest 0 + glueball to be 2.2 0.3 Several cosmic rays of extremely high energy ± GeV; similar calculations for the 0++ and (> 1020 eV) have been detected. Their shower 7For a review and primary references see [11]. 8W. Dunwoodie, private communication. 10 properties are consistent with those expected for a tion matching-scheme ambiguity is large. In par- or nucleus primary, but not with a ticular, ALEPH’s claimed limit on light gluinos or primary. On the other hand, (mg˜ > 6.3 GeV at 95% cl) must be set aside be- and nuclei of such high energy interact strongly cause it relies on an ansatz for reducing the scale with the cosmic microwave background radiation sensitivity which has been shown to be invalid via the ∆ resonance or nuclear breakup, lead- (see sec. 2.3). Using a more realistic estimate of ing to an upper bound on their energies if they the intrinsic theoretical uncertainty leads to the are to come from cosmological distances. This is conclusion that the ALEPH analysis is actually known as the GZK bound[47]. Thus if the high- less sensitive than earlier experiments employing est energy cosmic ray 3 1020 eV were a proton, only 4-jet angular distributions, for which system- its source would have to be closer than about 50 atic uncertainties were also too large to make a Mpc[48]. The problem is that in order to produce definitive statement. In order to reduce the the- such extremely high energy projectiles, the source oretical error in the ALEPH analysis to a useful is expected to be remarkable in other observable level, the two-loop correction to three-jet matrix ways. In particular it should be an exception- elements is needed. ally strong x-ray source[49]. There are no plau- It is still possible that all gauginos are massless, sible candidates with appropriate features in the aside from radiative corrections due to known relevant angular region, closer than 50 Mpc[48]. particles and their superpartners. This gives a However the two highest energy cosmic rays point gluino mass is of order 100 MeV and is consis- toward a good source at about 240 Mpc, and an tent with properties of the η′. Such a scenario excellent one beyond 1000 Mpc[48]. It was sug- provides an explanation for dark matter, predicts gested that these UHECR’s might be the lightest the ”extra” flavor singlet pseudoscalar (η(1410)), R-baryon, the S0 (udsg˜) mentioned above[4]. Its and accounts for the apparent violation of the interaction length in the CMBR is much longer GZK bound by ultra-high energy cosmic rays. than a ’s, and can accomodate even a Gpc This scenario should be completely excluded, or source[50]. Because its interactions with atmo- suggestive evidence for it found, in the next year spheric nuclei is similar to a nucleon’s, its shower of LEP running, using a combination of conven- development would be consistent with observa- tional signatures and limits on an excess in the tions. For further details, references, and discus- hadronic total cross section[27,36]. With planned sion of alternative ”uhecrons” see [50]. increases in integrated luminosity, the case that only the wino and gluino are light can be fully in- 6. Summary vestigated in the same way. The possibility that the wino and/or bino are light, but the gluino is The past two years have seen subtantial effort heavy, is already excluded by LEP. on many fronts to explore the various light gaug- The most difficult case to study experimentally ino possibilities. KTeV and E761 searches for ev- is when the gluino is the only light gaugino. With idence of decaying R-hadrons have yielded null a significant improvement on the determination − results, but they have not yet investigated the of the e+e total cross section at Q2 = m2 , the 6 Z most plausible regions of parameter space (see beta function can be determined with sufficient sec. 2.1). accuracy to unambiguously infer or exclude some Indirect searches are still either theoretically gluino mass ranges. The requisite 3-loop calcula- or statistically inadequate. The running of αs tions have been done and the method does not + − as determined by Rhad in e e hadrons is require knowledge of non-perturbative physics. theoretically clean but only gives→ a 70 % cl ex- When the 3-jet differential cross section in Z0 de- clusion of light gluinos[28]. Analysis of Z0 event cay has been calculated to 2-loop accuracy, it will shapes is statistically powerful but the theoretical probably be possible to use Z0 event shapes to ob- predictions are not known to high enough order, tain a consitent set of determinations of αs(mZ ) so that the renormalization scale and resumma- and nf . However further control of hadronization 11 and resummation uncertainties may also prove tional Conference on High Energy Physics, necessary. A final strategy if the gluino is not Munich, page Contributed paper no. 723., too heavy is to extend the search for the weak 1988. 0 + decay Rp S + π in the fashion of E761[4,26] 17. G. R. Farrar. Phys. Rev. Lett., 53:1029–1033, to shorter→ lifetimes and much lower production 1984. levels. 18. R. Plaga. Primordial gluinos. MPI-PhE/94- 09, Max Planck Institute, Munich, 1994. Phys. Lett. REFERENCES 19. E. Nardi and E. Roulet. , 245B:105, 1990. 1. R. Barbieri et al. Nucl. Phys., B243:429, 20. S. Nussinov. hep-ph/9610236, TPI-MINN- 1984. Phys. Lett., B127:429, 1983. 96/18-T, 1996. 2. G. R. Farrar and A. Masiero. RU-94-38 (hep- 21. G. R. Farrar and G. Gabadadze. Phys. Lett., ph/9410401) Rutgers Univ., 1994. B397:104, 1997. 3. G. R. Farrar. RU-95-25 (hep-ph/9508291) 22. G. R. Farrar and E. W. Kolb. Phys. Rev., Rutgers Univ., 1995. D53:2990, 1996. 4. G. R. Farrar. Phys. Rev. Lett., 76:4111, 1996. 23. D. J. Chung, G. R. Farrar, and E. W. 5. R. Mohapatra and S. Nandi. UMD-PP- Kolb. FERMILAB-Pub-96-097-A, RU-97-13 97-082 (hep-ph/9702291) 1997. Z. Chacko and astro-ph/9703145, FNAL and Rutgers et al. UMD-PP-97-102 (hep-ph/9704307) Univ, 1997. 1997. S. Raby. OHSTPY-HEP-T-97-002 24. The KTeV Collaboration. RU-97-26, Rut- (hep-ph/9702299) 1997. gers Univ., 1997, Phys. Rev. Lett., to be pub- 6. G. R. Farrar. RU-95-73. SUSY95, Paris, May lished. 1995, hep-ph/9704310. 25. G. R. Farrar. Phys. Rev. Lett., 76:4115, 1996. 7. E. W. N. Glover and D. J. Miller. Phys. 26. I. F. Albuquerque and others (E761 Collabo- Lett. B396, 257, 1997. Z. Bern et al. Nucl. ration). Phys. Rev. Lett., 78:3252, 1997. Phys., B489, 3, 1997. J. M. Campbell, 27. G. R. Farrar. RU-97-20, Rutgers Univ., 1997. E. W. N. Glover, and D. J. Miller. DTP- 28. F. Csikor and Z. Fodor. Phys. Rev. Lett., 97-44, hep-ph/9706297. Z. Bern, L. Dixon, 78:4335, 1997. and D. Kosower. SLAC-PUB-7529, hep- 29. B. Chibisov et al. hep-ph/9605465, TPI Min- ph/9606378, SLAC, 1996. nesota, 1996. 8. L. Dixon and A. Signer. SLAC-PUB-7528 30. J. Fischer. hep-ph/9704351, 1997. (hep-ph/9706285) SLAC, 1997. 31. The ALEPH Collaboration. CERN-PPE- 9. A. Signer. SLAC-PUB-7490 97/002, to be pub Z. Phys., CERN, 1997. (hep-ph/9705218) SLAC, 1997. 32. G. R. Farrar. RU-97-22, Rutgers Univ., 1997. 10. L. Clavelli and L. Surguladze. Phys. Rev. 33. P. N. Burrows. SLAC-OUB-7328, MIT-LNS- Lett., 78:1632, 1997. L. Clavelli, P. Coulter, 96-213, hep-ex/9612008, MIT, 1996. and L. Surguladze. 55:4268, 1997. 34. OPAL Collaboration. Z. Phys. C, 68, 11. F. E. Close, G. R. Farrar, and Z. P. Li. Phys. 1995. DELPHI Collaboration. DELPHI 96- Rev., D, 1997. 68 CONF 628 (ICHEP’96 Ref pa01-020), 12. G. R. Farrar and P. Fayet. Phys. Lett., CERN, 1996. The L3 Collaboration. L3 Note 79B:442–446, 1978. 1805, submitted to -photon conf 1995, 13. G. R. Farrar and P. Fayet. Phys. Lett., CERN, 1995. 76B:575–579, 1978. 35. J. Feng, N. Polonsky, and S. Thomas. Phys. 14. Particle Data Group. Phys. Rev., D54:1, 1996 Lett., B370:95, 1996. and http://pdg.lbl.gov. 36. The OPAL Collaboration. PPE 97-101, hep- 15. G. R. Farrar. Phys. Rev., D51:3904, 1995. ex/970802, CERN, 1997. 16. P. M. Tuts et al. Phys. Lett., 186B:233, 37. G. R. Farrar. RU-96-71 and hep-ph/9608387, 1987; In Proceedings of the XXIV Interna- Rutgers Univ., 1996. G. R. Farrar. invited 12

talk Warsaw ICHEP96, RU-96-93 and hep- ph/9612355, Rutgers Univ., 1996. 38. L. Clavelli et al. Phys. Lett., B291:426, 1992. G. Bhattacharyya and A. Raychaud- huri. Phys. Rev., D49:1156, 1994. 39. I. Terekhov and L. Clavelli. UAHEP964 (hep- ph/9603390), U. Alabama, 1996. 40. J. Hewitt, T. Rizzo, and M. Doncheski. SLAC-PUB-7372 and hep-ph/9612377, 1996. 41. I. Terekhov. UAHEP971 (hep-ph/9702301), U. Alabama, 1997. 42. D. Choudhury. MPI-PTh/96-74 (hep- ph/9608444), MPI, 1996. 43. CDF Collaboration. Phys. Rev. Lett., 77:438, 1996. 44. L. Clavelli and I. Terekhov. Phys. Rev. Lett., 77:1941, 1996. Z. Bern, A. Grant, and A. Mor- gan. Phys. Lett., B387:804, 1996. 45. CTEQ Collaboration. Phys. Rev., D55, 1997. 46. L. Clavelli and I. Terekhov. UAHEP974 (hep- ph/9703318), U. Alabama, 1997. 47. K. Greisen. Phys. Rev. Lett., 16:748, 1966. G. T. Zatsepin and V. A. Kuzmin. Sov. Phys.-JETP Lett., 4:78, 1966. 48. J. Elbert and P. Sommers. Astrophys. J., 441:151–161, 1995. 49. A. M. Hillas. Ann. Rev. Astron. Astrophys., 22:425, 1984. 50. D. J. Chung, G. R. Farrar, and E. W. Kolb. RU-97-14 and astro-ph/97??, in preparation, FNAL and Rutgers Univ, 1997.