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CERN-TH-97-195 hep-ph/9708437
HERA DATA AND LEPTOQUARKS IN SUPERSYMMETRY
G. Altarelli a aTheoretical Physics Division,CERN, CH-1211 Geneva 23, and Terza Universit`a di Roma, Rome, Italy
I present a concise review of the possible evidence for new physics at HERA and of the recent work towards a theoretical interpretation of the signal. It is not clear yet if the excess observed at large Q2 is a resonance or a continuum (this tells much about the quality of the signal). I discuss both possibilities. For the continuum case one considers either modifications of the quark structure functions or contact terms. In the case of a resonance, a leptoquark, the most attractive possibility that is being studied is in terms of s-quarks with R-parity violation. In writing this script I updated the available information to include the new data and the literature presented up to August 1, 1997.
1. Introduction + 2 = 5 events with about 1.2 + 0.8 = 2 expected. The distribution of the first H1 data suggested The HERA experiments H1 [1] and ZEUS [2], a resonance in the NC channel. In the interval recently updated in ref. [3], have reported an 187.5
> ently not completely [4], be due to the different ceivable at very large x, x ∼ 0.75, which is too methods of mass reconstruction used by the two large even for ZEUS. The compatibility with the experiments, or to fluctuations in the event char- Tevatron is also an important constraint. This is acteristics. Of course, at this stage, due to the because ep scattering is linear in the quark den- limited statistics, one cannot exclude the possi- sities, while pp¯ is quadratic, so that a factor of bility that the whole effect is a statistical fluctu- 1.5-2 at HERA implies a large effect also at the ation. All these issues will hopefully be clarified Tevatron. In addition, many possibilities includ- by the continuation of data taking. Meanwhile, ing intrinsic charm (unlessc ¯ 6= c at the relevant it is important to explore possible interpretations x values [11]) are excluded from the HERA data of the signal, in particular with the aim of identi- in the CC channel [12]. In conclusion, it is a fying additional signatures that might eventually fact that nobody sofar was able to even roughly be able to discriminate between different expla- fit the data. This possibility is to be kept in mind nations of the reported excess. if eventually the data will drift towards the SM and only a small excess at particularly large x and Q2 is left with comparable effects in NC and 2. Structure Functions CC, with e+ or e− beams.
Since the observed excess is with respect to the Standard Model (SM) expectation based on the 3. Contact Terms QCD-improved parton model, the first question is whether the effect could be explained by some in- Still considering the possibility that the ob- adequacy of the conventional analysis without in- served excess is a non-resonant continuum, a voking new physics beyond the SM. In the some- rather general approach in terms of new physics what analogous case of the apparent excess of jet is to interpret the HERA excess as due to an ef- production at large transverse energy ET recently fective four-fermionee ¯ qq¯ contact interaction [13] observed by the CDF collaboration at the Teva- with a scale Λ of order a few TeV. It is interest- tron [5], it has been argued [6] that a substan- ing that a similar contact term of theqq ¯ qq¯ type, tial decrease in the discrepancy can be obtained with a scale of exactly the same order of magni- by modifying the gluon parton density at large tude, could also reproduce the CDF excess in jet values of x where it has not been measured di- production at large ET [5]. (Note, however, that rectly. New results [7] on large pT photons ap- this interpretation is not strengthened by more re- pear to cast doubts on this explanation because cent data on the dijet angular distribution [14]). these data support the old gluon density and not One has studied in detail [15] [16] vector contact the newly proposed one. In the HERA case, a terms of the general form similar explanation appears impossible, at least for the H1 data. Here quark densities are in- 4πηij µ ∆L = η 2 e¯iγ ei q¯j γµqj . (1) volved and they are well known at the same x (Λij ) but smaller Q2 [8], [9], and indeed the theory fits the data well there. Since the QCD evolution is with i, j = L, R and η a ± sign. Strong believed to be safe in the relevant region of x,the limits on these contact terms are provided by proposed strategy is to have, at small Q2,anew LEP2 [17] (LEP1 limits also have been consid- component in the quark densities at very large x, ered but are less constraining [18,19]), Teva- beyond the measured region, which is then driven tron [20] and atomic parity violation (APV) ex- at smaller x by the evolution and contributes to periments [21]. The constraints are even more HERA when Q2 is sufficiently large [8]. One stringent for scalar or tensor contact terms. APV possible candidate for a non perturbative effect limits essentially exclude all relevant AeVq com- at large x is intrinsic charm [10]. However it ponent. The CDF limits on Drell-Yan produc- turns out that a large enough effect is only con- tion are particularly constraining. Data exist 3 both for electron and muon pairs up to pair the production at HERA occurs from valence u or masses of about 500 GeV and show a remark- d quarks, since otherwise the coupling would need able e − µ universality and agreement with the to be quite larger, and more difficult to reconcile SM. New LEP limits (especially from LEP2) have with existing limits. However production from been presented [17]. In general it would be the sea is also considered. Assuming an S-wave possible to obtain a reasonably good fit of the state, one may have either a scalar or a vector HERA data, consistent with the APV and the leptoquark. I only consider here the first option, LEP limits, if one could skip the CDF limits because vector leptoquarks are more difficult to [22]. But, for example, a parity conserving com- reconcile with their apparent absence at the Teva- µ µ bination (¯eLγ eL)(¯uRγµuR)+(¯eRγ eR)(¯uLγµuL) tron. The coupling λ for a scalar φ is defined + + with ΛLR =ΛRL ∼ 4 TeV still leads to a marginal by λφe¯LqR or λφe¯RqL, The corresponding width 2 fit to the HERA data and is compatible with all is given by Γ = λ Mφ/16π, and the production existing limits [22,23]. Because we expect con- cross section on a free quark is given in lowest π 2 tact terms to satisfy SU(2) U(1), as they re- order by σ = 4s λ . flect physics at large energy scales, the above phenomenological form is toN be modified into Including also the new ’97 run results, the com- µ µ µ bined H1 and ZEUS data, interpreted in terms L¯LγµLL(¯uRγ uR +d¯Rγ dR)+¯eRγµeRQ¯Lγ QL), where L and Q are doublets [24]. This form is of scalar leptoquarks lead to the following list of both gauge invariant and parity conserving. We couplings [15,33,34]: took into account the requirement that contact √ terms corresponding to CC are too constrained e+uλB∼0.017 − 0.025 to appear. More general fits have also been per- √ e+dλB∼0.025 − 0.033 formed [22]. √ e+sλB∼0.15 − 0.25 (2) In conclusion, contact terms are severely con- strained but not excluded. The problem of gen- erating the phenomenologically required contact where B is the branching ratio into the e-q mode. terms from some form of new physics at larger By s the strange sea is meant. For√ comparison energies is far from trivial [24,25]. Note also note that the electric charge is e = 4πα ∼ 0.3. e+u e+ ¯ that contact terms require values of g2/Λ2 ∼ Production via ¯ or d is excluded by the fact −u e−d 4π/(3−4 TeV)2, which would imply a very strong that in these cases the production in e or nearby interaction. Alternatively, for g2 of the or- would be so copious that it should have shown der of the SU(3) SU(2) U(1) couplings, Λ up in the small luminosity already collected in − would fall below 1 TeV, where the contact term the e p mode. The estimate of λ in the strange description is inadequate.N WeN recall that the ef- sea case is merely indicative due to the large un- fects of contact terms should be present in both certainties on the value of the small sea densities the e+ and the e− cases with comparable inten- at the relatively large values of x relevant to the sity. Definitely contact terms cannot produce a HERA data. The width is in all cases narrow with CC signal [26], as we shall see, and no events with respect to the resolution: for B ∼ 1/2wehave isolated muons and missing energy. Γ∼4−16 MeV for valence and 350 − 1000 MeV for sea densities.
It is important to notice that improved data 4. Leptoquarks from CDF and D0 [7] on one side and from APV [21] and LEP [17] on the other consider- I now focus on the possibility of a resonance ably reduce the window for leptoquarks. Con- with e+q quantum numbers, namely a leptoquark sistency with the Tevatron, where scalar lepto- [15,27–32], of mass M ∼ 190 − 210 GeV, accord- quarks are produced via model-independent (and ing to H1. The most obvious possibility is that λ-independent) QCD processes with potentially 4
+ > large rates, demands a value of B sizeably smaller edB∼0.2−0.4(5) than 1. In fact, the most recent NLO estimates of the squark and leptoquark production cross sec- For production off the strange sea quark the up- tions [35,36] allow to estimate that at 200 GeV per limit on λ is obtained from LEP2 [17], in that + approximately 6–7 events with e e−jj final states the t-channel exchange of the leptoquark con- should be present in the combined CDF and D0 tributes to the process e+e− → ss¯ (similar limits data sets. For B = 1 the CDF limit is 210 GeV, for valence quarks are not sufficiently constrain- the latest D0 limit is 225 GeV at 95%CL. The ing, because the values of λ required by HERA combined CDF+D0 limit is 240 GeV at 95%CL are considerably smaller). Recently new results [7]. We see that for consistency one should im- have been presented by ALEPH, DELPHI and pose: OPAL [17]. The best limit is from ALEPH:
< + B ∼ 0.5 − 0.7(3)e sλ∼<0.6(6)
< < Finally, the case of a 200 GeV vector leptoquark is (OPAL finds λ ∼ 0.7, DELPHI λ ∼ 0.9). This, most likely totally ruled out by the Tevatron data, given eq.(2), corresponds to since the production rate can be as much as a factor of 10 larger than that of scalar leptoquarks. + > e sB∼0.05 − 0.2(7) There are also lower limits on B, different for production off valence or sea quarks, so that only Recalling the Tevatron upper limits on B, given a definite window for B is left in all cases. For in eq.(3), we see from eqs. (5) and (7) that only production off valence the best limit arises from a definite window for B is left in all cases. APV [21], while for the sea case it is obtained Note that one given leptoquark cannot be from recent LEP2 data [17]. present both in e+p and in e−p (unlessitispro- One obtains a limit from APV because the s- duced from strange quarks). channel exchange amplitude for a leptoquark is equivalent at low energies to an (¯eq)(¯qe)contact 5. S-quarks with R-parity Violation term with amplitude proportional to λ2/M 2.Af- ter Fierz rearrangement a component on the rel- evant APV amplitude AeVq is generated, hence I now consider specifically leptoquarks and the limit on λ. The results are [26] SUSY [15,19,37–42]. In general, in SUSY one could consider leptoquark models without R- parity violation. It is sufficient to introduce to- e+uλ<0.058 ∼ gether with scalar leptoquarks also the associated + < e dλ∼0.055 (4) spin-1/2 leptoquarkinos [37]. In this way one has not to give up the possibility that neutrali- The above limits are for M = 200 GeV (they nos provide the necessary cold dark matter in the scale in proportion to M) and are obtained from universe. We find it more attractive to embed the quoted error on the new APV measurement a hypothetical leptoquark in the minimal super- on Cs. This error being mainly theoretical, one symmetric extension of the SM [43] with viola- could perhaps take a more conservative attitude tion of R parity [44]. The connection with the and somewhat√ relax the limit. Comparing with HERA events has been more recently invoked in the values for λ B indicated by HERA, given in ref. [15,39,41]. The corresponding superpotential eq.(2), one obtains lower limits on B: canbewrittenintheform
+ > c 0 c e uB∼0.1−0.2 WR ≡ µiHLi + λijkLiLjEk + λijkLiQj Dk + 5
00 c c c ˜ ˜ λijk Ui Dj Dk , (8) only observes t1 while ZEUS only sees t2!). How- ever, the presence of two light leptoquarks makes c c the APV limit more stringent. In fact it becomes where H, Li,Ej,Qk,(U, D)l denote superfields for the Y =1/2 Higgs doublet, left-handed lep- 2 ton doublets, lepton singlets, left-handed quark 2 m1 B>B∞[1 + tan θt 2 ] (12) doublets and quark singlets, respectively. The in- m2 dices i, j, k label the three generations of quarks and leptons. Furthermore, we assume the absence Thus, for the above mass and mixing choices, the of the λ00 couplings, so as to avoid rapid baryon above quoted APV limit [B∞ is given in eq. (5)] decay, and the λ couplings play no rˆole in our must be relaxed invoking a larger theoretical un- analysis. certainty on the Cs measurement.
The squark production mechanisms permitted Let us now discuss [15] if it is reasonable to 0 + by the λ couplings in (8) include e d collisions to expect thatc ˜ and t˜ decay satisfy the bounds on ˜ formu ˜L, c˜L or tL, which involve valence d quarks, the branching ratio B. A virtue of s-quarks as + and various collisions of the types e di (i =2,3) leptoquark is that competition of R-violating and + or e u¯i (i =1,2,3) which involve sea quarks. normal decays ensures that in general B<1. A careful analysis [15] leads to the result that the only processes that survive after taking into In the case ofc ˜L, the most important possi- account existing low energy limits are ble decay modes are the R-conserving channels 0 + c˜L → cχi (i =1, .., 4) andc ˜L → sχj (j =1,2), + + and the R-violating channelc ˜L → de ,where eRdR → c˜L χ0,χ+ denote neutralinos and charginos, respec- e+d → t˜ i j R R L tively. In this case it has been shown [15] that, e+s t˜ (9) R R → L if one assumes that m + > 200 GeV, then , in χj a sizeable domain of the parameter space, the + For example eR dR → u˜ L is forbidden by data on neutralino mode can be sufficiently suppressed so neutrinoless double beta decay which imply [45] that B ∼ 1/2 as required (for example, the cou- plings of a higgsino-like neutralino are suppressed 2 1 0 −3 mq˜ mg˜ 2 by the small charm mass). |λ111| < 7 × 10 . (10) 200 GeV 1TeV ˜ In the case of tL, it is interesting to notice that the neutralino decay mode t˜ tχ0 is kinemat- ˜ L → i where mq˜ is the mass of the lighter ofu ˜L and dR, ically closed in a natural way. Thus, in order to and mg˜ is the gluino mass. obtain a large value of B in the case of s-top pro- It is interesting to note [39] that the left s-top duction off d-quarks, in spite of the small value of λ, it is sufficient to require that all charginos could be a superposition of two mass eigenstates + are heavy enough to forbid the decay t˜L → bχ . t˜1, t˜2, with a difference of mass that can be large j However, we do not really want to obtain B too as it is proportional to mt: close to 1, so that in this case some amount of fine tuning is required. Or, with charginos heavy, ˜ ˜ ˜ tL =cosθt t1 +sinθtt2 (11) one could invoke other decay channels as, for ex- ample, t˜ → ˜bW + [46]. But the large splitting where θt is the mixing angle. With m1 ∼ needed between t˜and ˜b implies problems with the 2 200 GeV, m2 ∼ 230 GeV and sin θt ∼ 2/3one ρ-parameter of electroweak precision tests, unless can obtain a broad mass distribution, more sim- large mixings in both the s-top and s-bottom sec- ilar to the combined H1 and ZEUS data. (But tors are involved and their values suitably chosen. with the present data one has to swallow that H1 In the case of s-top production off s-quarks, val- 6 ues around B ∼ 1/2 are rather natural because ily diagonal quark currents in order to minimise of the larger value of λ, which is of the order of problems with the occurrence of flavour changing the gauge couplings [15,19]. neutral currents, the only possible vector contact term with valence quarks (and no Cabibbo sup- The interpretation of HERA events in terms of pression) is of the form s-quarks with R-parity violation requires a very peculiar family and flavour structure [47]. The 4πη flavour problem is that there are very strong µ 0 ∆LCC = 2 e¯Lγ νLu¯LγµdL +h.c. (13) limits on products of couplings from absence of Λη FCNC. The unification problem is that nucleon stability poses even stronger limits on products of i.e. the product of two isovector currents. Here 0 λ couplings that differ by the exchange of quarks dL is the left-handed d-quark current eigenstate, and leptons which are treated on the same foot- related to the mass eigenstate by the Cabibbo- ing in GUTS. However it was found that the uni- Kobayashi-Maskawa (CKM) matrix. It is simple fication problem can be solved and the required to see that such terms cannot have a sufficent pattern can be embedded in a grand unification magnitude. In fact the scale Λ associated with framework [47]. The already intricated problem this operator is too strongly constrained to pro- of the mysterious texture of masses and couplings duce any measurable effect at HERA. The con- is however terribly enhanced in these scenarios. straints arise from at least two experimental facts: lepton-hadron universality of weak charged cur- rents and electron-muon universality in charged- 6. Charged Current Events pion decays. The corresponding lower limits on Λ exceed 10 TeV in all cases [26].
In the Introduction, I have mentioned that in The possible scalar or tensor currents arising 2 > 4 2 the CC channel at Q ∼ 1.510 GeV H1 and from an SU(2)⊗U(1) invariant theory which can ZEUS see a total of 11 events with 5 expected. contribute to valence-parton CC processes are The statistics is even more limited than in the NC case, so one cannot at the moment derive any 4π 4π firm conclusion on the existence and on the na- L = 2 (¯eRνL)(¯uRdL)+ 2 (¯eRνL)(¯uLdR)+ ΛS ΛS0 ture of an excess in that channel. However, the 4π presence or absence of a simultaneous CC signal is (¯e σµν ν )(¯u σ d ) , (14) Λ2 R L R µν L extremely significant for the identification of the T underlying physical effect (as it would also be the µν case for the result of a comparable run with an while the operator (¯eRσ νL)(¯uLσµν dR) iden- e− beam, which however is further away in time). tically vanishes. The scalar interactions are In view of this, I now briefly discuss the implica- strongly limited by e–µ universality in pion de- tions for the CC channel of the various proposed cays [50], because they do not lead to electron- solutions of the HERA effect [26,46,48,49]. It is helicity suppression, in contrast with the SM case. found that in most of the cases the CC signal is The lower limit om Λ is about 500 TeV [50]. The not expected to arise. But if it is present at a tensor interaction can be dressed into a scalar in- comparable rate as for the NC signal, the corre- teraction of effective strength [51] sponding indications are very selective. 1 α Λ2 1 To see that contact terms cannot work recall '− log T , (15) Λ2 π M 2 Λ2 that for them it is natural to assume the validity Seff W T of the SU(2) U(1) symmetry, because they are associated with physics at a large energy scale. with the exchange of a photon between the elec- In the SU(2)N U(1) limit, restricting us to fam- tron and the quark fields. The upper limit re- N 7 mains sufficiently strong to prevent these terms the leptoquark exchange induces an effective in- from contributing as well. teraction of the form
Considering now also CC processes involving λuλd L = (¯e d )(¯u ν )+h.c. (18) sea quarks [26], we can introduce a contact term M 2 L R R L for second generation quarks + Note that in the transition eRdR → ν¯RuR the 4πη initial state has T =+1/2 while the final state ∆L = (¯e γµν )(¯c γ s0 )+h.c. (16) CC (2)2 L L L µ L Λη has T = −1/2. In this case the low energy ef- fective interaction gives a contribution to π → eν¯ which is helicity suppressed and so can be accept- Clearly since the strange sea in the proton is small able, as it can be checked. Since SU(2) ⊗ U(1) one needs relatively small values of Λ in order is broken only by the Higgs vacuum expectation to produce a sufficiently large effect. A detailed value (VEV), the leptoquark couplings could vi- study shows that one needs Λ ∼ 0.8 − 1TeV olate gauge invariance if the leptoquark couples with η = −1 in order to obtain an increase to the quark-lepton current through some higher- by a factor of two with respect to the SM at dimensional operator [26] and/or if the breaking 2 > 2 Q ∼ 15000 GeV . But bounds on the scales (2) induces a mixing between two leptoquarks of dif- Λη derived from lepton universality in D de- ferent electroweak properties [48]. cays [26,52] and, independently, from the unitar- ity of the CKM matrix, forbid such low values. Another viable alternative is a leptoquark which couples simultaneously to thee ¯(1)q(1) and In conclusion it appears very difficult to accom- R L `¯(i)u(2) currents (i =1,2,3). Here we have spec- modate a CC signal at HERA in the framework L R ified the generation indices of the different fields. of contact terms. If CC events were observed at HERA and such a Let us now consider a scalar leptoquark res- leptoquark was responsible for them, we expect onance that is coupled both to e+d and toνu ¯ the striking signature of leptonic D decays with so that it can generate both NC and CC events rates much larger than in the SM. In the case of from valence (note that e+u has charge +5/3 and a leptoquark produced in the e+s channel, the cannot go intoνq ¯ ). Assuming that the symme- possibility of aνc ¯ final state is still allowed. This try under SU(2) U(1) is conserved, the virtual leads to a remarkable signature in leptonic Ds leptoquark exchange gives a CC contribution to decays the low-energy effectiveN Lagrangian of the form Bνc BR(D− → e−ν¯) ' 6 × 10−3 s (1 −B )3 λuλd νc L = (¯e d )(¯u ν )+h.c. (17) 4 M 2 R L R L 200 GeV i =1,2. M Here λu and λd are the (real) couplings of a lep- (19) toquark with mass M to theν ¯LuR ande ¯RdL currents, respectively. This interaction corre- We are not aware of any existing experimental + sponds to the transition eL dL → ν¯RuR which has limit on this quantity. T = −1/2 both in the initial and final states. At low energies, the leptoquark exchange induces a To conclude, we recall that a leptoquark with contribution to π → eν¯ which is not helicity sup- branching ratio equal to 1 in e+q is excluded pressed. It is simple to verify that this clearly by the recent Tevatron limits. Therefore on one excludes any observable CC signal. An alterna- hand some branching fraction in the CC channel tive is to break SU(2) U(1) and assume that is needed. On the other hand, we find that there N 8 is limited space for the possibility that a lepto- vation of such events would make the model much quark can generate a CC signal at HERA with more constrained. one single parton quark in the final state. This occurrence would indicate SU(2) U(1) violat- It is a pleasure for me to thank Professors Mir- ing couplings or couplings to a current containing jam Cvetic and Paul Langacker for their kind in- the charm quark. N vitation and pleasant hospitality.
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