Don’t stop thinking about leptoquarks: Constructing new models

PHYSICAL REVIEW D, VOLUME 58, 055005

Don’t stop thinking about leptoquarks: Constructing new models

JoAnne L. Hewett and Thomas G. RizzoStanford Linear Accelerator Center, Stanford, California 94309

~Received 12 November 1997; published 20 July 1998!

We discuss the general framework for the construction of new models containing a single fermion numberzero scalar leptoquark of mass.200–220 GeV which can both satisfy the D0 and CDF search constraints aswell as low-energy data, and can lead to both neutral and charged currentlike final states at DESY HERA. Theclass of models of this kind necessarily contain new vectorlike fermions with masses at the TeV scale whichmix with those of the standard model after symmetry breaking. In this paper we classify all models of this typeand examine their phenomenological implications as well as their potential embedding into supersymmetric~SUSY! and non-SUSY grand unified theory scenarios. The general coupling parameter space allowed bylow-energy as well as collider data for these models is described and requires no fine-tuning of the parameters.@S0556-2821~98!03515-2#

PACS number~s!: 12.60.2i, 14.80.2j

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I. INTRODUCTION AND OVERVIEW

A. Current status of the leptoquark scenario

The observation of a possible excess of neutral cur~NC! events ine1p collisions at highQ2 by both the H1@1#and ZEUS@2# Collaborations have sparked much fervorboth the theoretical and experimental communities. Thiscitement has now been heightened by the recent annoument that both experiments may also be observing a cosponding excess in the charged-current~CC! channel@3#. Ifthese events are not merely a statistical fluctuation, it is cthat new physics must be invoked in order to provide a sable explanation, e.g., compositeness appearing in theof higher-dimensional operators@4#, exotic modifications ofthe parton densities@5#, or the resonant production of a neparticle @7,8# such as a leptoquark~LQ! or squark in super-symmetric models withR-parity violation.

If the excess is resonant in thex distribution@6#, a popularinterpretation@7,8# invoked in the NC case is thes-channelproduction of a.200–220 GeV scalar~i.e., spin-0! lepto-quark with fermion number (F) equal to zero. These quantum numbers arise from the requirements that~i! the ob-served excess appears in thee1p rather than thee2pchannel,~ii ! the Fermilab Tevatron search constraints@9# ex-clude vector~spin-1! leptoquarks with masses near 200 Geand ~iii ! any discussion of leptoquark models has beentorically based on the classic work by Buchmu¨ller, Ruckl,and Wyler~BRW! @10#. In that paper the authors provideset of assumptions under which consistent leptoquark mocan be constructed; these we now state in a somewhat sger form:~a! LQ couplings must be invariant with respectthe standard model~SM! gauge interactions,~b! LQ interac-tions must be renormalizable,~c! LQs couple to only a singlegeneration of SM fermions,~d! LQ couplings to fermions arechiral, ~e! LQ couplings separately conserve baryon and lton numbers, and~f! LQs only couple to the SM fermionand gauge bosons. Amongst these assumptions, both~a! and~b! are considered sacrosanct whereas~c!–~e! are data driven@11# by a host of low-energy processes. Assumption~f! ef-fectively requires that the leptoquark be the only new co

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ponent added to the SM particle spectrum which seems qunlikely in any realistic model. Based on these classicalsumptions it is easy to show@10# that all F50 scalar lepto-quarks must have a unit branching fraction into a charglepton plus jet~i.e., Bl 51!. This lack of flexibility presentsa new problem for the leptoquark interpretation of the DESe f collider HERA events for two reasons:~i! leptoquarkswith Bl 51 clearly cannot accommodate any excessevents in the CC channel at HERA since these would reqa sizeable leptoquark decay rate into neutrino plus jet,~ii !both the Collider Detector at Fermilab CDF@12# and D0@13#Collaborations have recently presented new limits forproduction of scalar leptoquarks at the Tevatron usingnext-to-leading order cross section formulas of Kra¨meret al.@14#. In particular, in theee j j channel, D0 finds a 95% C.Llower limit on the mass of aBl 51 first generation scalaleptoquark of 225 GeV. D0 has also performed a combinsearch for first generation leptoquarks by using theee j j,en j j , andnn j j channels. For fixed values of the leptoquamass below 225 GeV, these search constraints can be usplace an upper limit onBl . For MLQ5200(210,220) GeV,D0 obtains the constraintsBl <0.40~0.62, 0.84! at 95% C.L.Of course if the CDF and D0 Collaborations combine thsearches in the future, then the 225 GeV bound may ris.240 GeV, in which case even stronger upper bounds onBl

will be obtained.Besides the obvious need to provide an potential expla

tion for the HERA data which satisfies all other experimenconstraints, it is perhaps even more important to exploremore general fashion how one can go beyond the rathestrictive BRW scenarios. Even if the HERA events turn oto be statistical fluctuations, we will show that by the rmoval of the least tenable of the BRW assumptions, wefind important ways to extend the possible set of leptoquathat may be realised in nature. Since, as was mentioabove, it is difficult to believe that the addition of the leptquark would be the only extension to the SM spectrumany realistic model containing such a field, it is clear thassumption~f! should be abandoned. We now explore tconsequences of this possibility.

© 1998 The American Physical Society05-1

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JOANNE L. HEWETT AND THOMAS G. RIZZO PHYSICAL REVIEW D58 055005

B. Enlarging the framework of leptoquark models

In order to satisfy all the experimental constraints itclear that we need to have anF50 scalar leptoquark abefore, but now with a coupling to SM fermions given by

Lwanted5@lunuc1ldedc#LQ1H.c., ~1!

with comparable values of the Yukawa couplingslu andld .This fixes the leptoquark’s electric charge to beQLQ56 2

3 ;no other charge assignment will allow the leptoquark tomultaneously couple toe j andn j as is required by the combination of HERA and Tevatron data. An alternative posbility, if neutrinos are Dirac particles, or ifnc is light andappears as missingpT in a HERA or Tevatron detector, is thinteraction

Lwanted8 5@lu8ncu1ld8e

cd#LQ81H.c. ~2!

It is important for later analysis to note that these two intactions cannot simultaneously exist as the BRW assump~d! above would then be strongly violated. Unfortunateboth of these Lagrangians as they stand violate assump~a! above, in that they are not gauge invariant with respecSU(2)L . We must then arrive at one of these effective intactions indirectly by some other means than by direct funmental couplings. In order to do so it is clear that we mustwilling to abandon at least one of the BRW assumptio~a!–~f! and it is evident that~f! is the one most easily dismissed. Hence we will assume that the leptoquark has ational interactions besides those associated with SM gainteractions and the Yukawa couplings to the SM fermioWe note, however, that fine-tuning solutions can be fouwhich allow the assumption~c! to be dropped as a conditiothat applies in the mass eigenstate basis; these will nodiscussed in detail here although it is important to understhow flavor mixing plays a role in leptoquark dynamicsrealistic models.

In principle there are several alternatives as to what kiof new additional interactions one can introduce, twowhich we now briefly discuss. In a recent paper, BaKolda, and March-Russell@15# considered an interestinmodel with two different leptoquark doublets, one couplito Ldc and the other toLuc ~with L being the SM leptondoublet!. In this model the electric chargeQ5 2

3 membersare mixed through a renormalizable coupling to the SHiggs field with the mixed leptoquarks forming mass eigestates that can couple to bothe j andn j as desired with theratio of strengths controlled by the amount of mixing. Tnew interactions in this case are quite complex and a ceramount of fine-tuning is necessary to get the spectrumcouplings to come out as desired. The rich phenomenolof this scenario, which now involves four leptoquark maeigenstates of various charges, should be further studiedetail. A second scenario has only been briefly mentionethe recent paper by Altarelli, Giudice, and Mangano@16#who considered the possibility of at least temporarily violing both conditions~a! and~b! via nonrenormalizable operators. These authors show, however, that both~a! and~b! canbe restored by the introduction of new heavy fermions

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which the leptoquarks couple in a gauge invariant fashand which are then integrated out to obtain the desired eftive low-energy Lagrangian above. In this case there is oone isosingletQ5 2

3 leptoquark present, which turns out tbe quite advantageous.

In this paper we will consider and classify all modewherein heavy fermions are used to generate the effecinteractionsLwantedorLwanted8 at low energies. As we will seethe emphasis of our approach is somewhat different thanof Altarelli et al., in that we will keep the new heavy fermions as active ingredients in our models and not treat theman auxiliary device to produce the desired coupling structuIn particular, we will assume that exotic, vectorlike fermioexist and that the desired interactions are induced throtheir couplings to the leptoquark and their mixing with thSM fermions. The mixing between the new fermions athose of the SM will be generated by conventional spontaous symmetry breaking~SSB! via the usual Higgs doublemechanism. It is only through SSB that the above effectLagrangian can be obtained in the fermion mass eigensbasis from an originally gauge invariant interaction. Tsmall size of the effective Yukawa couplings in the aboLagrangians,Lwanted or Lwanted8 , are then directly explainedby the same mechanism that produces the ordinary-exfermion mixing and automatically sets the scale of the vtorlike fermion masses in the TeV region. We note thatuse of vectorlike fermions in this role is particularly suitabsince in their unmixed state they make essentially no conbution to the oblique parameters@18#, they are automaticallyanomaly free, and they can have bare mass terms whichSM gauge invariant.~Alternatively, their masses can be geerated by the vacuum expectation value of a SM singHiggs field.! Mixing with the SM fermions does not significantly detract from these advantages as we will see beAs is by now well known@8#, the leptoquark itself does nosignificantly contribute to the oblique parameters providedis either an isosinglet, which will be the case realized inof the models below, or in a degenerate multiplet.

Before discussing the construction of new leptoquamodels with vectorlike fermions, it is interesting to note thHERA will not be able to distinguish between the two scnarios described above, even if the relativee j andn j branch-ing fractions are precisely measured. The only means offerentiating the models is to either find the other neparticles anticipated in each scheme, or to directly prodthe .200–220 GeV leptoquarks at a high-energye1e2 col-lider such as the Next Linear Collider~NLC! @8#. As we willsee below, the charge and weak isospin of the leptoquarfixed in the models with vectorlike fermions and is indepedent of the value ofBl . However, in the Babuet al. ap-proach the leptoquark’s effective weak isospin is highly crelated with the value ofBl . Figure 1 displays a comparisoof the leptoquark pair production cross section and polartion asymmetry for these two models at a 500 GeV NLCis clear that unlessBl is very close to 50% the two scenariowill be easily separated at the NLC. These results also shthat a leptoquark with the quantum numbers anticipated

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DON’T STOP THINKING ABOUT LEPTOQUARKS: . . . PHYSICAL REVIEW D58 055005

vectorlike fermion models is trivially distinguishable fromthe more conventional BRW leptoquarks by the same ansis @8#.

C. Constraints on leptoquark coupling parameters

As we will find below, in models with vectorlike fermions, the only new physics at low energies introduced byleptoquark itself can be parametrized in terms of the intertions inLwanted. It is then straightforward to use existing dato constrain the effective Yukawa couplingslu,d ; here, wecan expresslu in terms ofBl 5ld

2/(ld21lu

2), since we as-sume that the leptoquark has no other decay modes. Ascussed above, the Tevatron searches place ald-independentconstraint onBl for any fixed value of the leptoquark mas

FIG. 1. Cross section~top! and associated polarization asymmtry ~bottom! for the production of a pair of 200 GeV leptoquarksa 500 GeV NLC. The dashed curve is the model of Babu, Koland March-Russell while the solid line is the prediction of tmodel with vectorlike fermions.

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Similarly, the recent measurements of atomic parity violat~APV! in cesium@19# placeBl -independent bounds onld

@20# for fixed values ofMLQ . In addition, universality inpdecay constrains the productluld @21#, while the observedrate of NC events at HERA constrains instead the prodld

2Bl ; in the later case QCD corrections are quite import@22#. The latest available results presented by both the ZEand H1 Collaborations@23# in the neutral current as well athe charged current are included in our estimate of the csection constraints for both channels.~We note that due tothe relatively low statistics and other uncertainties the errin this case are probably significantly underestimated sothis band is actually somewhat wider than what is shobelow.! Combining these constraints defines an approximallowed region in theBl 2ld plane which is presented inFig. 2 for MLQ5200,210,220 GeV. Here,l5l/e with e be-ing the conventional proton charge~this scaling of the cou-pling to e follows earlier tradition@24#!. We note that thesize of the~apart from the HERA data! 95% C.L. allowedregion is sensitive to the two possible choices of the signthe product ofluld . As we will see below, the region corresponding toluld.0 is preferred so that thep decay datahas little impact in restricting the parameter space. From F2 we see that the position of the allowed region movesand to the right as the mass of the leptoquark increases f200 to 220 GeV. For the caseluld.0, the size of the al-lowed region is not greatly affected as the leptoquark mincreases whereas, forluld,0 the region grows signifi-cantly in area with increasing mass. The size of the allowregion in each case would be substantially smaller ifCDF and D0 Collaborations could combine their results afurther constrain the value ofBl .

In addition to the constraints shown in Fig. 2, further letoquark coupling information can potentially be obtain@16# from examining the sum of the squares of the first roof the Cabibbo-Kobayashi-Maskawa~CKM! weak mixingmatrix ( i uVuiu2. In the SM this sum is, of course, unity, buleptoquark exchange inb decay can yield either an upwaror downward shift in the extracted value ofuVudu of

uVudueff2 .uVudu true

2 21.5231023S 200 GeV

MLQD 2S lu

0.15D S ld

0.15D ,

~3!

so that it would appear experimentally as if a unitarity vilation were occurring. Interestingly, the value of the abosum has recently been discussed by Buras@25#, who reports( i uVuiu250.997260.0013, which is more than 2s below theSM expectation. Clearly, ifluld.0, leptoquark exchangeprovides one possible additional contribution which, forlu

5ld50.15 ~implying Bl 5 12 ! and MLQ5200 GeV, would

increase the sum to the value 0.9987. If we take this ndetermination ofVud seriously, then the constraint on leptoquark parameters from CKM unitarity can be writtenterms ofld andBl at the 1s level as~for the case of samesign leptoquark couplings!

,

5-3

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FIG. 2. Allowed parameter space region in theBl 2ld plane for a leptoquark with mass 200 GeV~a!, 210 GeV~b!, or 220 GeV~c!. Theregion allowed by Tevatron searches is below the horizontal dotted line while that allowed by APV data is to the left of the verticaline. The region inside the solid band is required to explain the HERA excess in the NC channel at 1s. The region between the dashed curvcorresponds to the 1s range required to explain the apparent excess at HERA in the charge current channel. The region above the dacurve is allowed byp decay universality: the lower~upper! curve corresponds to the case whereluld.(,)0.

teenna

d

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2.861.351.52S 200 GeV

MLQD 2S ld

0.15D2A12Bl

Bl

, ~4!

which is easily satisfied over most of the allowed paramespace in Fig. 2. As we will see below, the mixing betwethe SM and vectorlike fermions can also yield an additiosmall positive or negative contribution touVudueff

2 which canhave an effect on the CKM unitarity condition in some moels.

II. ANALYSIS AND CONSTRUCTIONOF NEW LEPTOQUARK MODELS

Employing the BRW assumptions~a!–~e! listed above wecan construct our new extended set of leptoquark mo

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using the following prescription.~i! The leptoquark couples a SM fermion multiplet, one

@L,Q,uc,dc,ec,(nc)#, whereQ is the usual left-handed quardoublet, to an exotic vectorlike fermionXi ~or Xi

c! in agauge-invariant manner. For simplicity, the vectorlike femion is assumed to be an isosinglet or isodoublet unSU(2)L and either a singlet, triplet, or antitriplet with respeto SU(3)C . Xi(Xi

c) will denote the new fields with fermionnumberF.(,)0.

~ii ! If Xi(Xic) couples a SM fermion with a given helicit

to the leptoquark, thenXic(Xi) couples viaH or Hc to the SM

fermion of the opposite helicity, whereH/Hc are conven-tional doublet Higgs fields. We introduce bothH/Hc fields asindependent degrees of freedom to allow for supersymme

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zation of the models we construct.~iii ! To obtain the effective Lagrangian in Eq.~1! we re-

quire that terms of the formNUc1H.c. andEDc1H.c. mustboth appear in the original Lagrangian before spontanesymmetry breaking by theH/Hc vacuum expectation value~VEVs!, where one ofN(Uc) andE(Dc) must be a SM fer-mion field. This insures that aQ521(0) lepton will coupleto a Q521/3(12/3) quark to produce anF50 leptoquarkand that the type of structure inLwantedcan be obtained aftemixing.

~iv! Bare mass terms for the fieldsXi of the formMiXiXic

must be added to the original Lagrangian.~v! We follow the BRW assumptions~a!–~e! cataloged in

the Introduction.We note that in the supersymmetric version of these m

els, the conjugate leptoquark field LQc must also be presenand that it cannot couple directly to any of the SM fermifields, due to gauge invariance, unless it mixes with the ltoquark. This implies, in the zero LQ2LQc mixing limit, thatthe conjugate leptoquark field cannot be produced at HEand that its production signature at the Tevatron will necsarily be quite different than that of the leptoquark and whave thus escaped detection, even though the LQc pair pro-duction cross section is the same as that for leptoquark pof the same mass. We will briefly discuss the more compsituation which includes this type of mixing below.

We now begin to classify all possible models which eploy SM and vectorlike fermion mixing to obtain the desirleptoquark couplings. We will take one SM fermion multilet at a time and pair it with a vectorlike fermion andleptoquark. Since there are six SM fermion multiplets~al-lowing for the possibility ofnc! there are naively at most sipossible models that can be constructed.~As we will see theactual number is somewhat more than this since varicombinations of these models are feasible.! To demonstratehow these construction rules work in practice, we beginconsidering the first case in detail. Here, we couple an exfermion, denoted asX1 , to L plus a leptoquark, i.e.,LX1

c LQ.In this case~iii ! above requires thatX1 be an isodoublet, withmember charges of23 , 2 1

3 since the leptoquark chargefixed, as well as being an SU(3)C triplet. The BRW assump-tion ~a! then dictates that the leptoquark be an isosinglet.can thus writeX1

T5(U0,D0), where the superscript denotethe weak eigenstate fields.~ii ! and~iv! above then instruct usto add the SM gauge-invariant termsX1ucH1X1dcHc andM1X1X1

c to the Lagrangian. Including the Yukawa couplin~which we assume are of order unity! these terms, togethewith the gauge interactions of both the leptoquark andfermion doubletXi , form our new set of interactions that aadded to the SM. Denoting this as model A, we thus arrive

LA5lALX1c LQ1auX1ucH1adX1dcHc2M1X1X1

c

1gauge1H.c., ~5!

where gauge represents the new gauge interactions oleptoquark andX1 . We emphasize that all of the abovYukawa couplings are assumed to be of order unity.

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WhenH andHc receive vevs (v andvc), the au,d termsin the above Lagrangian induce off-diagonal couplingsboth theQ52 1

3 andQ5 23 quark mass matrices. Neglectin

the u- and d-quark masses, these are given in thecL0McR

0

weak eigenstate basis by

cL0MucR

05~ u0,U0!LS 0 0

auv 2M1D S u0

U0DR

, ~6!

cL0MdcR

05~ d0,D0!LS 0 0

advc 2M1D S d0

D0DR

. ~7!

Both Mu,d can be diagonalized by a bi-unitary transformtion which becomes biorthogonal under the assumptionthe elements ofMu,d are real, resulting in the diagonal mamatricesMu,d

diag5UL(u,d)Mu,dUR(u,d)†. Since UL,R(u,d) aresimple 232 rotations they can each be parametrized bsingle angleuL,R

u,d . For the case at handuLu,d50, whereas

uRu,d>au,dv(vc)/M1 . Taking the Yukawa couplings to be o

order unity andv, vc;100– 250 GeV, the size of the mixinis fixed by the scale ofM1 . Writing U0.U1uR

uu in termsof the mass eigenstate fields, and similarly forD0, the inter-action involving the SM fermions and the leptoquark thbecomes

Llight5F S lAauvM1

D nuc1S lAadvc

M1DedcGLQ1H.c., ~8!

which is the exact form we desired in Eq.~1!. This naturallyleads to a reasonable relative branching fraction for the→n j decay mode, and gives acceptable values forlu,d inEq. ~1! for M1 in the 1–5 TeV range.

At this point one may note that we have omitted a termLA of the form2M 8QX1

c , with M 8 being a bare mass parameter. Such a term is, of course, gauge invariantshould be present in principle but has little influence onscenario as far as the leptoquark interactions are concerOf course one can always invent a symmetry to forbid tterm if so desired as in practice such a term may produceuncomfortably large mass for the SM fermions, inducedmixing, and so additional care is required. However, to kethe following discussion as general as possible, such tewill be included in our discussion. WithM 8 being the sameorder asM1 there is essentially no change in our result fthe right-handed mixing above; we now obtainuR

u,d

.au,dv(vc)M1 /(M121M 82).au,dv(vc)/M1 . However,M 8

induces a nonzero mixing for the left-handed fields, but tdoes not influence either the leptoquark orZ boson couplingsto the light fermions. There is a new contribution in the caof the light fermions’ charged current couplings to theW, butit is quite suppressed being proportional toD512cos(uL

u

2uLd), with the differenceuL

u2uLd.(au

2v22ad2vc2)/M1

2 beingsmall. Note that while bothuL

u,d are large, neither is directlyobservable and it is thedifferencebetween the two, which isvery small, that is observable. It is also important to remeber that this mixing angle difference is also proportionalBl

22(12Bl )2, so that it is further suppressed for values

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Bl approaching 0.5. Even without considering these canlations, we estimate the effect to be very small sincedifference in the left-handed mixing angles is roughly givby uL

u2uLd;uR

2.(0.05)2, implying D,1025. In the nextsection we will return to the general question of whethereffects associated with the finite size of these mixing angcan lead to observable shifts in SM expectations.

To proceed with our systematic analysis, we first list tremaining five skeleton models that are obtained by simcombining the other SM representations with an approprvectorlike fermion and leptoquark field~note that both mod-els B and F involve the fieldnc!:

LB5lBQX2cLQ1aeX2ecHc1anX2ncH2M2X2X2

c ,

LC5lCX3ucLQ1a1LX3cH2M3X3X3

c ,

LD5lDX4dcLQ1a2LX4cHc2M4X4X4

c ,

LE5lEX5ecLQ1a3QX5cHc2M5X5X5

c ,

LF5lFX6ncLQ1a4QX6cH2M6X6X6

c , ~9!

where the usual gauge1H.c. terms have been dropped fsimplicity. Note that model B is essentially the leptonequivalent of model A; here, the vectorlike fermion fieldX2

is a color singlet, weak isodoublet, i.e.,X2T5(N0,E0), and

the leptoquark remains an isosinglet. This model requiresneutrino to be a light Dirac field or, at the very least,nc toappear as missingpT in the leptoquark decay process.

It is important to notice that some of these individuskeleton modelsdo notsatisfy all of the model building constraints listed above, in particular~iii !. However, this require-ment can be satisfied by taking combinations of the variskeletonLi above, taking care not to violate the BRW codition ~d! that the leptoquark couplings remain chiral. Tweaknesses in models C and D as well as E and F caovercome by simply pairing them:

LCD5@lCNuc1lDEdc#LQ1a1LNcH1a2LEcHc

2MNNNc2MEEEc,

LEF5@lEDec1lFUnc#LQ1a3QDcHc1a4QUcH

2MDDDc2MUUUc, ~10!

where the superscript 0 denoting the weak eigenstatebeen dropped for simplicity. Both models CD and EF nosatisfy all of our model building requirements, however, itimportant to realize that these two combinations are notonly set of alternatives. In this case, the fieldsU, D, N, andEare identified withX6,5,3,4, respectively, and are all weaisosinglets with the field notation designating the color acharge information. Note that the individual bare mass teare present for these fields, and that in both models thetoquark is again an isosinglet with charge2

3 . As in the caseof model B, model EF requiresnc to appear as missingpT inthe leptoquark decay, otherwise these models are excluby the apparent HERA CC excess and, possibly, by

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Tevatron constraints. We note that, as in the case of moA, additional gauge-invariant mass-mixing terms canadded to the Lagrangians of models B, CD, and EF. Thtake the form of 2ML8LX2

c for model B, 2MN8 Nnc

2ME8Eec for model CD, and2MD8 Ddc2MU8 Uuc for modelEF. They produce essentially no additional new physicsfects at a visible level in the latter two cases since nonethe SM fermion couplings to the gauge bosons are furtaltered. However, in model B, as was seen for model Amodification of the SM leptonic CC couplings to theW bo-son will occur and is proportional to the square of the diffeence in the left-handed mixing angles needed to diagonathe neutral and charged lepton mass matrices. For compness, the mass matrices for the vectorlike and SM fermsector for each of these models are as follows~using thesame weak eigenstate basis as above!. For model B,

M n5S 0 2ML8

anv 2M2D , ~11!

Me5S 0 2ML8

aevc 2M2

D , ~12!

whereas for model CD we find

M n5S 0 a1v

2MN8 2MND , ~13!

Me5S 0 a2vc

2ME8 2MED , ~14!

and for model EF we correspondingly obtain

Mu5S 0 a4v

2MU8 2MUD , ~15!

Md5S 0 a3vc

2MD8 2MDD , ~16!

where in all cases we have allowed for the additional gauinvariant terms discussed above. With the primed aunprimed bare mass terms of roughly the same magnituthe effectivelu,d ~or lu,d8 ! couplings can be read off directlfrom these matrices and the above Lagrangians are expible in the same form as in Eq.~8! with the appropriatesubstitutions of masses and Yukawa couplings. It is imptant to remember that in models CD and EF, which invomixings with isosinglet fermions, the roles of the left- anright-handed mixing anglesuL and uR are essentially inter-changed with respect to those in models A and B wherevectorlike fermions are in isodoublets. In all cases the revant mixing angles are of order 0.05 as obtained in the cof model A, due to the phenomenological constraints iposed on the effective Yukawa couplings by the HERA da

Lastly, we note that models A, B, CD, and EF are not tonly successful ones that can be constructed. We can,take either model A or B and combine it with one of th

5-6

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skeleton models C–F; for example, model B could be clesced with F. In principle, many potential hybrid modelsthis type can be constructed. This observation will be imptant below when we discuss the unification of these modwithin a grand unified theory~GUT! framework, as well asthe phenomenological implications of the SM and vectorlfermion mixing. We note that in these more complex modthe fermion mixing~s! that generate the SM fermion couplings to the leptoquark can arise from multiple sources.course, when we attempt to construct further hybrid modwe must take care not to violate the assumption thatleptoquark couplings are chiral. Given this very strong costraint, the entire list of models that can be constructedthis fashion are only ten in number: A, B, CD, EF; AC, ADACD, BE, BF, and BEF. We note that models A, CD, ACAD, and ACD produce the effective interactionLwanted,while models B, EF, BE, BF, and BEF produce insteLwanted8 . The models and the exotic fermions associated weach of them are cataloged in Table I.

III. IMPLICATIONS AND TESTS

Some phenomenological implications of these modelsexamined in this section. The detailed phenomenologypends on whether or not supersymmetry~SUSY! is also in-troduced. Clearly, the non-SUSY versions are more eaanalyzed but both classes of models share many comfeatures which we will discuss here. These include newteractions due to the mixing between the vectorlike and

TABLE I. Listing of models and the vectorlike fermions whicare contained in them.

Model Vectorlike fermions

A SUDDL,R

CD NL,R ;EL,R

AC SUDDL,R

;NL,R

AD SUDDL,R

;EL,R

ACD SUDDL,R

;NL,R ;EL,R

B SNEDL,R

EF UL,R ;DL,R

BE SNEDL,R

;DL,R

BF SNEDL,R

;UL,R

BEF SNEDL,R

;UL,R ;DL,R

05500

-fr-ls

s

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h

ree-

lyon-

fermions as well as from the existence of the leptoquarkthe vectorlike fermions themselves.

A. Direct production of vectorlike fermions

The production and decay of vectorlike fermions has beextensively discussed in the literature@24,26#, particularly inthe context ofE6 grand unified theories. The mixing inducebetween these new fields and the ordinary SM fermionsonly modifies the SM fermion couplings to theW andZ butalso leads to flavor-changingZ interactions involving asingle SM fermion and a vectorlike fermion. This impliethat the vectorlike fermions can be produced in pairs viausual mechanisms, or singly via mixing. Once producthey can decay through mixing into a SM fermion and aZ orW with comparable rates. However, unlike most models ctaining vectorlike fermions, it is more likely here that at leasome of these states will dominantly decay to leptoquainstead due to the large assumed size of the Yukawa cplings. Given the expected large mass of the new fermionthese models, they will only be accessible at the CELarge Hadron Collider~LHC! ~until As52210 TeV e1e2

or m1m2 colliders are constructed!. For masses of order 1TeV and an integrated luminosity of 100 fb21, we estimatethe yield of color triplet vectorlike fermion pairs at the LHto be of order 104 events, where they are produced bycombination ofgg andqq fusion. If theW andZ final statesproduced in the vectorlike fermion decays can be triggeon with reasonable efficiency this implies that the productof such heavy states should be relatively straightforw@27#. The production and detection of heavy color-singstates at a reasonable rate seems somewhat more proble@26# due to background issues.

B. Universality violations revisited

Do the vectorlike fermions have visible indirect effectslower energies? We first examine whether the vectorlikeSM fermion mixing itself induces a sizeable universality vilation. Here, the cases where the vectorlike fermionsisodoublets or isosinglets induce quite different effects;call that in the isodoublet vectorlike fermion scenario,uR

;0.05 and the differenceuLu2uL

d;(0.05)2, whereas the re-verse is true in the case of isosinglet fermions. We thus fithe following shifts in the CKM elementuVudu2 in each ofthe above principle models~to leading order in the mixingangles!:

A: 2~uLu2uL

d!21~uRuuR

d !2,

B: 0,

CD: 0,

EF: 2~uLu!22~uL

d!2. ~17!

Clearly the effect is very small in the models with isodoubquarks~model A!, but can be sizable in the isosinglet quacase~model EF!. In fact, for model EF we see that the effeof mixing is to decrease the value ofuVudueff

2 relative to theSM expectation by an amount of order 1023; this is at the

5-7

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the


level of current sensitivity, as discussed in the previous stion, and is comparable to the size of the present differebetween experiment and the expectations of unitarity.

The other consequence to notice above is the null resuthe case of models B and CD. In these scenarios, the smixing that affects nuclear decays also appears in the calation of m decay and is therefore absorbed into the definitof GF . However, a residual effect from the mixing will remain in the ratio of widths forp→en to p→mn. This re-sults in another shift in these models, in addition to that frthe leptoquark exchange discussed above, from the SMpectation for this ratio by an amount

B: 2~uLn2uL

e!22~uRn uR

e !2,

CD: 2~uLn !22~uL

e!2, ~18!

which is negative and can be sizeable in the case of mCD for mixing angles of order 0.05. Experimentally@21#, thevalue of this universality testing ratio to its SM expectatiis found to be 0.996660.0030; we note that the potentiadeviation from unity is comparable to the expectationmodel CD.

Lastly, we note that in model B a right-handed chargedcurrent is generated for the electron, which could in princibe observed inm decay ifnc appeared as missing energypT . However, the size of the right-handed amplitude genated through this mixing is far too small~by several orders omagnitude! to be detected in the Michel spectrum@21#.

C. g22 of the electron and electron neutrino

One reason for demanding that the leptoquark couplito fermions be chiral is to avoid the enhancement of a nuber of loop-order processes, e.g., theg22 of the electron.Here we have successfully constructed chirally coupledtoquark models and hence their contribution to the electrog22 is very small, however, there remains the possibithat the mixings between the SM and vectorlike fermiomay reinstate significant contributions toae . Model B pro-vides an example of this scenario, since in this case, bleft- and right-handed leptonic couplings to theW boson ex-ist and the heavyN can participate inae as an intermediatestate. The contribution in this case can be immediatelytained from Ref.@28# and directly compared with the prediction of the SM @29# and the experimental value. For thdifference between the latter two we find~with the total un-certainty in the difference given in parentheses!

aeexp2ae

SM5213.2~27.2!310212, ~19!

while the additional contribution in the case of model B cbe written as

Dae5~234346310212!F~x!sin~uLn2uL

e!sin uRe , ~20!

where F(x) is a kinematical function of the mass ratiox5MN

2 /MW2 . The large numerical size of the prefactor giv

some warning that the effect might be of a reasonable mnitude even though it is highly suppressed by several pow

05500

c-e

inmeu-n

x-

el

e

r-

s-

-’s

s

th

-

g-rs

of mixing angle factors. TakinguR;0.05 and the differenceuL

n2uLe;(0.05)2 as usual, we obtain the results displayed

Fig. 3; note that the absolute value of the shift is presensince the signs of the mixing angles are unknown. Tanalysis demonstrates that for typical ranges of the pareters in this model, the size ofDae is comparable to or largethan the present uncertainty in the value ofae ; hence valuesof MN*5 TeV are excluded for these suggestive sizes ofmixing angles.

In a similar fashion the corresponding contribution to tmagnetic moment of the electron neutrinokn can be ob-tained, provided thatne is a Dirac fermion.~We recall thatboth the electric and magnetic dipole moments of a Majorneutrino vanish identically.! In this case the amplitude arisefrom a penguin diagram with the vectorlike fermionE in theintermediate state. The results thus take similar form to tfor Dae above, except that the kinematic function is differeand with the replacement sinuR

e→sinuRn . The result of this

calculation is presented in Fig. 4 and should be comparethe present experimental limit@21# of uknu<180310212mBat 90% C.L. from elasticnee elastic scattering using reactoneutrinos. Stronger bounds~by factors of order 10! based onastrophysical constraints remain somewhat controver@21#. Note that a similar graph without the attached photoncapable of generating a mass forne in the range1023– 1022 eV.

D. Oblique parameters,Z pole observables, and APV

Vectorlike fermions are known to have negligible contbutions@17# to the oblique parameters@18#. However, oncevectorlike fermions mix with their SM counterparts it is po

FIG. 3. Contribution to the anomalous magnetic moment ofelectron in model B in units of 10212 due to mixing between theSM and the vectorlike fermions as a function of theN fermionmass.

5-8

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sible to induce nonzero shifts in the values of these pareters. As a numerical example, we examine the size of thcontributions in model A. In the case of the shift in therparameterDr[aT there are two sources which contribuhere: ~i! the modification of both the vector like and SMfermion couplings to theW andZ due to mixing;~ii ! the Uand D masses, originally degenerate, are now split byamountMU

2 2MD2 5au

2v22ad2vc2. Writing in this casecu,d

5cosuRu,d andsu,d5sinuR

u,d , one obtains

Dr53GF

8&p2 H cu4MU

2 1cd4MD

2 22cu2cd

2MU

2 MD2

MU2 2MD

2 lnMU

2

MD2 J .

~21!

Note that whencu5cd51, MU5MD and Dr vanishes asexpected. ForMU,D.5 TeV anduR

u,d.0.05,Dr is found tobe ,1024, far too small to be observed. In a similar veithe induced value for the parameterS is found to be less than531024 and is hence also vanishingly small. Thus, althouthe vectorlike fermions do not remain purely vectorlike afmixing, their contribution to the oblique parameters remnegligible. This same pattern is repeated in the case ofother models with only minor differences, e.g., color factoare present in the case of model B and the gauge invamass terms for the two isosinglet fields in either modelsor EF can be different. Numerically, however, similarsmall results are obtained for the oblique parameters in thremaining models.

Are there observable modifications in the SM fermicouplings to theZ boson? Recall that, for example, the miing of the u and d quarks with vectorlike fermions whichhave weak isospinT3u,3d8 produces a shift in theu and dcouplings to theZ of Dvu(au)5(T3u8 21/2)(sL

u)26T3u8 (sRu)2

FIG. 4. Mixing induced contribution to the magnetic momentthe electron neutrino in model B in units of 10212 Bohr magnetonsas a function of theE fermion mass.

05500

-se

n

hrnhesnt

se

andDvd(ad)5(T3d8 11/2)(sLd)26T3d8 (sR

d)2, respectively, us-ing the notation above.~The corresponding shifts in the casof leptonic mixing can be obtained from these expressionstrivial notational changes.! Two places where these couplinshifts may show up most clearly are in the partial widthsthe Z boson and in APV. In both these observables therean additional shift in the case of the leptonic couplings duethe overall change in the coupling normalization from tredefinition of GF from muon decay, as discussed abovHowever, theZ leptonic asymmetries, which are particularimportant observables, are insensitive to these ovechanges in the coupling normalization. For this case, takthe relevant mixing angle to be 0.05 as usual, we find thatZ partial width to thee1e2 final state is decreased~in-creased! by an amount of order.0.2 MeV for the isodoublet~isosinglet! model. Correspondingly, the apparent shift in tvalue of sin2uw

eff from the asymmetries increases~decreases!by an amount of order.0.0006 for these same two caseBoth of these shifts are essentially at the boundary ofcurrent level of sensitivity of the measurements at the CEe1e2 collider LEP at SLAC Large Detector~SLD! @30#.Similarly there is a corresponding shift in the numberneutrinos extracted from the measurement of theZ invisiblewidth by .0.005.

These shifts in the SM fermion couplings can modify texpectations for APV as well since the effective weak chaQw directly probes the two productsaevu andaevd in addi-tion to the shift in the overall normalization that occurs wileptonic mixing. In the case where the SM fermions mix wtheir leptonic vectorlike counterparts, the shift inQw is di-rectly given by

DQw /Qw5dr22~T3e8 11/2!~sLe!212T3e8 ~sR

e !2, ~22!

wheredr represents the change in the overall coupling nmalization and is given to leading order in the mixing angby

B: ~uLn2uL

e!22~uRn uR

e !2,

CD: ~uLn !21~uL

e!2. ~23!

We find that this fractional shift inQw is at the 1023 levelfor either isosinglet or isodoublet leptonic vectorlike fermons and is hence clearly too small to be observed. The mfication could be potentially larger when mixing occurstheu andd couplings and where there is no overall changethe normalization. However we find that the individual cotributions of theu and d quarks tend to cancel each othinstead of adding coherently, leaving, again, a relative sin Qw at the 1023 level.

E. Drell-Yan production in the e6ne channel

What future constraints can be placed on the leptoqucouplings? We know from earlier work@8# that theld cou-pling can be probed in high precision measurements at LII in e1e2→qq and also at the Tevatron via neutral curre~NC! Drell-Yan production. Can future colliders also probthe lu coupling? One possibility is to examine the corr

5-9

ege

sult


FIG. 5. ~a! The electron plus neutrino transverse mass distribution assuminguh l u<2.5 and~b! the folded lepton charge asymmetry in thcharged current Drell-Yan production channel at the 2 TeV Tevatron for the SM~solid curves! and with 200 GeV scalar leptoquark exchanassumingluld51 ~dashed curves!. In ~b!, from top to bottom in the center of the figure, the SM curves correspond toMT bins of 50–100,100–200, 200–400, and.400 GeV, respectively. Note that forMT in the 50–100 GeV range there is no distinction between the SM reand that with a leptoquark.

n

s

ft

eilto

an

on

t

ty

ede-

rehisar-

cu-on

to

tion

m-tri-luescan

s-

-

sponding charged current~CC! Drell-Yan process at hadrocolliders p( p)→e6n. In addition to the usual SMW-bosonexchange, leptoquarks can also contribute to this procest-channel exchange involving both theld andlu couplings.The subprocess cross section for this reaction is found to

ds~ ud→e2ne!

dz5

GF2MW

4

12p sF u2

~ s2MW2 !21~GWMW!2

1S luld

xD 2

t2

~ t2mLQ2 !2G , ~24!

wherex5GFMW2 /2&pa andz5cosu* , the parton center o

mass scattering angle between the incoming quark andoutgoing negatively charged electron; as usualt52 s(12z)/2 andu52 s(11z)/2. Note that there is no interferencbetween theW boson and leptoquark exchanges which wmake the leptoquark contribution somewhat more difficultobserve although the two distributions peak in oppositegular regions.

There are two useful observables in this case. First,can examine the transverse mass (MT) distribution beyondthe Jacobian peak associated withW-boson production. Forlarge values ofMT one would expect an increase inds/dMTdue to the leptoquark exchange. A second possibility isexamine the leptonic charge asymmetryA(h l ) for the caseof electrons in the final state as a function of their rapidiHereA(h l ) is defined as

05500

via

be

he

l

-

e

o

.

A~h l !5dN1 /dh l 2dN2 /dh l

dN1 /dh l 1dN2 /dh l

, ~25!

whereN6 are the number of positively or negatively chargelectrons of a given rapidity. In the SM, the charge asymmtry is sensitive to the ratio ofu-quark tod-quark parton den-sities and thev2a structure of theW decay@31#. Since thedecay structure of theW has been well measured elsewhe@32#, any observed deviations from SM expectations in tasymmetry have been attributed to modifications in the pton density functions@33#. The possibility of new physicscontributing to this channel has been overlooked. In callating the asymmetry it is essential to split the integratiover the parton densities into two regions, correspondingpositive and negative lepton rapidities in theW center ofmass frame, according to the prescription in Ref.@34#. Figure5 shows how both the binned transverse mass distribuand the lepton charge asymmetry, for fourMT bins corre-sponding to 50,MT,100 GeV, 100,MT,200 GeV, 200,MT,400 GeV, and 400,MT GeV, are modified by thepresence of a 200 GeV leptoquark with, for purposes of deonstration,luld51. We see that the transverse mass disbution does rise above the SM expectations for large vaof MT as expected, and that the lepton charge asymmetryalso be significantly modified for larger values ofMT . Notethat there is little deviation in the asymmetry in the tranverse mass bin associated with theW peak, 50,MT,100 GeV, so that thisMT region can still be used for determination of the quark densities.

5-10

alAu-

ea

ait

ng

oto

onre

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-

s, athe

antss ate

tedhis

eso-

of

ight


We now perform ax2 analysis to determine the potentisensitivity to leptoquark exchange at the main injector.shown in Fig. 5~a!, we divide the transverse mass distribtion into several bins corresponding to

7 bins in steps of 5 GeV in the range

50<MT<85 GeV,


85<MT<285 GeV,

6 bins in steps of 40 GeV in the range~26!

285<MT<525 GeV,


525<MT<725 GeV,

1 bin for the range 725<MT GeV.

This ensures that adequate statistics are maintained inbin. The apparent rise in the cross section in Fig. 5~a! atMT5285 GeV is an artifact of the increased bin width at thpoint. For the lepton charge asymmetry the lepton’s rapidis binned as

12 bins in steps ofDh l 50.2 in the range

50<MT<100 GeV.


100<MT<200 GeV,~27!


200<MT<400 GeV,

2 bins of uDh l u<0.4 and uDh l u>0.4 in the range

400<MT GeV,

subject, of course, to the constraintMT<Ase2uh l u. We noteagain, that there is no sensitivity to the leptoquark exchaon the W transverse mass peak (50,MT,100 GeV), andhence this region does not contribute to thex2 distribution.The bin integrated cross section and asymmetry are thentained for the SM and for the case of 200 GeV scalar lepquark exchange. We sum over bothe1ne ande2ne produc-tion for the cross section and employ an electridentification efficiency of 0.75. The statistical errors aevaluated asdN5AN anddA5A(12A2)/N, as usual. Theresulting 95% C.L. bound in theBl 2ld plane is presentedin Fig. 6 for 2 and 30 fb21 of integrated luminosity withAs52 TeV. We see that even for 30 fb21, the constraints areinferior to those obtained from present data onp decay uni-versality as shown in Fig. 2.

05500

s

ch

ty

e

b--

F. Like-sign leptoquark production at the Tevatron

In models B and C where theu quark couples to a heavneutral vectorlike fermionN new processes may arise ifN isa Majorana field.~Note that for simplicity we have only considered the Dirac case in the above discussions.! One suchunusual possibility is the production of pairs ofidenticalleptoquarks in hadronic collisions viau- or t-channelN ex-change which generates the processuu→2LQ. The lepto-quarks then decay to like-sign charged leptons plus jetrelatively clean signature at a hadron collider. Recall thatrelevant Yukawa coupling involved in thisDL52 reaction isof order unity so that this cross section may be significeven though it is a valence times sea-quark density procethe Tevatron. We find the subprocess cross section to b

ds

dz5

l4

128pbF MN~ t1u22MN

2 !

~ t2MN2 !~ u2MN

2 !G 2

, ~28!

wherel;1, z is defined in the previous section andMN isthe mass of the neutral vectorlike fermion. Here,t52 s(12bz)/2 and u52 s(11bz)/2, whereb5(124mLQ

2 / s)1/2.Note that asMN→0 the cross section vanishes as expecfor a Majorana fermion induced process. The rate for treaction at the Tevatron withAs52 TeV is shown in Fig. 7for l51. Here we see that the cross section initially riswith increasingMN but then begins to fall, scaling similar tMN

22 asMN→`. For MN51 TeV, this cross section corresponds to.100 events at the main injectorbeforeleptoquarkbranching fractions are taken into account. At theAs51.8 TeV collider the cross section is smaller by a factor.0.56.

FIG. 6. 95% C.L. bound onBl as a function ofld from a fit toboth theMT distribution andA(h l ) at the 2 TeV Tevatron for twointegrated luminosities as indicated. The area below and to the rof the curves are excluded.

5-11

sthhimd-Oth

ic

n-

donin

ceoware-s

ro

ar

tiaco

As

the.

the

oresereoricsnd

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arkro-is

that

as

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we

to

be-tothess

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G. Speculations on a realistic flavor coupling structure

Although one can impose discrete or other symmetriesthat leptoquarks only couple to a single generation inweak eigenstate basis it is difficult to understand how tmight hold in the physical basis. This issue is a major stubling block for the construction of realistic leptoquark moels and is one that we have carefully avoided until now.course the detailed exploration of possible solutions toproblem lies outside the scope of this paper@35#, however,there are directions that do show some promise@36#.

To be more specific, let us concentrate on models whyield the interactionLwanted in Eq. ~1! where thenc field isabsent, and also neglect the possibility of any large leptomixing. This implies that all of the traditional flavor changing neutral current~FCNC! constraints are only to be applieto the quark sector of the model as lepton number is cserved. Interestingly, in this case the relevant flavor changterms are induced by the right-handed unitary matriU(u,d)R of which there is no information since they play nrole in SM interactions. For purposes of demonstrationwill this simply assume that element for element theynumerically similar to the corresponding CKM matrix elments. Thus flavor mixing now leads us to make the subtutions uR→S i@U(u)R#1i(uR) i and similarly for dR inLwanted. This particular form guarantees that tree levelss→d andb→d, s transitions will be accompanied bye1e2,while c→u processes are accompanied only bynene . Thusleptoquarks will not mediate the potentially dangerous pcessesK→pnn or D→pe1e2 at tree level.

Are the tree-level rates induced by these leptoquarks dgerously large? Fortunately, the chirality of the leptoquacouplings automatically reduces the size of their potencontributions to rare processes and the fundamental

FIG. 7. Cross section for like-sign pairs of 200 GeV leptoquaat the 2 TeV Tevatron as a function of the neutral vectorlike fmion massMN . The Yukawa coupling is assumed to be unity.

05500

oes-

fis

h

ic

-gs

ee

ti-

-

n-klu-

plings present in the Lagrangian are already quite small.we saw from our discussion ofuVudu, for example, the effec-tive Fermi coupling for leptoquark exchange was belowlevel of 1023GF for typical values of the Yukawa couplingsIn fact, usinglu,d.0.15 andMLQ5200 GeV it is easy toshow that this class of models indeed satisfies all ofFCNC experimental constraints in Ref.@36# for values of@U(d)R#sd , @U(u)R#uc of order 0.1–0.2.~This result remainstrue even when these constraints are strengthened by mrecent experimental results@21#.! This observation leads uto believe that leptoquarks of the type under discussion hare not only compatible with present bounds from flavchanging data but may lead to new effects in flavor physthat are comparable in magnitude to SM contributions acan thus be searched for in charm orB factories@35#.

IV. UNIFICATION? NEVER BREAK THE CHAIN

A. Non-SUSY case

If leptoquarks exist and we also believe that there isperimental evidence for coupling constant unification thwe must begin to examine schemes which contain bothgredients as pointed out in our earlier work@8#. In the sce-narios at hand, the SM quantum numbers of the leptoquare fixed but new vectorlike fermions have now been intduced as well, all of which will alter the usual RGE analysof the running couplings.

Before discussing supersymmetric models we notecoupling constant unificationcanoccur in leptoquark modelscontaining exotic fermions even if SUSY is not introducedwas shown many years ago in Refs.@37,38#. Of course in thework of Murayama and Yanagida@37#, the leptoquark wasan isodoublet which was one of the BRW models, andnow excluded by the combined HERA and Tevatron datathe scenarios presented here the leptoquark is now aQ5 2

3

isosinglet so that the Murayama and Yanagida analysis dnot apply. Fortunately, we see from the results of Ref.@38#that a second unification possibility does exist for just thetypes of models: in addition to the SM spectrum, one addleptoquark and its conjugate as well as a vectorlike paircolor-triplet isodoublets together with the fieldHc. This isjust the particle content of model A. To verify and updathis earlier analysis, we assume for simplicity that all tnew matter fields are introduced at the weak scale andsin2uw50.2315 as input to a two-loop RGE study. The rsults are shown in Fig. 8 where we obtain the predictions tcoupling unification occurs at 3.531015 GeV andas(MZ) ispredicted to be 0.118. If unification does indeed occurcan estimate the proton lifetime@39# to betp51.63103461

years, safely above current constraints@21#. We find thissituation to be intriguing and we leave it to the readerponder further.

B. SUSY models

Of course there are other reasons to introduce SUSYyond that of coupling constant unification, so we now turnthe SUSY versions of the above leptoquark models withassumption thatR parity is preserved, i.e., the HERA exce

s-

5-12

uga

ra

heeaf

stmis

doinwes

allyisa

-le

d

ls,

alyark

ee-nta-

artva-letoprk

hisght.

hepionlse-

uc-ikedels

into

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tonn-

tionell

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ed.this

er-c-ndnd

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is due to a leptoquark and not a squark produced throR-parity violating interactions. This subject was discussedsome length in our earlier work@8# from a somewhat differ-ent view point but from which we are reminded of seveimportant points:

~i! To trivially preserve the successful unification of tSUSY-SM, only complete SU~5! representations can badded to the conventional minimal supersymmetric standmodel~MSSM! spectrum. As is well known, the addition oextra matter superfields in complete SU~5! representationsdelays unification and brings the grand unified theory~GUT!scale much closer to the string scale. Of course, thereremains the rather unnatural possibility of adding incoplete, but ‘‘wisely chosen,’’ split representations. Thiswhat happens, of course, in the case of the usual Higgsblets and is the basis for the famous doublet-triplet splittproblem. Employing split representations certainly allomore flexibility at the price of naturalness but still requirone to choose sets of SU(3)C3SU(2)L3U(1)Y representa-tions which will maintain asymptotic freedom and perturbtive unification. Of course one would still need to eventuaexplain why these multiplets were split. An example of thrather bizarre scenario is the possibility of adding

(2,3)(16 ) from a15 and a (1,1)(1)% (1,3)(2 2

3 ) from a10 tothe spectrum at low energy@8#. Here the notation refers tothe @SU(3)C ,SU(2)L#(Y/2) quantum numbers of the representation. We remind the reader that in this notation the

toquark itself transforms as (1,3)(23 ); the smallest standar

SU~5! representation into which the LQ1LQc can be embed-ded is a10% 10, while in flipped SU~5!3U~1! @40#, it can beplaced in a5% 5.

FIG. 8. Two-loop RGE evolution of the model with the SMparticle content together with a leptoquark and its conjugate asas with the vectorlike fermions and Higgs content of model A. TSU(3)C @SU(2)L ,U(1)Y# coupling corresponds to the dotte~dashed, solid! curve.

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~ii ! Since we only have vectorlike fermions in our modeit is clear that only pairs of representationsR1R can beadded to the MSSM spectrum in order to maintain anomcancelation. Of course this is also true for the leptoqusuperfield in that both the LQ and LQc fields must now bepresent as discussed above.

~iii ! To preserve perturbation theory and asymptotic frdom up to the GUT scale when adding complete represetions, at most one10110 pair or three515 pairs can beappended to the low-energy spectrum of the MSSM apfrom SM singlets. The reason for this is the general obsertion that if one adds more than three vectorlike color tripsuperfields to the MSSM particle content then the one-loQCD b function changes sign. Recall that the leptoquaitself already accounts for one of these color triplets. Tsame consideration also excludes the introduction of liexotic fields in higher-dimensional SU(3)C representationsComplete SU~5! representations larger than10110 arefound to contribute more than this critical amount to trunning of the QCD coupling which would then blow ulong before the GUT scale is reached. Whether unificatwith strong coupling is possible has been considered ewhere@41#, but we disregard this possibility here.

These are highly restrictive constraints on the constrtion of a successful GUT scenario containing both vectorlfermions and leptoquarks and we see that none of the modiscussed above can immediately satisfy themunlessthe lep-toquark and vectorlike fermion superfields can be placeda single SU~5! representation. In the standard SU~5! picture,we can then place (U,D)T, an isosingletEc and LQc into asingle10 with the corresponding conjugate fields in the10.This would form a hybrid of model A with the ‘‘skeleton’model D, which we have denoted by AD in Table I. Ocourse we pay no penalty for also including the skelemodel C here as well, which then yields model ADC. Istead, when we consider the flipped-SU~5!3U~1! case, itwould appear that we can place (N,E)T and LQc into a 5with the conjugate fields in the5; this is exactly model B. Itwould also seem that no penalty is paid as far as unificais concerned for including the skeleton model C here as wexcept that this would violate our assumption about tchirality of leptoquark couplings to fermions. However, thmodel is no longer truly unified since the hypercharge gerator is not fully contained within the SU~5! group itself andlies partly in the additional U~1!. While the SU(3)C andSU(2)L couplings will unify, U(1)Y will not join them evenwhen arbitrary additional vectorlike singlet fields are addThus unification no longer occurs in this scenario so thatpossibility is now excluded.

The leptoquark embedding situation becomes more pplexing if the leptoquark and vectorlike fermions cannot ocupy the same GUT multiplet. In this case unification aasymptotic freedom constraints become particularly tight awe are forced to consider the split multiplet approach m

tioned above. This means that we add the fields (2,3)16 )

% (1,1)(1)% (1,3)(2 23 ) and their conjugates at low energie

but constrain them to be from different SU~5! representa-

tions. In this case the combination (1,3)(23 ) % (1,3)(2 2

3 ) cor-

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responds to the isosinglet leptoquark and its conjugatewhat remains can only be the vectorlike fermion fields. Nthat we have again arrived back at models AD and ADC. Athese the only solutions? We have performed a systemscan over a very large set of vectorlike fermions with varioelectroweak quantum numbers under the assumptionthey are either color singlets or triplets, demanding only t~i! QCD remains asymptotically free and~ii ! the modelpasses the so-called ‘‘B test’’ @42# which is highly nontrivialto arrange. Essentially theB test takes advantage of the oservation that if we know the couplings at the weak scalewe demand that unification takes placesomewherethen thevalues of the one-loopb functions must be related. Note thit is a necessary but not sufficient test on our choice of mels but is very useful at chopping away a large regionparameter space. Using the latest experimental data@30#, wefind that

B5b32b2

b22b150.72060.030, ~29!

where the60.030 is an estimate of the corrections duehigher order as well as threshold effects and thebi are theone-loopb functions of the three SM gauge groups. NothatBMSSM5 5

7 .0.714 clearly satisfies the test. If we requithat ~i! and ~ii ! be satisfied and also require that the unifiction scale not be too low then only the solutions describabove survive after examining.73107 combinations ofmatter representations. While not completely exhaustive,search indicates the solutions above are fairly unique. Iinteresting to observe that models constructed around mA produce successful grand unification both with and wiout SUSY.

Finally we need to briefly comment on the possible retionship between the LQ and LQc masses and their SUSYpartners. In these SUSY models one might imagine thatfermionic partner of the leptoquark, the leptoquarkino, mhave a mass comparable to the vectorlike fermions, i.e.order 1–5 TeV or so. Why then is the leptoquark itselflight? One possible mechanism, discussed in another conby Deshpande and Dutta@7#, is to envision a large mixingbetween the leptoquark and its conjugate that producesee-saw effect analogous to what happens in light top sqscenarios@43#. This possibility will not be pursued furthehere.

V. SUMMARY AND CONCLUSIONS

In this paper, we have obtained a general frameworkthe construction of newF50 scalar leptoquark modelwhich go beyond the original classification by Buchmu¨ller,Ruckl, and Wyler. This approach is based on the observathat in any realistic extension of the SM containing lepquarks it is expected that the leptoquarks themselves willbe the only new ingredient. This construction technique iscourse, far more general than that required to addressspecific issue of the HERA excess and, as outlined, canbe used to obtain a new class ofF52 scalar leptoquarkmodels if so desired.

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To extend leptoquark models into new territories it is neessary to reexamine the assumptions that have gone intoclassic BRW framework. While the assumptions of gauinvariance and renormalizability are unquestionable requments of model building, it is possible that the other contions one usually imposes are much too strong—unlessare clearly demanded by data. This observation impliesfor leptoquarks to be experimentally accessible now, or atime soon, their couplings to SM fermions must be esstially chiral and separately conserve both baryon and lepnumbers. The assumption that leptoquarks couple to onsingle SM generation is surely convenient by way of avoing numerous low-energy flavor changing neutral currconstraints but is far from natural in the mass eigenstatesis. Our analysis indicates that the natural imposition of tcondition in the original weak basis, and then allowing fCKM-like intergenerational mixing does not obviously cauany difficulties with experimental constraints, especiallylepton generation number is at least approximately cserved. What is required to obtain a new class of leptoqumodels is that the leptoquarks themselves must be frecouple to more than just the SM fermions and gauge fiel

Given the fixed gauge structure of the SM the most likenew interactions that leptoquarks may possess are withHiggs field~s! responsible for spontaneous symmetry breing and with new vectorlike fermions that are a commfeature in many extensions of the SM. Such particles hthe advantages that are automatically anomaly free andessentially no significant contributions to the oblique paraeters. In the analysis presented above we have showntwo particular new forms of the effective interactions of letoquarks with the SM fermions, consistent with Tevatrsearches, the HERA excess in both the NC and CC chanand low-energy data, can arise through the action of veclike fermions and ordinary symmetry breaking. The typicvectorlike fermion mass was found to lie in the low Teregion and they could thus be directly produced at futcolliders with known rates. With our set of assumptions,obtained ten new models which fell into two broad classaccording to the chirality of the resulting leptoquark coplings to the SM fermions. The vectorlike fermions themselves were shown to lead to a number of model-depeneffects which are close to the boundary of present expmental sensitivity including~i! violations of quark-leptonuniversality~for which, as discussed, there is some evidenat the 2s level arising from the CKM matrix!, ~ii ! possiblesmall changes in theZ-pole observables for electrons,~iii ! asmall contribution to the shift in the value of the weak charmeasured by atomic parity violation experiments over aabove that induced by the leptoquark itself,~iv! a new con-tribution to the anomalous magnetic moments of the electand electron neutrino, and~v! the possible production olike-sign leptoquarks with a reasonable cross section atmain injector. We also showed that, as in the case of DrYan in thee1e2 channel at the Tevatron discussed in oearlier work, there is some potential sensitivity tot-channelleptoquark exchange in the correspondinge6n channelthrough the transverse mass distribution and the chargedton asymmetry.

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Leptoquarks within the framework of models containivectorlike fermions were shown to be consistent with graunification in both a supersymmetricandnonsupersymmetriccontext. The common feature of both schemes is the stture associated with model A, i.e., the vectorlike fermio

are color triplet, weak isodoublets in a (2,3)(16 ) representa-

tion and bothH and Hc Higgs fields are required to bpresent as is LQc field. In both scenarios the GUT scaleraised appreciably from the corresponding model wherleptoquarks and vectorlike fermions are absent. In the SUcase a~1,1!~1! field is also required with the optional addtion of a SM singlet, corresponding to models AD and ACIn some sense, ACD is the ‘‘anti-E6’’ model in that the colortriplet vectorlike fermions are in isodoublets while the cosinglet fields are all isosinglets. Interestingly, in this scenathere is a vectorlike fermion corresponding to every type

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SM fermion. Realistic leptoquark models provide a risource of new physics beyond the standard model.

ACKNOWLEDGMENTS

We appreciate comments, discussions, and input fromEno ~D0!, G. Landsberg~D0!, J. Conway~CDF!, and H.Frisch ~CDF! regarding the current Tevatron constraintsthe mass of the first generation scalar leptoquark. We thY. Sirois ~H1! and D. Krakauer~ZEUS! for discussions ofthe HERA data. We also thank H. Dreiner, M. Kra¨mer, R.Ruckl, and A. Kagan for informative theoretical discussioas well as N. Glover, T. Han, and L. Nodulman for informtive communications on the lepton rapidity asymmetry. Twork was supported by the Department of Energy, ContrDE-AC03-76SF00515.

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Documents

Don’t stop thinking about leptoquarks: Constructing new models