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Composite Vector Leptoquarks in e+e−, γe, and γγ Colliders

arXiv:hep-ph/9208242v1 24 Aug 1992IC/92/156hep-ph/9208242Composite Vector Leptoquarks in e+e−, γe, and γγ CollidersJ. E. Cieza Montalvo†Departamento de F´ısica Matem´aticaInstituto de F´ısica da Universidade de S˜ao PauloC.P.

20516, 01498 S˜ao Paulo, BrazilO. J. P. ´Eboli∗International Centre for Theoretical Physics, Trieste, ItalyWe study the signals for composite vector leptoquarks in e+e−colliders (LEPII, NLC, and CLIC) through their effects on the production of jet pairs, as well astheir single and pair productions.

We also analyze their production in γe and γγcollisions.Submitted to Phys. Rev.

DSeptember 24, 20181

I. INTRODUCTIONThe standard electroweak theory provides a very satisfactory description of most ele-mentary particle phenomena up to the presently available energies.However, there areexperimental facts such as the proliferation of the fermion generations and their complexpattern of masses and mixing angles, that are not predicted by the standard model. A rathernatural explanation for the existence of the fermion generations is that the known particles(leptons, quarks, and vector bosons) are composite.

In general, composite models exhibit avery rich spectrum which includes many new states such as excitations of the known particlesand bound states which cannot be viewed as excitations of the familiar particles, since theypossess rather unusual quantum numbers. Among these, there are leptoquarks, which areparticles carrying simultaneously leptonic and baryonic number.

Leptoquarks are naturallypresent in a variety of theories beyond the standard model such as some technicolor models[1], grand unified theories [2], E6 superstring-inspired models [3], and composite models [4].In the present work we study the production of vector leptoquarks in e+e−, eγ, andγγ collisions. We shall consider two sources of photons: they can be produced either bybremsstrahlung or by backscattering laser light of the incident positron (electron) beam [5].Here an intense hard-photon beam is generated by backward Compton scattering of softphotons from a laser of a few eV energy.

We shall not consider beamstrahlung photons sinceits spectrum depends strongly on the machine design.For definiteness we shall consider the vector leptoquarks predicted by the Abbott–Farhimodel [4]. The Lagrangian of this model has the same form as the standard model one.However, the parameters determining the potential for the scalar field and the strength ofthe SU(2)L gauge interaction, are such that no spontaneous symmetry breaking occurs andthe SU(2)L gauge interaction is confining.

The model is essentially the confining version ofthe standard model and is also called the strongly coupled standard model (SCSM). Thespectrum of physical particles in the SCSM consists of SU(2)L gauge singlets, includingfundamental particles which are neutral with respect to the SU(2)L force, such as the right-2

handed fermions and the U(1) gauge boson. For instance, the physical left-handed fermionsare bound states of a preonic scalar and a preonic dynamical left-handed fermion, whilethe vector bosons are P-wave bound states of the scalar preons.

Provided some dynamicalassumptions on the model hold true, it has been shown [6] that the predictions of the SCSMmodel are consistent with the present experimental data.We denote the preonic left-handed fermionic doublet by ψaL, with the flavor index arunning from 1 to 12 for three families. ψaL belongs to a 2 representation of the SU(2)Land to the (0, 12) representation of the Lorentz group.

The vector leptoquarks in the SCSMmodel are bound states of the form ψaL†ψbL, where ψaL carries baryon number while ψbL carrieslepton number. We define V abµas the interpolating field for the vector leptoquarks, which isan SU(2)L singlet, belongs to the ( 12, 12) representation of the Lorentz group and is a tripletunder SU(3)color.

From its preonic content it follows that these particles have an electriccharge −2/3.The SCSM model cannot be analyzed perturbatively since it is strongly interacting atthe energy scale of interest. Instead, we describe the interaction between leptoquarks andphysical left-handed fermions by an effective Lagrangian [7].

We assume thatLint = −Fe2√2 sin2 θWV abµ† ¯LaγµLb + h.c.(1)describes the low-energy interactions of V abµ , where La are physical left-handed doubletsunder the global SU(2) symmetry of the model [6], and θW is the weak mixing angle. Theparameter F is a measure of the strength of this interaction compared to the Wq¯q′ vertex.Notice that the vector leptoquarks couple to both upper (or lower) components of the leptonand quark doublets.

It is important to realize that the above Lint, conserves charge, color,and baryonic and leptonic numbers.It is also natural to assume that vector leptoquarks V abµinteract with the photon andthe physical Z. In this work we assume that the couplings of vector leptoquarks to Z’s andγ’s are similar to the W boson ones to these particles.

Therefore, we postulate the followingFeynman rules (see Fig. (1))3

ΓγV −V +αβρ= ieQV {gαβ(p1 −p2)ρ + gβρ(p2 −p3)α + gρα(p3 −p1)β} ,(2)ΓγγV +V −αβρσ= −ie2Q2V {2gαβgρσ −gασgβρ −gαρgβσ} ,(3)ΓZV −V +αβρ= −iF 2Ze cot θW {gαβ(p1 −p2)ρ + gβρ(p2 −p3)α + gρα(p3 −p1)β} ,(4)where QV (= −2/3) is the electric charge of the vector leptoquark and FZ is a free parameter.The couplings in Eqs. (2,3) were obtained via minimal substitution and assuming that V abµhas an anomalous magnetic moment κ = 1.The absence of experimental evidence for compositeness constrains the low energy phe-nomenology of the SCSM.

These constraints can, in principle, place bounds on the vectorleptoquark mass (MV ) and coupling constants (F and FZ). In fact, the analyzes of thecontribution of vector leptoquarks to the four-fermion Fermi interaction at low energies leadto the constraint [7]MV > 197 F (GeV) .

(5)In practice, contributions from other states soften this bound [8], so that MV and F arein reality free parameters. However, an educated guess for the coupling F can be madeas follows.

In the SCSM model the Z and the W are bound states of two preonic scalars,therefore it is natural to assume that the coupling of vector leptoquarks to physical left-handed fields is of the same order of the coupling of these fermions to W’s and Z’s, i.e. Fis of order 1.

Analogously, we expect that FZ ≃F ≃O(1).We can constrain the couplings F and FZ imposing that unitarity is respected at treelevel [9]. For instance, the process e+e−→V +V −violates unitarity at high energies forarbitrary values of the couplings.

However, if we choose F = FZ =q|QV | =q23, unitarityat tree level is restaured.The main decay mode of vector leptoquarks are into a pair lq or νq′, therefore its signalis a lepton plus a jet, or a jet plus missing energy. Using the couplings given above we obtainthat the width of a vector leptoquark is given by4

ΓV =αF 24 sin2 θWMV ,(6)where we neglected all the fermion masses and summed over the possible decay channels.The outline of this paper is the following. The analisis of the indirect signals for lepto-quarks is contained in Sec.

II: One way to look for vector leptoquarks in e+e−colliders isthrough their effects on the production of jet pair (e+e−→q¯q), since they can be exchangedin the t channel. Another way tho search for these particles is to study the forward–backwardasymmetry in the production of b¯b pairs.

In Sec. III, we study the single production of vec-tor leptoquarks through eγ →V eqq, where the photons comes either from bremsstrahlungor from laser backscattering.

In this Sec. we also discuss the signal and its potential back-grounds.

Pairs of vector leptoquarks can also be produced provided that there is enoughavailable energy. Sec.

IV exhibits the study of the production of vector-leptoquark pairs ine+e−and γγ colliders. We summarize our results on Sec.

V. The Appendix presents therelevant expressions for the photon distribution functions used throughout this paper.II. INDIRECT EVIDENCE FOR VECTOR LEPTOQUARKSWe can look for signals of leptoquarks even when the available center of mass energy isnot enough to produce these particles on shell.

This can be done through the study of theireffects as an intermediate state of reactions like e+e−→dijets and e+e−→b¯b.A. Total cross section e+e−→q¯qThe existence of vector leptoquarks can be investigated through the analyzes of thereaction e+e−→q¯q, where they lead to a new t channel contribution, in addition to theusual exchange of γ and Z in the s channel.

Using the vertices derived from the interactionLagrangian (1), the cross section for this process is given bydσdΩ= α2em4snQ2(1 + cos2 θ) +116 sin4 θW cos4 θWs2(s −M2Z)2 + Γ2ZM2Z5

×hCeV2 + CeA2 CqV2 + CqA2(1 + cos2 θ) + 8CeV CeACqV CqA cos θi−Q2 sin2 θW cos2 θWs(s −M2Z)(s −M2Z)2 + Γ2ZM2ZhCeV CqV (1 + cos2 θ) + 2CeACqA cos θi+F 2sin2 θW(1 + cos θ)2cos θ −ηhF 24 sin2 θW1cos θ −η + Q2(7)−18 sin2 θW cos2 θW(CqV + CqA)(CeV + CeA)s(s −M2Z)(s −M2Z)2 + Γ2ZM2Zio,where MZ is the mass of the Z boson, θW is the weak mixing angle, and η = 1 + 2M2V /s.According to our conventions the charge of a quark is Qe (e > 0), CV = Iz −2Q sin2 θW,and CA = Iz.The exchange of a vector particle in the t channel modifies the high energy behaviourof this process: within the scope of the standard model this cross section decreases as thecenter of mass energy increases, however, the new contribution alters this behaviour, yieldinga constant cross section at high energies which is given byσlimit(e+e−→q¯q) ≃π4α2F 4sin4 θW1M2V. (8)This is a dramatic signal once there will be many more dijets than the expected in the scope ofthe standard model at high energies.

In Fig. (2), we exhibit the cross section σ(e+e−→q¯q)as a function of center of mass energy for different values of the vector leptoquark massand for F =q2/3.

This figure was obtained imposing the cut | cos θ| < 0.9, and assumingthe existence of three vector leptoquarks (V ed, V es, V eb), which have the same mass andvalues for the coupling constants. Notice that, after the Z peak the results, which includethe leptoquark, depart significantly from the standard model prediction.In order to estimate the capabilities of the different colliders (LEP II, NLC, CLIC) tosearch for leptoquarks, we evaluate the largest mass of a vector leptoquark, keeping F fixed,for which the cross section for dijet production differs by 10% from the standard modelresult.

In our estimates we were conservative assuming that only one vector leptoquarkcontributes to this reaction. We have defined∆≡σ −σW SσW S,(9)6

where σ is the total cross section including the leptoquark contribution and σW S is thestandard model result. Fig.

(3) displays F as a function of MV , which satisfies the constraint∆(F, MV ) = 10%, for several collider center of mass energies. From this figure, we can learnthat an e+e−collider with center of mass energy of 200 (1000) GeV will be able to unravelthe existence of vector leptoquarks of masses up to 400 (2000) GeV, assuming F =q2/3.B.

Forward-backward asymmetry for b¯b pairsAnother indirect way to look for the vector leptoquark V eb is studying the forward-backward asymmetry in the production of b¯b pairs. Recently at LEP, this asymmetry hasbeen measured [10], and it is in agreement with the standard model prediction.

Imposingthat the contribution of this vector leptoquark to this reaction is at most of the size of theexperimental error (5%), we can exclude a region of the plane MV × F, as it is shown bythe dotted line in Fig. (4).

Assuming F =q23, the data constrains the mass of the ebleptoquark to be bigger than ≃370 GeV.From Fig. (4), we can also foresee the potential of the future e+e−machines for discov-ering the leptoquark V eb: The dashed, solid, and dot-dashed lines indicate the region forwhich the forward-backward asymmetry is 5%, for center of mass energies of 200, 500, and1000 GeV respectively.

For F =q23, LEP II (NLC, CLIC) should be able to look for V ebwith mass up to 600 (1300, 2300) GeV.III. SINGLE PRODUCTION OF VECTOR LEPTOQUARKSWe can produce a single vector leptoquark V eq (q = d, s, b) through the processγe−→V eqq.

This process can take place in e+e−colliders, with the γ being producedby bremsstrahlung, or in γe machines, with the γ originating from laser backscattering. Theelementary cross section for this reaction isdˆσdˆt = −Ncπ36F 2α2sin2 θWhˆs + 3(ˆt −M2q )i2M2V (ˆs + ˆt −M2q )2(ˆt −M2q )2ˆs37

n(ˆt −M2q )hM2q (ˆs + ˆt)2 + 2ˆs2M2V + 4M6V + M6qi−4ˆtM4V (ˆs + ˆt) + 2ˆtM2V M2qˆs −2ˆt + M2V + M2q )i(10)+2ˆsM6q + 2M4q M4V + 2ˆt3M2Vo,where Nc = 3 is the numbers of colors, ˆs is the center of mass energy squared of thesubprocess, ˆt = M2V −ˆs2(1 −β cos θ∗), with β being the V eq velocity in the subprocess c.m.and θ∗its angle with respect to the incident electron in this frame. In order to obtain thecross section for this reaction we must fold the above expression with the γ distributionfunction (fγ/e(x)) (see Appendix)σ =Z 1xmindx fγ/e(x)ˆσ(xs) ,(11)where xmin = (Mq + MV )2/s.

Fig. (5) exhibits the behaviour of σ as a function of MV .As expected, the process initiated by laser backscattering possess a cross section that is oneorder of magnitude larger than the processes initiated by bremsstrahlung photons, with thesame MV and s.Once the leptoquark couples to eq and νq′ with the same strength, the signal for its singleproduction is either (e)jjp/T or (e)jje, where the spectator e is usually lost in the beam pipein the case of e+e−colliders.

The main background for the signal (e)jjp/T ((e)jje) comesfrom the process γe →Wν (eγ →Ze) with the W (Z) decaying into two jets [11]. However,this background can be easily eliminated by requiring that the invariant mass of the jet pairis not close to MW (MZ).At first sight, another potential background is the Bethe-Heitler production of hadrons(γe →q¯q), which exhibits a large cross section.

However, the main contribution to thecross section in this case is due to the region of small transverse momenta of the producedparticles. This allow us to reject with a high efficiency this class of events by demandingthat the observed particles and jets have a sufficiently high pT.In order to access the capability of the future colliders to establish the existence of lep-toquarks through the reaction eγ →V eqq, we require the occurance of 5000 events per year8

with the final state jje−. Once the couplings V eqeq and V eqνq′ are expected to be approx-imately equal, we take that σ(jje−) = σ(V eqq)/2.

Assuming an integrated luminosity of1034 cm−2 s−1 for the future machines, the maximum observable mass for an e+e−collideris MV = 300 (400) GeV for √s = 500 (1000) GeV, while a collider γe using laser backscat-tering can unravel the existence of leptoquarks of mass up to MV = 450 (900) GeV for acenter of mass energy of 500 (1000) GeV.IV. PAIR PRODUCTION OF VECTOR LEPTOQUARKSA.

e+e−→V +V −Pairs of vector leptoquarks can be produced in e+e−collisions provided that there isenough available energy (√s ≥2MV ). This process takes place through the exchange ofa quark in the t channel and through a Z and γ in the s channel.

Using the interactionLagrangians of Sect. I, it is easy to evaluate the cross section for this reaction, resultingthatdσdt =F 4πα216s2t2M4V sin4 θWh3st2M2V −4sM6V + (t2 + 4M4V )(t −M2V )(u −M2V )i+πα2Q2V2s4M4Vht(s2 + tM2V )(u −M2V ) + s2M2V (s −u −10M2V ) + 2st2M2V + stuM2V−4sM4V (t −u) + 2su2M2V + tu2M2V + 8tuM4V −u2M4V −8M8Vi+F 2πα2QV4s3tM4V sin2 θWhs2tM2V + 4s2M4V + st2(u −3M2V ) −3stM2V (u −M2V ) + 4sM4V (u + M2V )−2t2M2V (u −M2V ) −2tM4V (u −M2V ) + 4M6V (u −M2V )i+F 4Zπα28s2M4V sin4 θW(C2V + C2A)1((s −M2Z)2 + Γ2ZM2Z)hs2M2V (s −t −u −10M2V ) + s2tu + 8tuM4V+stM2V (2t + u −4M2V ) + 2suM2V (u −2M2V ) + t2M2V (u −M2V ) + u2M2V (t −M2V ) −8M8Vi+ F 2Zπα2CV QV2s3M4V sin2 θWs −M2Z((s −M2Z)2 + Γ2ZM2Z)hs2M2V (s −u −10M2V ) + s2t(u −M2V ) + t2M2V (u −M2V )+stM2V (2t + u −4M2V ) + 2suM2V (u −2M2V ) + u2M2V (t −M2V ) + 8tuM4V −8M8Vi+F 2ZF 2α28s2tM4V sin4 θW(CV + CA)s −M2Z((s −M2Z)2 + Γ2ZM2Z)hs2tM2V + 4s2M4V + st2u−3stM2V (t + u −M2V ) + 4sM4V (u + M2V ) −2tM2V (u −M2V )(t + M2V ) + 4M6V (u −M2V )i9

where t = M2V −s2(1 −β cos θ), with θ being the scattering angle between the e−and thenegatively charged leptoquark in the laboratory frame, and β =q1 −4M2V /s. This crosssection exhibits a bad high energy behaviour (σ ∝s), and violates unitarity in this limitfor an arbitrary choice of the couplings F and FZ.

However, this violation of unitarity canbe avoided by a careful choice of the couplings: for F = FZ =q23 this cross section has agood high energy behaviour. Moreover, for these values of the couplings, the cross sectionfor this process is 4/9σ(e+e−→W +W −).

Therefore, we must make this choice if we wantto preserve unitary at tree level.Fig. (6) exhibits the total cross section for the process e+e−→V +V −as a function ofMV for F = FZ =q23.

The signal for such a process is either jjee, jjep/T, or jjp/T. Certainlythe identification of the leptoquark is very easy in the mode jjee since the backgrounds,like e+e−→ZZ, can be efficiently eliminated by looking at the invariant mass of the pairsee and/or jj.

Moreover, the signal is very striking since it consists of two pairs ej with(approximately) the same invariant mass. Assuming an integrated luminosity of 105 pb−1per year, there will be more than 105 events per year, which is more than enough to establishthe existence of the leptoquarks.B.

γγ →V +V −We can also produce pairs V +V −in γγ collisions, where the photons are generatedeither by bremsstrahlung or by laser backscattering. There are three Feynman diagramsthat contribute to this process: there is the exchange of a V in the t and u channels and thequartic vertex γγV V .

The cross section for this reaction is equal to the one for γγ →W +W −scaled by a factor Q4V , since the couplings V γ and Wγ are assumed to be proportional. Itis straightforward obtain that the subprocess cross section isdˆσdˆt = Q4V8πα2M2V"(16x2 + 3)M6V2(ˆt −M2V )2(ˆu −M2V )2 −(8x + 3)M2V8x(ˆt −M2V )(ˆu −M2V ) +364x2M2V#,(12)where we defined x = ˆs/4M2V .

One characteristic of this process is that the cross sectionis peaked at the forward region at high energies. Furthermore, due to exchange of a spin-110

particle in the t and u channels, the cross section goes to a constant at high energiesˆσlimit ≃12881πα2M2V. (13)We can obtain the total cross section for this process folding ˆσ with the photon distri-bution functions.σ =Zdx1Zdx2fγ/e(x1)fγ/e(x2)ˆσ(ˆs = x1x2s)(14)Figs.

(7) and (8) show the behaviour of the cross section of the process γγ →V +V −asa function of MV for bremsstrahlung and laser backscattering photons respectively. In thiscase also, the cross section for the process initiated by backscattered photons is one to twoorders of magnitude larger than the one for bremsstrahlung photons due to the distributionof backscattered photons being harder than the one for bremsstrahlung.

From Fig. (7) wecan infer that this reaction is observable for leptoquark masses up to ≃100 (200) GeV inan e+e−machine with √s = 500 (1000) GeV.

Analogously, we can see from Fig. (8), thatthis process is observable for masses up to ≃200 (400) GeV in a γγ collider with √s = 500(1000) GeV.V.

CONCLUSIONSWe studied the signals of vector leptoquarks in e+e−, eγ, and γγ machines. In order todo so, we postulated the interaction Lagrangian of the vector leptoquarks with the quarksand leptons.

Demanding that unitarity is satisfied at tree level, in the different processanalyzed [9], we discovered that the couplings F and FZ are constrained to the valueq2/3.In e+e−machines, we can look for these particles through their effect in e+e−→q¯q,and the existence of leptoquark can be established provided their masses are smaller thanO(2√s). In these machines, vector leptoquarks can also be single produced through thereaction eγ →V eqq, where the γ originates from bremsstrahlung.

This process is observablefor leptoquark masses up to 300 (400) GeV, in a collider with √s = 500 (1000) GeV. We11

have also studied the production of leptoquark pairs, either through e+e−→V +V −orγγ →V +V −, with the two photons coming from bremsstrahlung.In a eγ collider, leptoquarks can be produced in association with jets through eγ →V eqq.For hard photons produced by laser backscattering, we can detect this process provided thatthe leptoquark mass is smaller than 450 (900) GeV, for a collider with √s = 500 (1000)GeV. We also investigated the production of V +V −pairs in γγ collisions, and we foundthat this processes can be observed for leptoquarks with masses up to 200 (400) GeV, if√s = 500 (1000) GeV.ACKNOWLEDGMENTSThis work was partially supported by Conselho Nacional de Desenvolvimento Cient´ıficoe Tecnol´ogico (CNPq), Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (FAPESP),and Coordenadoria de Aperfei¸coamento de Pessoal de N´ıvel Superior (CAPES).

One of theauthors (OJPE) would like to thank the hospitality of the ICTP-Trieste, where part of thiswork was carried on. We also would like to thank prof. S.F.

Novaes for a careful reading ofthe manuscript.The contribution arising from the conventional bremsstrahlung photons were computedusing the well-known Weisz¨acker-Willians distribution [12]f wwγ/e(x) = α2π1 + (1 −x)2xln s4m2e!,(15)where me is the electron mass, and s is the center of mass energy of the e+e−pair. Thisspectrum is peaked at small x, i.e.

most of its photons are soft.Hard photons can be obtained by laser backscattering, which converts an e beam into aγ one. Here the intense photon beams is generated by backward Compton scattering of soft12

photons from a laser of a few eV energy. The energy spectrum of the backscattered laserphotons is [5]f Lγ/e(x, ξ) ≡1σcdσcdx =1D(ξ)"1 −x +11 −x −4xξ(1 −x) +4x2ξ2(1 −x)2#,(16)where σc is the total Compton cross section.

For the photons going in the direction of theinitial electron, the fraction x represents the ratio between the scattered photon and theinitial electron energy (x = ω/E). In writing Eq.

(16), we definedD(ξ) = 1 −4ξ −8ξ2!ln(1 + ξ) + 12 + 8ξ −12(1 + ξ)2 ,(17)withξ ≡4Eω0m2cos2 α02 ≃2√sω0m2,(18)where ω0 is the laser photon energy and (α0 ∼0) is the electron-laser collision angle. It iseasy to verify that the maximum value of x possible in this process isxm = ωmE =ξ1 + ξ .

(19)From Eq. (16) we can see that the fraction of photons with energy close to the maximumvalue grows with E and ω0.

Usually, the choice of ω0 is such that it is not possible for thebackscattered photon to interact with the laser and create e+e−pairs, otherwise the conver-sion of electrons to photons would be dramatically reduced. In our numerical calculations,we assumed ω0 ≃1.26 eV, which is below the threshold of e+e−pair creation (ωmω0 < m2).Thus for the NLC beams (√s = 500 GeV), we have ξ ≃4.8, D(ξ) ≃1.9, and xm ≃0.83.13

REFERENCES†E-mail address: CIEZA@USPIF.IF.USP.BR∗Permanent address: Instituto de F´ısica da USP, C.P. 20516, CEP 01498 S˜ao Paulo, SP,Brazil.

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FIGURESFIG. 1.

Feynman rules for the vertices γV +V −, γγV +V −, and Z0V +V −.FIG. 2.

Total cross section for the production of two jets as a function of the collider center ofmass energy. The solid line stands for the standard model result, while the dotted, dashed, anddot-dashed lines include the contribution of a vector leptoquark of mass 300, 700, and 1500 GeVrespectively.FIG.

3. F as a function of MV for several √s: the dotted, dashed, solid, and dot-dashed linesstand for √s = 100, 200, 500, and 1000 GeV respectively.FIG.

4. Allowed values of the coupling F and MV from the experimental results from LEPfor b¯b production (dotted line).

The dashed, solid, and dot-dashed lines are the region for whichthe forward-backward asymmetry is 5%, for center of mass energies of 200, 500, and 1000 GeVrespectively.FIG. 5.Total cross section for the process e−γ →V −q as a function of MV : (a) laserbackscattering at √s = 500 GeV (dotted line); (b) laser backscattering at √s = 1000 GeV (solidline); (c) bremsstrahlung at √s = 500 GeV (dot-dashed line); (d) bremsstrahlung at √s = 1000GeV (dashed line).FIG.

6. Cross section of the process e+e−→V +V −as a function of MV for several colliderenergies: √s = 500 (dotted line); 1000 (solid line); 2000 (dashed line) GeV.

It was assumed thatF = FZ =q23.FIG. 7.

Cross section for the process γγ →V +V −, with the γ originating from bremsstrahlung,for several energies: (a) √s = 500 (dotted line); (b) 1000 (solid line); (c) 2000 GeV (dot-dashedline).FIG. 8.

Same as in Fig. (7), but with the γ’s produced by laser backscattering.15

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