PHYSICAL REVIEW 0 VOLUME 47, NUMBER 11 1 JUNE 1993 sector in Zy production Probing the weak-boson at hadron colliders U. Baur Florida State University, Florida 32306 Physics Department, Tallahassee, E. L. Berger CERN, Geneva, Switzerland Illinois 60439 and High Energy Physics Division, Argonne National Laboratory, Argonne, (Received 5 November 1992) analysis of Zy production for general ZZy and Zyy cou- A detailed at hadron colliders is presented in terms of four plings. Deviations from the standard model gauge theory structure can be parametrized ZZy and four Zyy form factors. behavior of these form factors is severely The high-energy restricted of Z bosons and photons Tevat- by unitarity. Prospects for testing the self-interactions at the Fermilab ron, the CERN Large Hadron Collider and the Superconducting Super Collider are explored. Sensitivi- ZZy and Zyy couplings ty limits for anomalous are derived and compared to bounds from low-energy data and e+ e collider experiments. 13. 85. Qk, 12. 15. Cc, 13. 38. +c PACS number(s): I. INTRODUCTION ance Lorentz invariance [6]. Their properties are and Sec. II, where discussed in we also derive unitarity with the ZZy and bounds for the form factors associated at the Fermilab Tevatron pp collider are Experiments Zyy vertices. We assume the SM to be valid apart from expected to collect data corresponding to an integrated in the ZZy and Zyy in the 1992 — vertices. In particular, of approximately 100 pb 1993 anomalies luminosity of 8' and Z bosons to quarks run, an increase of more than one order of magnitude we assume the couplings in and leptons to be given by the SM and that there are no statistics over the data sample presently available. The couplings of the Zy pair to two gluons [7]. nonstandard increase in integrated will make it significant luminosity of helicity am- sectors of the stan- Our analysis is based on the calculation possible to probe previously untested plitudes for the complete processes dard model (SM) of electroweak interactions, such as the vector-boson self-interactions. Within the SM, at the tree qq~Zy~l I y level, these self-interactions are completely fixed by the SU(2) XU(1) gauge theory of the model. structure Their and is thus a crucial test of the model. observation Recently, qq ~Zy ~Vvy, the UA2 Collaboration [1] reported the first direct mea- 8'8'y of surement the vertex in the reaction I =e, p. In case of the l+/ y final state, timelike where pp~e — vyX. Within rather large errors the UA2 result and radiative Z decay diagrams also con- virtual photon is consistent with SM expectations. More precise infor- with effects of the finite Z width, tribute. Together these from 8' — mation can soon be expected y production in In Sec. III we dis- are included fully in our calculation. run [2]. the ongoing Tevatron and Zyy cuss the signatures of anomalous ZZy cou- to significantly In addition improved bounds on the in pp — y and pp — +l+t' tak- +Vvy at the Tevatron, plings structure of the 8'8 y vertex, the new Tevatron data will ing into account the form-factor of the anoma- behavior to search for evidence of nonzero also offer the possibility The l+I lous couplings. y invariant mass, the photon and Zyy in Zy production. All ZZy ZZy couplings the coseI are transverse momentum, and distributions and Zyy vanish in the SM at the tree level, couplings indicators of anomalous Here sensitive couplings. GI* is and the rates for 8'*y and Zy production are quite simi- rest frame with respect to the the polar angle in the I I lar [3]. In this paper of future we study the capabilities l+ l direction in the ll y rest frame. Cuts are described to probe the ZZy and Zyy hadron collider experiments which select a region in phase space particularly sensitive via Zy vertices production. In the past, the reaction In Sec. III we also consider the to anomalous pp — couplings. +Zy has usually for a restricted been considered set to (1. 1) and (1. 2). The sensi- most important backgrounds of anomalous only [4, 5]. We go a step further couplings tivity of experiments at the CERN Large Hadron Collid- and use the most general Zy V, V =y, Z, vertex which is er (LHC) and (SSC) to Superconducting Super Collider qq — of accessible in the annihilation process +Zy theory Zy V vertices is discussed in Sec. IV. In nongauge Four effectively massless quarks. different anomalous Sec. V we compare ZZy the limits on anomalous and are allowed by electromagnetic invari- couplings gauge Zyy expected from future hadron collider ex- couplings periments with low-energy bounds, and with the sensitivi- and future e+e ty from collider experiments. present In Sec. V we also present our conclusions. *Permanent address. 1993 The American 0556-2821/93/47(11)/4889(16)/$06. 00 47 4889 Physical Society
U. BAUR AND E. L. BERGER 4890 II. ZZy AND Zyy COUPLINGS Z In both processes the timelike and/or virtual photon boson couples to essentially en- massless fermions, which level, the reaction pp ~l+/ effectively B„V"=0, V =y, Z. that At the parton sures This together y proceeds shown in Figs. 1 and 2. Figure of the on-shell photon restricts the via the Feynman with gauge invariance graphs 1 of the Zy V vertex the full set of SM diagrams, the contri- tensor structure to allow whereas sufficiently displays and Zyy from anomalous ZZy are just four free parameters. The most general anomalous butions couplings in Fig. 2. For pp — ZyZ vertex function (see Fig. 3 for notation) shown +Vvy, only the timelike virtual is given by Z diagrams of Figs. 1(a) and 1(b) and Fig. 2(a) contribute. I P e"~~ P q2, I z~"z(q„q2, P) = A "~)+ ~]+h& e" ~~q2 + P [(P q2)g"~ ~ h, (qI2g qzg— (2. 1) q~zP— m' mz The most general Zyy mz is the Z-boson the electric and magnetic (electric) where mass. (magnetic) dipole from Eq. (2. 1) by the fol- quadrupole transition moment. h2 and h4 receive only vertex function can be obtained from operators of dimension 8. Within lowing replacements: contributions the SM, at tree level, all couplings vanish. At the h, P2 - q2 i =1, . . . , 4 . h, — one-loop level, only the CP-conserving h 3 and couplings +h, i', (2. 2) and For h 3, for example, one finds [9] h & are nonzero. mz mz to P" and + h 3 + 2. 5 X 10 Terms proportional q& have been omitted 2. 2 X 10 (2. 4) in to the cross section. Eq. (2. 1) since they do not contribute for a top-quark m, in the range 100 and mass between loss of generality Without we have chosen the overall 200 GeV. ZZy and Zyy coupling constant to be In Eq. (2. 1), without loss of generality, we have chosen zrr = e, (2. 3) the Z boson mass mz as the energy scale in the denomi- Rzzr nator of the overall factor and the terms proportional to e is the charge of the proton. The overall factor where h& 4. For a different mass scale M all subsequent results q, ) in E— (P of Bose symmetry, (2. 1) is a result q. & 3 (h z & ) by a factor M /mz can be obtained by scaling h the factor P in the Zyy whereas vertex function origi- (M /m ). gauge invariance. As a result nates from electromagnetic the ZZy and Zyy cou- Tree-level unitarity restricts the Zyy vertex function if both pho- vanishes identically to their SM values at asymptotically high plings uniquely tons are on shell [8]. h, ~ [10]. This implies that the Zy V couplings energies functions of q &, The form factors h, are dimensionless by form factors h, (q &, q 2, P have to be described ) which q2, and P . All couplings are C odd; h & and h2 violate q &, qz, or P In Zy produc- becomes large. vanish when to CP. Combinations of h 3 (h, ) and h~ (h 2 ) correspond tion q z =0 and q, = mz even when finite Z width effects large values of P =s are taken into account. However, will be probed in future hadron collider experiments, and the s dependence has to be included in order to avoid un- results that would violate unitarity. physical h, 0 =h; (mz, 0, 0) of the form factors at low The values (at s =0) are constrained energy by partial-wave unitarity of the inelastic vector-boson pair production amplitude in at arbitrary center-of- fermion antifermion annihilation mass energies. Since the couplings do not contribute h; to ff +ZZ [6], it is suffi— cient to consider partial-wave for ff ~Zy only. In deriving unitarity unitarity limits a) b) FIG. 1. Feynman FIG. 2. of ZZy graphs for the tree-level processes contrib- Contributions and Zy y diagrams to qq ~l+l uting to pp — +l+I y in the SM. y.
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