arXiv:hep-ph/0604200v1 24 Apr 2006
Next-to-leading order QCD corrections
to Z boson pair production via
Barbara J¨ ager1, Carlo Oleari2and Dieter Zeppenfeld1
1Institut f¨ ur Theoretische Physik, Universit¨ at Karlsruhe, P.O.Box 6980, 76128 Karlsruhe,
2Dipartimento di Fisica ”G. Occhialini”, Universit` a di Milano-Bicocca, 20126 Milano,
Vector-boson fusion processes are an important tool for the study of electroweak
symmetry breaking at hadron colliders, since they allow to distinguish a light Higgs
boson scenario from strong weak boson scattering. We here consider the channels
WW →ZZ and ZZ →ZZ as part of electroweak Z boson pair production in associ-
ation with two tagging jets. We present the calculation of the NLO QCD corrections
to the cross sections for pp→e+e−µ+µ−+ 2 jets and pp→e+e−νµ¯ νµ+ 2 jets via
vector-boson fusion at order αsα6, which is performed in the form a NLO parton-level
Monte Carlo program. The corrections to the integrated cross sections are found to
be modest, while the shapes of some kinematical distributions change appreciably at
NLO. Residual scale uncertainties typically are at the few percent level.
One of the primary goals of the CERN Large Hadron Collider (LHC) is the discovery
of the Higgs boson and a thorough investigation of the mechanism of electroweak (EW)
symmetry breaking [1, 2]. In this context, vector-boson fusion (VBF) processes have emerged
as a particularly interesting class of processes. Higgs boson production in VBF, i.e. the
reaction qq→qqH, where the Higgs decay products are detected in association with two
tagging jets, offers a promising discovery channel  and, once its existence has been verified,
will help to constrain the couplings of the Higgs boson to gauge bosons and fermions .
In order to distinguish possible signatures of strong weak-boson scattering from those of a
light Higgs boson, a good understanding of WW →ZZ and ZZ →ZZ scattering processes,
which are part of the VBF reaction qq→qqZZ, is needed. This requires the computation
of next-to-leading order (NLO) QCD corrections to the qq →qqZZ cross section, including
the leptonic decays of the Z bosons. Experimentally, very clean signatures are expected
from the ZZ →ℓ+ℓ−ℓ′+ℓ′−decays in VBF with four charged leptons in the final state, the
disadvantage of this channel being a rather small Z →e+e−or Z →µ+µ−branching ratio of
about 3%. The ZZ →ℓ+ℓ−ν¯ ν channel, with two undetected neutrinos, on the other hand,
results in a larger number of events due to the larger Z →ν¯ ν branching ratio .
LO results for EW ZZ jj production in VBF have been available for more than two
decades. The first calculations  were performed employing the effective W approxima-
tion , where the vector bosons radiated off the scattering quarks are treated as on-shell
particles and, therefore, kinematical distributions characterizing the tagging jets cannot be
predicted reliably. In the following years, exact calculations for qq →qqZZ have been com-
pleted, first without Z boson decay , and then including leptonic decays of the Z bosons
within the narrow width approximation .
We go beyond these approximations and develop a fully-flexible parton level Monte Carlo
program, which allows for the calculation of cross sections and kinematical distributions for
EW ZZ jj production via VBF at NLO QCD accuracy. The program is structured in com-
plete analogy to the respective code for EW W+W−jj production presented in Ref. .
Here, we calculate the t-channel weak-boson exchange contributions to the full matrix ele-
ments for processes like qq →qqe+e−µ+µ−and qq→qqe+e−νµ¯ νµat O(α6αs). We consider
all resonant and non-resonant contributions giving rise to a four charged-lepton and a two
charged-lepton plus two neutrino final state, respectively. Contributions from weak-boson
exchange in the s-channel are strongly suppressed in the phase-space regions where VBF
can be observed experimentally and therefore disregarded throughout. We do not specifi-
cally require the leptons and neutrinos to stem from a genuine VBF-like production process,
but also include diagrams where one or two of the Z bosons are emitted from either quark
line. Diagrams, where the final state leptons stem from a γ →ℓ+ℓ−decay or non-resonant
We are grateful to Gunnar Kl¨ amke for useful discussions and to Stefan Gieseke for support
with our computer system. This research was supported in part by the Deutsche Forschungs-
gemeinschaft under SFB TR-9 “Computergest¨ utzte Theoretische Teilchenphysik”.
 ATLAS Collaboration,
E. Richter-Was and M. Sapinski, Acta Phys. Pol. B 30, 1001 (1999); B. P. Kersevan
and E. Richter-Was, Eur. Phys. J. C 25, 379 (2002) [arXiv:hep-ph/0203148].
ATLAS TDR, Report No. CERN/LHCC/99-15 (1999);
 G. L. Bayatian et al., CMS Technical Proposal, Report No. CERN/LHCC/94-
38x (1994); R. Kinnunen and D. Denegri, CMS Note No. 1997/057; R. Kinnunen
and A. Nikitenko, Report No. CMS TN/97-106; R. Kinnunen and D. Denegri,
arXiv:hep-ph/9907291; V. Drollinger, T. M¨ uller and D. Denegri, arXiv:hep-ph/0111312.
 D. L. Rainwater, PhD thesis, arXiv:hep-ph/9908378.
 D. Zeppenfeld, R. Kinnunen, A. Nikitenko and E. Richter-Was, Phys. Rev. D 62, 013009
(2000) [arXiv:hep-ph/0002036]; D. Zeppenfeld, in Proc. of the APS/DPF/DPB Summer
Study on the Future of Particle Physics, Snowmass, 2001 edited by N. Graf, eConf
C010630, p. 123 (2001) [arXiv:hep-ph/0203123]; A. Belyaev and L. Reina, JHEP 0208,
041 (2002) [arXiv:hep-ph/0205270]; M. D¨ uhrssen et al., Phys. Rev. D 70, 113009 (2004)
 R. N. Cahn and M. S. Chanowitz, Phys. Rev. Lett. 56, 1327 (1986).
 M. J. Duncan, Phys. Lett. B 179, 393 (1986); A. Abbasabadi and W. W. Repko, Nucl.
Phys. B292, 461 (1987).
 R. N. Cahn and S. Dawson, Phys. Lett. B 136, 196 (1984) [Erratum-ibid. B 138, 464
(1984)]; S. Dawson, Nucl. Phys. B249, 42 (1985); M. J. Duncan, G. L. Kane and
W. W. Repko, Nucl. Phys. B272, 517 (1986).
 D. A. Dicus, S. W. Wilson and R. Vega, Phys. Lett. B 192, 21 (1987).
 U. Baur and E. W. N. Glover, Nucl. Phys. B347, 12 (1990); U. Baur and
E. W. N. Glover, Phys. Rev. D 44 99 (1991).
 B. J¨ ager, C. Oleari and D. Zeppenfeld, arXiv:hep-ph/0603177.
 K. Hagiwara and D. Zeppenfeld, Nucl. Phys. B274, 1 (1986); K. Hagiwara and D. Zep-
penfeld, Nucl. Phys. B313, 560 (1989).
 A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Nucl. Phys. B560, 33 (1999)
 C. Oleari and D. Zeppenfeld, Phys. Rev. D 69, 093004 (2004) [arXiv:hep-ph/0310156].
 Warren Siegel, Phys. Lett. B 84, 193 (1979); Warren Siegel, Phys. Lett. B 94, 37 (1980).
 S. Catani and M. H. Seymour, Nucl. Phys. B485, 291 (1997) [Erratum-ibid. B510, 503
 T. Figy,
C. Oleari and D. Zeppenfeld,Phys. Rev. D 68, 073005 (2003)
 G. Passarino and M. J. Veltman, Nucl. Phys. B160, 151 (1979).
 T.Stelzer andW. F. Long,Comput.Phys. Commun.
F. Maltoni and T. Stelzer,
 J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP
0207, 012 (2002) [arXiv:hep-ph/0201195].
 S. Catani, Yu. L. Dokshitzer and B. R. Webber, Phys. Lett. B 285 291 (1992); S. Catani,
Yu. L. Dokshitzer, M. H. Seymour and B. R. Webber, Nucl. Phys. B406 187 (1993);
S. D. Ellis and D. E. Soper, Phys. Rev. D 48 3160 (1993).
 G. C. Blazey et al., arXiv:hep-ex/0005012.