Vector Boson Pair Production via Vector Boson Fusion at NLO QCD
Giuseppe Bozzi, Barbara Jäger, Carlo Oleari, Dieter Zeppenfeld
VVector Boson Pair Production via VectorBoson Fusion at NLO QCD ∗ Giuseppe Bozzi , Barbara J¨ager , Carlo Oleari and Dieter Zeppenfeld Institut f¨ur Theoretische Physik, Universit¨at Karlsruhe, P.O.Box 6980, 76128Karlsruhe, Germany KEK Theory Division, Tsukuba 305-0801, Japan Universit`a di Milano Bicocca and INFN Sezione di Milano Bicocca, 20126Milano, Italy
Abstract.
NLO QCD corrections to Vector Boson Pair Production via VectorBoson Fusion have recently been calculated and implemented in a parton-level Monte-Carlo program with full experimental cuts. We briefly sketch theelements of the calculation and show numerical results for the Large HadronCollider.
Introduction
The Vector Boson Fusion (VBF) process qq → qqH is one of the most promis-ing channels for the discovery of the Higgs particle and the measurement ofits properties at the Large Hadron Collider (LHC) [1]. It proceeds through a t − channel scattering of the two initial-state quarks mediated by a weak bo-son, with the Higgs emitted off the boson propagator. The kinematic featuresthat make this process phenomenologically relevant are: the presence of twohighly-energetic jets in the final state, the large rapidity interval between thesejets and the absence of noticeable jet activity inside this rapidity interval.Moreover the Next-to-Leading Order (NLO) QCD corrections to the totalcross sections [2] and for the differential distributions [3] have been found tobe quite modest (enhancing the Leading Order (LO) result by 5-10%), thuspointing towards a good stability of the perturbative result.Even though the cross section for the VBF process is somewhat smallerthan the one for the gluon fusion gg → H channel at the LHC, the distinctivefeatures cited above greatly help in distinguishing the signal from the back-grounds and make VBF an ideal candidate for Higgs discovery and precisionmeasurements.One of the most relevant backgrounds to a VBF H → V V signal is theprocess qq → qqV V , i.e. vector boson pair production via VBF [4]. It shows ∗ Presented by G. Bozzi at IFAE 2007 (Napoli, April 2007) and HEP 2007 (Manch-ester, July 2007) a r X i v : . [ h e p - ph ] O c t Giuseppe Bozzi, Barbara J¨ager, Carlo Oleari and Dieter Zeppenfeld exactly the same kinematical features as VBF Higgs production, thus beingan irreducible background. In addition, it is known that the scattering of lon-gitudinal vector bosons is intimately related to the mechanism of electroweaksymmetry breaking (EWSB), and an enhancement of qq → qqV V over theStandard Model predictions at high center-of-mass energies could be a possiblesignal of strong EWSB (see, for instance, [5] and references therein).It is thus clear that an accurate prediction for the electroweak productionof a vector boson pair plus two jets is mandatory for new physics searches atthe LHC.In the following we will present the results obtained in three recent pa-pers where we computed the NLO QCD corrections to the processes qq → qqW + W − [6], qq → qqZZ [7], qq → qqW ± Z [8], including the full leptonicdecays of the vector bosons. The calculations have been implemented in afully-flexible parton level Monte-Carlo program, allowing for the computationof jet observables and a straightforward implementation of experimental cuts. Selected topics from the calculation
The main challenges of the calculation were the huge number of Feynmandiagrams involved and the numerical instabilities arising from pentagon con-tributions to the virtual part of the cross section.When computing a multi-parton process (in this case, a 2 → identical in form to the onesappearing in Higgs production via VBF [3].The EW bosons exchanged in the t − channel are colour-singlets, thus therecannot be any virtual contribution at O ( α S ) from gluons attached both to theupper and lower quark lines. This allows us to consider virtual radiative cor-rections separately for the single quark lines, leading to diagrams containingloops with up to five external legs ( pentagons ). After the cancellation of the in-frared poles between real and virtual contributions, the finite remainder of theloop amplitudes can be computed by means of the Passarino-Veltman reduc-tion formalism [10] in the case of two-, three- and four-point tensor integrals.In the case of pentagons, numerical instabilities show up when kinematicalinvariants, such as the Gram determinant, become small for some regions ofphase space. For the pentagons, we have thus used the recently proposed al-ternative reduction formalism by Denner and Dittmaier [11], which results in ector Boson Pair Production via Vector Boson Fusion at NLO QCD 3 a fraction of numerically unstable events at the per-mille level (for details, see[8]). Numerical results
In the following we will present numerical results at NLO QCD accuracyobtained with our Monte-Carlo code for EW + W − W jj, ZZjj, W ± Zjj pro-duction at the LHC.We used the CTEQ6M parton distributions with α S =0.118 at NLO andthe CTEQ6L1 set at LO [12]. We chose m Z =91.188 GeV, m W =80.419 GeVand G F =1.166 × − as EW input parameters, obtaining α QED =1/132.54and sin θ W =0.22217. We have set fermion masses to zero, neglecting externalbottom and top quark contributions. Jets have been reconstructed by meansof the k T -algorithm [13, 14] with resolution parameter D =0.8.Typical VBF cuts have been imposed: here we show those used in the W ± Z case: • two hard ”tagging” jets: p T j ≥
20 GeV, | y j |≤ M jj >
600 GeV • large rapidity separation between jets: ∆y jj > y j × y j < • lepton cuts: p T l ≥
20 GeV, | η l | ≤ m ll ≥
15 GeV • ”separation” cuts: ∆R jl ≥ ∆R ll ≥ ∆R jl and ∆R ll denote the jet-lepton and lepton-lepton separationin the rapidity-azimuthal angle plane, respectively, and m ll the invariant massof an electron or muon pair. Fig. 1.
Scale dependence of the total cross section for W ± Z production via VBFfor two values of the central scale (see text). Giuseppe Bozzi, Barbara J¨ager, Carlo Oleari and Dieter Zeppenfeld In Figure 1 (from [8]) we show the total cross section displayed as a functionof the factorization and renormalization scales µ F,R = ξ F,R µ in the case of W ± Zjj production. We have considered two possible values for the centralscale: µ = ( m Z + m W ) / µ = Q , where Q is the momentum transfercarried by the exchanged vector boson in VBF graphs (for details, see [8]).The K-factor is K =0.97 in the first case and K =1.04 in the second one. Inboth cases the scale dependence, for instance in the range 0 . < ξ <
2, isgreatly reduced when passing from LO (about 10%, dotted black curves) toNLO (about 2%). At NLO, we have considered three cases: ξ F = ξ R = ξ (solidred lines), ξ F = 1 , ξ R = ξ (dashed green lines), ξ F = ξ, ξ R = 1 (dot-dashedblue lines). Fig. 2.
Transverse-momentum distribution of the tagging jet with the highest p T in W + W − production via VBF (left), with the corresponding K -factor (right). Thecuts of Ref. [6] are used. In Figure 2 (from [6]) we present the transverse-momentum distributionof the tagging jet with the highest p T in the W W jj case, together with thecorresponding K-factor. The figure shows a strong change in shape when goingfrom LO to NLO, with a 10-20% enhancement of the cross section at low valuesof p T ( p T <
100 GeV) and a corresponding decrease at higher p T values: thiseffect is mainly due to the extra parton coming from real emission at NLO.Finally, in Figure 3 (from [7]) we show the differential distribution for EW ZZjj production with respect to the invariant mass M ZZ without (left) andwith (right) the inclusion of the Higgs contribution for a scale µ = Q . Apartfrom the pronounced resonance behaviour visible in the right plot, we notethat the LO and NLO predictions are virtually indistinguishable in both cases, ector Boson Pair Production via Vector Boson Fusion at NLO QCD 5 Fig. 3.
Distribution of the invariant mass M ZZ in ZZ production via VBF without(left) and with (right) the Higgs boson contribution. The cuts of Ref. [7] are used. indicating an excellent stability of the perturbative calculation for this scalechoice. Acknowledgements.
The work of B.J. is supported by the Japan Societyfor the Promotion of Science. The work of G.B. is supported by the DeutscheForschungsgemeinschaft under SFB TR-9 “Computergest¨utzte TheoretischeTeilchenphysik”.
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