W+W-, WZ and ZZ production in the POWHEG BOX V2
aa r X i v : . [ h e p - ph ] N ov Preprint typeset in JHEP style - PAPER VERSION W + W − , W Z and
Z Z production in the
POWHEG-BOX-V2
Paolo Nason
INFN, Sezione di Milano Bicocca, ItalyE-mail:
Giulia Zanderighi
Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, University of Oxford, UKE-mail: [email protected]
Abstract:
We present an implementation of the vector boson pair production processes ZZ , W + W − and W Z within the
POWHEG-BOX-V2 . This implementation, derived from the
POWHEG BOX version, has several improvements over the old one, among which the inclusionof all decay modes of the vector bosons, the possibility to generate different decay modesin the same run, speed optimization and phase space improvements in the handling ofinterference and singly resonant contributions.
Keywords:
POWHEG, SMC, NLO, QCD. ontents
1. Introduction 12. Matrix Elements 23. Phase space 24. Generation of the subprocesses 35. Availability 3
1. Introduction
In ref. [1] an implementation of vector boson pair production at NLO in QCD, that canbe interfaced to a shower generator according to the
POWHEG method, was presented. Onlydecays into leptons and neutrinos were considered. Singly resonant contributions andinterference effects were included, and in fact all diagrams relevant to the production offour leptons were accounted for, with the exception of interference effects between W + W − and ZZ production when the decay products are the same. These last effects were shownto be fully negligible at Born level.In the present work, we present a new implementation of these processes that has thefollowing improvements over the old one: • all possible decay modes are allowed; • different decay modes can be produced in a single run; • there is a considerable speed improvement; • there is an improvement in the treatment of the phase space and interference terms.Although hadronic final states are all allowed, no NLO corrections to the vector bosondecays are included. W and Z decays are in fact properly handled by the shower MonteCarlo programs, like PYTHIA [2, 3] and
HERWIG [4, 5], that can be interfaced to the
POWHEGBOX , their resonance decay machinery being tuned to closely reproduce collider data.The new implementation exploits the fact that in the
POWHEG-BOX-V2 version one canspecify if final state particles arise from a resonance decay. The algorithm for finding theradiation region in real graphs, checks if a parton arises from a resonance rather thanfrom the production vertex, and handles the radiation accordingly. In the present imple-mentation, where no radiative corrections to decaying resonances are considered, the onlysingular regions that are produced by
POWHEG are thus relative to the production vertex.– 1 – . Matrix Elements
We have used the same MCFM matrix elements [6] as in the old implementation, extendingthem to deal with hadronic decays. A considerable increase in performance was achievedby storing intermediate results in the matrix element calculation. Strong corrections inhadronic decays, of the form 1 + α S ( M V ) /π , are also included.A non diagonal Cabibbo matrix is used by default (an arbitrary CKM matrix can beentered in input by the user). This is done in the following way. The only process inwhich flavour changing interactions can arise in production is W Z (in fact, in W + W − production flavour changing interactions are suppressed by the GIM mechanism). In the W Z case we thus generate explicitly from the beginning all CKM allowed flavour changingprocesses. In W decays, one generates the matrix elements for the decay into ¯ ud ′ , ¯ cs ′ (and the corresponding ones for the W + ), where d ′ and s ′ are the electroweak flavoureigenstates. Once the event is generated, the d ′ or s ′ are transformed randomly into a d or s mass eigenstate, with a probability corresponding to the square of the appropriate CKMentry.
3. Phase space
The treatment of the phase space, especially when handling processes with interference,has been changed with respect to the original version.When interference is present, we compute both the amplitudes A and A exch , where A exch is the amplitude with the final state identical particles exchanged. In the previousversion we computed the cross section using the squared amplitude |A| + |A exch | + 2Re( AA ∗ exch ) . (3.1)This had the disadvantage that the regions for the importance sampling of the resonanceswere mixed up, and had to be handled with care [1]. In the present version, we instead dothe following. We rewrite eq. (3.1) as (cid:0) |A| + |A exch | (cid:1) × (cid:26) AA ∗ exch ) |A| + |A exch | (cid:27) . (3.2)Noticing that both factors are symmetric for the exchange of the momenta of the identicalparticles, and that |A| and |A exch | go into each other by this exchange, we can as welluse the expression 2 |A| × (cid:26) AA ∗ exch ) |A| + |A exch | (cid:27) , (3.3)that yields the same result upon integration. We then assign the resonances according tothe structure of the |A| term. The ambiguity in the assignment is only present now in thesmall interference term, which is ignored, and no particular importance sampling tricks areneeded to handle it.Notice that what would seem to be the most obvious choice2 |A| + 2Re( AA ∗ exch ) . (3.4)– 2 –s in fact problematic, since it does not yield a positive definite cross section.A further improvement was given by generating the partonic s variable in the un-derlying Born configuration with Lorenzian importance sampling over the possible single-resonant contribution. This leads to a better description of the single-resonant region.
4. Generation of the subprocesses
In this version of the
V V production codes it is possible to generate the matrix elements forall possible decays of the vector bosons. This leads to a large proliferation of amplitudes.For example, there are 880 Born parton level configurations that arise in
W Z production.Generating all processes at once slows down the program considerably. Furthermore, evenif the total result is computed with a satisfactory accuracy, it is not easy to check that alldecay processes have been accurately probed. This is particularly critical when computingthe upper bounds for radiation, since they are computed individually for each underlyingBorn configuration. Because of this reason a new feature was introduced in
POWHEG-BOX-V2 ,such that the upper bound for radiation of equivalent amplitudes (i.e. amplitudes that areequal up to constant couplings) are combined. This feature is activated by default forthe processes at hand, but can also be activated for other processes by including the line evenmaxrat 1 in the powheg.input file. Still it is often convenient to restrict the generateddecay modes to the ones one is really interested into. All generators offer a number of pre-defined options to select specific decay modes (e.g. leptonic, semi-leptonic, hadronic, etc.).It is however difficult to anticipate all interesting possibilities. For this reason, the codehas been written in such a way that the selection of decay modes can also be carried outby the user by editing the subroutine alloweddec in the init processes.f file. Furtherexplanations on how to do this are given in the respective manual.
5. Availability
The new code has been made available in the
POWHEG BOX svn repository, and instructionsfor downloading the V2 version of
POWHEG and the corresponding user processes are givenat the URL http://powhegbox.mib.infn.it .If you use this code, please quote the present note, and ref. [1]. Furthermore we remindthat the matrix elements were obtained from ref. [6], and the
POWHEG BOX framework hasbeen developed in the sequel of publications [7–9].
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