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Manual for W and Z Production via Vector Boson Fusion in the POWHEG BOX This document describes the settings and input parameters that are specific to the implementation of W and Z production via vector boson fusion at the LHC within the POWHEG BOX framework. The parameters that are common to all POWHEG BOX implementations are given in the manual-BOX.pdf document in the POWHEG-BOX/Docs directory. Since there are singular configurations in the Born contributions, due care has to be exercised to avoid these regions when generating the Born phase space. Two available options are described in the Input parameters section. On this account, the code is not expected to give reliable results when used with very inclusive cuts. If you use our program, please cite Refs. [?, ?, ?]. Running the program Go to the directory $ cd POWHEG-BOX/VBF W-Z and create a directory where you want to run the code: $ mkdir testrun The directory must contain the powheg.input and vbfnlo.input file. To compile the code with gfortran, type $ make The code needs fastjet and lhapdf, so make sure that fastjet-config and lhapdf-config are in the path. After compiling, enter the testrun directory: $ cd testrun The program can be run sequentially by deactivating the variable manyseeds in powheg.input. Execute the program with $../pwhg main The program can also be run in parallel by setting manyseeds to 1 in powheg.input and in several steps as for instance described in the manual for VBF Z production [?]. 1 Input parameters To have more flexible choices for the input parameters of the calculation, a new input file (vbfnlo.input) was added in addition to the standard powheg.input file. The use of this new file and some special parameters for powheg.input will be explained in the following. powheg.input • mll gencut : cut on the invariant dilepton mass for Zjj production, set to 15 GeV if lower than 15 GeV. This cut is needed to avoid singularities when a virtual photon decays into two massless leptons. • bornsuppfact: 0 No Born suppression factor. You should use generation cuts via ptj gencut when using this option. 1 Use a Born suppression factor F (Φn ) with F (Φn ) = p2T,j1 p2T,j1 + Λ2pT j !n p2T,j2 p2T,j2 + Λ2pT j !n . ΛpT j is set to the value given in ptsuppfact and F (Φn ) vanishes whenever a singular region in the Born phase space Φn is reached. The underlying Born kinematics are then generated in the Powheg-Box according to a modified B function, B supp = B(Φn )F (Φn ). • ptj gencut: Generation cut on the jets’ pT in the phase space generator. Should be used when bornsuppfact is set to 0. • Phasespace: 1 Default value, use the standard phase space (with bornsuppfact or ptj gencut). 2 Use unweighted events as phase space generator. To use this option, unweighted events with very inclusive cuts have to be generated with Vbfnlo in a seperate run. Each event which survives the unweighting procedure has to be reweighted by the factor Ji = σLO /(|MB (Φi )|2 pdf(Φi )), the Born cross section over the respective numerical value of the squared Born matrix element including pdfs. This factor Ji is exactly the Jacobian factor of the Born phase space. Place the file with the reweighted events called event.total.lhe in the running directory. • bornxsec: Born cross section in nb of the unweighted events used for Phasespace 2. Not needed otherwise. • fakevirt : If the program is run in several steps, the generation of the grid can be performed with fakevirt 1, where the virtual amplitude is set to a factor proportional to the Born amplitude. 2 vbfnlo.input The input parameters which can be changed by the user are explained in the Vbfnlo Manual [?] in detail. Here we give a list of the supported parameters with a short description. • PROC ID: 120 pp → Z jj → `+ `− jj 130 pp → W + jj → `+ ν` jj 140 pp → W − jj → `− ν̄` jj • DECAYMODE: 11 ` = e (electron) 13 ` = µ (muon) • HMASS: Standard Model Higgs boson mass in GeV. Default value is 126 GeV. • HWIDTH: It is possible to set the Higgs boson width with this input parameter. Default is -999 GeV, which means that the internally calculated value of the width is used. • EWSCHEME: Sets the scheme for the calculation of electroweak parameters. A summary of the four available options is given in Table ??. Note that if EWSCHEME = 4 is chosen, all variables in Table ?? are taken as inputs. As the parameters are not independent, this can lead to problems if the input values are not consistent. In this scheme, all photon couplings are set according to the input variable INVALFA and all other couplings are set according to FERMI CONST. Default value is 3. • ANOM CPL: If set to 1, anomalous gauge boson couplings are used if available for the selected process. Anomalous coupling parameters are set via the file anomV.dat which has to be located in the running directory. For details on the possible choices and parameterisations of the anomalous couplings see the Vbfnlo Manual [?]. This is not a tested feature and should always be compared to the NLO result of Vbfnlo. Default value is 0. • TOPMASS: Top-quark mass in GeV. Default value is 172.4 GeV. • TAU MASS: Tau mass in GeV used in the calculation of the Higgs boson width and branching ratios. Default value is 1.77684 GeV. • BOTTOMMASS: Bottom-quark pole mass in GeV, used in the calculation of the Higgs boson S width and branching ratios. Default value is 4.855 GeV, which corresponds to mM b (mb ) = 4.204 GeV. • CHARMMASS: Charm-quark pole mass in GeV used in the calculation of the Higgs boson S width and branching ratios. Default value is 1.65 GeV, corresponding to mM c (mc ) = 1.273 GeV. • FERMI CONST: Fermi constant, used as input for the calculation of electroweak parameters in EWSCHEME = 1-4. Default value is 1.16637 × 10−5 GeV−2 . • INVALFA: One over the fine structure constant, used as input for EWSCHEME = 1 and 4. Within the other schemes this parameter is calculated. The default value depends on the choice of EWSCHEME, as given in Table ??. 3 EWSCHEME Parameter Default Value 1 FERMI CONST INVALFA SIN2W WMASS ZMASS 1.16637 × 10−5 GeV−2 128.944341122 0.230990 79.9654 GeV 91.1876 GeV Input Input Calculated Calculated Input 2 FERMI CONST INVALFA SIN2W WMASS ZMASS 1.16637 × 10−5 GeV−2 132.340643024 0.222646 80.3980 GeV 91.1876 GeV Input Calculated Input Calculated Input 3 FERMI CONST INVALFA SIN2W WMASS ZMASS 1.16637 × 10−5 GeV−2 132.340705199 0.222646 80.3980 GeV 91.1876 GeV Input Calculated Calculated Input Input 4 FERMI CONST INVALFA SIN2W WMASS ZMASS 1.16637 × 10−5 GeV−2 137.035999679 0.222646 80.3980 GeV 91.1876 GeV Input Input Input Input Input Input/Calculated Table 1: Electroweak input parameter schemes. To compare the code with [?], the flag consistency in the qqbqq.f and qqZWjqqi.f file in the vbfnlo-files directory has to be set to .true.. Than, all amplitudes with Q2 < 4 GeV are provided with a large damping factor, not only the ones with photons in the t-channel. After that, the code has to be recompiled. References [1] F. Schissler, and D. Zeppenfeld, Parton Shower Effects on W and Z Production via Vector Boson Fusion at NLO QCD, arXiv:1302.2884. [2] C. Oleari and D. Zeppenfeld, QCD corrections to electroweak nu(l) j j and l+ l- j j production, Phys. Rev. D 69, 093004 (2004) [hep-ph/0310156]. 4 [3] S. Alioli, P. Nason, C. Oleari, and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 1006 (2010) 043 [arXiv:1002.2581 [hep-ph]]. [4] B. Jäger, S. Schneider, G. Zanderighi, Next-to-leading order QCD corrections to electroweak Zjj production in the POWHEG BOX, arXiv:1207.2626 [hep-ph]. [5] K. Arnold, M. Bähr, G. Bozzi, F. Campanario, C. Englert, T. Figy, N. Greiner and C. Hackstein et al., Comput. Phys. Commun. 180, 1661 (2009) [arXiv:0811.4559 [hep-ph]]; K. Arnold, J. Bellm, G. Bozzi, F. Campanario, C. Englert, B. Feigl, J. Frank and T. Figy et al., [arXiv:1207.4975 [hep-ph]]; K. Arnold, J. Bellm, G. Bozzi, M. Brieg, F. Campanario, C. Englert, B. Feigl and J. Frank et al., [arXiv:1107.4038 [hep-ph]]. 5
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