PROPHECY4f: a PROPer description of the Higgs dECaY into 4 fermions =============================================================================== Prophecy4f, Version 2.0.1, released on Dec 03, 2014 Prophecy4f can be downloaded from http://omnibus.uni-freiburg.de/~sd565/programs/prophecy4f/prophecy4f.html ------------------------------------------------------------------------------- Summary of changes in PROPHECY4f 2.0.1: 12/03/14: * random number generator RANLUX is added to provide seedable random numbers Summary of changes in PROPHECY4f 2.0: 08/08/11: * Production of unweighted events for leptonic final states * optional inclusion of a fourth fermion generation * a bug in the renormalization of the W-boson mass corrected. This leads to an increase of the partial widths of the WW-mediated channels by up to 0.5%. ------------------------------------------------------------------------------- Prophecy4f has been tested under Operating Systems: LINUX (Scientific Linux, Ubuntu) Compilers: gfortran ifort pgf90 Language: Fortran 77 (g77 is no longer supported) ------------------------------------------------------------------------------- Authors: Axel Bredenstein (until 2009 at KEK Tsukuba, Japan) Ansgar Denner Wuerzburg University, Germany (denner@physik.uni-wuerzburg.de) Stefan Dittmaier Freiburg University, Germany (stefan.dittmaier@physik.uni-freiburg.de) Alexander Mueck RWTH Aachen University, Germany (mueck@physik.rwth-aachen.de) Marcus M. Weber MPI fuer Physik, Munich, Germany (mmweber@mppmu.mpg.de) BRIEF DESCRIPTION: Prophecy4f is a Monte Carlo integrator for H -> WW/ZZ -> 4fermions. It includes: - all four-fermion final states - NLO QCD and electroweak corrections - all interferences at LO and NLO - corrections beyond NLO from heavy-Higgs effects - alternatively an Improved Born Approximation (IBA) with leading effects of the corrections - production of unweighted events for leptonic final states - optional inclusion of a 4th fermion generation (w/ or w/o leading two-loop improvements) The present version does not (yet) include: - multi-photon final-state radiation - interface to parton showers - anomalous HWW and HZZ couplings - production of unweighted events for semi-leptonic and hadronic final states (at present unweighted events only for Born and IBA for these channels) PUBLICATIONS: [1] A. Bredenstein, A. Denner, S. Dittmaier, M.M. Weber Precise predictions for the Higgs-boson decay H --> W W / Z Z --> 4 leptons Phys. Rev. D 74 (2006) 013004 [arXiv:hep-ph/0604011], [2] A. Bredenstein, A. Denner, S. Dittmaier, M.M. Weber Precision calculations for the Higgs decays H --> Z Z / W W --> 4leptons Nucl. Phys. Proc. Suppl. 160 (2006) 131 [arXiv:hep-ph/0607060]. [3] A. Bredenstein, A. Denner, S. Dittmaier, M.M. Weber Radiative corrections to the semileptonic and hadronic Higgs-boson decays H --> W W / Z Z --> 4 fermions JHEP 0702 (2007) 080 [arXiv:hep-ph/0611234], INSTALLATION: Gunzip and untar Prophecy4f-2.0.1.tar.gz (it will unpack into the directory ./Prophecy4f-2.0.1) Edit the makefile to choose compiler. The code is self-contained. No other libraries are needed. COMPILATION By issuing "make" in the command line the executable "Prophecy4f" is generated. For removing *.o files issue "make clean". EXECUTION For execution "Prophecy4f" needs an inputfile for the standard input. The program can be executed using ./Prophecy4f < inputfile All output is written to standard output or to a file if a name is specified in the inputfile. INPUT All input should be delivered via the inputfile. Its general format can be seen from the default inputfile "defaultinput". Only those values that differ from default have to be specified in the input file. So the file "sampleinput" is equivalent to "defaultinput" apart from the number of events. Do not forget the "d0" after "double precision" quantities. An inputfile has to be specified via standard input, otherwise Prophecy4f does not start. In the following we present the content of the file "defaultinput" with additional comments added. The specified values correspond to the default. # global parameters outputfile='' ! output is written to standard output ******************************************************************************* * Output will be written to standard output or a given file * if a name is provided here. The plot data will be written * to files named plot.* in directory HISTOGRAMS. 'plot' is * replaced by the file name of the output file if provided. * Unweighted events are written to the directory UNWEIGHTEDEVENTS * (*.lhe files) in the same manner. Unweighted events are also binned * into distributions written to the directory HISTUNWEIGHTED. ******************************************************************************* nevents=10000000 ! nevents: number of weighted events ******************************************************************************* * Number of weighted events, we recommend to use at least 10^7 * events for the integrated partial decay width, for histograms * about 5*10^7 should be used. ******************************************************************************* nunwevents=0 ! nevents: number of weighted events ******************************************************************************* * Number of unweighted events, which are produced in the Les Houches * event file format after the generation of 'nevents' weighted events * to find the maximal weights used for unweighting. * Unweighted events have weight 1 or very rarely weight -1. * For nunwevents>0 one has to use: * qsoftcoll = 2 (slicing) * qrecomb = 0 (no recombination) * For nunwevents>0 the two parameters are set accordingly. ******************************************************************************* lheoutput=1 ! do (not) write lhe event files: 1 (0) ******************************************************************************* * Controls whether to write unweighted events to *.lhe file in * Les Houches Event File format. * The default is lheoutput=1, i.e. do write a *.lhe file. * There will be two separate *.lhe files per channel, one for the Born * (*_born.lhe) result and one including radiative corrections. ******************************************************************************* contrib=1 ! contrib: 1=best 2=IBA 3=Born ******************************************************************************* * Specifies whether to calculate the partial decay width including * complete corrections (NLO corrections as defined by qqcd (see * below) and some higher order effects), the Improved-Born * Approximation (see publications for details) or the leading-order result ******************************************************************************* qqcd=1 ! qqcd: 0=EW 1=EW+QCD 2=QCD corrections incl. ******************************************************************************* * Specifies whether to use only EW corrections, both EW and QCD * corrections or only QCD corrections. For purely leptonic final * states only EW corrections contribute. ******************************************************************************* qsoftcoll = 1 ! qsoftcoll: 1=subtraction, 2=slicing ******************************************************************************* * Soft and collinear singularities can be treated with the subtraction * or the slicing method. For calculations of partial decay widths * subtraction is the preferred option while for the production of * unweighted events slicing has to be used. ******************************************************************************* channel= e anti-e mu anti-mu ! final state ******************************************************************************* * Final state fermions (e,mu,nue,num,dq,uq,sq,cq). The old input format * of Version 1.0 is also still supported. If more than one channel is * specified, Prophecy will calculate the different channels subsequently. * In addition one can choose the special cases: * channel= total * channel= leptonic * channel= semi-leptonic * channel= hadronic * Integrated partial widths usually do not differ between different * generations of fermions (For example, the integrated partial decay * width for H -> e anti-e e anti-e is the same as for * H -> mu anti-mu mu anti-mu). Symmetric final states * are an exception, here effects of identical particles are, * of course, taken into account (i.e., H -> e anti-e e anti-e is * different from H -> e anti-e mu anti-mu). * Moreover, in distributions (or unweighted events) fermion-mass logarithms do * show up if no photon recombination is applied, i.e. fermions of different * generations will in general yield different results. * Third generation fermions cannot be used as input. However, the partial * width including third generation particles like bottom quarks, tau * leptons or tau neutrinos do not differ in the massless approximation * from those into fermions of the first and second generation, * i.e. use e.g. H -> mu anti-mu sq anti-sq * to calculate the H -> mu anti-mu bq anti-bq partial width. * Top quarks in the final state are not supported. ******************************************************************************* qrecomb=1 ! qrecomb: 0=no recomb., 1=photon recomb. invrecomb=5d0 ! recombination condition (for qrecomb=1) ******************************************************************************* * For qrecomb=0 photons and fermions are not recombined. * For qrecomb=1 photons and fermions are recombined if their invariant mass * in GeV is smaller than invrecomb, i.e. their 4-momenta are added and * attributed to the fermion. (Note that we cannot use a proper * jet-algorithm for recombination since the lab frame of the Higgs decay * is not specified). For inclusive partial widths recombination does not * affect the result. * Independent of qrecomb we always recombine the two QCD partons with * the smallest invariant mass in events with gluon emission to form two * jets in semileptonic decays or 4 jets in hadronic decays. * When producing unweighted events for leptonic final states one should * use qrecomb=0 since recombination can be performed on the event files * after production. ******************************************************************************* qrecombcolle=0 ! 1=recomb. electrons and photons inside the slicing cone, 0=do not recomb. ******************************************************************************* * For qrecombcolle=1 photons and electrons are recombined inside the slicing * cone around electrons (for qsoftcoll = 2). In the slicing approximation * these recombined electron-photon pairs are strictly collinear. * For qrecombcolle=0 no electron-photon recombination is performed. * This option for recombination might be useful to avoid large numbers * of negative unweighted events for electron final states. ******************************************************************************* mh = 140d0 ! Higgs boson mass 1/alpha0 = 137.0359997d0 ! alpha(0) alphas = 0.119d0 ! strong coupling constant gf = 1.16637d-5 ! Fermi constant mz = 91.1876d0 ! on-shell Z-boson mass mw = 80.398d0 ! on-shell W-boson mass gammaz = 2.4952d0 ! on-shell Z-boson width (only to calculate pole mass) gammaw = 2.141d0 ! on-shell W-boson width (only to calculate pole mass) me = 0.510998910d-3 ! electron mass mmu = 105.658367d-3 ! muon mass mtau = 1.77684d0 ! tau mass md = 0.190d0 ! d-quark mass mu = 0.190d0 ! u-quark mass ms = 0.190d0 ! s-quark mass mc = 1.4d0 ! c-quark mass mb = 4.75d0 ! b-quark mass mt = 172.5d0 ! t-quark mass ******************************************************************************* * Input parameters * The values of the fermion masses are needed but the results are * practically independent of the specific values in the alpha_GF scheme * for inclusive quantities. Only if photons and fermions are not recombined * logarithms of the fermion masses may appear in distributions. * * The values of the on-shell gauge-boson masses and widths as given in the * input are only used to calculate the pole masses of the gauge bosons. * For the actual evaluation of the Higgs decay, the gauge-boson widths * are calculated from the gauge-boson pole masses and the remaining input. * The required complex gauge-boson masses are built from these calculated * widths and the pole masses. Upon using calculated W/Z widths, we can assure * that the effective branching ratios of W and Z bosons add up to 1. * More details are provided below. ******************************************************************************* qsm4=0 ! 0,1,2 4th fermion gen. off,NLO,NLO+improvements ******************************************************************************* * SM4 option for 4th generation * A 4th fermion generation of massive fermions can be optionally included * upon setting qsm4=1 or 2. For both values the full mass dependence of the * additional closed fermion loops is taken into account at NLO, comprising the * HWW/HZZ/HZA/HAA vertex corrections as well as all gauge-boson self-energies. * The qsm4=2 option additionally takes into account the leading corrections * ~ Gf^2*mf4^4, alpha_s*Gf*mf4^2 to the HVV vertices, which are taken from * hep-ph/9712330 and hep-ph9602304, respectively. ******************************************************************************* ml4 = 600d0 ! mass of l in 4th fermion generation mn4 = 600d0 ! mass of nu in 4th fermion generation md4 = 600d0 ! mass of d in 4th fermion generation mu4 = 650d0 ! mass of u in 4th fermion generation ******************************************************************************* randomseed = -1 ! use random numbers of version 2.0 ******************************************************************************* * other positive integer values or zero switch to the usage of RANLUX for * random number generation, where randomseed is used as a seed for the * random number generator to obtain statistically independet samples. ******************************************************************************* OUTPUT: All output is written to standard output or the output file specified in the input. In the output, the input used for the calculation is provided. The result of the narrow-width approximation is also given. It is simply zero below the H->WW/ZZ threshold. Along with the full result and its integration error we separately show the born result and the corresponding contributions due to EW and QCD corrections (if non-zero). HISTOGRAMS: A few default histograms corresponding to the distributions presented in the publications are produced in the directory HISTOGRAMS. They can be modified in the subroutine 'create_histo' in public.f. There, a subroutine called 'histogram' is called. Its first two parameters correspond to the range of the histogram, the third parameter to the variable of the distribution, and the number 50 refers to the number of bins. The output format of the histograms is detailed in the corresponding output files. The default histograms are: The invariant-mass distributions for final-state particles 1/2 or 3/4 for different ranges (75-85 GeV, 85-95 GeV, 50-90 GeV, 60-100 GeV). The corresponding files read: outputfile.inv12.5090 outputfile.inv12.7585 outputfile.inv12.60100 outputfile.inv12.8595 outputfile.inv34.5090 outputfile.inv34.7585 outputfile.inv34.60100 outputfile.inv34.8595 outputfile.cthv2f2: The cosine of the angle between (k(3)+k(4)) and k(2) in the Higgs rest frame, see e.g. Fig. 12 in hep-ph/0611234 (however, the particle numbering is different there). outputfile.cthv2f3: The cosine of the angle of k(3) with respect to (k(3)+k(4)) in the (k(3)+k(4)) rest frame, see e.g. Fig. 14 in hep-ph/0604011. outputfile.phitrf2f3: Transverse angle between particle 2 and 3 according to Fig. 15 in hep-ph/0604011. outputfile.cthf1f3: The cosine of the angle between particle 1 and 3 according to Fig. 16 in hep-ph/0604011. outputfile.phi: The distribution of the angle between the decay planes according to Eq. (7.9) hep-ph/0604011. The ordering of the momenta corresponds to the ordering of the final-state particles in the input file. This is only used for fully leptonic final states. outputfile.cphihad: The distribution of the absolute value of the cosine of the angle between the decay planes (one plane spanned by particles 1 and 2, the second plane spanned by particles 3 and 4), as defined in Eq. (4.2) of hep-ph/0611234. This is only used for semi-leptonic final states. The present version of the program does not provide histograms for hadronic final states and only a smaller set of distributions for semi-leptonic final states. UNWEIGHTED EVENTS: Unweighted events are written to the directory UNWEIGHTEDEVENTS in the Les Houches event file format (*.lhe). These files contain also the complete output in their header. As a cross check the unweighted events are also binned into distributions written to the directory HISTUNWEIGHTED. These histograms should be reproduced by binning the events in the *.lhe files accordingly. COMMENTS: Electromagnetic coupling constant: The electromagnetic coupling constant is derived from the Fermi constant. This procedure takes into account some higher-order effects already at tree level. Treatment of gauge-boson resonances: Gauge-boson resonances are treated using the complex-mass scheme. (A. Denner, S. Dittmaier, M. Roth, L.H. Wieders, Nucl.Phys.B724:247-294,2005, hep-ph/0505042) As input, the program expects the on-shell W/Z masses and widths. From these it calculates internally the real parts of the complex pole masses. The imaginary pars of the complex pole masses, i.e. the vector-boson widths are calculated from the pole masses and the other input parameters as described in the next paragraph. The thus calculated pole masses are then used in propagators and the complex weak mixing angle and other couplings. Decay widths of vector bosons: The decay widths of the W and Z bosons that enter the complex pole masses are calculated from the pole masses and the other input parameters as follows: If only LO order results are requested (i.e. for contrib=3) the LO widths are used. For NLO results and the IBA (contrib=1 or contrib=2) we apply the NLO widths (also for the LO sub-contribution). This ensures that the effective branching fractions for the W- and Z-boson decays in both LO and NLO add up to one. Note that in the publications we have presented the LO results with NLO widths. At LO, the difference is, of course, only a higher-order effect. Leading-logarithmic final-state radiation: Higher-order effects of collinear photon radiation are not yet supported in this version. Parton shower An interface to a parton shower is not provided yet. In fact, naively using a shower algorithm in combination with the NLO corrections would lead to a double counting of real radiation. Runtime of the program For 10^7 weighted events the program will roughly run 1-3 hours depending on the final state, hardware, and compilers. The production of 10^6 unweighted events will take about 1-2 days. Total width The total width for H -> 4 fermions can be obtained by summing over all possible final states: Gamma(H->4f) = 3*Gamma(nue anti-nue num anti-num) + 3*Gamma(e anti-e mu anti-mu) + 6*Gamma(nue anti-nue mu anti-mu) + 6*Gamma(nue anti-e mu anti-num) + 3*Gamma(nue anti-nue nue anti-nue) + 3*Gamma(e anti-e e anti-e) + 3*Gamma(nue anti-e e anti-nue) + Gamma(uq anti-uq cq anti-cq) + 3*Gamma(dq anti-dq sq anti-sq) + 4*Gamma(uq anti-uq sq anti-sq) + 2*Gamma(uq anti-dq sq anti-cq) + 2*Gamma(uq anti-uq uq anti-uq) + 3*Gamma(dq anti-dq dq anti-dq) + 2*Gamma(uq anti-dq dq anti-uq) + 6*Gamma(nue anti-nue uq anti-uq) + 9*Gamma(nue anti-nue dq anti-dq) + 6*Gamma(uq anti-uq e anti-e) + 9*Gamma(dq anti-dq e anti-e) + 12*Gamma(nue anti-e dq anti-uq). The above three blocks correspond to the leptonic, hadronic, and semi-leptonic width, respectively. EXAMPLES: Examples for inputfiles and the resulting output are given in the directories example-paper/ and example-channels/ example-paper/ This directory contains input files for the decay modes H -> ZZ -> 2e 2mu, H -> ZZ -> 4e, H -> WW -> e mu nue numu and H -> WW -> 2e 2nue with Higgs masses of 140, 170, and 200 GeV for the input parameters of Ref.[1]. For reference the corresponding output files are provided in 'out.*' and the histograms in the directory example-paper/HISTOGRAMS. The results for the WW-mediated channels differ by up to 0.5% from those given in Table 1 of Ref.[1] due to the bug in the renormalization of the W-boson mass. The ZZ-mediated channels give slightly different results from those in the publication since the top-mass effects in the Z width calculation are treated in an improved manner in Prophecy4f. example-channels/ This directory contains input and corresponding output files for all final states for a Higgs mass of 140 GeV for the default input parameter set. example-unweighted/ This directory contains input and corresponding output files for unweighted events, leptonic final states, a Higgs mass of 140 GeV and the default input parameter set. MPI: PROPHECY4f supports parallel computing using MPI. Simply edit the makefile appropriately. The program will produce nevents weighted events in total and nunwevents unweighted events per core. Large unweighted event samples: In unweighting runs with more than 10^6 unweighted events in a single run it is possible that fewer unweighted events are generated than requested. This is caused by a 32bit integer overflow and can be solved by using 64bit integers everywhere. The default size of all integers can be controlled using the following compiler options for the Fortran compiler: gfortran: -fdefault-integer-8 ifort: -integer-size 64 pgf90: -i8 These options are the default in the supplied makefile.