David G. CHARLTON$^{a}$, Guido MONTAGNA$^{b,c}$,\
Oreste NICROSINI$^{c,b}$ and Fulvio PICCININI$^{c}$

[*$^a$Royal Society University Research Fellow, School of Physics and Space Research, University of Birmingham, Birmingham B15 2TT, UK*]{}\
[*$^b$Dipartimento di Fisica Nucleare e Teorica, Università di Pavia, via A. Bassi n. 6 - 27100 PAVIA - ITALY*]{}\
[*$^c$ INFN, Sezione di Pavia, via A. Bassi n. 6 - 27100 PAVIA - ITALY*]{}

Program classification: 11.1\

[The Monte Carlo program [WWGENPV]{}, designed for computing distributions and generating events for four-fermion production in $e^+ e^- $ collisions, is described. The new version, 2.0, includes the full set of the electroweak (EW) tree-level matrix elements for double- and single-$W$ production, initial- and final-state photonic radiation including $p_T / p_L$ effects in the Structure Function formalism, all the relevant non-QED corrections (Coulomb correction, naive QCD, leading EW corrections). An hadronisation interface to [JETSET]{} is also provided. The program can be used in a three-fold way: as a Monte Carlo integrator for weighted events, providing predictions for several observables relevant for $W$ physics; as an adaptive integrator, giving predictions for cross sections, energy and invariant mass losses with high numerical precision; as an event generator for unweighted events, both at partonic and hadronic level. In all the branches, the code can provide accurate and fast results. ]{}

[*Program obtainable from:*]{} CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue)

[*Reference to original program:*]{} [WWGENPV]{}; [*Cat. no.:*]{} ACNT; [*Ref. in CPC:* ]{} [**90**]{} (1995) 141

[*Authors of original program:*]{} Guido Montagna, Oreste Nicrosini and Fulvio Piccinini

[*The new version supersedes the original program*]{}

[*Computer for which the new version is designed:*]{} DEC ALPHA 3000, HP 9000/700 series; [*Installation:*]{} INFN, Sezione di Pavia, via A. Bassi 6, 27100 Pavia, Italy

[*Keywords:*]{} $e^+ e^-$ collisions, LEP, $W$-mass measurement, radiative corrections, QED corrections, QCD corrections, Minimal Standard Model, four-fermion final states, electron structure functions, Monte Carlo integration/simulation, hadronisation.

The precise measurement of the $W$-boson mass $M_W$ constitutes a primary task of the forthcoming experiments at the high energy electron–positron collider LEP2 ($2 M_W \leq \sqrt{s} \leq 210$ GeV). A meaningful comparison between theory and experiment requires an accurate description of the fully exclusive processes $e^+ e^-  \to 4f$, including the main effects of radiative corrections, with the final goal of providing predictions for the distributions measured by the experiments.

Same as in the original program, as far as weighted event integration and unweighted event generation are concerned. Adaptive Monte Carlo integration for high numerical precision purposes is added. Optional hadronic interface in the generation branch is supplied.

The most promising methods for measuring the $W$-boson mass at LEP2 are the so called “threshold” and “direct reconstruction” methods \[5\]. For the first one, a precise evaluation of the threshold cross section is required. For the second one, a precise description of the invariant-mass shape of the hadronic system in semileptonic decays is mandatory. In order to meet these requirements, the previous version of the program has been improved by extending the class of the tree-level EW diagrams taken into account, by including $p_T / p_L $ effects both in initial- and final-state QED radiation, by supplying an hadronic interface in the generation branch.

While the semileptonic decay channels are complete at the level of the Born approximation EW diagrams ([CC11/CC20]{} diagrams), neutral current backgrounds are neglected in the fully hadronic and leptonic decay channels. QED radiation is treated at the leading logarithmic level. Due to the absence of a complete ${\cal O}
(\alpha)$/${\cal O} (\alpha_s)$ diagrammatic calculation, the most relevant EW and QCD corrections are effectively incorporated according to the recipe given in \[6\]. No anomalous coupling effects are at present taken into account.

As adaptive integrator, the code provides cross section and energy and invariant-mass losses with a relative accuracy of about 1% in 8 min on HP 9000/735. As integrator of weighted events, the code produces about $10^5$ events/min on the same system. The generation of a sample of $10^3$ hadronised unweighted events requires about 8 min on the same system.

Subroutines from the library of mathematical subprograms [NAGLIB]{} \[3\] for the numerical integrations are used in the program, when the adaptive integration branch is selected.

\[1\] CERN Program Library, CN Division, CERN, Geneva. \[2\] NAG Fortran Library Manual Mark 16 (Numerical Algorithms Group, Oxford, 1991). \[3\] T. Sjöstrand, Comp. Phys. Commun. [**82**]{} (1994) 74; Lund University Report LU TP 95-20 (1995). \[4\] F. James, Comput. Phys. Commun. 79 (1994) 111. \[5\] [*Physics at LEP2*]{}, CERN Report 96-01, Theoretical Physics and Particle Physics Experiments Divisions, G. Altarelli, T. Sjöstrand and F. Zwirner, eds., Vols. 1 and 2, Geneva, 19 February 1996. \[6\] W. Beenakker, F. Berends et al., “WW cross-sections and distributions”, in \[5\], Vol. 1, pag. 79.

Introduction
============

The precise measurement of the $W$-boson mass $M_W$ constitutes a primary task of the forthcoming experiments at the high energy electron–positron collider LEP2 ($2 M_W \leq \sqrt{s} \leq 210$ GeV). A meaningful comparison between theory and experiment requires an accurate description of the fully exclusive processes $e^+ e^-  \to 4f$, including the main effects of radiative corrections, with the final goal of providing predictions for the distributions measured by the experiments. A large effort in the direction of developing tools dedicated to the investigation of this item has been spent within the Workshop “Physics at LEP2”, held at CERN during 1995. Such an effort has led to the development of several independent four-fermion codes, both semianalytical and Monte Carlo, extensively documented in [@wweg]. [WWGENPV]{} is one of these codes, and the aim of the present paper is to describe in some detail the developments performed with respect to the original version [@cpcww], where a description of the formalism adopted and the physical ideas behind it can be found.

As discussed in [@wmass], the most promising methods for measuring the $W$-boson mass at LEP2 are the so called “threshold” and “direct reconstruction” methods. For the first one, a precise evaluation of the threshold cross section is required. For the second one, a precise description of the invariant-mass shape of the hadronic system in semileptonic and hadronic decays is mandatory. In order to meet these requirements, the previous version of the program has been improved, both from the technical and physical point of view.

On the technical side, in addition to the “weighted event integration” and “unweighted event generation” branches, the present version can also be run as an “adaptive Monte Carlo” integrator, in order to obtain high numerical precision results for cross sections and other relevant observables. In the “weighted event integration” branch, a “canonical” output can be selected, in which several observables are processed in parallel together with their most relevant moments [@wweg]. Moreover, the program offers the possibility of generating events according to a specific flavour quantum number assignment for the final-state fermions, or of generating “mixed samples”, namely a fully leptonic, fully hadronic or semileptonic sample.

On the physical side, the class of tree-level EW diagrams taken into account has been extended to include all the single resonant diagrams ([CC11/CC20]{}), in such a way that all the charged current processes are covered. Motivated by the physical relevance of keeping under control the effects of the transverse degrees of freedom of photonic radiation, both for the $W$ mass measurement and for the detection of anomalous couplings, the contribution of QED radiation has been fully developed in the leading logarithmic approximation, going beyond the initial-state, strictly collinear approximation, to include $p_T / p_L $ effects both for initial- and final-state photons. Last, an hadronic interface to [JETSET]{} in the generation branch has been added.

In the present version the neutral current backgrounds are neglected in the fully hadronic and leptonic decay channels, but this is not a severe limitation of the program since, at least in the LEP2 energy range, these backgrounds can be suppressed by means of proper invariant mass cuts. On the other hand, the semileptonic decay channels are complete at the level of the Born approximation EW diagrams ([CC11/CC20]{} diagrams), and this feature allows to treat at best those channels that are expected to be the most promising for the direct reconstruction of the $W$ mass, because free of systematics such as the “color reconnection” and the “Bose-Einstein correlation” problems.

In the development of the code, particular attention has been paid to the possibility of obtaining precise results in relatively short CPU time. As shown in [@wweg], [WWGENPV]{} is one of the most precise four fermion Monte Carlo’s from the numerical point of view. This feature allows the use of the code also for fitting purposes.

The most important new features
===============================

In the following we list and briefly describe the most important technical and physical developments implemented in the new version of [WWGENPV]{}.

TECHNICAL IMPROVEMENTS

The present version of the program consists of three branches, two of them already present in the original version but upgraded in some respect, the third one completely new.

-   Unweighted event generation branch. This branch, meant for simulation purposes, has been improved by supplying an option for an hadronisation interface (see more details later on).

-   Weighted event integration branch. This branch, intended for computation only, includes as a new feature an option for selecting a “canonical” output containing predictions for several observables and their most relevant moments together with a Monte Carlo estimate of the errors. According to the strategy adopted in [@wweg], the first four Chebyshev/power moments of the following quantities are computed: the production angle of the $W^+$ with respect to the positron beam ([TNCTHW, N=1,2,3,4]{}), the production angle $\vartheta_{d}$ of the down fermion with respect to the positron beam ([TNCTHD]{}), the decay angle $\vartheta_{d}^*$ of the down fermion with respect to the direction of the decaying $W^-$ measured in its rest frame ([TNCTHSR]{}), the energy $E_{d}$ of the down fermion normalized to the beam energy ([XDN]{}), the sum of the energies of all radiated photons ([XGN]{}) normalized to the beam energy, the lost and visible photon energies normalized to the beam energy ([XGNL]{} and [XGNV]{}), respectively, and, finally $$\begin{aligned}
    <x_m> \, = \, {1 \over \sigma} \, \int \left( { { \sqrt{s_+} +
    \sqrt{s_-} -2 M_W} \over {2 E_b} } \right) \, d \sigma\end{aligned}$$ where $s_+$ and $s_-$ are the invariant masses of the $W^+$ and $W^-$ decay products, respectively ([XMN]{}).

-   Adaptive integration branch. This new branch is intended for computation only, but offers high precision performances. On top of the importance sampling, an adaptive Monte Carlo integration algorithm is used. The code returns the value of the cross section together with a Monte Carlo estimate of the error. Moreover, if QED corrections are taken into account, also the average energy and invariant mass losses are printed. The program must be linked to NAG library for the Monte Carlo adaptive routine. Full consistency between non-adaptive and adaptive integrations has been explicitly proven.

In each of these three branches the user is asked to specify the four-fermion final state which is required. The final states at present available are those containing [CC03]{} diagrams as a subset. Their list, as appears when running the code, is the following:

    PURELY LEPTONIC PROCESSES
    [0]  ---> E+ NU_E E- BAR NU_E
    [1]  ---> E+ NU_E MU- BAR NU_MU
    [2]  ---> E- BAR NU_E MU+ NU_MU
    [3]  ---> E+ NU_E TAU- BAR NU_TAU
    [4]  ---> E- BAR NU_E TAU+ NU_TAU
    [5]  ---> MU+ NU_MU MU- BAR NU_MU
    [6]  ---> MU+ NU_MU TAU- BAR NU_TAU
    [7]  ---> MU- BAR NU_MU TAU+ NU_TAU
    [8]  ---> TAU+ NU_TAU TAU- BAR NU_TAU
    SEMILEPTONIC PROCESSES
    [9]  ---> E+ NU_E D BAR U
    [10] ---> E- BAR NU_E BAR D U
    [11] ---> E+ NU_E S BAR C
    [12] ---> E- BAR NU_E BAR S C
    [13] ---> MU+ NU_MU D BAR U
    [14] ---> MU- BAR NU_MU BAR D U
    [15] ---> MU+ NU_MU S BAR C
    [16] ---> MU- BAR NU_MU BAR S C
    [17] ---> TAU+ NU_TAU D BAR U
    [18] ---> TAU- BAR NU_TAU BAR D U
    [19] ---> TAU+ NU_TAU S BAR C
    [20] ---> TAU- BAR NU_TAU BAR S C
    HADRONIC PROCESSES
    [21] ---> D BAR U BAR D U
    [22] ---> D BAR U BAR S C
    [23] ---> S BAR C BAR D U
    [24] ---> S BAR C BAR S C
    MIXED SAMPLES
    [25] ---> LEPTONIC SAMPLE
    [26] ---> SEMILEPTONIC SAMPLE
    [27] ---> HADRONIC SAMPLE

It is worth noting that in the weighted event integration and unweighted event generation branches, besides the possibility of selecting a specific four-fermion final state, an option is present for considering three realistic mixed samples corresponding to the fully leptonic, fully hadronic or semileptonic decay channel, respectively. When the generation of a mixed sample is required, as a a first step the cross section for each contributing channel is calculated; as a second step, the unweighted events are generated for each contributing channel with a frequency given by the weight of that particular channel with respect to the total.

In the generation branch, if the hadronisation interface is not enabled, an $n$-tuple is created with the following structure:

    'X_1','X_2','EB'         ! x_{1,2} represent the
                             ! energy fractions of incoming e^- and
                             ! e^+ after ISR; EB is the beam energy;
    'Q1X','Q1Y','Q1Z','Q1LB' ! x,y,z components of the momentum
                             ! of particle 1 and the particle label
                             ! according to PDG; the final-state
                             ! fermions are assumed to be massless;
    'Q2X','Q2Y','Q2Z','Q2LB' ! as above, particle 2
    'Q3X','Q3Y','Q3Z','Q3LB' ! "  "          "    3
    'Q4X','Q4Y','Q4Z','Q4LB' ! "  "          "    4
    'AK1X','AK1Y','AK1Z'     ! x,y,z components of the momentum of
                             ! the photon from particle 1;
                             ! they are 0 if no FSR has been chosen
                             ! and/or if particle 1 is a neutrino;
    'AK2X','AK2Y','AK2Z'     ! as above, particle 2
    'AK3X','AK3Y','AK3Z'     ! "  "          "    3
    'AK4X','AK4Y','AK4Z'     ! "  "          "    4
    'AKEX','AKEY','AKEZ'     ! x,y,z components of the momentum of
                             ! the photon from the initial-state
                             ! electron; they are 0 if no ISR has
                             ! been chosen;
    'AKPX','AKPY','AKPZ'     ! as above, initial-state positron;

If the hadronisation interface is enabled, fully hadronised events are instead made available to a user routine in the [/HEPEVT/]{} format (see below).

PHYSICAL IMPROVEMENTS\
The main theoretical developments with respect to the original version concern the inclusion of additional matrix elements to the tree-level kernel and a more sophisticated treatment of the photonic radiation, beyond the initial-state, strictly collinear approximation. Moreover, an hadronisation interface to [ JETSET]{} has been also provided.

[*Tree-level EW four-fermion diagrams*]{} – In addition to double-resonant charged-current diagrams [CC03]{} already present in the previous version, the matrix element includes also the single-resonant charged-current diagrams [CC11]{} for $\mu $ and $\tau$’s in the final state, and [CC20]{} for final states containing electrons. This allows a complete treatment at the level of four-fermion EW diagrams of the semileptonic sample, which appears the most promising and cleanest for the direct mass reconstruction method due to the absence of potentially large “interconnection” effects [@wmass]. Concerning [CC20]{} diagrams, the importance sampling technique has been extended to take care of the peaking behaviour of the matrix element when small momenta of the virtual photon are involved. As a consequence of the fact that the tree-level matrix-element is computed in the massless limit, a cut on the minimum electron (positron) scattering angle must be imposed. The inclusion of such a cut eliminates the problems connected with gauge-invariance in the case of [CC20]{} processes, for which the present version does not include any so-called “reparation” scheme [@bhf; @wwcd]. Anyway, when for instance a set of “canonical cuts” [@wweg] is used, the numerical relevance of such gauge-invariance restoring schemes has been shown [@bhf; @wwcd] to be negligible compared with the expected experimental accuracy.

[*Photonic corrections*]{} – As far as photonic effects are concerned, the original version, as stated above, included only leading logarithmic initial-state corrections in the collinear approximation within the SF formalism. The treatment has been extended in a two-fold way: the contribution of final-state radiation has been included and the $p_T / p_L$ effects have been implemented both for initial- and final-state radiation. The inclusion of the transverse degrees of freedom has been achieved by generating the fractional energy $x_{\gamma}$ of the radiated photons by means of resummed electron structure functions $D(x; s)$ [@sf] ($x_{\gamma} = 1 - x$) and the angles using an angular factor inspired by the pole behaviour $1 / (p \cdot k)$ for each charged emitting fermion. This allows to incorporate leading QED radiative corrections originating from infrared and collinear singularities, taking into account at the same time the dominant kinematic effects due to non-strictly collinear photon emission, in such a way that the universal factorized photonic spectrum is recovered. According to this procedure, the leading logarithmic corrections from initial- and final-state radiation are isolated as a gauge-invariant subset of the full calculation (not yet available) of the electromagnetic corrections to $e^+ e^- \to 4f$. Due to the inclusion of $p_T$-carrying photons at the level of initial-state radiation, the Lorentz boost allowing the reconstruction of the hard-scattering event from the c.m. system to the laboratory one has been generalized to keep under control the $p_T$ effects on the beam particles. Final state radiation and $p_T / p_L$ effects are not taken into account in the adaptive integration branch.

[*Non-QED corrections*]{} – Coulomb correction is treated as in the original version on double-resonant [CC03]{} diagrams. QCD corrections are implemented in the present version in the naive form according to the recipe described in [@wweg; @wwcd]. The treatment of the leading EW contributions is unchanged with respect to the original version.

[*Hadronisation*]{} – Final-state quarks issuing from the electroweak 4-fermion scattering are not experimentally observable. An hadronisation interface is provided to the [JETSET]{} package [@jetset] to allow events to be extrapolated to the hadron level, for example for input to a detector simulation program. Specifically, the 4-fermion event structure is converted to the [/HEPEVT/]{} convention, then [JETSET]{} is called to simulate QCD partonic evolution (via routines [LUJOIN]{} and [LUSHOW]{}) and hadronisation (routine [LUEXEC]{}). In making this conversion, masses must be added to the outgoing fermions, considered massless in the hard scattering process. This is done by rescaling the fermion momenta by a single scale factor, keeping the flight directions fixed in the rest frame of the four fermion system. In the QCD evolution phase, strings join quarks coming from the same W decay. The virtuality scale of the QCD evolution is taken to be the invariant mass-squared of each evolving fermion pair. No colour reconnection is included by default, although it could be implemented by appropriate modification of routine [WWGJIF]{} if required. Bose - Einstein correlations are neglected in the present version. The resulting event structure is then made available to the user in the [/HEPEVT/]{} common block via a routine [WWUSER]{} for further analysis, such as writing out for later input to a detector simulation program. The [WWUSER]{} routine is also called at program initialisation time to allow the user to set any non-standard [JETSET]{} program options, for example, and at termination time to allow any necessary clean-up. A dummy [WWUSER]{} routine is supplied with the program. The only [JETSET]{} option which is changed by [WWGENPV]{} from its default value controls emission of gluons and photons by final-state partons[^1], turning off final-state photon emission simulation from [JETSET]{} if activated in [WWGENPV]{}, to avoid double counting.\
All the new features of the program can be switched on/off by means of separate flags, as described in the following.

Input
=====

Here we give a short explanation of the input parameters and flags required when running the program.

****

    OGEN(CHARACTER*1)

It controls the use of the program as a Monte Carlo event generator of unweighted events ([OGEN = G]{}) or as a Monte Carlo/adaptive integrator for weighted events ([OGEN = I]{}).

****

    RS(REAL*8)

The centre-of-mass energy (in GeV).

****

    OFAST(CHARACTER*1)

It selects ([OFAST = Y]{}) the adaptive integration branch, when [OGEN = I]{}. When this choice is done, the required relative accuracy of the numerical integration has to be supplied by means of the [REAL\*8]{} variable [EPS]{}.

****

    NHITWMAX(INTEGER)

Required by the Monte Carlo integration branch. It is the maximum number of calls for the Monte Carlo loop.

****

    NHITMAX(INTEGER)

Required by the event-generation branch. It is the maximum number of hits for the hit-or-miss procedure.

****

    IQED(INTEGER)

This flag allows the user to switch on/off the contribution of the initial-state radiation. If [IQED = 0]{} the distributions are computed in lowest-order approximation, while for [IQED = 1]{} the QED corrections are included in the calculation.

****

    OPT(CHARACTER*1)

This flag controls the inclusion of $p_T / p_L$ effects for the initial-state radiation. It is ignored in the adaptive integration branch where only initial-state strictly collinear radiation is allowed.

****

    OFS(CHARACTER*1)

It is the option for including final-state radiation. It is assumed that final-state radiation can be switched on only if initial-state radiation including $p_T / p_L$ effects is on, in which case final-state radiation includes $p_T / p_L$ effects as well. Ignored in the adaptive integration branch.

****

    ODIS(CHARACTER*1)

Required by the integration branch. It selects the kind of experimental distribution. For [ODIS = T]{} the program computes the total cross section (in pb) of the process; for [ODIS = W]{} the value of the invariant-mass distribution $d \sigma / d M$ of the system $d \bar u$ ([IWCH = 1]{}) or of the system ${\bar d} u$ ([IWCH = 2]{}) is returned (in pb/GeV).

****

    OWIDTH(CHARACTER*1)

It allows a different choice of the value of the $W$-width. [OWIDTH = Y]{} means that the tree-level Standard Model formula for the $W$-width is used; [OWIDTH = N]{} requires that the $W$-width is supplied by the user in GeV.

****

    NSCH(INTEGER)

The value of [NSCH]{} allows the user to choose the calculational scheme for the weak mixing angle and the gauge coupling. Three choices are available. If [NSCH=1]{}, the input parameters used are $G_F, M_W, M_Z$ and the calculation is performed at tree level. If [NSCH = 2]{} or [3]{}, the input parameters used are $\alpha(Q^2), G_F, M_W$ or $\alpha(Q^2), G_F, M_Z$, respectively, and the calculation is performed using the QED coupling constant at a proper scale $Q^2$, which is requested as further input. The recommended choice is [NSCH = 2]{}, consistently with [@wweg].

****

    OCOUL(CHARACTER*1)

This flag allows the user to switch on/off the contribution of the Coulomb correction. Unchanged with respect to the old version of the program.

****

    OQCD(CHARACTER*1)

This flag allows the user to switch on/off the contribution of the naive QCD correction.

****

    ICHANNEL(INTEGER)

A channel corresponding to a specific flavour quantum number assignment can be chosen.

****

    ANGLMIN(REAL*8)

The minimum electron (positron) scattering angle (deg.) in the laboratory frame. It is ignored when [CC20]{} graphs are not selected.

****

    SRES(CHARACTER*1)

Option for switching on/off single-resonant diagrams ([CC11]{}).

****

    OCC20(CHARACTER*1)

Option for switching on/off single-resonant diagrams when electrons (positrons) occur in the final state ([CC20]{}).

****

    OOUT(CHARACTER*1)

Option for “canonical” output containing results for several observables and their most important moments. It is active only in the Monte Carlo integration branch.

****

    OHAD(CHARACTER*1)

Option for switching on/off hadronisation interface in the unweighted event generation branch.

Test run output
===============

The typical new calculations that can be performed with the updated version of the program are illustrated in the following examples.

An example of adaptive integration is provided. The process considered is $e^+ e^- \to e^+ \nu_e d \bar u$ ([CC20]{}). The output gives the cross section, together with the energy and invariant-mass losses from initial-state radiation. “Canonical” cuts are imposed as in [@wweg]. The input card is as follows:

    OGEN = I
    RS = 190.D0
    OFAST = Y
    EPS = 1.D-2
    IQED = 1
    OPT = N
    OFS = N
    ODIS = T
    OWIDTH = Y
    NSCH = 2
    ALPHM1 = 128.07D0
    OCOUL = N
    OQCD = N
    ICHANNEL = 9
    ANGLMIN = 10.D0
    SRES = Y
    OCC20 = Y
    OOUT = N

An example of weighted event integration is provided. Here the process considered is $e^+ e^- \to \mu^+ \nu_{\mu} 
d \bar u$ ([CC11]{}). “Canonical” cuts are imposed as before. The “canonical” output is provided. The input card differs from the previous one as follows:

    RS = 175.D0
    OFAST = N
    NHITWMAX = 100000
    OPT = Y 
    OFS = Y
    OCOUL = Y
    OQCD = Y
    ICHANNEL = 13
    OCC20 = N
    OOUT = Y

An example of unweighted event generation including hadronisation is provided. A sample of 100 events corresponding to the full semileptonic channel is generated. The detailed list of an hadronised event is given. The input card differs from the first one as follows:

    OGEN = G
    RS = 175.D0
    NHITMAX = 100
    OPT = Y 
    OFS = Y
    OCOUL = Y
    OQCD = Y
    ICHANNEL = 26
    ANGLMIN = 5.D0
    OHAD = Y

Conclusions
===========

The program [WWGENPV 2.0]{} has been described. In its present version it allows the treatment of all the four-fermion reactions including the [CC03]{} class of diagrams as a subset. This means that all the semileptonic channels are complete from the tree-level diagrams point of view, whereas fully leptonic and fully hadronic channels are treated in the CC approximation. Since the most promising channels for the $W$ mass reconstruction are the semileptonic ones, the present version of the code allows a precise analysis of such data. Moreover, NC backgrounds can be suppressed by proper invariant mass cuts, so that the code is also usable for fully hadronic and leptonic events analysis, with no substantial loss of reliability. Initial- and final-state QED radiation is taken into account within the SF formalism, including finite $p_T / p_L$ effects in the leading logarithmic approximation. The Coulomb correction is included for the [CC03 ]{} graphs. Naive QCD and leading EW corrections are implemented as well. An hadronic interface to [JETSET]{} is also provided.

The code as it stands is a valuable tool for the analysis of LEP2 data, with particular emphasis to the threshold and direct reconstruction methods for the measurement of the $W$-boson mass. Speed and high numerical accuracy allow the use of the program also for fitting purposes.

The code is supported. Future releases of [WWGENPV]{} will include:

-   an interface to the code [HIGGSPV]{} [@wweg; @egdp] in order to treat all the possible four-fermion processes in the massless limit, including Higgs-boson signals;

-   implementation of anomalous couplings;

-   implementation of CKM effects;

-   the extension of the hadronic interface to [HERWIG]{} [@herwig].

[99]{}

D. Bardin, R. Kleiss et al., “Event generators for WW physics”, in [*Physics at LEP2*]{}, CERN [**96-01**]{}, Theoretical Physics and Particle Physics Experiments Divisions, G. Altarelli, T. Sjöstrand and F. Zwirner, eds., Vol. 2, pag. 3, Geneva, 19 February 1996.

G. Montagna, O. Nicrosini and F. Piccinini, Comput. Phys. Commun. [**90**]{} (1995) 141.

Z. Kunszt, W.J. Stirling et al., “Determination of the mass of the $W$ boson”, in [*Physics at LEP2*]{}, CERN [**96-01**]{}, Theoretical Physics and Particle Physics Experiments Divisions, G. Altarelli, T. Sjöstrand and F. Zwirner, eds., Vol. 1, pag. 141, Geneva, 19 February 1996.

E. N. Argyres et al., Phys. Lett. [**B358**]{} (1995) 339.

W. Beenakker, F. Berends et al., “WW cross-sections and distributions”, in [*Physics at LEP2*]{}, CERN [**96-01**]{}, Theoretical Physics and Particle Physics Experiments Divisions, G. Altarelli, T. Sjöstrand and F. Zwirner, eds., Vol. 1, pag. 79.

T. Sjöstrand, Comp. Phys. Commun. [**82**]{} (1994) 74; Lund University Report LU TP 95-20 (1995).

M.L. Mangano, G. Ridolfi et al., “Event Generators for Discovery Physics”, in [*Physics at LEP2*]{}, CERN [**96-01**]{}, Theoretical Physics and Particle Physics Experiments Divisions, G. Altarelli, T. Sjöstrand and F. Zwirner, eds., Vol.2, pag. 299.

G. Marchesini, B. R. Webber et al., Comput. Phys. Commun. [**67**]{} (1992) 465.


     HADRONISATION VIA JETSET
     WWGJIF: Initialising WWGENPV to JETSET interface
     PHOTON FSR WILL BE HANDLED BY WWGENPV:
     TURNING OFF PHOTON FSR FROM JETSET
    1
     SQRT(S) =  175.0  GEV
     M_Z =  91.1888  GEV
     G_Z =  2.4974  GEV
     M_W =  80.23  GEV
     G_W =  2.08823657515165  GEV
     STH2 =  .2310309124510679

     GVE =  -1.409737267299689E-02
     GAE =  -.185794027211796
     GWF =  .230409927395451
     GWWZ =  -.571479454308384


                                Event listing (summary)

        I  particle/jet KS     KF orig    p_x      p_y      p_z       E        m

        1  !e+!         21    -11    0     .000     .000  -87.500   87.500     .001
        2  !e-!         21     11    0     .000     .000   87.500   87.500     .001
        3  !e+!         21    -11    1     .000     .000  -87.500   87.500     .001
        4  !e-!         21     11    2     .000     .000   87.500   87.500     .001
        5  gamma         1     22    1     .000     .000     .000     .000     .000
        6  nu_e          1     12    0   45.589   -8.504   -7.296   46.945     .000
        7  e+            1    -11    0  -32.518    1.009  -24.213   40.555     .001
        8  gamma         1     22    7    -.063    -.003    -.054     .083     .000
        9  (c~)      A  11     -4    0   -6.482    5.087  -14.629   16.844    1.350
       10  (g)       V  11     21    0    -.912    -.166   -1.330    1.621     .000
       11  (g)       A  11     21    0   -1.717    2.148     .149    2.754     .000
       12  (g)       V  11     21    0    -.404    -.150    -.153     .457     .000
       13  (g)       A  11     21    0     .524     .257    -.485     .759     .000
       14  (g)       V  11     21    0     .568    5.813   -3.909    7.028     .000
       15  (g)       A  11     21    0    -.833     .123    -.634    1.054     .000
       16  (g)       V  11     21    0   -1.616    -.218     .984    1.904     .000
       17  (g)       A  11     21    0    -.893    -.594    -.345    1.127     .000
       18  (g)       V  11     21    0    -.064   -1.133     .124    1.141     .000
       19  (u)       A  11      2    0   -1.275    -.657    4.823    5.032     .006
       20  (u~)      V  11     -2    0   -1.276     .758    3.201    3.528     .006
       21  (g)       A  11     21    0     .733    -.103    2.158    2.281     .000
       22  (g)       V  11     21    0     .691    -.234    2.326    2.438     .000
       23  (g)       A  11     21    0     .410   -1.788   16.927   17.027     .000
       24  (s)       V  11      3    0    -.461   -1.646   22.354   22.420     .199
       25  (string)     11     92    9  -13.104   10.511  -15.404   39.722   32.532
       26  (D~0)        11   -421   25   -6.057    4.073  -13.996   15.894    1.865
       27  (pi0)        11    111   25   -1.112    1.280    -.302    1.728     .135
       28  (rho-)       11   -213   25   -1.158    1.158   -2.172    2.803     .676
       29  (omega)      11    223   25    -.792     .558     .401    1.303     .774
       30  (Sigma*~+)   11  -3114   25     .123    2.038   -1.332    2.787    1.351
       31  (K*-)        11   -323   25     .319    1.963   -1.639    2.729     .896
       32  (Delta+)     11   2214   25    -.155    1.330   -1.314    2.263    1.266
       33  (rho-)       11   -213   25   -1.026     .221     .345    1.292     .670
       34  (pi0)        11    111   25    -.256     .036    -.546     .619     .135
       35  (rho0)       11    113   25    -.488    -.118     .538    1.103     .822
       36  pi+           1    211   25    -.420     .013    -.275     .521     .140
       37  pi-           1   -211   25    -.612    -.620     .002     .882     .140
       38  (rho+)       11    213   25    -.474   -1.082    1.048    1.662     .520
       39  (rho0)       11    113   25    -.997    -.339    3.839    4.136    1.122
       40  (string)     11     92   20     .096   -3.014   46.967   47.695    7.733
       41  p~-           1  -2212   40    -.233     .669    3.532    3.723     .938
       42  p+            1   2212   40     .259    -.320    2.633    2.826     .938
       43  (Delta~--)   11  -2224   40    -.208    -.282    7.298    7.431    1.357
       44  pi+           1    211   40     .568    -.518    3.830    3.909     .140
       45  (Lambda0)    11   3122   40    -.290   -2.562   29.673   29.806    1.116
       46  (K*+)        11    323   26   -3.673    2.525   -9.054   10.129     .875
       47  (rho-)       11   -213   26   -2.384    1.548   -4.942    5.765     .856
       48  gamma         1     22   27   -1.055    1.186    -.310    1.617     .000
       49  gamma         1     22   27    -.058     .094     .008     .111     .000
       50  pi-           1   -211   28    -.837    1.095   -1.923    2.370     .140
       51  (pi0)        11    111   28    -.321     .063    -.249     .433     .135
       52  pi+           1    211   29    -.610     .314     .197     .727     .140
       53  pi-           1   -211   29    -.236     .248     .217     .429     .140
       54  (pi0)        11    111   29     .055    -.005    -.014     .146     .135
       55  (Lambda~0)   11  -3122   30     .085    1.705    -.918    2.237    1.116
       56  pi+           1    211   30     .038     .333    -.414     .551     .140
       57  (K~0)        11   -311   31     .462    1.760   -1.507    2.414     .498
       58  pi-           1   -211   31    -.143     .203    -.133     .315     .140
       59  n0            1   2112   32     .123     .910   -1.024    1.665     .940
       60  pi+           1    211   32    -.277     .420    -.290     .598     .140
       61  pi-           1   -211   33     .005     .082     .159     .227     .140
       62  (pi0)        11    111   33   -1.031     .138     .186    1.065     .135
       63  gamma         1     22   34    -.201    -.017    -.301     .362     .000
       64  gamma         1     22   34    -.055     .053    -.245     .257     .000
       65  pi-           1   -211   35    -.071    -.134     .622     .655     .140
       66  pi+           1    211   35    -.417     .016    -.084     .448     .140
       67  pi+           1    211   38     .032    -.277     .386     .497     .140
       68  (pi0)        11    111   38    -.506    -.804     .661    1.166     .135
       69  pi-           1   -211   39    -.186     .113     .094     .275     .140
       70  pi+           1    211   39    -.811    -.452    3.745    3.861     .140
       71  p~-           1  -2212   43    -.135    -.544    5.493    5.600     .938
       72  pi-           1   -211   43    -.073     .262    1.805    1.831     .140
       73  n0            1   2112   45    -.262   -2.385   26.596   26.721     .940
       74  (pi0)        11    111   45    -.028    -.177    3.077    3.085     .135
       75  (K0)         11    311   46   -2.419    1.634   -6.536    7.176     .498
       76  pi+           1    211   46   -1.253     .891   -2.517    2.953     .140
       77  pi-           1   -211   47    -.404     .604   -1.633    1.792     .140
       78  (pi0)        11    111   47   -1.980     .945   -3.310    3.973     .135
       79  gamma         1     22   51    -.223     .051    -.091     .246     .000
       80  gamma         1     22   51    -.098     .012    -.158     .187     .000
       81  gamma         1     22   54     .048    -.066     .004     .082     .000
       82  gamma         1     22   54     .006     .062    -.017     .064     .000
       83  p~-           1  -2212   55     .064    1.274    -.756    1.755     .938
       84  pi+           1    211   55     .021     .431    -.161     .482     .140
       85  (K_S0)       11    310   57     .462    1.760   -1.507    2.414     .498
       86  gamma         1     22   62    -.111     .044    -.011     .120     .000
       87  gamma         1     22   62    -.920     .094     .197     .945     .000
       88  gamma         1     22   68    -.034    -.065     .012     .074     .000
       89  gamma         1     22   68    -.472    -.740     .649    1.091     .000
       90  gamma         1     22   74    -.035    -.088    2.449    2.451     .000
       91  gamma         1     22   74     .007    -.089     .628     .634     .000
       92  (K_S0)       11    310   75   -2.419    1.634   -6.536    7.176     .498
       93  gamma         1     22   78   -1.877     .868   -3.149    3.768     .000
       94  gamma         1     22   78    -.103     .077    -.160     .205     .000
       95  pi-           1   -211   85     .270     .383    -.379     .618     .140
       96  pi+           1    211   85     .192    1.377   -1.128    1.796     .140
       97  pi+           1    211   92    -.563     .463   -2.034    2.165     .140
       98  pi-           1   -211   92   -1.857    1.171   -4.502    5.011     .140
                       sum:   .00          .000     .000     .000  175.000  175.000
     NHIT =  100

     XSECT FOR UNWEIGHTED EVENTS

     EFF =  1.887112905965163E-03
     XSECT =  6.79360646147459 +-  .6787193283232224 (PB)
     NBIAS/NMAX =  .0
      USER TERMINATION
      A TOTAL OF  100 EVENTS WERE GENERATED
      THE TOTAL CROSS-SECTION WAS: 6.793606281280517E-09 MB

[^1]: parameter [MSTJ(41)]{}
