[Paper Review] GRAPE-Dilepton (Version 1.1) A generator for dilepton production in ep collisions

K. Abe|arXiv (Cornell University)|Dec 4, 2000

Particle physics theoretical and experimental studies10 references66 citations

TL;DR

GRAPE-Dilepton (v1.1) is a Monte Carlo event generator for precise simulation of dilepton production in ep collisions using exact tree-level electroweak matrix elements. It includes γγ, γZ⁰, Z⁰Z⁰, and internal conversion processes, accounts for Z⁰ on/off-shell production, and features full interference effects in e±e± final states, with interfaces to PYTHIA and SOPHIA for full hadronic final states.

ABSTRACT

Abstract GRAPE-Dilepton is a Monte Carlo event generator for dilepton production in ep collisions. The cross-section calculation is based on the exact matrix elements in the electroweak theory at tree level. The dilepton productions via γγ, γZ^0 , Z^0 Z^0collisions and via photon internal conversion are taken into account. In addition, the effects of the Z^0on/off-shell production are also included. The relevant Feynman amplitudes are generated by the automatic calculation system GRACE. The calcul... Title of program: GRAPE-Dilepton (v1.1) Catalogue Id: ADNR_v1_0 Nature of problem A precise estimation of the cross-section of the electroweak dilepton production in ep collisions is required in various physics analyses, where 8~48 Feynman diagrams can contribute. Versions of this program held in the CPC repository in Mendeley Data ADNR_v1_0; GRAPE-Dilepton (v1.1); 10.1016/S0010-4655(00)00246-0 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

Motivation & Objective

• To provide a precise Monte Carlo generator for dilepton production in ep collisions beyond the two-photon Bethe-Heitler approximation.
• To include all relevant electroweak processes: γγ, γZ⁰, Z⁰Z⁰, and internal conversion (CO) diagrams.
• To account for interference effects in e±e± final states, which are missing in prior generators like LPAIR and EPVEC.
• To cover the full kinematical region of the proton vertex via elastic, quasi-elastic, and deep inelastic scattering (DIS) channels.
• To enable accurate simulation of initial and final state radiation (ISR/FSR) and to interface with PYTHIA and SOPHIA for complete event generation.

Proposed method

• Uses the GRACE automatic amplitude calculation system to generate exact tree-level helicity amplitudes for all relevant electroweak diagrams.
• Divides the proton vertex kinematics into three regions: elastic (Mhad = Mp), quasi-elastic (Q²p < Q²min or Mp + Mπ⁰ < Mhad < Mcut), and DIS (Q²p > Q²min and Mhad > Mcut).
• Applies dipole form factors for the proton vertex in elastic processes and parameterized hadron tensors (Brasse et al. for Mhad < 2 GeV, ALLM97 for Mhad > 2 GeV) in quasi-elastic processes.
• Uses PDFLIB with QCD scale Q²p for parton densities in DIS, and PYTHIA for proton remnant and hadronization.
• Implements ISR and FSR using structure functions and parton shower methods.
• Supports user-defined cuts via input cards for dilepton mass, final-state lepton kinematics, and detector-like acceptance.

Experimental results

Research questions

• RQ1 How do γZ⁰ and Z⁰Z⁰ contributions affect dilepton cross sections in ep collisions compared to dominant two-photon processes?
• RQ2 What is the impact of internal conversion (CO) diagrams on dilepton production at low invariant masses?
• RQ3 How do interference effects in e±e± final states influence the total cross section and kinematic distributions?
• RQ4 To what extent do Z⁰ on-shell and off-shell production contribute in the high-mass region?
• RQ5 How accurately can the full kinematical region of the proton vertex (elastic, quasi-elastic, DIS) be modeled with consistent matrix elements and hadronic final states?

Key findings

• The generator includes all tree-level electroweak diagrams for dilepton production, including γγ, γZ⁰, Z⁰Z⁰, and internal conversion, with full interference in e±e± final states.
• The Z⁰ on/off-shell production is accurately modeled, with significant contributions in the high-mass region.
• The dipole form factor GpE(Q²p) = (1 + Q²p/0.71 GeV²)⁻² is used for the elastic proton vertex, ensuring accurate low-Q²p behavior.
• For quasi-elastic processes, the hadron tensor is parameterized using Brasse et al. (Mhad < 2 GeV) and ALLM97 (Mhad > 2 GeV), based on experimental γ*p cross-section data.
• The DIS region is simulated with PDFLIB and PYTHIA, valid for u ≳ 25 GeV², where u is the virtuality of the u-channel quark.
• Event generation runs at ~1 msec per event, with cross-section integration taking ~1 hour, enabling efficient precision studies.