[Paper Review] The event generator for the two-photon process e^+e^- --> e^+e^- R (J^{PC}=0^{-+}) in the single-tag mode

V. P. Druzhinin, L. A. Kardapoltsev+1 more|arXiv (Cornell University)|Oct 28, 2010

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the GGRESRC Monte Carlo event generator for simulating two-photon processes e⁺e⁻ → e⁺e⁻R (R = pseudoscalar meson) in the single-tag mode, where one final-state electron is detected at large angle. It implements full radiative corrections, including initial- and final-state radiation, and accurately models transition form factors via the vector dominance model, enabling high-precision measurements of meson-photon form factors in experiments like BABAR and KEDR.

ABSTRACT

The Monte Carlo event generator GGRESRC is described. The generator is developed for simulation of events of the two-photon process e^+e^- --> e^+e^- R, where R is a pseudoscalar resonance, \pi^0, \eta, \eta', \eta_c, or \eta_b. The program is optimized for generation of two-photon events in the single-tag mode. For single-tag events, radiative correction simulation is implemented in the generator including photon emission from the initial and final states.

Motivation & Objective

• To develop an efficient event generator for two-photon resonance production e⁺e⁻ → e⁺e⁻R in the single-tag mode, where one electron is detected at large angle.
• To enable high-precision measurements of meson-photon transition form factors by including radiative corrections in the simulation.
• To support experimental analyses at BABAR and KEDR by accurately modeling the kinematics and dynamics of pseudoscalar meson production via virtual photons.
• To implement both the constant form factor and vector dominance model (VDM) for the transition form factor F(Q²₁, Q²₂), with Λ = mρ, mJ/ψ, or mΥ depending on the resonance.
• To ensure simulation accuracy by including interference terms (τTT) and full four-dimensional phase space integration with invariant variables t₁, t₂, s₁, s₂.

Proposed method

• The generator uses four-dimensional Monte Carlo integration over invariants t₁ = −Q²₁, t₂ = −Q²₂, s₁, s₂ to simulate the differential cross section for pseudoscalar resonance production.
• It implements the Born cross section using the Gram determinant ∆₄ and the function B, which encodes the spin and polarization structure of virtual photons.
• Radiative corrections are simulated via initial-state radiation (ISR) and final-state radiation (FSR), with dedicated subroutines GGRFSR and GGRINV for photon emission and invariant generation.
• The transition form factor is modeled using the vector dominance model: |F|² = 1 / [(1 + Q²₁/Λ²)²(1 + Q²₂/Λ²)²], with Λ set to mρ, mJ/ψ, or mΥ for π⁰, ηc, or ηb respectively.
• The generator uses the CERN library routines RANLUX for random number generation and DZEROX for root-finding in phase space integration.
• Final-state decays of π⁰, η, η′, ηc, and ηb are simulated using known branching fractions and phase space models, with dedicated subroutines like GGRPI0D, GGRETCD, and GGRSPC3.

Experimental results

Research questions

• RQ1 How can a high-precision event generator be constructed for two-photon processes in the single-tag mode, where one electron is detected at large angle?
• RQ2 What is the impact of the τTT interference term on the differential cross section dσ/dQ²₂, especially at large Q²₂?
• RQ3 How accurately can the vector dominance model describe the Q² dependence of the transition form factor F(Q²₁, Q²₂) in e⁺e⁻ → e⁺e⁻R processes?
• RQ4 To what extent do initial- and final-state radiation effects affect the measured form factor in single-tag experiments?
• RQ5 How can four-dimensional phase space integration be efficiently performed to maximize event generation efficiency in single-tag configurations?

Key findings

• The GGRESRC generator successfully simulates two-photon processes e⁺e⁻ → e⁺e⁻R in the single-tag mode with full radiative corrections, including ISR and FSR, enabling precision measurements at the ∼1% level.
• The inclusion of the τTT interference term is essential for accurate simulation, as it contributes significantly to dσ/dQ²₂ at large Q²₂, especially in single-tag events.
• The vector dominance model with Λ = mρ (0.7755 GeV) accurately describes the Q²₂ dependence of |F|² for π⁰, η, and η′, as shown in Fig. 2.
• For resonances with broad widths like ηc and ηb, the generator uses Breit-Wigner distributions to correctly model their mass distributions.
• The generator has been validated and used in real experimental analyses, including the BABAR measurements of transition form factors for π⁰, η, η′, and ηc.
• The event generation efficiency is significantly improved by fixing Q²₂ early in the generation process using the t₂, t₁, s₁, s₂ ordering, as implemented via the GALUGA-inspired integration method.