STARlight: A Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions

Spencer R. Klein; Joakim Nystrand; Janet Seger; Yuri Gorbunov; Joey Butterworth

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STARlight: A Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions

Spencer R. Klein, Joakim Nystrand, Janet Seger, Yuri Gorbunov, Joey Butterworth

arXiv:1607.03838v2Jul 13, 2016hep-phnucl-ex

TL;DR

UPCs require modeling electromagnetic interactions while excluding hadronic collisions, with geometry shaping the resulting final states. STARlight calculates cross-sections and generates decayed Monte Carlo events for two-photon and photonuclear processes. It reproduces important features of RHIC and LHC data, while specific approximations limit some kinematic descriptions and resonance modeling.

Problem
UPC studies need cross-sections and detector-efficiency events for varied two-photon and photonuclear final states, whose production depends strongly on collision geometry.
Method
STARlight integrates impact-parameter-dependent photon fluxes subject to no hadronic interaction, builds look-up tables, and generates Monte Carlo events with particle decays and spin treatment.
Results
STARlight has been found to describe most important features of RHIC and LHC data very well and supports acceptance and efficiency calculations.
Takeaways & Limitations
STARlight provides a versatile event generator for UPC cross-sections, kinematic distributions, and detector acceptance and efficiency studies.
Takeaways & Limitations
The EPA treatment of lepton pairs gives lower average pT than data, while higher-order corrections and their kinematic effects are not well known; the ρ′ is represented by a single resonance because its details are poorly known.

Abstract

from arXiv · show

Ultra-peripheral collisions (UPCs) have been a significant source of study at RHIC and the LHC. In these collisions, the two colliding nuclei interact electromagnetically, via two-photon or photonuclear interactions, but not hadronically; they effectively miss each other. Photonuclear interactions produce vector meson states or more general photonuclear final states, while two-photon interactions can produce lepton or meson pairs, or single mesons. In these interactions, the collision geometry plays a major role. We present a program, STARlight, that calculates the cross-sections for a variety of UPC final states and also creates, via Monte Carlo simulation, events for use in determining detector efficiency.

Program summary

STARlight calculates ultra-peripheral-collision cross-sections and generates Monte Carlo events for detector-efficiency studies. It uses selectable look-up-table accuracy and includes particle decays and final angular distributions.

Program summary: STARlight is distributed as a C++ program for PCs and workstations running Linux, with external PYTHIA 8.2 and DPMJET 3.0 routines needed for some final states.The distributed version contains 53,188 lines and 2,965,010 bytes, including test data.
Program summary: STARlight calculates cross-sections for ultra-peripheral-collision reactions as functions of W, Y, and pT, then generates Monte Carlo events.The events support cross-section studies under kinematic constraints and detector-efficiency determination.
Program summary: The program generates a two-dimensional production-cross-section look-up table as a function of final-state rapidity and mass.For certain final states, it also uses a rapidity-dependent transverse-momentum look-up table.
Program summary: Look-up-table dimensions are selectable, allowing users to choose the desired accuracy when generating final states.Particle decays and final angular distributions are calculated for each event.

1. Introduction

STARlight models electromagnetic interactions in ultra-peripheral collisions, where nuclei avoid hadronic contact, and simulates two-photon and photonuclear final states. It incorporates collision geometry, interference, multiple interactions, nuclear structure, and updated parameterizations.

1. Introduction: In ultra-peripheral collisions, nuclei interact electromagnetically through two-photon or photonuclear processes while physically missing each other.STARlight simulates single mesons, vector mesons, lepton pairs, and general photonuclear interactions.
1. Introduction: Photonuclear vector-meson production is treated coherently at small momentum transfer and incoherently at higher transverse momentum.Coherent amplitudes from target nucleons are handled using a Glauber formalism.
1. Introduction: Photon-emitter and target interchange contributes interference: for symmetric collisions, negative-parity vector-meson amplitudes subtract and production vanishes as pT approaches zero.For proton-antiproton collisions, the corresponding CP transformation makes the amplitudes add for CP-positive vector mesons.
1. Introduction: Multiple interactions between one ion pair enable studies of correlations among several final-state particles and require unitarization for multiple subreactions.STARlight calculates and generates interactions accompanied by mutual Coulomb excitation, involving three or four photons.
1. Introduction: STARlight supports dissimilar nuclei, selectable Z and A, several nuclear-density models, asymmetric beam energies, and laboratory-frame boosts.The code is optimized for RHIC and LHC energies, while other energy ranges should be usable.
1. Introduction: STARlight 2.2 replaces some A^1/3-based nuclear radii with measured values, reducing gold-beam cross-sections by about 7% while barely affecting lead beams.The γ + p → J/ψ + p and γ + p → Υ + p cross-section parameterizations were also improved.

2. Photon spectra and form factors

STARlight computes photon spectra and no-hadronic-interaction probabilities in impact-parameter space, using nuclear form factors and collision-specific models. The non-interaction prescription materially changes the usable two-photon luminosity.

2. Photon spectra and form factors: The photon spectrum is obtained by integrating the equivalent-photon flux over impact parameters while requiring that the projectiles do not interact hadronically.For photonuclear interactions, the flux is treated with a corresponding no-hadronic-interaction condition.
2. Photon spectra and form factors: The two-photon cross-section integrates both photon densities over photon energies and transverse positions, weighted by the probability of no hadronic interaction.The separation |b_1 − b_2| is the impact parameter between the nuclei.
2. Photon spectra and form factors: No-hadronic-interaction probabilities are implemented differently for nucleus-nucleus, proton-nucleus, and proton-proton collisions.These probabilities reduce usable luminosity, and the resulting cross-section is sensitive to how non-interaction is defined.
2. Photon spectra and form factors: For nucleus-nucleus collisions, P_NOHAD uses a nuclear overlap function derived from Woods-Saxon density profiles and nucleon-nucleon cross-sections parameterized for pp collisions.For proton-nucleus collisions, the hadronic interaction probability is also calculated using the Glauber model.
2. Photon spectra and form factors: 20%: applying P_NOHAD(b) can reduce γγ luminosities by up to 20% relative to the simpler b > 2R_A requirement.The difference reflects substantial residual hadronic-interaction probability at impact parameters larger than 2R_A.
2. Photon spectra and form factors: The nuclear form factor uses a hard-sphere convolution with a Yukawa potential, while light nuclei use a Gaussian form factor and proton collisions use a dipole form factor.The Yukawa range is 0.7 fm, and the resulting form factor is close to a Woods-Saxon distribution.

3. Two-photon interactions

STARlight models two-photon production through invariant-mass, rapidity, and transverse-momentum distributions, then generates decayed final states for several lepton and meson channels. Its lepton-pair treatment is useful for most purposes but uses a lowest-order EPA approximation with known kinematic and higher-order limitations.

Two-photon kinematics: STARlight transforms two-photon luminosity into invariant-mass and rapidity distributions, using user-selected W and |Y| integration limits.The resulting lookup table provides the basis for invariant-mass and rapidity sampling.
Two-photon kinematics: Final-state transverse momentum is the vector sum of the two photon transverse momenta and is sampled using rejection sampling.The photon azimuthal angle is assumed uniformly distributed, while its pT distribution depends on photon energy and the nuclear form factor.
Implemented final states: Three two-photon interaction classes are implemented: lepton pairs, single mesons, and γγ →ρ0ρ0 with subsequent ρ decays.The ρ0ρ0 mode is simulated at threshold with σρ0ρ0 = 100 nb to represent an observed two-photon excess.
Lepton pairs: Lepton pairs use a lowest-order equivalent photon approximation in which photons are treated as massless.The predicted kinematic distributions generally agree with data, but the average pT is lower; higher-order corrections are expected and their kinematic effects are not well known.
Lepton pairs: Lepton-pair cross-sections use the Breit-Wheeler formula, and accurate integration near threshold requires at least 100 W bins per GeV/c^2.The cross-section falls rapidly with increasing W in the W ≥2m region.
Mesonic final states: Single-meson production depends on Γγγ, mass, total width, and spin, and STARlight simulates spin 0 and spin 2 mesons using standard Γγγ values.The program supports narrow and wide resonances, with user-selectable W limits for wide resonances.

4. Overview of photonuclear interactions

STARlight models photonuclear production of vector mesons and general final states using parameterized photon-proton cross-sections, nuclear form factors, and configurable event-generation choices.

STARlight simulates photoproduction and decay for ρ, ω, φ, J/ψ, ψ′, Υ(1S), Υ(2S), and Υ(3S), plus general photonuclear interactions using DPMJET III.
Photon-proton cross-sections for vector mesons are parameterized versus Wγp, with Pomeron exchange dominant and meson exchange included for ρ and ω.
Near-threshold suppression supplements the power law for J/ψ, ψ′, and Υ production, while excited-state shapes use corresponding mass substitutions or coupling-based scalings.
The ρ′ is represented by a single resonance with mass 1540 MeV and width 570 MeV because its overlapping-resonance structure and couplings are poorly known.
Coherent production uses nuclear form factors, while transverse-momentum modeling uses photon fluxes constrained by the no-hadronic-interaction condition and selectable narrow- or wide-resonance treatments.
Using a wide resonance reduces the ρ0 cross-section by about 5% in heavy-ion collisions, while event generation still uses a Breit-Wigner invariant-mass distribution.

5. Photonuclear breakup

STARlight models photonuclear breakup as an impact-parameter-dependent accompaniment to UPC reactions, with selectable neutron-emission modes and beam-dependent excitation limitations.

Photonuclear breakup is experimentally useful because emitted neutrons near beam rapidity can be detected in forward calorimeters.
Breakup probabilities multiply the two-photon luminosity and photonuclear cross-section at each impact parameter, incorporating multiple independent photon interactions without new integrals.
STARlight supports Xn breakup with any neutron multiplicity and GDR excitation usually producing single-neutron emission, with one- or two-nucleus selection controlled by BREAKUPMODE.
Excitation probabilities are unitarized because the non-unitarized P1(b) can exceed one at sufficiently high collision energies.
The excitation code works only for gold or lead beams; proton-proton and proton-nucleus interactions support only modes without Coulomb-excitation restrictions.
Photons below 30 MeV/c in the target rest frame are assigned to GDR excitation and single-neutron emission, whereas higher energies produce higher excitations and multiple neutrons.

6. Program overview

STARlight separates cross-section calculation from Monte Carlo event generation, using look-up tables to sample kinematics and rapidly produce decayed final states.

STARlight first calculates cross-sections and kinematic distributions, then uses the results to simulate nuclear-interaction events.
Look-up table structure: Its primary two-dimensional look-up table stores the event mass–rapidity distribution d2N/dYdW, with mass shapes selected according to the interaction type.
Look-up table structure: Photonuclear channels may use a second d2N/dpTdY table, while γγ transverse momentum is generated semi-analytically without a table.
Look-up table structure: Table ranges and bin counts are user settable, and normalized integral tables enable random sampling with linear interpolation.
The C++ package includes build, configuration, documentation, conversion, and analysis components, including ROOT utilities for trees and histograms.
Event production selects energies and rapidities, creates parent systems, decays them when appropriate, boosts daughters to the laboratory frame, and writes ASCII output.

7. Description of input data

STARlight input data configure the collision beams, production channels, nuclear breakup, interference, kinematic cuts, cross-section methods, event generation, and external interfaces. Supported channels include two-photon and vector-meson production.

Beam parameters: Beam inputs specify each projectile’s charge, atomic number, and Lorentz boost for the two colliding nuclei.The distributed examples use Z=82, A=208, and γ=1470 for both beams.
Kinematic ranges: W and rapidity settings define the lookup-table ranges and binning used for cross-section calculations.The input includes minimum and maximum γγ energy, W bins, maximum rapidity, and rapidity bins.
Production modes: PROD_MODE selects coherent or incoherent vector-meson production and photonuclear exchange modes, including DPMJET-based options.Modes distinguish narrow or wide resonances, incoherent production, and one- or two-photon exchange configurations.
Event and analysis controls: Optional inputs configure photon-emission interference, decay-product pT and pseudorapidity cuts, γγ cross-section methods, and event counts and random seeds.Interference affects very small transverse momentum, while cuts can constrain decay products in pT and η.
External interfaces: External interfaces support DPMJET and PYTHIA settings, including photon-energy limits, PYTHIA parameters, and optional full event-record output.PYTHIA handles selected two-photon decays, while DPMJET is required for some photonuclear final states.

8. Description of output

STARlight writes event information to the ASCII file slight.out, recording event-level, vertex-level, and daughter-track data. The output format includes identifiers, kinematics, ancestry, and particle codes.

Event records: Each event begins with an EVENT line containing the event number, track count, and vertex count.STARlight currently produces events with no more than one vertex.
Vertex records: A VERTEX line records the vertex four-vector, vertex number, process number, parent track, and daughter count.The process number is always set to 0, and primary vertices have parent track 0.
Track records: TRACK lines record particle identifiers, momentum components, event and track indices, terminating vertex, and PDG codes.The format includes Geant and Particle Data Group identifiers plus track ancestry through the stopping vertex.

9. Description of test data

The paper identifies the parameters used to generate Fig. 1 and notes that additional figure-generation input files are included in the code distribution. These materials support reproduction of the test figure.

Figure-generation parameters: The parameters used to produce Fig. 1 are specified in the accompanying input description.The passage directly links the test-data settings to Fig. 1.
Test-data package: The test-data materials connect documented parameters with distributed configuration files for figure production.Together, these passages identify both the settings and their supplementary files.
Reproducibility files: Additional input files used to generate the paper’s figures are available in the distribution’s config folder.The files are included with the code distribution.

10. Summary

STARlight is presented as a versatile C++ event generator for relativistic heavy-ion UPCs. Its outputs have been tested against RHIC and LHC data and used for detector acceptance and efficiency corrections.

Scope: STARlight simulates a variety of important ultra-peripheral collisions between relativistic heavy nuclei.The program is implemented as versatile C++ code.
Validation: STARlight outputs cross-sections, rapidity distributions, and pT distributions that have been tested against experimental results.The reported tests cover results from RHIC and the LHC.
Experimental use: Experiments have used STARlight-generated events to calculate acceptance and efficiency corrections.The paper emphasizes reasonable phase-space distributions for produced particles in these calculations.