[Paper Review] Fully Differential Monte-Carlo Generator Dedicated to TMDs and Bessel-Weighted Asymmetries

M. Aghasyan, H. Avakian|arXiv (Cornell University)|Mar 15, 2013

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper presents a fully differential Monte Carlo generator for semi-inclusive deep inelastic scattering (SIDIS) that models quark intrinsic transverse momentum within the generalized parton model, enabling accurate simulation of transverse momentum dependent (TMD) parton distributions. Using Bessel-weighting of simulated events, it extracts double longitudinal spin asymmetries with 2.5% accuracy for $ b_T < 6~\text{GeV}^{-1} $, while identifying systematic shifts due to kinematic constraints and momentum conservation effects.

ABSTRACT

We present studies of double longitudinal spin asymmetries in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator, which includes quark intrinsic transverse momentum within the generalized parton model based on the fully differential cross section for the process. Additionally, we apply Bessel-weighting to the simulated events to extract transverse momentum dependent parton distribution functions and also discuss possible uncertainties due to kinematic correlation effects.

Motivation & Objective

• To develop a fully differential Monte Carlo generator that simulates quark intrinsic transverse momentum ($k_\perp$) in SIDIS within the generalized parton model.
• To enable model-independent extraction of the ratio of polarized to unpolarized TMD distributions ($g_{1L}/f_1$) using Bessel-weighted asymmetries.
• To investigate systematic biases in TMD extraction due to experimental kinematic cuts and momentum conservation effects.
• To compare model-dependent data corrections with model-independent integration limits in asymmetry calculations.
• To validate the accuracy of Bessel-weighted asymmetry extraction under realistic experimental constraints.

Proposed method

• Utilizes the fully differential SIDIS cross section from Ref. [1], incorporating quark TMD distributions $f_{1,q}(x,k_\perp)$ and $g_{1L,q}(x,k_\perp)$, and unpolarized fragmentation functions $D_{1,q}(z,p_\perp)$.
• Employs the Foam Monte Carlo generator to sample events in $n$-dimensional phase space according to the user-defined cross section, including $k_\perp$ and $p_\perp$ distributions.
• Applies Bessel-weighting via $J_0(b_T P_{hT})$ to extract Fourier-transformed TMDs, enabling access to $\tilde{g}_{1L}/\tilde{f}_1$ ratios in impact parameter space.
• Uses modified Gaussian (MG) ansatz for TMDs: $f_1(x,k_\perp) \propto \exp\left(-k_\perp^2 / [x(1-x)\langle k_\perp^2 \rangle_{f_1}]\right)$, with non-factorized $x$ and $k_\perp$ dependence.
• Corrects for kinematic distortions by estimating missing $P_{hT}$ contributions using a Gaussian model (data correction), and by limiting integration to accessible $P_{hT}$ ranges (model-independent method).
• Compares extracted asymmetries with analytical predictions to quantify systematic shifts due to experimental acceptance and resolution.

Experimental results

Research questions

• RQ1 How accurately can Bessel-weighted asymmetries extract the $g_{1L}/f_1$ ratio in SIDIS when constrained by realistic $P_{hT}$ acceptance cuts?
• RQ2 What is the impact of energy and momentum conservation on the reconstructed $k_\perp$ and $p_\perp$ distributions in Monte Carlo simulations?
• RQ3 To what extent do binning effects and $P_{hT}$ range restrictions distort the Gaussian shape of transverse momentum distributions?
• RQ4 Can systematic shifts in extracted asymmetries be corrected without introducing model dependence?
• RQ5 How do model-dependent data corrections compare with model-independent integration limits in recovering true TMD asymmetries?

Key findings

• The Bessel-weighted double spin asymmetry $A^{J_0(b_T P_{hT})}_{LL}(b_T)$ can be extracted with 2.5% accuracy for $b_T < 6~\text{GeV}^{-1}$, corresponding to about 1 fm in impact space.
• A systematic shift of ~2.5% is observed between extracted and theoretical asymmetries due to kinematic constraints and momentum conservation, particularly affecting $k_\perp$ and $p_\perp$ distributions.
• The distortion of Gaussian shapes in $k_\perp$ and $p_\perp$ distributions arises from experimental $P_{hT}$ cutoffs at high and low values, where resolution and acceptance degrade.
• Model-dependent correction of missing $P_{hT}$ regions (e.g., via Gaussian extrapolation) successfully restores agreement with the theoretical asymmetry curve for $b_T < 6~\text{GeV}^{-1}$.
• Model-independent integration limits that match the accessible $P_{hT}$ range yield a calculated asymmetry that agrees with simulated data without introducing bias.
• The effective $\langle k_\perp^2 \rangle$ extracted from MC events is consistently lower than the input value due to energy and momentum conservation, confirming kinematic suppression effects.