[Paper Review] Potential PDF sensitivity at LHCb

R. McNulty|ArXiv.org|Oct 14, 2008

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper demonstrates that the LHCb experiment can significantly improve constraints on proton parton distribution functions (PDFs), particularly at small momentum fractions $ x \sim 2 \times 10^{-6} $, by measuring Z, W, and low-mass Drell-Yan dimuon production in the forward region. Using high-purity triggers and kinematic asymmetries, LHCb achieves 1% experimental precision on cross-section ratios, enabling sensitivity to PDF uncertainties of 2–5% at $ Q^2 \approx 90 \, \text{GeV}/c^2 $, with potential to reduce theoretical uncertainties on small-$ x $ gluons by up to 60% at high rapidities.

ABSTRACT

A review of the potential sensitivity of the LHCb experiment to the parton distribution functions is given. Studies of dimuon events coming from Z, W and low mass Drell Yan production are presented and compared to MSTW theoretical predictions.

Motivation & Objective

• To assess LHCb's sensitivity to proton parton distribution functions (PDFs) in unexplored kinematic regions.
• To address the lack of experimental constraints on small-$ x $ PDFs, especially the small- $ x $ gluon distribution.
• To develop and validate triggers and analysis techniques for high-purity selection of Z, W, and low-mass Drell-Yan dimuon events at high rapidity.
• To quantify how LHCb measurements can reduce theoretical uncertainties in PDFs, particularly in the $ x \sim 10^{-6} $ regime.
• To demonstrate that ratios of cross-sections (e.g., $ R_{ZW} $, $ R_{\pm} $) minimize dependence on PDF uncertainties and enable precise electroweak tests.

Proposed method

• Utilizes a loose dimuon trigger requiring $ p_T^{\text{sum}} > 1.6 \, \text{GeV}/c $, followed by offline selections to enhance purity.
• Applies kinematic asymmetries $ A(x,y) = \frac{x - y}{x + y} $ to distinguish signal from background, especially for W boson decays.
• Combines five observables—muon momenta, cone momenta, and rest momentum—into a likelihood-based selection for low-mass Drell-Yan events.
• Uses MCFM generator with MSTW07 PDF eigenvectors to simulate theoretical predictions and compare with expected experimental uncertainties.
• Analyzes differential cross-sections $ d\sigma/dy $ and $ d^2\sigma/dQ^2dy $ to assess sensitivity to PDF variations.
• Employs ratios like $ R_{ZW} = \sigma_Z / (\sigma_{W^+} + \sigma_{W^-}) $ to minimize PDF dependence and enhance precision.

Experimental results

Research questions

• RQ1 Can LHCb achieve 1% precision in measuring Z and W boson production cross-sections in the forward region?
• RQ2 To what extent can LHCb constrain the small- $ x $ gluon PDF, particularly at $ x \sim 2 \times 10^{-6} $, using low-mass Drell-Yan dimuon events?
• RQ3 How effective are kinematic asymmetries and likelihood-based selection in isolating Drell-Yan signals down to $ Q^2 = 5 \, \text{GeV}/c^2 $?
• RQ4 Can ratios of cross-sections such as $ R_{ZW} $ and $ R_{\pm} $ reduce sensitivity to PDF uncertainties and serve as precise electroweak tests?
• RQ5 What is the statistical precision achievable on $ d^2\sigma/dQ^2dy $ with 1 fb$^{-1}$ of data, and how does it compare to current PDF theoretical uncertainties?

Key findings

• LHCb achieves a Z boson dimuon selection efficiency of $ 91 \pm 1\% $ and purity of $ 97 \pm 3\% $, with dominant background from misidentified hadrons ($ 3 \pm 3\% $).
• With 50 pb$^{-1}$, Z cross-section measurements are limited to ~1% systematic uncertainty, assuming precise luminosity knowledge.
• For W boson decays, a selection efficiency of 33% and purity of 83% are achieved using muon momentum asymmetry $ A(p^\mu, p^{\text{rest}}) > 0.85 $, with misidentified pions as the dominant background.
• Low-mass Drell-Yan events can be selected with >95% purity at $ Q^2 > 10 \, \text{GeV}/c^2 $, retaining 15–50% of signal events.
• At $ Q^2 = 5 \, \text{GeV}/c^2 $, LHCb can probe $ x \sim 2 \times 10^{-6} $, a region previously unmeasured, with 70% purity at 5% signal retention.
• With 1 fb$^{-1}$ of data, statistical precision of a few percent per bin is achievable on $ d^2\sigma/dQ^2dy $, and LHCb can reduce theoretical PDF uncertainties on small- $ x $ gluons by up to 60% at high rapidities.