[Paper Review] Top production at the LHC: the impact of PDF uncertainties and correlations

Alberto Guffanti, Juan Rojo|arXiv (Cornell University)|Aug 27, 2010

Particle physics theoretical and experimental studies2 references6 citations

TL;DR

This paper investigates the impact of PDF uncertainties and correlations on top quark pair and single-top production at the LHC, showing that the bottom quark mass is a dominant theoretical uncertainty in single-top production. Using the NNPDF2.0 global fit, it demonstrates strong anti-correlations between top quark and electroweak vector boson cross-sections, suggesting that precise measurements of $W^\pm$ and $Z^0$ production can reduce PDF uncertainties in top cross-section determinations at early LHC data.

ABSTRACT

In this contribution we discuss the impact of PDF uncertainties on t\bar{t} and t-channel single-top production at the LHC. We present predictions for total cross-sections computed at NLO accuracy with different PDF sets. For single- top production, we point out that the uncertainty arising from the choice of the bottom quark mass is one of the dominant theoretical uncertainties on the total cross-section. Finally, the possibility of using PDF induced correlations between top quark and electroweak vector boson production cross-sections to improve the accuracy of LHC measurements is investigated.

Motivation & Objective

• To assess the impact of PDF uncertainties on $t\bar{t}$ and $t$-channel single-top production cross-sections at the LHC.
• To identify the dominant theoretical uncertainties in single-top production, particularly the role of the bottom quark mass $m_b$.
• To explore PDF-induced correlations between top quark and electroweak vector boson ($W^\pm, Z^0$) production cross-sections for improved measurement accuracy.
• To evaluate the potential of using vector boson cross-sections as a calibration tool to reduce PDF uncertainties in top quark cross-section measurements.
• To compare predictions across multiple NLO PDF sets (NNPDF2.0, CTEQ6.6, MSTW2008, ABKM09, HERAPDF1.0) and trace discrepancies to parton luminosities and input parameters.

Proposed method

• Computed NLO QCD cross-sections for $t\bar{t}$ and $t$-channel single-top production using the MCFM code with various PDF sets.
• Used the NNPDF2.0 global fit, which employs Monte Carlo techniques to estimate PDF uncertainties and correlations.
• Quantified correlations between parton densities and cross-sections using the correlation coefficient $\rho$ defined in Eq. (1), derived from PDF error propagation.
• Analyzed correlations between top quark and electroweak vector boson cross-sections ($\sigma_{W^+}, \sigma_{W^-}, \sigma_{Z^0}$) using the same NNPDF2.0 framework.
• Compared predictions across PDF sets to isolate contributions from differences in $\alpha_s$, $m_b$, and parton luminosities.
• Plotted correlation ellipses and parton density correlations to visualize the sensitivity of cross-sections to specific PDFs at different $x$ values.

Experimental results

Research questions

• RQ1 How do PDF uncertainties affect the theoretical predictions for $t\bar{t}$ and $t$-channel single-top production at the LHC?
• RQ2 What is the relative impact of the bottom quark mass $m_b$ on the theoretical uncertainty of single-top production cross-sections?
• RQ3 To what extent are the $t\bar{t}$ and $t$-channel single-top cross-sections correlated with electroweak vector boson production cross-sections?
• RQ4 Can measurements of $W^\pm$ and $Z^0$ production be used to reduce PDF uncertainties in top quark cross-section measurements?
• RQ5 How do differences in PDF sets (e.g., NNPDF2.0 vs. ABKM09) affect cross-section predictions, and what are the underlying causes?

Key findings

• The $t\bar{t}$ cross-section at 7 TeV varies by up to ~10% across different PDF sets, with NNPDF2.0, CTEQ6.6, and MSTW2008 agreeing within 1-sigma uncertainties.
• The $t$-channel single-top cross-section shows larger discrepancies between PDF sets, with differences exceeding 1-sigma uncertainties, largely due to variations in $m_b$ and $\alpha_s$.
• The uncertainty from the bottom quark mass $m_b$ is identified as a dominant theoretical uncertainty in single-top production, especially when using $N_f=4$ calculations.
• The $t\bar{t}$ cross-section is strongly anti-correlated with $W^\pm$ and $Z^0$ cross-sections, with correlation coefficients of $\rho = -0.716$, $-0.694$, and $-0.773$, respectively.
• The $t$-channel single-top cross-section shows only mild correlations with $W^\pm$ and $Z^0$ cross-sections ($\rho \approx 0.14$ to $0.33$), limiting its potential for calibration via vector boson measurements.
• The $t\bar{t}$ cross-section is most sensitive to the gluon PDF at $x \sim 0.1$, while the $t$-channel single-top cross-section is most sensitive to $b$-quark and $s$-quark PDFs at $x \sim 0.01$.