[Paper Review] MRST partons and uncertainties

A. D. Martin, Richard G. Roberts+2 more|ArXiv.org|Jul 21, 2003

Particle physics theoretical and experimental studies19 citations

TL;DR

This paper introduces conservative MRST parton distribution sets (MRST03(cons)) at NLO and NNLO, derived from global fits with stabilized data cuts ($x_{\text{cut}} > 0.005$, $Q^2_{\text{cut}} > 10~\text{GeV}^2$, $W^2_{\text{cut}} > 15~\text{GeV}^2$) to minimize sensitivity to input choices. The conservative sets yield stable predictions for $\alpha_S(M_Z^2)$ and $W$-boson production cross sections, with NNLO results showing improved convergence and reduced uncertainty, particularly at the Tevatron, where the conservative NNLO prediction is $2.67~\text{nb}$ with ~2% total uncertainty.

ABSTRACT

We discuss uncertainties in the extraction of parton distributions from global analyses of DIS and related data. We present conservative sets of partons, at both NLO and NNLO, which are stable to x,Q^2,W^2 cuts on the data. We give the corresponding values of alpha(M_Z^2) and the cross sections for W production at the Tevatron.

Motivation & Objective

• To reduce uncertainties in global parton distribution fits by identifying data cut choices that yield stable results across varying $x$, $Q^2$, and $W^2$ thresholds.
• To develop conservative parton sets (MRST03(cons)) that are robust against changes in data selection criteria, particularly $x_{\text{cut}}$, $Q^2_{\text{cut}}$, and $W^2_{\text{cut}}$.
• To assess the stability and convergence of $\alpha_S(M_Z^2)$ and $W$-boson production cross sections at both NLO and NNLO, using conservative fits.
• To provide a reliable benchmark for $\alpha_S(M_Z^2)$ and $W$-boson cross sections by minimizing theoretical and fitting uncertainties from data cuts and truncation effects.

Proposed method

• A stability measure $\Delta_i^{i+1}$ is defined as the normalized difference in $\chi^2$ contributions between adjacent $x_{\text{cut}}$ values, quantifying sensitivity to data cut changes.
• Systematic variation of $x_{\text{cut}}$, $Q^2_{\text{cut}}$, and $W^2_{\text{cut}}$ is performed to identify a stable domain where parton distributions remain insensitive to further cut increases.
• Global NLO and NNLO fits are performed using the same data sets but with different data cut combinations, and the resulting parton distributions are compared for consistency.
• The $\alpha_S(M_Z^2)$ values are extracted from fits with varying $\Delta\chi^2$ tolerances to assess theoretical and model uncertainties.
• The $W$-boson production cross section at the Tevatron ($\sqrt{s} = 1.96~\text{TeV}$) is computed using both default and conservative parton sets to evaluate stability across perturbative orders.
• The conservative parton sets are validated by comparing their predictions to default sets and observing reduced sensitivity to data cut variations, especially at NNLO.

Experimental results

Research questions

• RQ1 What is the optimal choice of $x_{\text{cut}}$ that ensures stability in global parton distribution fits across different $\chi^2$ values?
• RQ2 How do variations in $Q^2_{\text{cut}}$ and $W^2_{\text{cut}}$ affect the stability and reliability of extracted parton distributions?
• RQ3 To what extent do NNLO corrections improve the stability and convergence of $\alpha_S(M_Z^2)$ and $W$-boson cross section predictions compared to NLO?
• RQ4 How do conservative parton sets (MRST03(cons)) reduce uncertainties in $\alpha_S(M_Z^2)$ and $W$-boson production cross sections compared to default fits?
• RQ5 Can the conservative parton sets serve as a robust benchmark for luminosity monitoring at the Tevatron?

Key findings

• The conservative parton set MRST03(cons) is defined by $x_{\text{cut}} > 0.005$, $Q^2_{\text{cut}} > 10~\text{GeV}^2$, and $W^2_{\text{cut}} > 15~\text{GeV}^2$, where further increases in cuts do not alter the fit quality significantly.
• The stability measure $\Delta_i^{i+1}$ shows that raising $x_{\text{cut}}$ from 0.005 to 0.01 yields no further improvement, confirming $x_{\text{cut}} \approx 0.005$ as a safe choice.
• At NLO, the conservative parton set yields $\alpha_S(M_Z^2) = 0.1165 \pm 0.002 \pm 0.003$, with a $\chi^2$ tolerance of $\Delta\chi^2 = 5$.
• At NNLO, the conservative parton set yields $\alpha_S(M_Z^2) = 0.1153 \pm 0.002 \pm 0.003$, showing improved convergence and reduced sensitivity to data cuts.
• The NNLO conservative prediction for the $W$-boson production cross section at the Tevatron is $2.67~\text{nb}$, with a total uncertainty of about 2%, and it shows a 0.7% decrease relative to the default NNLO prediction.
• The NNLO conservative parton set exhibits greater stability under $x_{\text{cut}}$ variations than the NLO default, indicating improved convergence with higher perturbative order.