[Paper Review] Update of the NNLO PDFs in the 3-, 4-, and 5-flavour scheme

S. Alekhin, J. Blümlein+1 more|arXiv (Cornell University)|Jul 21, 2010

Particle physics theoretical and experimental studies2 references20 citations

TL;DR

This paper presents an updated set of next-to-next-to-leading order (NNLO) parton distribution functions (PDFs) in the 3-, 4-, and 5-flavor schemes, incorporating combined HERA Run I deep-inelastic scattering data and partial NNLO corrections to heavy-quark electroproduction. The update yields a refined strong coupling constant αs(MZ) = 0.1147(12) and improves the description of low-x PDF behavior, particularly for the non-strange sea and gluon distributions, with significant impacts on standard candle cross sections at the Tevatron and LHC.

ABSTRACT

We report on an update of the next-to-next-to-leading order (NNLO) ABKM09 parton distributions functions. They are obtained with the use of the combined HERA collider Run I inclusive deep-inelastic scattering (DIS) data and the partial NNLO corrections to the heavy quark electro-production taken into account. The value of the strong couplig constant $α^{ m NNLO}_{ m s}(M_{ m Z})=0.1147(12)$ is obtained. The standard candle cross sections for the Tevatron collider and the LHC estimated with the updated PDFs are provided.

Motivation & Objective

• To improve the precision and theoretical consistency of NNLO parton distribution functions (PDFs) for hadron collider phenomenology.
• To address the tension between HERA data and previous PDF fits, particularly at low Bjorken-x, by refining the low-x asymptotics of PDF parametrization.
• To incorporate partial NNLO corrections to heavy-quark electroproduction, enhancing theoretical accuracy in the 3-flavor scheme.
• To provide updated standard candle cross sections for W, Z, top quark, and Higgs production at the Tevatron and LHC using the improved PDFs.
• To determine a more accurate value of the strong coupling constant αs(MZ) through simultaneous PDF and αs fitting.

Proposed method

• A model-independent analysis of the combined HERA Run I inclusive structure function F2 is performed by fitting F2 as a function of ln(Q²) in x-bins, correcting for longitudinal structure function FL using NNLO PDFs from the previous fit.
• A new flexible PDF parametrization (Eq. 1) is introduced, incorporating parameters a, β, γ1–γ3, and b to better describe low-x behavior, particularly for the non-strange sea and gluon distributions.
• The fit includes partial NNLO corrections to heavy-quark electroproduction in the 3-flavor scheme, specifically O(αs²) threshold corrections from Ref. [8], improving theoretical accuracy.
• Systematic error correlations are carefully accounted for in the χ² evaluation, with a focus on minimizing bias in the F2-slope determination using data in the 2 < Q² < 100 GeV² range.
• The strong coupling constant αs is simultaneously fitted with the PDFs, resulting in αs(MZ) = 0.1147(12) in the 5-flavor scheme.
• Standard candle cross sections at the Tevatron and LHC are recalculated using the updated PDFs in the NNLO and NLO approximations, respectively, with comparisons to the previous ABKM09 set.

Experimental results

Research questions

• RQ1 How does the inclusion of combined HERA Run I DIS data affect the low-x behavior of parton distribution functions compared to previous fits?
• RQ2 To what extent do partial NNLO corrections to heavy-quark electroproduction modify the gluon and sea quark distributions at small x?
• RQ3 What is the impact of the updated PDFs on the determination of the strong coupling constant αs(MZ)?
• RQ4 How do the updated PDFs alter the predictions for standard candle cross sections at the Tevatron and LHC?
• RQ5 Can a more flexible PDF parametrization (Eq. 1) better describe the tension between HERA data and NNLO predictions, particularly in the low-x region?

Key findings

• The updated NNLO PDFs yield a value of αs(MZ) = 0.1147(12), which is 1σ higher than the previous ABKM09 result of 0.1135(14), primarily due to the updated HERA data.
• The non-strange sea quark distribution increases at small x, while the gluon distribution decreases at small x compared to ABKM09, due to improved data and momentum sum rule constraints.
• The inclusion of partial NNLO corrections to heavy-quark electroproduction leads to a suppression of the gluon distribution at small x, yet the gluon remains positive down to the factorization scale of ~2 GeV².
• The χ²/NDP for the updated fit on the high-precision HERA data subset (Q² < 300 GeV²) is 365/202 = 1.2, indicating a statistically acceptable fit with minor overestimation of fluctuations.
• Standard candle cross sections at the Tevatron show a significant shift: W± production increases from 26.2±0.3 nb to 26.8±0.3 nb, and Z production from 7.73±0.08 nb to 7.88±0.07 nb, driven by the upward shift in quark distributions at small x.
• At the LHC (7 TeV), the updated PDFs yield a 2.1 nb increase in W± cross section (100.9±1.3 nb vs. 98.8±1.5 nb) and a 0.6 pb increase in Higgs production cross section (9.4±0.2 pb vs. 8.8±0.3 pb), reflecting the combined effects of αs and PDF changes.