Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data (1710.05935v2)

Abstract: We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep inelastic structure functions are computed consistently at NLO+NLLx or NNLO+NLLx, while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the recent NNPDF3.1 analysis. We demonstrate that the inclusion of small-x resummation leads to a quantitative improvement in the perturbative description of the HERA inclusive and charm-production reduced cross-sections in the small x region. The impact of the resummation in our fits is greater at NNLO than at NLO, because fixed-order calculations have a perturbative instability at small x due to large logarithms that can be cured by resummation. We explore the phenomenological implications of PDF sets with small-x resummation for the longitudinal structure function $F_L$ at HERA, for parton luminosities and LHC benchmark cross-sections, for ultra-high energy neutrino-nucleus cross-sections, and for future high-energy lepton-proton colliders such as the LHeC.

• The paper applies NLLx small-x resummation with fixed-order calculations to stabilize parton distribution functions at low x.
• The study demonstrates that resummation yields a significantly improved fit to HERA data, evidenced by reduced χ² values.
• The enhanced gluon PDFs provide more accurate predictions for low-x sensitive processes at the LHC and future colliders.

Parton Distributions with Small-$x$ Resummation: Evidence for BFKL Dynamics in HERA Data

The paper presented is a comprehensive paper on the impact of small-$x$ resummation on parton distribution functions (PDFs) and their significance in the analysis of data from the HERA collider, emphasizing evidence for BFKL dynamics. The authors undertake a detailed approach to understand how small-$x$ resummation influences the behavior of PDFs, especially in the regime where $x$ is approaching very small values, an area where the fixed-order calculations might face perturbative instabilities due to large logarithms.

Theoretical Framework and Methodology

The research deploys a framework where next-to-leading logarithmic (NLL$x$) resummation is applied alongside fixed-order calculations (NLO and NNLO) to evaluate its effects on PDF evolution and deep-inelastic structure functions. The theoretical foundation is structured on the BFKL (Balitsky–Fadin–Kuraev–Lipatov) equation, used to perform small-$x$ resummation essential for managing the large logarithmic corrections in partonic processes.

The paper incorporates data from the HERA collider, evaluating both inclusive and charm production reduced cross-sections. The importance of the resummation is quantitatively assessed against NNLO predictions that might suffer from computational inaccuracies at small-$x$. The inclusion of small-$x$ resummation offers a substantial improvement in the quantitative description of the small-$x$ data compared to fixed-order NNLO calculations.

Key Findings

The inclusion of NLL$x$ resummation notably enhances the perturbative description of the HERA data, particularly in the small $x$ region, where fixed-order NNLO analyses encounter apparent deficiencies. The analysis reveals significant stability in the small-$x$ region, embodying the BFKL dynamics that align more effectively with precision DIS data from HERA. The impact of resummation manifests strongly in the gluon PDFs, evident from a quantifiable improvement in both the total $\chi^2$ for the fit and in direct data comparisons across various $Q^2$ bins.

Practical and Theoretical Implications

The implications of this paper are twofold. Practically, PDFs enhanced by small-$x$ resummation are more accurate, leading to enhanced predictions for processes sensitive to low $x$, such as those encountered at the LHC and potential future colliders like the FCC-eh. This can lead to improved predictions for cross-sections where gluon dominance is prevalent, such as in Higgs and high-energy neutrino interactions.

Theoretically, the paper bridges a significant gap in perturbative QCD by effectively integrating resummation methods within standard PDF evolution, providing a more stable perturbative series at small $x$. This research paves the way for future works to explore beyond current small-$x$ frameworks, utilizing extended datasets and considering higher-order logarithms.

Potential Future Developments

Future developments could extend this framework by including resummed partonic cross-sections across a wider array of collider processes, integrating NLL$x$ and potentially NNLL$x$ corrections for a more comprehensive understanding of small-$x$ QCD phenomena. More intricate studies involving combined resummation (collinear and small-$x$) effects might yield further insights, particularly for high-rapidity processes such as forward Drell-Yan and prompt photon production.

Engagement with future lepton-hadron colliders and additional neutrino-nucleus interactions data could open avenues to further validate and optimize PDFs using small-$x$ resummation methodologies, thereby advancing the precision frontier in particle physics. The adaptation of these techniques to higher-order calculations like N$^3$LO will be essential for managing the theoretical uncertainties associated with next-generation QCD analyses.