Redetermination of proton sea distributions

This paper presents a redetermination of the proton's light flavor sea quark distributions using NNLO global analyses of HERA and ATLAS data, revealing an unexpected asymmetry where the anti-up quark distribution exceeds the anti-down quark distribution in the momentum fraction range $x\in(10^{-2}, 1)$, leading to a Gottfried Sum Rule value that significantly differs from previous experimental results.

The Gist

Imagine a proton not as a solid marble, but as a bustling, chaotic city. Inside this city, there are three main types of residents: the "Valence" citizens (the permanent, named residents who define the city's identity), the "Gluon" workers (the glue holding everything together), and the "Sea" citizens.

The "Sea" is a swirling crowd of temporary particles that pop in and out of existence. Among these Sea citizens, there are two specific groups the scientists were curious about: the Anti-Up crowd and the Anti-Down crowd.

For decades, physicists believed these two groups were perfectly balanced, like two equal-sized teams in a game. This belief was based on a famous rule called the Gottfried Sum Rule, which predicted that if you counted all the Anti-Up and Anti-Down citizens, the numbers should be exactly the same.

The Mystery

However, previous experiments suggested this rule was broken. It looked like there were more Anti-Down citizens than Anti-Up ones. But there was a catch: those earlier experiments used "nuclear targets" (like mixing the proton city with other cities to make a bigger target). This introduced "noise" and confusion, making it hard to tell if the imbalance was real or just a side effect of the mixing.

The New Investigation

The authors of this paper decided to look at the proton city directly, without mixing it with anything else. They acted like detectives using two different high-tech surveillance tools:

1. The HERA Camera: This tool looked at electrons bouncing off protons. It was great at seeing the general crowd, but it had a blind spot: it couldn't easily tell the difference between the Anti-Down citizens and the Strange citizens (another temporary group). It was like trying to count red and blue marbles when some of the blue ones look exactly like green ones.
2. The ATLAS Camera: This tool looked at collisions between two protons (like two cities crashing into each other). This provided a different angle that helped separate the different types of citizens more clearly.

The Findings

The researchers ran their analysis in two rounds, like refining a sketch:

• Round 1 (HERA only): They relaxed some old, rigid rules about how these citizens were supposed to behave. They found that the "Strange" population was actually larger than previously thought. When they adjusted for this, the Anti-Down numbers dropped.
• Round 2 (HERA + ATLAS): By combining the data from both cameras, they got a crystal-clear picture.

The Big Reveal:
Contrary to the old belief that there were more Anti-Down citizens, the new data shows the opposite. There are actually more Anti-Up citizens than Anti-Down citizens in the proton, especially in the "busy" parts of the city (where the momentum fraction is higher).

Think of it like a concert hall where everyone thought the section for "Section A" was empty, but after using better microphones, they realized "Section B" was actually packed, and "Section A" was surprisingly sparse.

The Conclusion

The authors recalculated the Gottfried Sum Rule (the rule that said the two groups should be equal) using their new, clearer data. The result was a surprise: the rule is indeed broken, but not in the way everyone thought. Instead of having an excess of Anti-Down, the proton has an excess of Anti-Up.

In short, the proton's internal "sea" is lopsided, but it leans toward the Anti-Up side, not the Anti-Down side as previously suspected. This changes our fundamental understanding of what makes up the building blocks of our universe.

Technical Summary

Technical Summary: Redetermination of Proton Sea Distributions

Problem Statement
The internal structure of the nucleon, quantified by Parton Distribution Functions (PDFs), is well-established for valence quarks and gluons. However, the distributions of light flavor sea quarks, specifically the asymmetry between anti-up ($\bar{u}$) and anti-down ($\bar{d}$) quarks, remain ambiguous. Previous experimental evidence, primarily from the New Muon Collaboration (NMC), the NA51 experiment, and the NuSea collaboration, suggested an excess of $\bar{d}$ over $\bar{u}$, leading to a violation of the Gottfried Sum Rule (GSR). However, these earlier studies relied on nuclear targets (hydrogen and deuterium), introducing uncertainties related to target mass effects, higher-order corrections, and nuclear shadowing. Furthermore, the interpretation of the GSR violation is complicated by the assumption of isospin symmetry between protons and neutrons; a violation could stem from isospin symmetry breaking rather than an intrinsic asymmetry in the proton's sea. Consequently, a direct examination of the proton's light sea flavor shapes using pure proton-related data is necessary to resolve these ambiguities.

Methodology
The authors perform a Next-to-Leading Order (NNLO) perturbative QCD global analysis using the xFitter framework to extract light sea quark distributions. The study proceeds in two distinct rounds of fitting:

1. HERAshape Analysis:

   • Data: Combined inclusive $e^\pm p$ Deep Inelastic Scattering (DIS) cross-section measurements from the H1 and ZEUS experiments at HERA.
   • Kinematics: Covers $0.045 \le Q^2 \le 50,000$ GeV$^2$ and $6 \times 10^{-7} \le x \le 0.65$ (Neutral Current) and $200 \le Q^2 \le 50,000$ GeV$^2$ with $1.3 \times 10^{-2} \le x \le 0.40$ (Charged Current).
   • Parameterization: The authors relax the constraints imposed in the standard HERAPDF2.0 analysis. Specifically, they free the normalization ($A$) and shape ($B$) parameters for the $\bar{u}$ and $\bar{d}$ distributions, rather than enforcing equality as $x \to 0$.
   • Strangeness: Unlike HERAPDF2.0, which assumes a suppressed strange sea, this analysis adopts an unsuppressed strange sea scenario. The strange quark fraction factor $f_s$ is set to 0.54, consistent with recent ATLAS measurements of the $\bar{s}/\bar{d}$ ratio, rather than the arbitrary 0.4 used previously.

2. ATLASshape Analysis:

   • Data: Combines the HERA $e^\pm p$ data with ATLAS measurements of $W^\pm/Z$ boson production cross-sections in $pp$ collisions at $\sqrt{s} = 7$ TeV.
   • Purpose: The inclusion of $W^\pm/Z$ data provides additional constraints on the flavor decomposition of the sea, valence quarks, and gluons, particularly helping to distinguish between $\bar{d}$ and strange quark contributions which HERA data alone cannot fully separate.
   • Parameterization: Utilizes a functional form similar to ATLAS-series PDFs, allowing independent parameterization for $\bar{u}$, $\bar{d}$, and $\bar{s}$.

The theoretical cross-sections are calculated by convoluting PDFs (evolved via DGLAP equations) with hard scattering cross-sections. The $\chi^2$ minimization is performed using the CERN MINUIT program, with experimental uncertainties handled via the Hessian Error method.

Key Results

• Sea Asymmetry: Both the HERAshape and ATLASshape analyses reveal an asymmetric distribution between $\bar{u}$ and $\bar{d}$. Contrary to the traditional view of an excess of $\bar{d}$, the results indicate that the anti-up quark distribution exceeds the anti-down quark distribution in the momentum fraction range $x \in (10^{-2}, 1)$.
• Impact of ATLAS Data: The inclusion of ATLAS $W^\pm/Z$ data significantly reduces the uncertainties in the extracted PDFs. While the HERAshape analysis shows a decrease in the $\bar{d}$ distribution and an increase in the strange quark distribution compared to HERAPDF2.0, the ATLASshape analysis further refines these results, confirming the suppression of $\bar{d}$ relative to $\bar{u}$ with higher precision.
• Gottfried Sum Rule (GSR): The GSR ($S_G$) is reevaluated using the extracted PDFs.
  • In the range $0.004 \le x \le 0.8$, the calculated $S_G$ from the new analyses is larger than the NMC result ($0.240 \pm 0.016$), consistent with an excess of $\bar{u}$ over $\bar{d}$.
  • In the full range $0 \le x \le 1$, the results from HERAshape, ATLASshape, and other modern global fits (such as ATLAS-epWZ) are consistent with each other and indicate an excess of $\bar{u}$, differing from the NMC and NuSea findings which suggested $\bar{d} > \bar{u}$.
• Strange Quark: The analysis supports an unsuppressed strange sea, with the strange quark distribution increasing significantly compared to HERAPDF2.0, aligning with recent ATLAS findings.

Significance and Claims
The paper claims to provide a more direct and reliable determination of the proton's light sea quark shapes by eliminating the nuclear target effects inherent in previous fixed-target experiments. By utilizing pure proton data from HERA and ATLAS, and relaxing restrictive parameterizations regarding strangeness and isospin symmetry, the authors conclude that the proton possesses more anti-up quarks than anti-down quarks in the intermediate to high momentum fraction region. This finding challenges the long-standing interpretation of the Gottfried Sum Rule violation as evidence for a $\bar{d}$ excess. The authors assert that their results, particularly the ATLASshape PDFs which offer reduced uncertainties, provide a solid basis for this revised understanding of the proton's sea structure.