[Paper Review] Comment on "Searching for flavor dependence in nuclear quark behavior"

O. Hen, F. Hauenstein+7 more|arXiv (Cornell University)|May 6, 2019

High-Energy Particle Collisions Research4 citations

TL;DR

This paper critiques Arrington and Fomin's (2019) comparison of high-virtuality (HV) and high-local-density (LD) pair modifications in nuclei, demonstrating inconsistencies in their derivation of universal modification functions (UMFs). It shows that their use of combinatorial scaling and asymmetric nucleus corrections introduces artificial differences between UMFs, contradicting ab-initio Quantum Monte Carlo calculations and violating physical consistency, especially regarding flavor dependence and center-of-mass corrections.

ABSTRACT

Weinstein, et. al [1] [PRL 106, 052301 (2011)] and Hen, et. al [2] [PRC 85, 047301 (2012)] observed a correlation between the EMC effect and the amount of short range correlated (SRC) pairs in nuclei which implies that quark distributions are different in SRC pairs as compared with free nucleons. Schmookler, et. al [3] [Nature 566, 354 (2019)] bolstered this by showing that the EMC data can be explained by a universal modification of the structure of nucleons in neutron-proton SRC pairs and presented the first data-driven extraction of this universal modification function (UMF). Arrington and Fomin [4] [arxiv 1903.12535] attempt to gain insight into the correlation between the EMC effect and SRCs by distinguishing between correlated nucleon pairs at high-virtuality (HV) vs. high local-density (LD). However, there is an inconsistency in their derivations of the UMFs, FLD univ and FHV , causing a non-physical difference between them for asymmetric nuclei. In addition, the univ combinatorial scaling they used to extract high-LD np, pp and nn pairs from measured HV np pairs is contradicted by realistic ab-initio Quantum Monte-Carlo (QMC) calculations.

Motivation & Objective

• To identify and correct inconsistencies in Arrington and Fomin’s (2019) derivation of universal modification functions (UMFs) for high-virtuality (HV) and high-local-density (LD) nucleon pairs in nuclei.
• To challenge the validity of combinatorial scaling used to extract LD $pp$, $nn$, and $np$ pairs from measured HV $np$ pairs, showing it contradicts ab-initio Quantum Monte Carlo (QMC) calculations.
• To demonstrate that the artificial difference between $F_{\text{univ}}^{HV}$ and $F_{\text{univ}}^{LD}$ arises from inconsistent treatment of isospin asymmetry and the removal of the $(Z-N)F_2^p/F_2^d$ term only in the LD case.
• To show that center-of-mass (c.m.) motion corrections are inconsistently applied—only to LD pairs—leading to unphysical discrepancies in the UMFs.
• To establish that ab-initio QMC calculations support a single, universal scaling factor for both high-momentum and small-separation pairs, contradicting Arrington and Fomin’s assumption of distinct HV and LD scaling factors.

Proposed method

• Re-derive the universal modification function (UMF) for high-local-density (LD) pairs using a consistent many-body formalism that accounts for $np$, $pp$, and $nn$ pairs, correcting Arrington and Fomin’s incomplete treatment.
• Apply the same UMF framework to both HV and LD cases, showing that the only consistent comparison is under symmetric nuclei ($N=Z$), where the expressions reduce to the same form.
• Use ab-initio Quantum Monte Carlo (QMC) calculations to validate the physical equivalence of high-momentum and small-separation pair distributions, showing they factorize via a single nucleus-dependent scaling factor $C_{NN,\alpha}^A$ in both $k$- and $r$-space.
• Re-evaluate the center-of-mass (c.m.) motion correction by comparing simplistic 1D smearing models with more realistic 3D spectral function modeling, showing a 70% correction is more accurate than the 20% used by Arrington and Fomin.
• Re-analyze the $A$-dependence of UMF slopes using both logarithmic and constant fits, demonstrating that the one-parameter constant fit is more appropriate and eliminates artificial differences between $F_{\text{univ}}^{HV}$ and $F_{\text{univ}}^{LD}$.
• Contrast the combinatorial scaling assumption with QMC results showing equal abundances of $nn$, $pp$, and $np$ pairs at small $r$, even in asymmetric nuclei, proving the scaling is not valid.

Experimental results

Research questions

• RQ1 Why does Arrington and Fomin’s (2019) derivation of $F_{\text{univ}}^{LD}$ lead to a non-physical difference from $F_{\text{univ}}^{HV}$ in asymmetric nuclei?
• RQ2 Is the combinatorial scaling used to extract $pp$, $nn$, and $np$ pairs from HV $np$ pairs consistent with ab-initio QMC calculations?
• RQ3 Does the assumption that $R_{\text{EMC}}^{A}$ for asymmetric nuclei equals that of a symmetric nucleus with the same $A$ have theoretical justification?
• RQ4 Can distinct scaling factors for high-momentum and small-separation pairs be supported by QMC calculations, or is there a single universal scaling factor?
• RQ5 Is the inconsistent application of center-of-mass (c.m.) corrections to LD pairs only responsible for an artificial discrepancy between $F_{\text{univ}}^{HV}$ and $F_{\text{univ}}^{LD}$?

Key findings

• The difference between $F_{\text{univ}}^{HV}$ and $F_{\text{univ}}^{LD}$ in asymmetric nuclei is not physical but arises from the unjustified removal of the $(Z-N)F_2^p/F_2^d$ term in the LD derivation while retaining it in the HV case.
• Ab-initio QMC calculations show that the number of small-$r$ $nn$, $pp$, and $np$ pairs is nearly equal in symmetric and asymmetric nuclei, contradicting the combinatorial scaling used by Arrington and Fomin.
• The QMC-derived pair distributions factorize as $n_{NN,\alpha}^A(k>k_F) = C_{NN,\alpha}^A |\psi_{NN,\alpha}(k)|^2$ and $\rho_{NN,\alpha}^A(r<1\text{fm}) = C_{NN,\alpha}^A |\psi_{NN,\alpha}(r)|^2$, proving a single universal scaling factor for both high-$k$ and small-$r$ pairs.
• The center-of-mass (c.m.) motion correction is not 20% as assumed by Arrington and Fomin but closer to 70%, based on 3D spectral function modeling, and its inconsistent application distorts the UMF comparison.
• The logarithmic fit of the $A$-dependence of UMF slopes used by Arrington and Fomin is invalid; a one-parameter constant fit is more appropriate and reduces the difference between $F_{\text{univ}}^{HV}$ and $F_{\text{univ}}^{LD}$ from a factor of 2.5 to about 1.5.
• The physical equivalence of HV and LD pairs is confirmed by QMC: the same scaling factor $C_{NN,\alpha}^A$ applies to both momentum and coordinate space, invalidating the assumption of distinct dynamics.