Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Evidence of isospin-symmetry violation in high-energy collisions of atomic nuclei -- Supplementary Information

Wojciech Brylinski, Marek Gazdzicki, Francesco Giacosa, Mark Gorenstein, Roman Poberezhnyuk, Subhasis Samanta

TL;DR

The supplement analyzes isospin-symmetry violation in high-energy nucleus-nucleus collisions, grounding the discussion in the QCD ud-flavour symmetry. It presents both a conceptual and analytical framework showing that a charge-uniform initial ensemble yields equal mean multiplicities for charged and neutral kaons, leading to the RK ratio equal to unity in the exact symmetry limit. The work then quantifies known strong-interaction sources of charge-symmetry breaking via HRG and charm-sector considerations, finding that these effects produce only modest deviations from unity, and cannot by themselves explain the NA61/SHINE observations. The findings emphasize the robustness of charge-symmetry predictions for kaons under conventional mechanisms while highlighting potential new physics or systematic effects as avenues for further study. Overall, the analysis strengthens the theoretical interpretation of the experimental anomaly by detailing the symmetry structure, its QCD origins, and the limitations of known symmetry-breaking sources.

Abstract

Recently, the NA61/SHINE collaboration at the CERN SPS reported evidence of isospin-symmetry violation in high-energy nuclear collisions [Nature Communications 16, 2849 (2025)]. The effect was observed in the relative yields of charged and neutral kaons and cannot be explained by known sources of isospin symmetry breaking. In this work, we provide supplementary information on the theoretical aspects of that study. We discuss the historical background and introduce the concepts of isospin transformations and symmetry. Importantly, we relate isospin symmetry to the QCD flavour symmetry, and we present both conceptual and analytical proofs demonstrating the equality of the mean multiplicities of charged and neutral kaons for an initial ensemble of colliding systems that is invariant under charge-symmetry transformation.

Evidence of isospin-symmetry violation in high-energy collisions of atomic nuclei -- Supplementary Information

TL;DR

The supplement analyzes isospin-symmetry violation in high-energy nucleus-nucleus collisions, grounding the discussion in the QCD ud-flavour symmetry. It presents both a conceptual and analytical framework showing that a charge-uniform initial ensemble yields equal mean multiplicities for charged and neutral kaons, leading to the RK ratio equal to unity in the exact symmetry limit. The work then quantifies known strong-interaction sources of charge-symmetry breaking via HRG and charm-sector considerations, finding that these effects produce only modest deviations from unity, and cannot by themselves explain the NA61/SHINE observations. The findings emphasize the robustness of charge-symmetry predictions for kaons under conventional mechanisms while highlighting potential new physics or systematic effects as avenues for further study. Overall, the analysis strengthens the theoretical interpretation of the experimental anomaly by detailing the symmetry structure, its QCD origins, and the limitations of known symmetry-breaking sources.

Abstract

Recently, the NA61/SHINE collaboration at the CERN SPS reported evidence of isospin-symmetry violation in high-energy nuclear collisions [Nature Communications 16, 2849 (2025)]. The effect was observed in the relative yields of charged and neutral kaons and cannot be explained by known sources of isospin symmetry breaking. In this work, we provide supplementary information on the theoretical aspects of that study. We discuss the historical background and introduce the concepts of isospin transformations and symmetry. Importantly, we relate isospin symmetry to the QCD flavour symmetry, and we present both conceptual and analytical proofs demonstrating the equality of the mean multiplicities of charged and neutral kaons for an initial ensemble of colliding systems that is invariant under charge-symmetry transformation.
Paper Structure (12 sections, 24 equations, 2 figures)

This paper contains 12 sections, 24 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Historical background
  3. Isospin transformation and symmetry
  4. Isospin symmetry from ud-flavour symmetry
  5. Charge-uniform ensembles and kaons
  6. Conceptual proof
  7. Analytical proof
  8. Comments on isospin-uniform ensembles
  9. Neutral kaons and $R_K$
  10. Violation of charge-symmetry invariance by known effects
  11. Violation in the kaon sector
  12. Violation in the charm sector

Figures (2)

  • Figure 1: Left:$R_K$ as function of $\sqrt{s_{NN}}$ calculated within HRG Vovchenko:2019pjl for $Q/B=0.5$ for different cases (from down upwards): assuming exact isospin symmetry: $R_K=1$ as expected; including PDG kaon masses; including PDG $\phi(1020)$ branching ratios; including PDG data for all particles. Right: as in the left panel, but for $Q/B = 0.4$.
  • Figure 2: Left:$R_K$ as function of $\sqrt{s_{NN}}$ calculated within HRG Vovchenko:2019pjl for $Q/B=0.5$ setting different branching ratios of $a_0(980)$ and $f_0(980)$ resonances (from down upwards): $a_0(980)$ and $f_0(980)$ with isospin symmetric decays; $a_0(980)$ and $f_0(980)$ with realistic isospin breaking branching ratios; $a_0(980)$ and $f_0(980)$ with $K\bar{K}$ mode going entirely into $K^+K^-$ (unrealistic extreme choice). Right: as in the left panel, but for $Q/B = 0.4$.