#
Isospin Symmetry Breaking in Non-Perturbative QCD^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Formalism

#### 2.1. PLSM at Finite Chemical Potential

#### 2.2. Isospin Asymmetry and Meson Potential

## 3. Results and Discussion

- Both u- and d-quark chiral condensates become distinguishable. As the temperature approaches a critical value, the normalized nonstrange condensates are split into two different curves. At this point, the critical chiral temperatures, ${T}_{\chi}$, can be at least qualitatively estimated. We notice that the value of the resulting ${T}_{\chi}$ decreases with increasing ${\mu}_{I}$.
- Both Ployakov-loop variables $\varphi $ and $\overline{\varphi}$ also become distinguishable. Increasing ${\mu}_{I}$ decreases $\overline{\varphi}$ but increases $\varphi $. Moreover, both $\varphi $ and $\overline{\varphi}$ become more distinguishable with a further increase in ${\mu}_{I}$.
- Both nonstrange quark susceptibilities become distinguishable as well. The critical chiral temperature ${T}_{\chi}$ is positioned in the middle of the deconfinement phase transition. The resulting ${T}_{\chi}$ decreases with the increase in ${\mu}_{I}$.

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Table 1.**Various LSM parameters fixed at ${m}_{\sigma}=800\phantom{\rule{3.33333pt}{0ex}}$MeV and ${h}_{3}=0$ [16].

${\mathit{m}}_{\mathit{\sigma}}$ [MeV] | c [MeV] | ${\mathit{h}}_{\mathit{ud}}$ [MeV${}^{3}$] | ${\mathit{h}}_{3}$ [MeV${}^{3}$] | ${\mathit{h}}_{\mathit{s}}$ [MeV${}^{3}$] | ${\mathit{m}}^{2}$ [MeV${}^{2}$] | ${\mathit{\lambda}}_{1}$ | ${\mathit{\lambda}}_{2}$ |
---|---|---|---|---|---|---|---|

800 | $4807.84$ | ${\left(120.73\right)}^{3}$ | 0 | ${\left(336.41\right)}^{3}$ | $-{\left(306.26\right)}^{2}$ | $13.49$ | $46.48$ |

${\mathit{m}}_{\mathit{\sigma}}$ [MeV] | c [MeV] | ${\mathit{h}}_{\mathit{ud}}$ [MeV${}^{3}$] | ${\mathit{h}}_{3}$ [MeV${}^{3}$] | ${\mathit{h}}_{\mathit{s}}$ [MeV${}^{3}$] | ${\mathit{m}}^{2}$ [MeV${}^{2}$] | ${\mathit{\lambda}}_{1}$ | ${\mathit{\lambda}}_{2}$ |
---|---|---|---|---|---|---|---|

800 | $4807.84$ | ${\left(120.73\right)}^{3}$ | $-{\left(78.31\right)}^{3}$ | ${\left(336.41\right)}^{3}$ | $-{\left(306.26\right)}^{2}$ | $13.49$ | $46.48$ |

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**MDPI and ACS Style**

Tawfik, A.N.
Isospin Symmetry Breaking in Non-Perturbative QCD. *Phys. Sci. Forum* **2023**, *7*, 22.
https://doi.org/10.3390/ECU2023-14047

**AMA Style**

Tawfik AN.
Isospin Symmetry Breaking in Non-Perturbative QCD. *Physical Sciences Forum*. 2023; 7(1):22.
https://doi.org/10.3390/ECU2023-14047

**Chicago/Turabian Style**

Tawfik, Abdel Nasser.
2023. "Isospin Symmetry Breaking in Non-Perturbative QCD" *Physical Sciences Forum* 7, no. 1: 22.
https://doi.org/10.3390/ECU2023-14047