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Abstract <p>One-loop electromagnetic corrections to the masses of the pseudoscalar <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi \)</EquationSource> <!--JETP2560145Osipov-m1--> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(K\)</EquationSource> <!--JETP2560145Osipov-m2--> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <!--JETP2560145Osipov-m3--> </InlineEquation>, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\eta '\)</EquationSource> <!--JETP2560145Osipov-m4--> </InlineEquation> mesons have been calculated. For this purpose, the effective mesonic Lagrangian is used, the vertices of which are classified from the powers of momenta, masses of current quarks, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(1{\text{/}}{{N}_{c}}\)</EquationSource> <!--JETP2560145Osipov-m5--> </InlineEquation>. It is shown that the electromagnetic interactions lead to mixing of singlet–octet states. As a result, due to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(U{{(1)}_{A}}\)</EquationSource> <!--JETP2560145Osipov-m6--> </InlineEquation> axial anomaly admixture, the contribution of virtual photons in elements <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(M_{{08}}^{2}\)</EquationSource> <!--JETP2560145Osipov-m7--> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(M_{{03}}^{2}\)</EquationSource> <!--JETP2560145Osipov-m8--> </InlineEquation> of the mesonic mass matrix is enhanced, which substantially suppresses the effect of isospin symmetry breaking in the whole. This mechanism is important in precision calculations with the participation of the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\({{\pi }^{0}}\)</EquationSource> <!--JETP2560145Osipov-m9--> </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <!--JETP2560145Osipov-m10--> </InlineEquation>, and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\eta '\)</EquationSource> <!--JETP2560145Osipov-m11--> </InlineEquation> mesons.</p>

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Virtual Photons and π0-η-η' Mixing

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. A. Osipov

摘要

Abstract

One-loop electromagnetic corrections to the masses of the pseudoscalar \(\pi \) , \(K\) , \(\eta \) , and \(\eta '\) mesons have been calculated. For this purpose, the effective mesonic Lagrangian is used, the vertices of which are classified from the powers of momenta, masses of current quarks, and \(1{\text{/}}{{N}_{c}}\) . It is shown that the electromagnetic interactions lead to mixing of singlet–octet states. As a result, due to \(U{{(1)}_{A}}\) axial anomaly admixture, the contribution of virtual photons in elements \(M_{{08}}^{2}\) and \(M_{{03}}^{2}\) of the mesonic mass matrix is enhanced, which substantially suppresses the effect of isospin symmetry breaking in the whole. This mechanism is important in precision calculations with the participation of the \({{\pi }^{0}}\) , \(\eta \) , and \(\eta '\) mesons.