Charge dependence of mesons with flavored contact-interaction couplings

Effective interaction models of quantum chromodynamics, based on quark degrees of freedom, have been successfully employed to compute the properties of a large array of ground and excited meson and baryon states, along with their electromagnetic form factors, distribution functions, and thermal behavior. Amongst them, the contact-interaction model, while nonrenormalizable, implements confinement, satisfies Lorentz covariance, and correctly describes chiral symmetry and its dynamical breaking pattern. Original studies focused on the light hadron sector in the isospin limit and were thereafter extended to heavy mesons and baryons. The strong effective couplings, as well as infrared and ultraviolet regulators, are flavor-dependent model parameters adjusted to reproduce hadronic observables. In contrast, in this study we combine SU(4) flavor-symmetry breaking couplings, obtained from one-loop vacuum polarization amplitudes in the presence of background constituent quark currents, with the contact-interaction model. This allows us to reduce the number of mass-dimensioned parameters and to consistently relate all flavored couplings to a single mass scale, while the masses and weak decay constants of the pions, kaons, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>D</c:mi> <c:mi>s</c:mi> </c:msub> </c:math> mesons are in good agreement with average reference values. Allowing for realistic isospin breaking, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msub> <e:mrow> <e:mi>m</e:mi> </e:mrow> <e:mrow> <e:mi>d</e:mi> </e:mrow> </e:msub> <e:mo>/</e:mo> <e:msub> <e:mrow> <e:mi>m</e:mi> </e:mrow> <e:mrow> <e:mi>u</e:mi> </e:mrow> </e:msub> <e:mo>=</e:mo> <e:mn>1.7</e:mn> </e:mrow> </e:math> , in conjunction with the effect of the flavored couplings, leads to a mass splitting, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi>m</g:mi> </g:mrow> <g:mrow> <g:msup> <g:mrow> <g:mi>π</g:mi> </g:mrow> <g:mrow> <g:mo>+</g:mo> </g:mrow> </g:msup> </g:mrow> </g:msub> <g:mo>−</g:mo> <g:msub> <g:mrow> <g:mi>m</g:mi> </g:mrow> <g:mrow> <g:msup> <g:mrow> <g:mi>π</g:mi> </g:mrow> <g:mrow> <g:mn>0</g:mn> </g:mrow> </g:msup> </g:mrow> </g:msub> <g:mo>≈</g:mo> <g:mn>0.3</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>MeV</g:mi> </g:mrow> </g:math> , that agrees with lattice QCD values. For the kaons, the mass difference is <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msub> <i:mrow> <i:mi>m</i:mi> </i:mrow> <i:mrow> <i:msup> <i:mrow> <i:mi>K</i:mi> </i:mrow> <i:mrow> <i:mn>0</i:mn> </i:mrow> </i:msup> </i:mrow> </i:msub> <i:mo>−</i:mo> <i:msub> <i:mrow> <i:mi>m</i:mi> </i:mrow> <i:mrow> <i:msup> <i:mrow> <i:mi>K</i:mi> </i:mrow> <i:mrow> <i:mo>±</i:mo> </i:mrow> </i:msup> </i:mrow> </i:msub> <i:mo>≈</i:mo> <i:mn>2.3</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>MeV</i:mi> </i:mrow> </i:math> , whereas <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>m</k:mi> <k:msup> <k:mi>D</k:mi> <k:mo>±</k:mo> </k:msup> </k:msub> <k:mo>−</k:mo> <k:msub> <k:mi>m</k:mi> <k:msup> <k:mi>D</k:mi> <k:mn>0</k:mn> </k:msup> </k:msub> <k:mo>≈</k:mo> <k:mn>0.5</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>MeV</k:mi> </k:math> and the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>η</m:mi> <m:mi>c</m:mi> </m:msub> </m:math> is 6% lighter than the experimental mass.