Violations of Dashen’s Theorem

The electromagnetic contribution to the K − K mass difference is calculated in the 1/Nc approach including the SU(3) breaking contributions due to a non-zero strange quark mass. The short-distance contribution can be unambiguously determined in terms of the known parameters of the next-to-leading order chiral lagrangian. The long distance part is estimated using the 1/Nc approach by Bardeen et al. Relatively large corrections are found. 1) Introduction: The values of the quark masses are important physical quantities. Determining the values of the quark masses is, however, not such a simple task because quarks are confined and do not exist as free particles whose mass can be measured directly. At high energies they can be identified with jets but the effects due to their masses at these high energies are so small that jet-physics cannot be used to determine the masses of the light quarks. Therefore a recourse to other methods is needed. For a review of the values of the quark masses see [1]. A more recent discussion of some of the issues arising in this context can be found in [2]. Good theoretical results exist for certain ratios of the quark masses in terms of the masses of the pseudoscalar meson octet, π, K and η. As an example we give here the relation that determines the isospin breaking parameter mu −md, valid to next-to-leading order [3]. md −mu ms − m̂ 2m̂ ms + m̂ = m2K0 −m 2 K+ −m 2 π0 +m 2 π+ m2K −M 2 π m2π m2K ×