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 Physics , 2009, DOI: 10.1016/j.physletb.2009.05.068 Abstract: We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.
 Physics , 1995, DOI: 10.1016/0375-9474(95)00373-9 Abstract: The $\rho\omega$--mixing generated by the isospin breaking of the current quark masses $m_{u} \neq m_{d}$ is studied within the bosonized NJL model in the gradient expansion. The resulting effective meson lagrangian naturally incorperates vector meson dominance. By including pion loops an excellent description of both the pion electromagnetic form factor and of the $\pi^+\pi^-$ phase shifts in the vector--isovector channel is obtained. The $\rho\omega$--mixing can be treated in the static approximation but is absolutely necessary to reproduce the fine structure of the electromagnetic form factor, while the pion loops are necessary to obtain the correct energy dependence of the phase shifts.
 Physics , 2009, Abstract: We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory. The so-called triangle relation is found to be violated by about 1.5 %. We encounter a substantial isospin-breaking correction to neutral-pion-nucleon scattering beyond Weinberg's prediction due to a cusp effect. Finally, the application to hadronic atoms is briefly discussed.
 Physics , 2005, DOI: 10.1016/j.physletb.2006.07.001 Abstract: It is shown that isospin-breaking corrections to the pion-deuteron scattering length can be very large, because of the vanishing of the isospin-symmetric contribution to this scattering length at leading order in chiral perturbation theory. We further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and pionic deuterium. We also give the first determination of the electromagnetic low-energy constant f1.
 Xuemin Jin Physics , 1996, Abstract: The isospin breaking in the nucleon isovector axial charge, $g_A^3$, are calculated within the external field QCD sum-rule approach. The isospin violations arising from the difference in up and down current quark masses and in up and down quark condensates are included; electromagnetic effects are not considered. We find $\delta g^3_A/g^3_A \approx (0.5-1.0)\times 10^{-2}$, where $\delta g^3_A = (g^3_A)_p + (g^3_A)_n$ and $g^3_A = [(g^3_A)_p - (g^3_A)_n]/2$. Using the Goldberger-Treiman relation, we also obtain an estimate of the isospin breaking in the pion-nucleon coupling constant, $(g_{pp\pi_0}-g_{nn\pi_0})/g_{NN\pi} \approx (2-7) \times 10^{-3}$.
 High Energy Physics - Phenomenology , 2007, DOI: 10.1142/S0217751X08039931 Abstract: The chiral effective Lagrangian for pseudoscalar nonet is constructed in consideration of isospin breaking. And the difference of quark condensates is taken accounted. The SU(3) singlet eta0 is not taken as Goldstone-boson. The mixing with and without isospin symmetry is considered. The quark mass ratios are obtained through solving the mass equations of mesons. We estimate the change of quark mass ratios according to the change of the masses of pion+ and kaon+ to see how the electromagnetic corrections affect our results. It turn out that massless up quark is possible. The upper limit for mu/md is around 0.39. 2ms/(mu+md)=24.23~25.12. The values for quark condensate ratios and other constants are limited in narrow ranges.
 J. A. Niskanen Physics , 2001, DOI: 10.1103/PhysRevC.65.037001 Abstract: The effect of isospin breaking pion s-wave rescattering is included in elastic NN scattering at low energies using effective field theory. Although this mechanism gave a large contribution to charge symmetry breaking in np --> d pi0, the effect is rather small in pp vs. nn scattering parameters and in the 3H-3He binding energy difference. This smallness is caused by large cancellation of the up-down quark mass difference contribution and electromagnetic effects to the np mass difference.
 Physics , 1996, DOI: 10.1103/PhysRevC.55.3093 Abstract: We use QCD sum rules for the three point function of a pseudoscalar and two nucleonic currents in order to estimate the charge dependence of the pion nucleon coupling constant $g_{NN\pi}$ coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates $<{\bar u}u>$ and $<{\bar d}d>$. For the splitting $(g_{pp\pi_0} - g_{nn\pi_0}) / g_{NN\pi}$ we obtain an interval of $1.2 * 10^{-2}$ to $3.7 * 10^{-2}$, the uncertainties coming mainly from the input parameters. The charged pion nucleon coupling is found to be the average of $g_{pp\pi_0}$ and $g_{nn\pi_0}$. Electromagnetic effects are not included.
 Physics , 2012, Abstract: In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon-nucleon scattering. Based on the pi^{+/-} p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a^{1/2}=(170.5 +/- 2.0) x 10^{-3} mpi^{-1} and a^{3/2}=(-86.5 +/- 1.8) x 10^{-3} mpi^{-1}.
 Physics , 2004, DOI: 10.1103/PhysRevC.72.065205 Abstract: Coulomb and mass difference corrections to low-energy pion-nucleon scattering are calculated and compared with previous work including potential models, dispersion relation methods and chiral perturbation theory calculations. Particular attention is paid to their role in testing isospin breaking.
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