Isospin–violating nucleon–nucleon forces using the method of unitary transformation

Recently, we have derived the leading and subleading isospin–breaking three–nucleon forces using the method of unitary transformation. In the present work we extend this analysis and consider the corresponding two–nucleon forces using the same approach. Certain contributions to the isospin– violating one– and two–pion–exchange potential have already been discussed by various groups within the effective field theory framework. Our findings agree with the previously obtained results. In addition, we present the expressions for the subleading charge–symmetry–breaking two–pion exchange potential which were not considered before. These corrections turn out to be numerically important. Together with the three–nucleon force results presented in our previous work, the results of the present study specify completely isospin–violating nuclear forces up to the order q/Λ, where q (Λ) denotes the soft (hard) scale.