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

Abstract

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 5 / 5 , where q ( ) denotes the soft (hard) scale.

Chiral effective field theory and nuclear forces

“…For a more comprehensive and systematic study, the interested reader is referred to Ref. [186]. It is well known that the pion-mass difference is mainly due to electro-magnetic interactions among the quarks and, thus, according to Eq.…”

Local chiral effective field theory interactions and quantum Monte Carlo applications

“…(3), (4), (6)- (8), (13)- (15), (23), and (24), we take into account isospin-symmetrybreaking corrections [35]. We include long-range chargeindependence breaking (CIB) terms due to the pion mass splitting in the OPE potential,…”

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

“…However, this difference is ignored in the NLO and N2LO loop corrections which have been evaluated with m π = (2 m π + + m π 0 ) /3. Additional (and small) isospin symmetry breaking terms arising from OPE [49] and TPE [50] and from OPE and one-photon exchange [51,52] have also been neglected.…”