Quark masses

Electric dipole moments of light nuclei from chiral effective field theory

“…The electromagnetic contribution isδm N = O(α em M QCD /4π), which is O(εm 3 π /M 2 QCD ) and about the 20% of δm N . From the Cottingham sum rule [57] one findsδm N = −(0.76 ± 0.30) MeV, which is consistent with dimensional analysis. In order to achieve the form (6) for L P T , we have used a field redefinition [53] to eliminate the nucleon mass difference term in favor of pionic mass and interaction terms.…”

Charge symmetry violation in pn→dπ0 and chiral effective field theory

“…Most models estimate thatδm N ≈ −α/R N ≃ −1.5 MeV [2], in which case δm N ≃ 3 MeV. We will refer to these values, which are also consistent with the results of Gasser and Leutwyler [11], as "quark model estimates" .…”

“…Indeed, A f b nearly vanishes if this is 1 MeV instead of 4 MeV. However, there are estimates cited in the reviews [1,2,11] which would obtain δm N −δm N /2 significantly greater than 4 MeV. The energy dependence of the amplitudes around this energy is as expected (s wave independent of momentum, p wave proportional to q).…”

Cosmology and the standard model

“…Even for the smallest universe that we shall consider, with radius 100 microns, there is good separation (a factor [10][11][12][13][14][15][16][17][18][19][20] between the electroweak scale and the strong interaction scale. Heavy quarks, electroweak gauge bosons, Higgs particles, etc.…”

“…It is composed of two pieces. The dominant one is due to the mass difference of the up and down (current-) quarks, and the other is electromagnetic [11]. Schematically we may write…”