Johannes Najjar

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

Abstract We analyze N f = 2 nucleon mass data with respect to their dependence on the pion mass down to m π = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion–nucleon σ-term. Our lattice data below m π = 435 MeV is well described by O ( p 4 ) BChPT and we find σ = 37 ( 8 ) ( 6 ) MeV for the σ-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r 0 = 0.501 ( 10 ) ( 11 ) fm .

Isospin breaking in octet baryon mass splittings

Using an SU(3) flavour symmetry breaking expansion in the quark mass, we determine the QCD component of the nucleon, Sigma and Xi mass splittings of the baryon octet due to up-down (and strange) quark mass differences in terms of the kaon mass splitting. Provided the average quark mass is kept constant, the expansion coefficients in ourprocedure can be determined from computationally cheaper simulations with mass degenerate sea quarks and partially quenched valence quarks. Both the linear and quadratic terms in the SU(3) flavour symmetry breaking expansion are considered; it is found that the quadratic terms only change the result by a few percent, indicating that the expansion is highly convergent.

The moment

We present an update of our analysis [1] which includes additional ensembles at different quark masses, lattice spacings and volumes, all with high statistics. We use

\langle x\rangle_{u-d}

N_f=2

of the nucleon from

mass-degenerate quark flavours, employing the non-perturbatively improved clover action. The lattice matrix elements are converted to the

N_f=2

\overline{\rm MS}

lattice QCD down to nearly physical quark masses

scheme via renormalization factors determined non-perturbatively in the RI

Lattice determination of Sigma-Lambda mixing

^\prime

SU(3) flavour symmetry breaking and charmed states

-MOM scheme. We have systematically investigated excited state contributions, in particular, at the smallest, near physical, pion mass. While our results~(with much increased precision) are consistent with Ref.~[1], comparing with previous determinations we find that excited state contributions can be significant if the quark smearing is not suitably optimized, in agreement with other recent studies. The difference with respect to the value for

Moments of structure functions for

\langle x\rangle_{u-d}