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By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to about 190 MeV in large volumes (M_pi L > 4), and three values of the lattice spacing. Our main results are the nucleon sigma term sigma_{pi N} = 39(4)(^{+18}_{-7}) and the strangeness content y_{N} = 0.20(7)(^{+13}_{-17}). Under the assumption of validity of covariant baryon chi PT in our range of masses one finds y_{N} = 0.276(77)(^{+90}_{-62}).
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A status report is given for a joint project of the Budapest-Marseille-Wuppertal collaboration and the Regensburg group to study the quark mass-dependence of octet baryons in SU(3) Baryon XPT. This formulation is expected to extend to larger masses than Heavy-Baryon XPT. Its applicability is tested with 2+1 flavor data which cover three lattice spacings and pion masses down to about 190 MeV, in large volumes. Also polynomial and rational interpolations in M_pi^2 and M_K^2 are used to assess the uncertainty due to the ansatz. Both frameworks are combined to explore the precision to be expected in a controlled determination of the nucleon sigma term and strangeness content.
We evaluate the strangeness-conserving $N N$, $SigmaSigma$, $XiXi$, $LambdaSigma$ and the strangeness-changing $Lambda N$, $Sigma N$, $LambdaXi$, $SigmaXi$ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson-octet-baryon coupling constants so as to include $piXiXi$, $KLambdaXi$ and $KSigmaXi$ coupling constants. We find that the axial charges have rather weak quark-mass dependence and the breaking in SU(3)-flavor symmetry is small at each quark-mass point we consider.
We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039,mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.
We present results for the $sigma$-terms and axial charges for various hyperons and charmed baryons using $N_f=2+1+1$ twisted mass fermions. For the computation of the three-point function we use the fixed current method. For one of the $N_f=2+1+1$ ensembles with pion mass of 373 MeV we compare the results of the fixed current method with those obtained with a stochastic method for computing the all-to-all propagator involved in the evaluation of the three point functions.
The pion-nucleon $sigma$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3sigma$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.
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