We determine non-perturbatively the normalisation parameter Z m Z P /Z A as well as the Symanzik coefficients b m and b A − b P , required in O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N f = 3 QCD with O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N f = 2+1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm, are of particular use for the non-perturbative calculation of O(a) improved renormalised quark masses.

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We have calculated the masses of bound states numerically in N = 1 supersymmetric Yang-Mills theory with gauge group SU(2). Using the suitably optimised variational method with an operator basis consisting of smeared Wilson loops and mesonic operators, we are able to obtain the masses of the ground states and first excited states in the scalar, pseudoscalar and spin-½ sectors. Extrapolated to the continuum limit, the corresponding particles appear to be approximately mass degenerate and to fit into the predicted chiral supermultiplets. The extended operator basis including both glueball-like and mesonic operators leads to improved results compared to earlier studies, and moreover allows us to investigate the mixing content of the physical states, which we compare to predictions in the literature.