Lattice determinations of the strange quark mass

The importance of the strange quark mass, as a fundamental parameter of the Standard Model (SM) and as an input to many interesting quantities, has been highlighted in many reviews, eg in Ref [1]. A first principles calculation of ms is possible in lattice QCD but to date there has been a rather large spread in values from lattice calculations. This review aims to clarify the situation by explaining the particular systematic errors and their effects and illustrating the emerging consenus. In addition, a discussion of the strange quark mass is timely given the recent results from KTeV [2] and NA48 [3] for ǫ/ǫ which firmly establish direct CP-violation in the SM and when combined with previous measurements give a world average ǫ/ǫ = (21.2 ± 2.8) × 10. This is in stark disagreement with the theoretical predictions which favour a low ǫ/ǫ [4]. Although in principle ǫ/ǫ does not depend directly on ms in practice it has been an input in current phenomenological analyses. This dependence arises because the matrix elements of the gluonic, 〈Q6〉0, and electroweak, 〈Q8〉2, penguin operators 1 are of the form 〈ππ|Qi|K〉 and final state interactions make them notoriously difficult to calculate directly. They have been, therefore, parameterised in terms of bag parameters, Bi, the strange quark mass, ms and the top quark mass, mt, as discussed in detail in Ref. [4]. A recent review of lattice calculations of the matrix elements is in Ref. [5]. In this talk I will focus on some recent and careful lattice determinations of ms, illustrating the reasons for the large spread in earlier results.