QCD Sum-Rule Bounds on the Light Quark Masses

QCD sum-rules are related to an integral of a hadronic spectral function, and hence must satisfy integral inequalities which follow from positivity of the spectral function. Development of these Hölder inequalities and their application to the Laplace sum-rule for pions lead to a lower bound on the average of the non-strange 2GeV light-quark masses in the MS scheme. The light quark masses are fundamental parameters of QCD, and determination of their values is of importance for high-precision QCD phenomenology and lattice simulations involving dynamical quarks. In this paper the development of Hölder inequalities for QCD Laplace sum-rules [1] is briefly reviewed. These techniques are then used to obtain bounds on the non-strange (current) quark masses mn = (mu +md) /2 evaluated at 2GeV in the MS scheme, updating and extending the Hölder inequality results of ref. [2]. Although it is possible to obtain quark mass ratios in various contexts [3], the only methods which have been able to determine the absolute non-strange quark mass scales are the lattice (see [4] for recent results with two dynamical flavours) and QCD sum-rules [2, 5, 6, 7, 8, 9]. In sum-rule and lattice approaches, the pseudoscalar or scalar channels are used since they have the strongest dependence on the quark masses. This is exemplified by the correlation function Π5 (Q ) of renormalization-group (RG) invariant pseudoscalar currents with quantum numbers of the pion: Π5 ( Q )