Strange and charm quark contributions to the anomalous magnetic moment of the muon

Abstract

We describe a new technique to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarization using lattice QCD. Our method reconstructs the Adler function, using Padé approximants, from its derivatives at q 2 = 0 obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators on large-volume gluon field configurations that include the effect of up and down (at physical masses), strange and charm quarks in the sea at multiple values of the lattice spacing and multiple volumes and show that 1% accuracy is achievable. For the charm quark contributions we use our previously determined moments with up, down and strange quarks in the sea on very fine lattices. We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarization to be a s µ = 53.41(59) × 10 −10 , and from charm to be a c µ = 14.42(39) × 10 −10 . These are in good agreement with flavour-separated results from non-lattice methods, given caveats about the comparison. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward.

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

“…The second method uses the so-called "time-momentum representation" (TMR) discussed in [51,54,57]. As another variant we consider time moments of the vector correlator [34] to describe the low-momentum region of Π(Q 2 ). We focus primarily on controlling the various sources of systematic uncertainties associated with the lattice approach to a hvp µ , and in particular the problem of constraining the deep infrared region.…”

“…This includes the use of twisted boundary conditions [61][62][63] that are designed to penetrate more deeply into the region near Q 2 = 0 [32,64,65], and the direct determination of the additive renormalization Π(0), either via operator insertions [53] or by computing time moments of the vector correlator [34]. In order to avoid introducing any model dependence it has been proposed to represent Π(Q 2 ) by either Padé approximants…”

“…Therefore, lattice calculations of a hvp µ suffer from the additional difficulty of controlling the small-momentum regime. Various strategies for a model-independent description of the small-Q 2 regime have been discussed in the literature [32,34,[51][52][53][54][55][56].…”

“…A closely related method for determining the subtracted vacuum polarization function Π(Q 2 ) is based on the calculation of the time moments of the vector correlator [34]. The starting point is the expansion of Π(Q 2 ) at low Q 2 , i.e.…”

“…This concerns both a hvp µ , studied in [28][29][30][31][32][33][34][35][36][37][38][39][40], as well as a hlbl µ [41][42][43][44][45][46][47][48][49]. Lattice calculations of a hvp µ proceed by evaluating a convolution integral over Euclidean momenta Q 2 [28,50].…”