$α_s$ from the Lattice Hadronic Vacuum Polarisation

Abstract

We present a determination of the QCD coupling constant, α s , obtained by fitting lattice results for the flavour ud hadronic vacuum polarisation function to continuum perturbation theory. We use n f = 2 + 1 flavours of Domain Wall fermions generated by the RBC/UKQCD collaboration and three lattice spacings a −1 = 1.79, 2.38 and 3.15 GeV. Several sources of potential systematic error are identified and dealt with. After fitting and removing expected leading cut-off effects, we find for the five-flavour MS coupling the value α s (M Z ) = 0.1181(27) +8−22 , where the first error is statistical and the second systematic.

Determination of the QCD coupling from the static energy and the free energy

“…Our result agrees with the very recent lattice determination in terms of pseudoscalar quarkonium correlators [25], α s (M Z , N f = 5) = 0.1159 (12), or the preceding analysis of charmonium correlators [26], α s (M Z , N f = 5) = 0.11622(83), or the analyses of higher quarkonium moments [27] α s (M Z , N f = 5) = 0.1176 (26). Moreover, our result is consistent within errors with the recent lattice determinations from the hadronic vacuum polarization [28] α s (M Z , N f = 5) = 0.1181(27) +0.0008 −0.0022 , or from the gauge-fixed gluon propagator in Landau gauge [29], α s (M Z , N f = 5) = 0.1172 (11).…”

Hadronic vacuum polarization contribution to the muon g−2 with ( 2+1 )-flavor lattice QCD on a larger than Shintani1, Kuramashi2 2019Phys. Rev. DSelf Cite815660View full textAdd to dashboardCite

“…( 5) has extra contributions of O((aQ) n ) with n ≥ 2 due to the Lorentz symmetry breaking on the discretized space-time in LQCD. After subtracting these lattice artifacts [25][26][27] Π(Q 2 ) computed with LQCD is consistent with the perturbative representation of the Adler function [28] in high Q 2 > 1 GeV 2 except for the nonperturbative objects such as the d-dimensional operator condensate term given by O d /Q 2d appearing in the operator product expansion (OPE) [29]. For the actual computation of a hvp µ , the LQCD evaluation of the integral of Eq.…”

Spectral sum of current correlators from lattice QCD

“…The Borel transformation reduces the dependence on this assumption. The integral in (7) with ρ ph (s) should correspond to the OPE expression in (11). Namely,…”

“…In principle, the test of perturbative expansion and OPE can be performed using nonperturbatively calculated correlation functions using lattice QCD. Comparison of the lattice correlators at short distances with perturbative QCD may be found, e.g., in [4][5][6][7] for lighthadron current-current correlators and in [8,9] for charmonium correlators. The energy scale where the comparison is made has to be sufficiently low to avoid discretization effects in the lattice calculations, while the OPE analysis is more reliable at high energy scales.…”

“…The energy scale where the comparison is made has to be sufficiently low to avoid discretization effects in the lattice calculations, while the OPE analysis is more reliable at high energy scales. It has been pointed out that the convergence of OPE is a crucial problem in the energy region for which lattice QCD can provide reliable calculations by now [7,10].…”