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Register a new userNonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
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Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.
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Within the covariant formulation of light-front dynamics, we calculate the state vector of a fermion coupled to identical scalar bosons (the Yukawa model). The state vector is decomposed in Fock sectors and we consider the first three ones: a single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, and these contributions are calculated with no approximations. The divergences of the amplitudes are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we developed. This renormalization scheme is a necessary condition in order to avoid uncancelled divergences when Fock space is truncated. As an example, we present preliminary numerical results for the anomalous magnetic moment of a fermion in the Yukawa model.
A non-perturbative approach based on the Fock decomposition of the state vector and its truncation is discussed. In order the non-perturbative renormalization procedure after truncation could eliminate infinities, it should be the sector dependent. We clarify the meaning of this procedure in a toy model. Then we demonstrate stability, relative to the increasing cutoff, of the anomalous magnetic moment found using the sector dependent renormalization scheme in Yukawa model.
We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be $a_mu^{rm HVP~LO}=715.4(16.3)(9.2) times 10^{-10}$, where the first error is statistical and the second is systematic. By supplementing lattice data for very short and long distances with experimental R-ratio data using the compilation of Ref. [1], we significantly improve the precision of our calculation and find $a_mu^{rm HVP~LO} = 692.5(1.4)(0.5)(0.7)(2.1) times 10^{-10}$ with lattice statistical, lattice systematic, R-ratio statistical, and R-ratio systematic errors given separately. This is the currently most precise determination of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. In addition, we present the first lattice calculation of the light-quark QED correction at physical pion mass.
The quark-connected part of the hadronic light-by-light scattering contribution to the muons anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6;mathrm{fm})^3$ spatial volume using the $32^3times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.
We report our (HPQCD) progress on the calculation of the Hadronic Vacuum Polarisation contribution to the anomalous magnetic moment of muon. In this article we discuss the calculations for the light (up/down) quark connected contribution using our method described in Phys.Rev. D89(2014) 11, 114501 and give an estimate for the disconnected contribution. Our calculation has been carried out on MILC Collaborations $n_f = 2+1+1$ HISQ ensembles at multiple values of the lattice spacing, multiple volumes and multiple light sea quark masses (including physical pion mass configurations).
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