TY - JOUR

T1 - New strategy for the lattice evaluation of the leading order hadronic contribution to (g-2)μ

AU - Golterman, Maarten

AU - Maltman, Kim

AU - Peris, Santiago

PY - 2014/10/22

Y1 - 2014/10/22

N2 - © 2014 American Physical Society. A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval Q2>Qmin2, coupled with an N-parameter Padé or other representation of the polarization in the interval 0<Q2<Qmin2, for sufficiently high Qmin2 and sufficiently large N. Using a physically motivated model for the I=1 polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of Qmin2 and N can be reduced to well below the 1% level for Qmin2 as low as 0.1GeV2 and rather small N. For such low Qmin2, both a next-to-next-to-leading-order (NNLO) chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-Q2 contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a subpercent-precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

AB - © 2014 American Physical Society. A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval Q2>Qmin2, coupled with an N-parameter Padé or other representation of the polarization in the interval 0<Q2<Qmin2, for sufficiently high Qmin2 and sufficiently large N. Using a physically motivated model for the I=1 polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of Qmin2 and N can be reduced to well below the 1% level for Qmin2 as low as 0.1GeV2 and rather small N. For such low Qmin2, both a next-to-next-to-leading-order (NNLO) chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-Q2 contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a subpercent-precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

U2 - 10.1103/PhysRevD.90.074508

DO - 10.1103/PhysRevD.90.074508

M3 - Article

SN - 1550-7998

VL - 90

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 7

M1 - 074508

ER -