# ICHEP 2014

2-9 July 2014
Valencia, Spain

## Fits and Related Systematics for the Hadronic Vacuum Polarization on the Lattice

5 Jul 2014, 13:10
20m
Sala 6+7 ()

### Sala 6+7

Oral presentation Lattice QCD

### Speaker

Santiago Peris (U. Autonoma de Barcelona, Spain)

### Description

(See Attached file.) In order to test the systematic error coming from the extrapolation at low $Q^2$ carried out in present lattice determinations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, we employ a physically motivated model for the isospin-one non-strange vacuum polarization function $\Pi(Q^2)$ [1]. The model is based on the OPAL experimental vector-channel spectral function for energies below the $\tau$ mass and a successful parametrization, including perturbation theory and a model for quark-hadron duality violations, for higher energies. Using the same covariance matrix and $Q^2$ values as in a recent lattice simulation, we then generate fake data for $\Pi(Q^2)$. The fake data is then used to extrapolate to low $Q^2$ and evaluate the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, after which the result is compared to the exact model value. From this comparison we unravel a systematic error much larger than the few-percent total error sometimes claimed for such extractions in the literature. We find that errors deduced from fits using a Vector Meson Dominance ansatz are misleading, typically turning out to be much smaller than the actual discrepancy between the fit and exact model results. The use of a sequence of multipoint Pade approximants appears to provide a safer fitting strategy [2]. Alternatively, the use of one-point Pades based on the coefficients of the Taylor expansion of $\Pi(Q^2)$ at $Q^2=0$ could also prove effective, as recently emphasized in Ref. [3], but only if these coefficients are accurately known, not only for the $s,c$ quarks but also for $u$ and $d$. BIBLIOGRAPHY [1] M.~Golterman, K.~Maltman and S.~Peris, Tests of hadronic vacuum polarization fits for the muon anomalous magnetic moment,'' Phys. Rev. D88, 114508 (2013) [arXiv:1309.2153 [hep-lat]]. [2] C.~Aubin, T.~Blum, M.~Golterman and S.~Peris, Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice,'' Phys. Rev. D86, 054509 (2012) [arXiv:1205.3695 [hep-lat]]. [3] B.~Chakraborty, C.~T.~H.~Davies, G.~C.~Donald, R.~J.~Dowdall, J.~Koponen, G.~P.~Lepage and T.~Teubner, The strange and charm quark contributions to the anomalous magnetic moment of the muon,'' arXiv:1403.1778 [hep-lat].

### Primary author

Santiago Peris (U. Autonoma de Barcelona, Spain)

### Co-authors

Christopher Aubin (Fordham Univ., USA) Kim Maltman (York Univ., Canada) Maarten Golterman (San Francisco State Univ., USA) Tom Blum (Univ. of Connecticut, USA)

 Slides

### Paper

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