Exclusive Channel Study of the Muon HVP

Article
Report number	arXiv:1910.11745 ; CERN-TH-2019-179
Title	Exclusive Channel Study of the Muon HVP
Author(s)	Bruno, Mattia (CERN) ; Izubuchi, Taku (Brookhaven ; RIKEN BNL) ; Lehner, Christoph (U. Regensburg (main) ; Brookhaven) ; Meyer, Aaron S. (Brookhaven)
Publication	SISSA, 2019-11-26
Imprint	2019-10-25
Number of pages	7
In:	PoS LATTICE2019 (2019) 239
In:	37th International Symposium on Lattice Field Theory, Wuhan, Hubei, China, 16 - 22 Jun 2019, pp.239
DOI	10.22323/1.363.0239
Subject category	hep-lat ; Particle Physics - Lattice
Abstract	The Hadronic Vacuum Polarization (HVP) is a dominant contribution to the theoretical uncertainty of the muon anomalous magnetic moment. The uncertainty in a lattice QCD calculation of the connected light-quark contribution to the HVP is dominated by the long-distance region of the vector correlation function. Explicit studies of the exclusive channels of the HVP diagram make it possible to reconstruct the long-distance behavior of the correlation function. This removes most of the statistical uncertainty of the correlation function. In these proceedings, preliminary results of an exclusive study of the isospin symmetric connected-only vector-vector correlation function using a hybrid of distillation and A2A techniques are presented. The computation is performed on 2+1 flavor M\"obius Domain Wall Fermion ensembles with physical pion mass. Reconstruction of the long-distance correlation function will enable lattice-only calculations of the HVP to achieve precision similar to estimates of the HVP from the R-ratio method on the timescale of the new experimental measurements of the muon anomalous magnetic moment.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020-2024 The authors (License: CC-BY-NC-ND-4.0)

$Bounding method applied to the local vector current correlation function. The upper bound and lower bound are applied as a function of $t_{\text{max}}/a$ along the horizontal axis. The vertical axis is $a_\mu^{HVP}$ in units of $10^{-10}$ as measured from summing up the timeslices on the lattice. The left plot shows the bounding method with no improvement, and the right plot shows the improved bounding method with a 4-state reconstruction applied. As more states are added to the reconstruction, the upper and lower bounds converge at shorter $t_{\text{max}}$. The red point on the left side of both plots shows the optimal value obtained by picking the timeslice that minimizes the uncertainty (numerical values given in the text). In the right plot, the intermediate values from the $N$-state reconstructions with $N<4$ are shown as well.$ $Same as Fig.~\ref{fig:gevp2pi}, except for a GEVP with 2 additional $4\pi$ operators. The new states that appear as a result of the addition of the $4\pi$ operators are denoted as black crosses, while the colors and symbols for the other states are kept consistent with Fig.~\ref{fig:gevp2pi}. Even with the additional operators, the spectrum and overlaps are very strongly correlated with those without the additional operators. The large statistical error for $t_0=4$ in the right plot is associated with overlapping error bars, which results in eigenvalues that are not sorted properly.$ $Left: spectrum obtained from solving the GEVP for a $C(t_0)C^{-1}(t_0+\delta t)$ for fixed $\delta t$. Small values of $t_0$ are subject to contamination from excited states, which is observed as an exponential approach to the asymptotic value at large $t_0$. Right: overlap of the states with the local vector current operator. Both left and right plots should asymptote to the true value in the large $t_0$ limit. In this figure, the GEVP is solved for a 6-operator basis and $\delta t=3$ is used.$ Show more plots

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