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The Light Quark Connected Hadronic Vacuum Polarization Contribution to the muon anomaly via Sparsened Meson Fields

Vaishakhi Moningi, Christopher Aubin, Thomas Blum, Maarten Golterman, Luchang Jin, Santiago Peris

Abstract

We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, $a_μ$, on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size $144^3 \times 288$ sites. Within the low-mode averaging (LMA) framework, the HVP correlator is decomposed into low-low (LL), high-low (HL), low-high (LH) and high-high (HH) components. Since the LL part dominates the total statistical uncertainty but is also the most computationally expensive to evaluate, we implement a sparsening strategy to construct the meson fields efficiently. This approach significantly reduces the computational cost while preserving signal quality. By combining the sparsened LL contribution with HL, LH and HH components, we achieve an improved determination of the light-quark connected HVP contribution to $a_μ$.

The Light Quark Connected Hadronic Vacuum Polarization Contribution to the muon anomaly via Sparsened Meson Fields

Abstract

We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, , on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size sites. Within the low-mode averaging (LMA) framework, the HVP correlator is decomposed into low-low (LL), high-low (HL), low-high (LH) and high-high (HH) components. Since the LL part dominates the total statistical uncertainty but is also the most computationally expensive to evaluate, we implement a sparsening strategy to construct the meson fields efficiently. This approach significantly reduces the computational cost while preserving signal quality. By combining the sparsened LL contribution with HL, LH and HH components, we achieve an improved determination of the light-quark connected HVP contribution to .
Paper Structure (11 sections, 11 equations, 6 figures, 3 tables)

This paper contains 11 sections, 11 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Lattice details
  4. Motivation
  5. Low-low contribution to $C(t)$
  6. Sparsening of Meson Fields
  7. Results
  8. Window Quantities
  9. Window 0.4-1.0 fm
  10. Window 1.5-1.9 fm
  11. Conclusion

Figures (6)

  • Figure 1: Left: Sparsening of factor (s=4,t=1) on 6 different configurations on $144$c ensemble. Right: Sparsening of factor (s=2,t=1) on the same 24 configurations on $48$I ensemble
  • Figure 2: Left: Summand in $w(t)C(t)$ Eq. (\ref{['C(t)_sep']}). Middle: Quantitative breakdown of the statistical error in terms of LL, HH, HL on the summand. Right: $(a_\mu(T; t_b))$ using the bounding method, as a function of the switch-point $t_b$.
  • Figure 3: Left: SChPT NNLO fits -- linear, blue (dashed=no TB, solid=TB). Right: ChVM fits -- linear, red (dashed=no TB, solid=TB). Data points match fit colors; continuum limits in black. Gray points show uncorrected values from Table \ref{['tab:lattice_data']}.
  • Figure 4: Comparison of our lattice determinations for $a_\mu^{\mathrm{HVP,lqc}}$(red circles) with other lattice results (black circles) and data-driven results (green squares)
  • Figure 5: Left: SChPT fits - NNLO quadratic, blue (dashed = no TB, solid = with TB). NLO yellow: quadratic (dotted = no TB) and linear (dot-dashed = with TB). Right: ChVM quadratic, red (dashed = no TB, solid = with TB). Continuum limits in black. Gray points show uncorrected values from Table \ref{['tab:lattice_data']}.
  • ...and 1 more figures