[Paper Review] Strange and charm contributions to the HVP from C* boundary conditions

Anian Altherr, Lucius Bushnaq+14 more|arXiv (Cornell University)|Jan 1, 2023

Particle physics theoretical and experimental studies1 citations

TL;DR

This study presents preliminary lattice QCD calculations of the leading strange and charm quark contributions to the hadronic vacuum polarization (HVP) of the muon's anomalous magnetic moment using C★ boundary conditions. Employing two ensembles with 3+1 flavor O(a)-improved Wilson fermions at unphysical pion mass and one lattice spacing, the work finds that the charm quark contribution is highly sensitive to vector current discretization, while the strange quark contribution is robust across methods, with results consistent at the 2σ level for finite-volume effects.

ABSTRACT

We present preliminary results for the determination of the leading strange and charm quark-connected contributions to the hadronic vacuum polarization contribution to the muon's $g-2$. Measurements are performed on the RC$^{\star}$ collaboration’s QCD ensembles, with $3+1$ flavors of $O(a)$ improved Wilson fermions and C$^{\star}$ boundary conditions. The HVP is computed on a single value of the lattice spacing and two lattice volumes at unphysical pion mass. In addition, we compare the signal-to-noise ratio for different lattice discretizations of the vector current.

Motivation & Objective

• To compute the connected strange and charm quark contributions to the leading-order hadronic vacuum polarization (HVP) of the muon g−2.
• To assess the impact of different vector current discretizations (local vs. conserved) on the HVP signal-to-noise ratio and numerical stability.
• To evaluate finite-volume effects using two lattice volumes at the same unphysical pion mass and lattice spacing.
• To lay the groundwork for future inclusion of isospin-breaking effects and disconnected diagrams in the full HVP calculation.

Proposed method

• Lattice QCD simulations are performed on two RC★ collaboration ensembles with 3+1 flavor O(a)-improved Wilson fermions and C★ boundary conditions in spatial directions.
• The hadronic vacuum polarization is computed in the time-momentum representation using the convolution of vector current correlators with the QED kernel.
• Two discretizations of the vector current are employed: local current (V𝑙) and conserved (point-split) current (V𝑐), to assess discretization effects.
• The correlators are fitted to a single-exponential model to extract the ground state contribution, with tail approximations for the strange quark using a cut-off.
• Statistical errors are estimated via bootstrap resampling, and systematic errors are propagated from lattice spacing, ZV, fit range, and cut-off choices.
• Results are obtained at one lattice spacing and two volumes to assess finite-size effects, with no continuum or physical point extrapolation yet performed.

Experimental results

Research questions

• RQ1 How do the strange and charm quark contributions to the HVP depend on the choice of vector current discretization (local vs. conserved)?
• RQ2 What is the magnitude and statistical significance of finite-volume effects on the strange and charm HVP contributions?
• RQ3 How do the signal-to-noise ratios compare between different current discretizations for the HVP computation?
• RQ4 To what extent do the current results support the inclusion of isospin-breaking and disconnected contributions in future HVP determinations?
• RQ5 How do the results compare across two lattice volumes at the same unphysical pion mass and lattice spacing?

Key findings

• The strange quark contribution to the HVP is insensitive to the choice of vector current discretization, with results from local-local and conserved-local currents agreeing within uncertainties.
• The charm quark contribution shows a significant 2σ difference between the local-local and conserved-local discretizations, indicating strong discretization sensitivity.
• For ensemble A400a00b324, the strange quark contribution is 46.7(7)×10−10 (local-local) and 46.2(7)×10−10 (conserved-local), while for B400a00b324 it is 48.5(7)×10−10 and 48.0(7)×10−10 respectively.
• The charm quark contribution is 7.83(8)×10−10 (local-local) and 6.18(7)×10−10 (conserved-local) on ensemble A400a00b324, with similar values on ensemble B400a00b324.
• Finite-volume effects are found to be negligible for the charm contribution, but contribute to the 2σ discrepancy in the strange quark result between the two ensembles.
• The study identifies the need for improved lattice spacing determination and a more accurate tail model for the strange quark correlator to reduce systematic uncertainties.