[Paper Review] Isospin breaking corrections to the HVP at the physical point

Vera Gülpers, Andreas Jüttner+2 more|arXiv (Cornell University)|Dec 22, 2018

Particle physics theoretical and experimental studies15 references4 citations

TL;DR

This paper presents the first lattice QCD calculation of isospin breaking corrections to the hadronic vacuum polarization (HVP) at the physical quark masses, including both QED and strong isospin breaking effects using Domain Wall fermions. The results show isospin breaking corrections to the muon's anomalous magnetic moment are at the 1% level, with key contributions from connected and disconnected QED corrections and connected strong isospin breaking, enabling precision lattice QCD determinations of $a_\mu^{HVP}$ at the 1% level.

ABSTRACT

A determination of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon from lattice QCD aiming at a precision of $1\%$ requires to include isospin breaking corrections in the computation. We present a lattice calculation of the QED and strong isospin breaking corrections to the hadronic vacuum polarization with Domain Wall fermions. The results are obtained using quark masses which are tuned such that pion and kaon masses agree with their physical values including isospin breaking corrections.

Motivation & Objective

• To compute isospin breaking corrections to the hadronic vacuum polarization (HVP) at the physical point for the muon's anomalous magnetic moment.
• To include both QED and strong isospin breaking effects in lattice QCD simulations using physical quark masses.
• To enable lattice QCD determinations of $a_\mu^{HVP}$ with a precision goal of 1% by accounting for isospin breaking.
• To tune quark masses to reproduce physical pion and kaon masses, including electromagnetic and mass splitting effects.
• To estimate systematic uncertainties from neglected diagrams and fit ansatz, ensuring robustness of the final $a_\mu$ result.

Proposed method

• Use an expansion in $\alpha$ and $\Delta m_f$ around the isospin symmetric limit to compute QED and strong isospin breaking corrections to the HVP correlation function.
• Calculate connected QED corrections (diagrams V, S) and the leading disconnected QED correction (diagram F) using local vector currents and $Z_V$-improved renormalization.
• Compute the quark-connected strong isospin breaking correction (diagram M) via mass insertion with $\Delta m_f = m_f - m_f^0$.
• Tune up, down, and strange quark masses to reproduce physical $m_{\pi^+}$, $m_{K^+}$, and $m_{K^0}$, including QED and mass splitting effects.
• Use a $48^3 \times 96$ lattice with $N_f=2+1$ Mobius Domain Wall fermions at $a^{-1} = 1.730(4)$ GeV and apply chiral perturbation theory for finite volume corrections.
• Fit correlation functions using a two-state ansatz with $\pi\pi$ intermediate states, and vary fit parameters to estimate systematic errors.

Experimental results

Research questions

• RQ1 What is the magnitude of QED isospin breaking corrections to the HVP at the physical point?
• RQ2 What is the contribution of strong isospin breaking due to the $m_d - m_u$ mass splitting to the HVP at physical quark masses?
• RQ3 How do disconnected QED diagrams contribute to the HVP, and what is their impact on $a_\mu^{HVP}$?
• RQ4 Can lattice QCD achieve 1% precision in $a_\mu^{HVP}$ by including isospin breaking effects at the physical point?
• RQ5 What are the dominant systematic uncertainties in the current calculation, and how can they be reduced in future work?

Key findings

• The connected QED correction to $a_\mu^{HVP}$ is $a_\mu^{\text{QED, conn}} = 1.6(1.4)_{S}(0.4)_{E}(0.1)_{C}(0.1)_{V}(0.0)_{A}(0.0)_{Z} \times 10^{-10}$.
• The leading disconnected QED correction is $a_\mu^{\text{QED, disc}} = -6.9(2.1)_{S}(1.3)_{E}(0.4)_{C}(0.4)_{V}(0.0)_{A}(0.0)_{Z} \times 10^{-10}$.
• The connected strong isospin breaking correction is $a_\mu^{\text{sIB}} = 10.6(4.3)_{S}(1.3)_{E}(0.6)_{C}(6.6)_{V}(0.1)_{A}(0.0)_{Z} \times 10^{-10}$.
• The total isospin breaking correction to $a_\mu^{HVP}$ is found to be at the 1% level, consistent with the target precision of 1% for lattice QCD determinations.
• Systematic errors from neglected diagrams are estimated as 30% of the QED correction and 10% of the strong isospin breaking correction, with finite volume effects estimated via chiral perturbation theory.
• The results represent the first direct lattice QCD calculation of isospin breaking corrections to HVP at the physical point, enabling future improvements toward 1% precision.