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Neutral mesons and disconnected diagrams in Twisted Mass QCD

ETM Collaboration, Chris Michael, Carsten Urbach

TL;DR

This work studies neutral mesons in $N_f=2$ twisted mass QCD at maximal twist, with a focus on disconnected diagrams essential for neutral states. It introduces and validates a variance-reduction strategy, notably the one-end-trick, to efficiently evaluate disconnected loops, enabling detailed analyses of $\pi^0$, $\eta_2$, vector mesons, and flavour-singlet scalars. Key results show the $\pi^0$–$\pi^+$ mass splitting scales as $a^2$, an $\eta_2$ mass around $0.88$ GeV, negligible flavor splitting for vector mesons with accessible decay channels, and a flavour-singlet scalar channel dominated by the two-pion state. The findings illuminate practical TMQCD techniques for neutral hadrons and underscore challenges posed by disconnected noise and multi-hadron contributions in light-quark regimes.

Abstract

We evaluate properties of neutral mesons in Nf=2 dynamical simulations of TMQCD at maximal twist. The pion is explored - establishing the size of the isospin splitting (an order a^2 effect). We investigate the eta' (the Nf=2 flavour singlet pseudoscalar meson) and neutral rho and scalar mesons. We show that disconnected diagrams can be evaluated very efficiently in TMQCD using variance reduction methods.

Neutral mesons and disconnected diagrams in Twisted Mass QCD

TL;DR

This work studies neutral mesons in twisted mass QCD at maximal twist, with a focus on disconnected diagrams essential for neutral states. It introduces and validates a variance-reduction strategy, notably the one-end-trick, to efficiently evaluate disconnected loops, enabling detailed analyses of , , vector mesons, and flavour-singlet scalars. Key results show the – mass splitting scales as , an mass around GeV, negligible flavor splitting for vector mesons with accessible decay channels, and a flavour-singlet scalar channel dominated by the two-pion state. The findings illuminate practical TMQCD techniques for neutral hadrons and underscore challenges posed by disconnected noise and multi-hadron contributions in light-quark regimes.

Abstract

We evaluate properties of neutral mesons in Nf=2 dynamical simulations of TMQCD at maximal twist. The pion is explored - establishing the size of the isospin splitting (an order a^2 effect). We investigate the eta' (the Nf=2 flavour singlet pseudoscalar meson) and neutral rho and scalar mesons. We show that disconnected diagrams can be evaluated very efficiently in TMQCD using variance reduction methods.

Paper Structure

This paper contains 7 sections, 1 equation, 5 figures.

Table of Contents

  1. Introduction
  2. Disconnected diagrams - variance reduction
  3. Pion order($a^2$) effects
  4. Flavour singlet PS meson: $\eta_2$
  5. Vector mesons
  6. Flavour singlet scalar mesons
  7. Summary

Figures (5)

  • Figure 1: Ratio of correlators between neutral and charged pions. The left plot is for local operators $\bar{\chi} I \chi$ for $\pi^0$ and $\bar{\chi} \gamma_5 \chi$ for $\pi^+$ and the right plot for local operators $\bar{\chi} \gamma_4 \gamma_5 \tau_3 \chi$ for $\pi^0$ and $\bar{\chi} \gamma_4 \chi$ for $\pi^+$. The curves give the ratio arising from the mass difference determined by the full fit.
  • Figure 2: Pion charge splitting
  • Figure 3: $\eta_2$ mass versus quark mass. Here we summarise results with light pions and $a < 0.1$ fm ($r_0/a> 4.5$).
  • Figure 4: Ratios of correlator for neutral $\rho$-mesons to charged. The dotted lines guide the eye in the case that there is no mass splitting.
  • Figure 5: Transition $\rho^0 \to \pi^+ \pi^-$ from the lattice (with $M(\pi^+)\approx 300$ MeV, $a=0.086$ fm, $La=2.1$ fm ). The solid line is from a two state model ($\rho$ at rest and two pions with momentum $q=\pm 2 \pi/L$) with energy gap $\Delta m a =2aE(\pi)-am(\rho)=0.19$ and transition amplitude $x/a$.