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Baryon masses with C-periodic boundary conditions

Anian Altherr, Isabel Campos, Roman Gruber, Tim Harris, Francesca Margari, Marina Krstić Marinković, Letizia Parato, Agostino Patella, Sara Rosso, Paola Tavella

Abstract

Isospin-breaking corrections pose a significant challenge to lattice simulations, both because of the splitting between the up and down quark masses and, in particular, the need to include QED effects. The RC* collaboration has developed the openQxD code, based on openQCD, which enables fully dynamical QCD+QED simulations through the implementation of C-periodic boundary conditions. We use this code to measure baryon masses, with a special focus on the {Ω^-} baryon mass, whose precise determination is especially important since it has been used to set the scale of lattice simulations. Due to the use of C-periodic boundary conditions, the two-point function of the {Ω^-} baryon gets additional partially connected contributions, which vanish in the infinite-volume limit and which we are computing for the first time. We will present preliminary results for baryon masses obtained on QCD ensembles with C-periodic boundary conditions, at an unphysical pion mass of approximately 400 MeV.

Baryon masses with C-periodic boundary conditions

Abstract

Isospin-breaking corrections pose a significant challenge to lattice simulations, both because of the splitting between the up and down quark masses and, in particular, the need to include QED effects. The RC* collaboration has developed the openQxD code, based on openQCD, which enables fully dynamical QCD+QED simulations through the implementation of C-periodic boundary conditions. We use this code to measure baryon masses, with a special focus on the {Ω^-} baryon mass, whose precise determination is especially important since it has been used to set the scale of lattice simulations. Due to the use of C-periodic boundary conditions, the two-point function of the {Ω^-} baryon gets additional partially connected contributions, which vanish in the infinite-volume limit and which we are computing for the first time. We will present preliminary results for baryon masses obtained on QCD ensembles with C-periodic boundary conditions, at an unphysical pion mass of approximately 400 MeV.
Paper Structure (6 sections, 19 equations, 5 figures, 2 tables)

This paper contains 6 sections, 19 equations, 5 figures, 2 tables.

Table of Contents

  1. Isospin breaking and C-periodic boundary conditions
  2. Two-point function of the $\Omega^-$ baryon
  3. Numerical results
  4. 3-q connected contributions
  5. 1-q connected contributions
  6. Conclusions and outlook

Figures (5)

  • Figure 1: 2-dimensional section of a 4-dimensional lattice representing the orbifold construction used to implement C-periodic boundary conditions. Figure taken from open.code
  • Figure 2: Proton and $\Omega^-$ effective masses together with the selected plateaux and the fits to a constant for the ensemble B400a00b324. Values in MeV are obtained by using the reference value $(8t_0 )^{1/2} =$ 0.415 fm.
  • Figure 3: Proton and $\Omega^-$ effective masses together with the selected plateaux and the fits to a constant for the ensemble A400a00b324. Values in MeV are obtained by using the reference value $(8t_0 )^{1/2} =$ 0.415 fm.
  • Figure 4: Results for the $\Omega^-$ 2-point function with no smearing. In the left plot are the 3-q connected contributions, in red, and the 1-q connected, in black, with a zoom of the high $t$ region. In the right plot is a comparison of the 3-q correlator with the absolute error on the 1-q correlator, in a logarithmic scale for the y axis.
  • Figure 5: Results for the $\Omega^-$ 2-point function with maximum smearing on the source and none on the sink. In the left plot are the 3-q connected contributions, in red, and the 1-q connected, in black, with a zoom of the high $t$ region. In the right plot is a comparison of the 3-q correlator with the absolute error on the 1-q correlator, in a logarithmic scale for the y axis.