Detecting the flavor content of the vacuum using the Dirac operator spectrum
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arXiv
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| Format: | Preprint |
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2021
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| author | Liang, Jian Alexandru, Andrei Bi, Yu-Jiang Draper, Terrence Liu, Keh-Fei Yang, Yi-Bo |
| author_facet | Liang, Jian Alexandru, Andrei Bi, Yu-Jiang Draper, Terrence Liu, Keh-Fei Yang, Yi-Bo |
| contents | We compute the overlap Dirac spectrum on three gauge ensembles generated using $2+1$-flavor domain wall fermions. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. The spectral density is determined up to $λ\sim$100 MeV with subpercentage statistical uncertainty. We find that the density is close to a constant below $λ\sim$ 20 MeV as predicted by chiral perturbative theory ($χ$PT), and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order $χ$PT form and using the non-perturbative RI/MOM renormalization, the $\rm SU(2)$ (keeping the strange quark mass at the physical point) and $\rm SU(3)$ chiral condensates at $\overline{\textrm{MS}}$ 2 GeV are determined to be $Σ=(265.4(0.5)(4.2)\ \textrm{MeV})^3$ and $Σ_0=(234.3(0.5)(25.8)\ \textrm{MeV})^3$, respectively. The pion decay constants are also determined to be $F=84.1(1.9)(8.0)$ and $F_0=58.6(0.5)(10.0)$ MeV. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant $L_6$. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with {$\sim10\%-20\%$} statistical uncertainties using the Dirac spectral density. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_05380 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Detecting the flavor content of the vacuum using the Dirac operator spectrum Liang, Jian Alexandru, Andrei Bi, Yu-Jiang Draper, Terrence Liu, Keh-Fei Yang, Yi-Bo High Energy Physics - Lattice High Energy Physics - Phenomenology We compute the overlap Dirac spectrum on three gauge ensembles generated using $2+1$-flavor domain wall fermions. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. The spectral density is determined up to $λ\sim$100 MeV with subpercentage statistical uncertainty. We find that the density is close to a constant below $λ\sim$ 20 MeV as predicted by chiral perturbative theory ($χ$PT), and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order $χ$PT form and using the non-perturbative RI/MOM renormalization, the $\rm SU(2)$ (keeping the strange quark mass at the physical point) and $\rm SU(3)$ chiral condensates at $\overline{\textrm{MS}}$ 2 GeV are determined to be $Σ=(265.4(0.5)(4.2)\ \textrm{MeV})^3$ and $Σ_0=(234.3(0.5)(25.8)\ \textrm{MeV})^3$, respectively. The pion decay constants are also determined to be $F=84.1(1.9)(8.0)$ and $F_0=58.6(0.5)(10.0)$ MeV. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant $L_6$. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with {$\sim10\%-20\%$} statistical uncertainties using the Dirac spectral density. |
| title | Detecting the flavor content of the vacuum using the Dirac operator spectrum |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2102.05380 |