Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD (1403.4504v3)

Abstract: We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 - 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI-MOM method. The results for the quark masses converted to the bar{MS} scheme are: mud(2 GeV) = 3.70(17) MeV, ms(2 GeV) = 99.6(4.3) MeV and mc(mc) = 1.348(46) GeV. We obtain also the quark mass ratios ms/mud = 26.66(32) and mc/ms = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate mu/md = 0.470(56), leading to mu = 2.36(24) MeV and md = 5.03(26) MeV.

Up, Down, Strange and Charm Quark Masses in Twisted Mass LQCD

This paper presents a comprehensive lattice QCD determination of the masses of up, down, strange, and charm quarks using gauge configurations from the European Twisted Mass Collaboration (ETMC). The setup includes $N_f = 2+1+1$ dynamical quarks, facilitating an examination that considers light, strange, and charm quarks with masses near their physical values. The calculations leverage three lattice spacings and encompass pion masses ranging from 210 to 450 MeV, allowing precise continuum and chiral extrapolations. A mixed action approach is utilized for the strange and charm sectors, enhancing the accuracy of quark mass estimates.

The renormalization of quark masses follows the RI$^\prime$-MOM method, applied non-perturbatively to achieve the masses in the $\overline{\rm MS}$ scheme: $m_{ud}(2~) = 3.70 (17)$ MeV, $m_s(2~) = 99.6 (4.3)$ MeV, and $m_c(m_c) = 1.348 (46)$ GeV. The paper further expands on quark mass ratios, calculating $m_s / m_{ud} = 26.66 (32)$ and $m_c / m_s = 11.62 (16)$. The mass splitting between neutral and charged kaons is analyzed, leading to $m_u / m_d = 0.470 (56)$, and thus, $m_u = 2.36 (24)$ MeV and $m_d = 5.03 (26)$ MeV.

Key Analysis Details

• Lattice Parameters: Three β values (1.90, 1.95, 2.10) are used, with different lattice volumes for β = 1.90 and 1.95, enabling controlled continuum extrapolations.
• Chiral Extrapolation: Several fit procedures are applied, ranging from ChPT to polynomial expansions, to account for light quark mass dependencies effectively.
• Finite Size Effects (FSE): Predictions for FSE are integrated using the resummed asymptotic formula for pion sectors and additional established formulae for kaon sectors.
• Quark Mass Renormalization: Utilization of different methods ensures comprehensive determination of renormalization constants, helping validate the consistency of the physical quark mass determinations.

Results and Implications

The determination of these quark masses and ratios aids in testing the Standard Model's validity and serves as a benchmark for identifying potential new physics. This comprehensive lattice QCD approach is essential for pinning down the uncertainties in quark masses and exploring their effects on phenomenology. Furthermore, advancements in computational techniques and the refined lattice spacing used here could guide future designs of lattice QCD studies and inform theoretical models with enhanced precision.

Conclusion and Future Prospects

Overall, this paper provides a meticulous analysis of quark masses relevant for advancing QCD studies. While the present work achieves a significant level of precision, ongoing developments in computational power and algorithms may further enhance the precision measurement of non-perturbative elements in QCD. Future directions involve refining lattice spacings and sea quark configurations to achieve even greater accuracy and possibly explore other quark flavors or transition into more complex hadronic structures. Such studies will be pivotal in advancing theoretical and practical insights into the behavior of fundamental particles within the strong force regime.