[Paper Review] Light quark masses and pseudoscalar decay constants from Nf=2 twisted mass QCD

V. Lubicz, Silvano Simula+1 more|ArXiv.org|Oct 1, 2007

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This lattice QCD study computes light quark masses and pseudoscalar decay constants using $N_f=2$ twisted mass fermions at maximal twist, ensuring ${\cal O}(a)$ improvement. Non-perturbative RI-MOM renormalization yields $m_{ud}^{\overline{\text{MS}}}(2\,\text{GeV}) = 3.85 \pm 0.12 \pm 0.40\,\text{MeV}$, $m_s^{\overline{\text{MS}}}(2\,\text{GeV}) = 105 \pm 3 \pm 9\,\text{MeV}$, $f_K = 161.7 \pm 1.2 \pm 3.1\,\text{MeV}$, and $f_K/f_\pi = 1.227 \pm 0.009 \pm 0.024$, with $|V_{us}| = 0.2192(5)(45)$ in agreement with unitarity and $K_{\ell 3}$ decays.

ABSTRACT

We present the results of the lattice QCD calculation of the average up-down and strange quark masses and of the light meson pseudoscalar decay constants, recently performed with Nf=2 dynamical fermions by the ETM Collaboration. The simulation is carried out at a single value of the lattice spacing with the twisted mass fermionic action at maximal twist, which guarantees automatic O(a)-improvement of the physical quantities. Quark masses are renormalized by implementing the non perturbative RI-MOM renormalization procedure. Our results for the light quark masses are m_{ud}^{MSbar}(2 Gev)=3.85 +- 0.12 +- 0.40 MeV, m_s^{MSbar}(2 Gev)=105 +- 3 +- 9 MeV and m_s/m_{ud}=27.3 +- 0.3 +- 1.2. We also obtain f_K=161.7 +- 1.2 +- 3.1 MeV and the ratio f_K/f_pi=1.227 +- 0.009 +- 0.024. From this ratio, by using the experimental determination of Gamma(K -> mu {bar nu}_mu (gamma))/Gamma(pi -> mu {bar nu}_mu (gamma)) and the average value of |V_{ud}| from nuclear beta decays, we obtain |V_{us}|=0.2192(5)(45), in agreement with the determination from K_{l3} decays and the unitarity constraint.

Motivation & Objective

• To determine the average up-down and strange quark masses in the $\overline{\text{MS}}$ scheme at $2\,\text{GeV}$ using lattice QCD with $N_f=2$ dynamical fermions.
• To compute the pseudoscalar decay constants $f_K$ and $f_\pi$, and their ratio $f_K/f_\pi$, with high precision.
• To test the consistency of the CKM matrix unitarity by combining the lattice result for $f_K/f_\pi$ with experimental $K_{\ell 3}$ decay data to extract $|V_{us}|$.
• To assess the impact of non-perturbative renormalization on quark mass determinations, particularly the role of $Z_P^{\text{RI-MOM}}$ in reducing systematic uncertainties.

Proposed method

• Simulations performed using the twisted mass fermionic action at maximal twist on $N_f=2$ dynamical fermions with the tree-level improved Symanzik gauge action at $\beta=3.9$, corresponding to $a \approx 0.087\,\text{fm}$.
• Non-perturbative RI-MOM scheme used to determine the quark mass renormalization constant $Z_P^{\text{RI-MOM}}(1/a) = 0.39(1)(2)$, significantly smaller than one-loop perturbative estimates.
• Two-point correlation functions of charged pseudoscalar mesons computed using stochastic Z(2) noise sources on 240 gauge configurations, with jackknife and bootstrap methods for error estimation.
• Pseudoscalar decay constants extracted via the relation $f_{PS} = (\mu_1 + \mu_2) \cdot |\langle 0|P^1(0)|P\rangle| / M_{PS}^2$, with matrix elements from time-slice fits in $t/a \in [10,21]$.
• Quark mass dependence of meson masses and decay constants analyzed using polynomial, partially quenched chiral perturbation theory (PQChPT), and constrained PQChPT (C-PQChPT) fits.
• Final results obtained via weighted average of three fit types, with systematic errors conservatively estimated from spread across fits and uncertainties in lattice scale and $Z_P$.

Experimental results

Research questions

• RQ1 What are the precise values of the up-down and strange quark masses in the $\overline{\text{MS}}$ scheme at $2\,\text{GeV}$, using $N_f=2$ twisted mass fermions?
• RQ2 How does the use of non-perturbative RI-MOM renormalization affect the determination of quark masses compared to perturbative estimates?
• RQ3 What is the value of the ratio $f_K/f_\pi$ from lattice QCD, and how does it compare with experimental $K_{\ell 3}$ decays and CKM unitarity?
• RQ4 To what extent do chiral perturbation theory fits, including NNLO terms, describe the quark mass dependence of pseudoscalar masses and decay constants?

Key findings

• The average up-down quark mass is determined as $m_{ud}^{\overline{\text{MS}}}(2\,\text{GeV}) = 3.85 \pm 0.12 \pm 0.40\,\text{MeV}$, with the systematic error dominated by uncertainties in the lattice scale and $Z_P$.
• The strange quark mass is found to be $m_s^{\overline{\text{MS}}}(2\,\text{GeV}) = 105 \pm 3 \pm 9\,\text{MeV}$, in good agreement with other non-perturbative lattice determinations.
• The kaon decay constant is computed as $f_K = 161.7 \pm 1.2 \pm 3.1\,\text{MeV}$, with a precision of 0.7% on the statistical error.
• The ratio $f_K/f_\pi = 1.227 \pm 0.009 \pm 0.024$ is in excellent agreement with the experimental $K_{\ell 3}$ determination and CKM unitarity.
• The resulting $|V_{us}| = 0.2192(5)(45)$ is consistent with the $K_{\ell 3}$ value of $0.2255(19)$ and satisfies the unitarity constraint within $2\sigma$.
• Non-perturbative renormalization is found to be crucial: using perturbative $Z_P$ would have led to a $m_{ud}$ value $30\%$ smaller, highlighting its dominant impact over quenching effects.