Strange quark mass frome+e−revisited and present status of light quark masses

2005/10/31 by Stéphan Narison, Stephan Narison
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ex #hep-lat #hep-ph #nucl-th

paper · pdf · doi:10.1103/physrevd.74.034013

published as Phys.Rev.D74:034013,2006 · Updated and improved average values. Version to appear in Phys. Rev. D

arxiv created 2006/07/20 · openalex publication_date 2006/08/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We reconsider the determinations of the strange quark mass m_s from e⁺e^\ensuremath- into hadrons data using a new combination of finite energy sum rules (FESR) and revisiting the existing \ensuremathτ-like sum rules by including nonresonant contributions to the spectral functions. To order \ensuremathα_s³ and including the tachyonic gluon mass \ensuremathλ² contribution, which phenomenologically parametrizes the UV renormalon effect into the perturbative series, we obtain the invariant mass \stackrel^m_s=(119\ifmmode±\else\textpm\fi17) MeV leading to m_s(2 GeV)=(104\ifmmode±\else\textpm\fi15) MeV. Combining this value with the recent and independent phenomenological determinations from some other channels, to order \ensuremathα_s³ and including \ensuremathλ², we deduce the weighted average m_s(2 GeV)=(96.1\ifmmode±\else\textpm\fi4.8) MeV. The positivity of the spectral functions in the (pseudo)scalar (resp. vector) channels leads to the lower (resp. upper) bounds of m_s(2 GeV): (71\ifmmode±\else\textpm\fi4) MeV\ensuremath≤m_s(2 GeV)\ensuremath≤(151\ifmmode±\else\textpm\fi14) MeV, to order \ensuremathα_s³. Using the chiral perturbation theory (ChPT) mass ratio r₃\ensuremath≡2m_s/(m_u+m_d)=24.2\ifmmode±\else\textpm\fi1.5, and the average value of m_s, we deduce (m_u+m_d)(2 GeV)=(7.9\ifmmode±\else\textpm\fi0.6) MeV, consistent with the pion sum rule result, which, combined with the ChPT value for m_u/m_d, gives m_d(2 GeV)=(5.1\ifmmode±\else\textpm\fi0.4) MeV and m_u(2 GeV)=(2.8\ifmmode±\else\textpm\fi0.2) MeV. Finally, using (m_u+m_d) from the pion sum rule and the average value of m_s (without the pion sum rule), the method gives r₃=23.5\ifmmode±\else\textpm\fi5.8, in perfect agreement with the ChPT ratio, indicating the self-consistency of the sum rule results. Using the value m_b(m_b)=(4.23\ifmmode±\else\textpm\fi0.06) GeV, we also obtain the scale-independent mass ratio m_b/m_s=50\ifmmode±\else\textpm\fi3, which is useful for model-buildings. Absolute values of the light quark masses from QCD spectral sum rules reported in this paper are the most accurate determinations to date.

Citations

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