Strange quark mass from e+e- revisited and present status of light quark masses
Abstract
We reconsider the determinations of the strange quark mass ms from e+e- into hadrons data using a new combination of FESR and revisiting the existing tau-like sum rules by including non-resonant contributions to the spectral functions. To order alphas3 and including the tachyonic gluon mass lambda2 contribution, which phenomenologically parametrizes the UV renormalon effect into the PT series, we obtain the invariant mass ms=(119 +- 17)MeV leading to: ms(2 GeV)=(104+- 15)MeV. Combining this value with the recent and independent phenomenological determinations from some other channels, to order alphas3 and including lambda2, we deduce the weighted average: ms (2 GeV)=(96.1 +- 4.8)MeV . The positivity of the spectral functions in the (pseudo)scalar [resp. vector] channels leads to the lower [resp. upper] bounds of ms(2 GeV): (71 +- 4) MeV < ms(2 GeV) < (151 +- 14) MeV, to order alphas3. Using the ChPT mass ratio r3 = 2ms/(mu+md)=24.2 +- 1.5, and the average value of ms, we deduce: (mu+md)(2 GeV)=(7.9 +- 0.6) MeV, consistent with the pion sum rule result, which, combined with the ChPT value for mu/md, gives: md(2 GeV)=(5.1 +- 0.4)MeV and mu(2 GeV)=(2.8 +- 0.2)MeV. Finally, using (mu+md) from the pion sum rule and the average value of ms (without the pion sum rule), the method gives: r3= 23.5 +- 5.8 in perfect agreement with the ChPT ratio, indicating the self-consistency of the sum rule results. Using the value: mb(mb)=(4.23 +- 0.06) GeV, we also obtain the model-building useful scale-independent mass ratio: mb/ms=50 +- 3.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.