Quark Masses in Qcd: A Progress Report

Abstract

Recent progress on QCD sum rule determinations of the light and heavy quark masses is reported. In the light quark sector a major breakthrough has been made recently in connection with the historical systematic uncertainties due to a lack of experimental information on the pseudoscalar resonance spectral functions. It is now possible to suppress this contribution to the 1% level by using suitable integration kernels in Finite Energy QCD sum rules. This allows to determine the up-, down-, and strange-quark masses with an unprecedented precision of some 8 − 10 %. Further reduction of this uncertainty will be possible with improved accuracy in the strong coupling, now the main source of error. In the heavy quark sector, the availability of experimental data in the vector channel, and the use of suitable multipurpose integration kernels allows to increase the accuracy of the charm-and bottom-quarks masses to the 1% level.

B meson decay constants f B c $$ {f}_{B_c} $$ , f B s $$ {f}_{B_s} $$ and f B from QCD sum rules

“…Of the various inputs, the largest error comes from the running mass of the bottom quark, m b (M S). We use the Particle Data Group world average m b (m b ) = 4.18 ± 0.03 GeV [53], very close to the most recent and accurate value m b (m b ) = 4.171 ± 0.009 GeV [38,[54][55][56][57]. In table II we show the change in the decay constants when m b (M S) is changed by ± 1σ.…”

“…In table II we show the change in the decay constants when m b (M S) is changed by ± 1σ. Despite the relatively large uncertainty in the s-quark mass [50,[54][55][56][57], m s (2 GeV) = 94 ± 9 MeV, it only has a small effect on f Bs , reflecting the relative smallness of this correction. The uncertainty in the larger c-quark mass m c (m c ) = 1.278 ± 0.009 GeV [54][55][56][57][58][59] has also a small impact on f Bc .…”

Strange quark mass from sum rules with improved perturbative QCD convergence

“…Also negligible is the contribution of the strange-quark condensate. This leaves the dimension d = 2 quark mass correction, the light-quark condensate [14]: qq = (−267±5 MeV) 3 , the dimension d = 6 condensate, and the d = 4 gluon condensate [12]- [13]: results from both determinations. The input valuem s /m ud = 27 ±1 from [15] has been used.…”

Determination of the m_u and m_d quark masses from eta\rightarrow 3pi decay

“…We proceed now to the recent determinations of r. Progress report on sum rules [2] quotes the value denoted by r 4 . The method of [21] inspired by large N c considerations enables to determine r from the ratio of Γ(η→γγ) Γ(η →γγ) .…”

“…The presented results of the η → 3π analysis stem from the work done in collaboration with K. Kampf, M. Knecht and J. Novotný. * Email address: zdrahal@ipnp.mff.cuni.cz quark masses we refer to [1,2]. Note that a computation of electromagnetic (EM) corrections within SR methods would be very difficult since the inclusion of long-range interactions changes significantly analytic properties of the amplitudes, which makes it impossible to write dispersion relations in the regular form.…”