QCD sum rule determination of the charm-quark mass

Abstract

QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the M S scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form p(s) = 1 − (s0/s) 2 , where s0 is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range s ≃ 20 − 25 GeV 2 . This feature leads to a substantial reduction in the sensitivity of the results to changes in s0, as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the M S scheme at a scale of 3 GeV is mc(3 GeV) = 987 ± 9 MeV, where the error includes all sources of uncertainties added in quadrature. is based on inverse (Hilbert) moment QCD sum rules, requiring QCD knowledge of the vector correlator in the low energy, as well as in the high energy region. In [18] an alternative approach was used which involves only QCD information at short distances, together with (a) a simple integration kernel p(s) = 1 − s/s 0 (local constraint), and (b) Legendre-type polynomial kernels (global constraint). In this paper we describe an improved analysis based on the use of direct as well as inverse moment kernels of the form p(s) = 1 − (s 0 /s) n , with n ≥ 1.These kernels enhance considerably the impact of the well known narrow resonances, as compared with e.g. a simple kernel p(s) = 1/s 2 , or p(s) = 1 − s/s 0 . They also provide a welcome stronger suppression of the contribution of data in the range s ≃ 20 − 25 GeV 2 . In comparison with simple inverse moments without pinching, this means that results are less sensitive to assumptions about the onset of perturbative QCD (PQCD), as well as to the treatment of the higher resonance data. For instance, changes in s 0 in the range s 0 ≃ 15 − 23 GeV 2 lead to a variation in m c (3 GeV) of only 4 MeV (for n = 2) as opposed to a variation of 14 MeV for p(s) = 1/s 2 , as used in [17] We consider the vector current correlator Π µν (q 2 ) = i d 4 x e iqx 0|T (V µ (x) V ν (0))|0

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

“…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 .…”

Analytical determination of the QCD quark masses

“…In connection with the charm-quark mass application, this kernel enhances the contribution from the first two narrow resonances, J/ψ and ψ(2S), and reduces the weight of the broad resonance region, particularly near the onset of the continuum. The latter feature is better achieved with the alternative kernel [76] f…”

“…The correlator, Eq. (9), involves the vector current Table 2: Results for the charm-quark mass at different orders in PQCD, and for two integration kernels from [76]. The result for f (s) = 1/s 2 is obtained using slightly different values of the QCD parameters, and a different integration procedure as in [77].…”

“…The result for f (s) = 1/s 2 is obtained using slightly different values of the QCD parameters, and a different integration procedure as in [77]. Table 3: The various uncertainties due to the data (EXP), the value of αs (∆αs), changes of ±35% in the renormalization scale around µ = 3 GeV (∆µ), and the value of the gluon condensate (NP) [76].…”

“…Two of the most recent results for m c (3 GeV) [71], [72], together with the weighted FESR value [76] …”