Charm Quark Mass with Calibrated Uncertainty

Modern Physics Letters A, 2016

In this paper, we present preliminary results of the determination of the charm quark mass [Formula: see text] from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at [Formula: see text]. Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty.

Physical Review D, 2011

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.

Using the new non-analytic reconstruction method obtained from Mellin-Barnes properties, one can extract the value $m_c(\bar{\text{MS}}) = 1.12 \pm 0.08 \;\; \text{GeV}$ from experimental data of the radiation-corrected measured hadronic cross section to the calculated lowest-order cross section for muon pair production in the heavy-quark approximation.

Physical Review D, 2006

Using a new result for the first moment of the hadronic production cross section at order O(α 3 s), and new data on the J/ψ and ψ ′ resonances for the charm quark, we determine the MS masses of the charm and bottom quarks to be mc(mc) = 1.295 ± 0.015 GeV and m b (m b) = 4.205 ± 0.058 GeV. We assume that the continuum contribution to the sum rules is adequately described by pQCD. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of mc is related to the experimental data. On the other hand, the value of m b is not changed by our calculation to the assumed precision.

Physical Review D, 2010

The running charm-quark mass in the M S scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of s, the squared energy. The optimal kernels are found to be a simple pinched kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three different methods, fixed order perturbation theory (FOPT), contour improved perturbation theory (CIPT), and a fixed renormalization scale µ (FMUPT). The final result ismc(3 GeV) = 1008 ± 26 MeV, in a wide region of stability against changes in the integration radius s0 in the complex s-plane.

Nuclear physics, 2001

In this work, the charm quark mass is obtained from a QCD sum rule analysis of the charmonium system. In our investigation we include results from non-relativistic QCD at next-to-next-to-leading order. Using the pole mass scheme, we obtain a value of Mc = 1.70 ± 0.13 GeV for the charm pole mass. The introduction of a potential-subtracted mass leads to an improved scale dependence. The running MS-mass is then determined to be mc(mc) = 1.23 ± 0.09 GeV.

The European Physical Journal C

We determine the bottom quark mass $${\hat{m}}_b$$ m ^ b from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD to $${{\mathcal {O}}} ({\hat{\alpha }}_s^3)$$ O ( α ^ s 3 ) . Our approach is based on the mutual consistency across a set of moments where experimental data are required for the resonance contributions only. Additional experimental information from the continuum region can then be used for stability tests and to assess the theoretical uncertainty. We find $${\hat{m}}_b({\hat{m}}_b) = (4180.2 \pm 7.9)$$ m ^ b ( m ^ b ) = ( 4180.2 ± 7.9 ) MeV for $${\hat{\alpha }}_s(M_Z) = 0.1182$$ α ^ s ( M Z ) = 0.1182 .

1994

Ratios of Laplace QCD sum rules are used in order to determine the on-shell charmand beauty-quark masses. After confronting the experimental data in the charmonium and bottonium systems with theory1 we obtain me = 1.46 ± 0.07 Ge V and mb = 4. 70 ± 0.07 Ge V. The error is due to the uncertainties in the values of A and the gluon condensate.

Nuclear Physics B - Proceedings Supplements, 2009

The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are m u (Q = 2 GeV) = 2.9 ± 0.2 MeV, m d (Q = 2 GeV) = 5.3 ± 0.4 MeV, and m s (Q = 2 GeV) = 102 ± 8 MeV, for Λ = 381 ± 16 MeV, corresponding to α s (M 2 τ) = 0.344 ± 0.009. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2-3 %. The remaining uncertainties above arise from those in Λ, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement.

Physics Letters B, 2003

We present a new QCD sum rule with high sensitivity to the continuum regions of charm and bottom quark pair production. Combining this sum rule with existing ones yields very stable results for the MS quark masses,mc(mc) andm b (m b ). We introduce a phenomenological parametrization of the continuum interpolating smoothly between the pseudoscalar threshold and asymptotic quark regions. Comparison of our approach with recent BES data allows for a robust theoretical error estimate. The parametric uncertainty due to αs is reduced by performing a simultaneous fit to the most precise sum rules and other high precision observables. This includes a new evaluation of the lifetime of the τ lepton, ττ , serving as a strong constraint on αs. Our results aremc(mc) = 1.289 +0.040 −0.045 GeV, m b (m b ) = 4.207 +0.030 −0.031 GeV (with a correlation of 29%), and αs(MZ)[ττ ] = 0.1221 +0.0026 −0.0023 .