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Register a new userThe charm quark mass from non-relativistic sum rules
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Adrian Signer
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We present an analysis to determine the charm quark mass from non-relativistic sum rules, using a combined approach taking into account fixed-order and effective-theory calculations. Non-perturbative corrections as well as higher-order perturbative corrections are under control. For the PS mass we find m_{PS}(0.7 GeV) = 1.50pm 0.04 GeV, which translates into a MS-bar mass of m = 1.25pm 0.04 GeV.
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In this paper, we present preliminary results of the determination of the charm quark mass $hat{m}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${cal O} (hat alpha_s^3)$. 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.
The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: $bar{m}_u (2, mbox{GeV}) = (2.6 , pm , 0.4) , {mbox{MeV}}$, $bar{m}_d (2, mbox{GeV}) = (5.3 , pm , 0.4) , {mbox{MeV}}$, and the sum $bar{m}_{ud} equiv (bar{m}_u , + , bar{m}_d)/2$, is $bar{m}_{ud}({ 2 ,mbox{GeV}}) =( 3.9 , pm , 0.3 ,) {mbox{MeV}}$.
It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates $R_{su} = frac{<bar{s} s>}{<bar{q} q>}$ with ($q=u,d$). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are $Lambda_{QCD}$, and to a major extent the strange quark mass. From the positivity of $R_{su}$ there follows an upper bound on the latter: $bar{m_{s}} (2 {GeV}) leq 121 (105) {MeV}$, for $Lambda_{QCD} = 330 (420) {MeV} .$
We report results of our recent works [1,2] where we where the correlations between the c,b-quark running masses{m}_{c,b}, the gluon condensate<alpha_s G^2> and the QCD coupling alpha_s in the MS-scheme from an analysis of the charmonium and bottomium spectra and the B_c-meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the mu-subtraction stability point where higher orders PT and D< 6-8-dimensions non-perturbative condensates corrections are included. We obtain [1] alpha_s(2.85)=0.262(9) and alpha_s(9.50)=0.180(8) from the (pseudo)scalar M_{chi_{0c(0b)}}-M_{eta_{c(b)}} mass-splittings at mu=2.85(9.50) GeV. The most precise result from the charm channel leads to alpha_s(M_tau)=0.318(15) and alpha_s(M_Z)=0.1183(19)(3) in excellent agreement with the world average: alpha_s(M_Z)=0.1181(11)[3,4]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [1] combined with the one from M_{B_c} [2] lead to the new tentative QCD spectral sum rules (QSSR) average : m_c(m_c)|_average= 1266(6) MeV and m_b(m_b)|_average=4196(8) MeV. The values of the gluon condensate <alpha_s G^2> from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average [1]: <alpha_s G^2>_average=(6.35pm 0.35)x 10^{-2} GeV^4. Our results clarify the (apparent) discrepancies between different estimates of <alpha_s G^2> from J/psi sum rule but also shows the sensitivity of the sum rules on the choice of the mu-subtraction scale. As a biproduct, we deduce the B_c-decay constants f_{B_c}=371(17) MeV and f_{B_c}(2S)< 139(6) MeV.
In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous Holder-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $sigma$ and $f_0(980)$, we obtain a prediction for light quark mass $m_q(2,textrm{GeV})$ = $frac{1}{2}(m_u(2,textrm{GeV})$ + $m_d(2,textrm{GeV}))$ = $4.7^{+0.8}_{-0.7},textrm{MeV}$, which is consistent with the PDG (Particle Data Group) value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $sigma$ and $f_0(980)$ at 2 GeV, which are approximately $0.64-0.83$ GeV and $0.40-0.48$ GeV respectively.
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