Search results for "Sum rule in quantum mechanics"
showing 10 items of 153 documents
Bottom-quark mass from finite energy QCD sum rules
2011
Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the $\bar{\text {MS}}$ scheme at a reference scale of $10\, {GeV}$ is $\bar{m}_b(10\,\text{GeV})= 3623(9)\,\text{MeV}$. This value translates into a scale invariant mass $\bar{m}_b(\bar{m}_b) = 4171 (9)\, {MeV}$. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.
Order-$\alpha_s^3$ determination of the strange quark mass
1996
We present a QCD sum rule calculation of the strange-quark mass including four-loop QCD corrections to the correlator of scalar currents. We obtain $\bar m_s(1$ GeV$)=205.5\pm 19.1$ MeV.
Improved determination of the mass of the1−+light hybrid meson from QCD sum rules
2003
We calculate the next-to-leading order (NLO) ${\ensuremath{\alpha}}_{s}$ corrections to the contributions of the condensates $〈\ensuremath{\alpha}{G}^{2}〉$ and $〈\overline{q}q{〉}^{2}$ in the current-current correlator of the hybrid current $g\overline{q}(x){\ensuremath{\gamma}}_{\ensuremath{\nu}}{\mathrm{iF}}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}{T}^{a}q(x)$ using the external field method in the Feynman gauge. After incorporating these NLO contributions into the Laplace sum rules, the mass of the ${J}^{\mathrm{PC}}{=1}^{\ensuremath{-}+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO ${\ensuremath{\alp…
Comparison between two strictly local QCD sum rules
1989
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex {ital q}{sup 2} plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic ({ital g}{minus}2) factor of the muon. Their effectiveness is demonstrated in the calculati…
Off-forward Matrix Elements in Light-front Hamiltonian QCD
2002
We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.
Exclusive/inclusive ratio of semileptonicΛbdecays
2000
We present theoretical evidence that the exclusive/inclusive ratio of semileptonic ${\ensuremath{\Lambda}}_{b}$ decays exceeds that of semileptonic B decays where the experimental exclusive/inclusive ratio amounts to about 66%. We start from the observation that the spectator quark model provides a lower bound on the leading order Isgur-Wise function of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}$ transition in terms of the corresponding $\stackrel{\ensuremath{\rightarrow}}{B}{D,D}^{*}$ mesonic Isgur-Wise function. Using experimental data for the $\stackrel{\ensuremath{\rightarrow}}{B}{D,D}^{*}$ mesonic Isgur-Wise functions this bound is established. Ap…
Strange quark mass from Finite Energy QCD sum rules to five loops
2007
The strange quark mass is determined from a new QCD Finite Energy Sum Rule (FESR) optimized to reduce considerably the systematic uncertainties arising from the hadronic resonance sector. As a result, the main uncertainty in this determination is due to the value of $\Lambda_{QCD}$. The correlator of axial-vector divergences is used in perturbative QCD to five-loop order, including quark and gluon condensate contributions, in the framework of both Fixed Order (FOPT), and Contour Improved Perturbation Theory (CIPT). The latter exhibits very good convergence, leading to a remarkably stable result in the very wide range $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration co…
LIGHT QUARK MASSES FROM QCD SUM RULES
2013
Recent QCD sum rule determinations of the light quark masses are reviewed. In the case of the strange quark mass, possible uncertainties are discussed in the framework of finite energy sum rules.
Asymptotic 3-loop heavy flavor corrections to the charged current structure functions FLW+−W−(x,Q2) and F2W+−W−(x,Q2)
2016
We derive the massive Wilson coefficients for the heavy flavor contributions to the nonsinglet charged current deep-inelastic scattering structure functions ${F}_{L}^{{W}^{+}}(x,{Q}^{2})\ensuremath{-}{F}_{L}^{{W}^{\ensuremath{-}}}(x,{Q}^{2})$ and ${F}_{2}^{{W}^{+}}(x,{Q}^{2})\ensuremath{-}{F}_{2}^{{W}^{\ensuremath{-}}}(x,{Q}^{2})$ in the asymptotic region ${Q}^{2}\ensuremath{\gg}{m}^{2}$ to 3-loop order in quantum chromodynamics at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production, also the single heavy flavor excitation $s\ensuremath{\rightarrow}c$ contributes. Numerical results are presented for the charm quark contributions, …
Charm quark mass with calibrated uncertainty
2016
We determine the charm quark mass ${\hat m}_c({\hat m}_c)$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretical error. Our result is ${\hat m}_c({\hat m}_c) = 1272 \pm 8$ MeV for $\hat\alpha_s(M_Z) = 0.1182$. Special attention is given to the question how to quantify and justify the uncertainty.