Heavy Quark Current Correlators Research Articles

Small-momentum expansion of heavy-quark correlators in the large-\u03b20 limit and \u03b1s extractions

We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-β0 limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, αs, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can guide the design of combinations of moments with improved perturbative behaviour.

Charmonium spectroscopy in strong magnetic fields by QCD sum rules:S-wave ground states

We investigate quarkonium mass spectra in external constant magnetic fields by using QCD sum rules. We first discuss a general framework of QCD sum rules necessary for properly extracting meson spectra from current correlators computed in the presence of strong magnetic fields, that is, a consistent treatment of mixing effects caused in the mesonic degrees of freedom. We then implement operator product expansions for pseudoscalar and vector heavy-quark current correlators by taking into account external constant magnetic fields as operators, and obtain mass shifts of the lowest-lying bound states $\eta_c$ and $J/\psi$ in the static limit with their vanishing spatial momenta. Comparing results from QCD sum rules with those from hadronic effective theories, we find that the dominant origin of mass shifts comes from a mixing between $\eta_c$ and $J/\psi$ with a longitudinal spin polarization, accompanied by other subdominant effects such as mixing with higher excited states and continua.

Low-energy moments of heavy quark current correlators at four loops

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moments in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using the Ward identity, we obtain the third and fourth moments for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for σ ( e + e − → hadrons ) .

Reconstruction of heavy quark current correlators at [formula omitted

We construct approximate formulas for the O ( α s 3 ) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Padé approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.

Moments of heavy quark current correlators at four-loop order in perturbative QCD

We present the result for the first moment of the scalar and axial-vector current correlator in third order of the strong coupling constant αs and give the details of a recent evaluation of the pseudo-scalar correlator. The results can be used to reduce the theoretical uncertainty due to higher order corrections for the determination of fundamental parameters of QCD in the context of lattice calculations.

Correlator of heavy-quark currents at small q 2 in the large- $\beta_0$ limit

The correlator of vector heavy-quark currents at small q^2 is considered in the large-beta_0 limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. Asymptotic behaviour of the perturbative series is obtained in a model-independent way, up to a single unknown normalization factor. Gluon-virtuality distribution functions for the perturbative correction are calculated.

Heavy quark induced effective action for gauge fields in the $SU(N_c)\otimes U(1)$ model and the low-energy structure of heavy quark current correlators

We calculate the low-energy limit of heavy quark current correlators within an expansion in the inverse heavy quark mass. The induced low-energy currents built from the gluon fields corresponding to the initial heavy quark currents are obtained from an effective action for gauge fields in the one-loop approximation at the leading order of the 1/m expansion. Explicit formulae for the low-energy spectra of electromagnetic and tensor heavy quark current correlators are given. Consequences of the appearance of a nonvanishing spectral density below the two-particle threshold for high precision phenomenology of heavy quarks are discussed quantitatively.

Calculation of the renormalized charmed-quark mass in lattice QCD

The correlator of heavy-quark currents is calculated in quenched Lattice QCD on a 16 3 × 32-lattice for β = {6,6.3}. The renormalized charmed quark mass is extracted from the short-distance part of that correlator: m c MS (m c) = 1.22(5) GeV . We study the sensitivity of our data to the strong coupling constant.

Determination of the renormalized heavy-quark mass in lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte Carlo data on a small 8 3 × 16 lattice for β = 6. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit both the short-distance part and long-distance part of the correlator in such a small volume.

Two-loop gluon-condensate contributions to heavy-quark current correlators: exact results and approximations

The coefficient functions of the gluon condensate 〈 G 2〉, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z = q 2 4m 2 . In the limiting cases z → 0, z → 1, and z → − ∞, comparison are made previous results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A single moment, combined with only the leading threshold and asymptotic behaviour, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields 〈 α s πG 2〉 ≈ 0.021 GeV 4 .