Two-loop Anomalous Dimension Research Articles

Two-loop renormalization scale dependence of the Isgur-Wise function

The two-loop anomalous dimension of a current consisting of two heavy quarks with velocities ν and ν′ (relevant to the renormalization scale dependence of the Isgur-Wise function) is computed within the framework of the Heavy Quark Effective Theory. Our result agrees with Korchemsky and Radyushkin's calculation of the cusp anomalous dimension of Wilson lines, thus resolving previous discrepancies in the literature.

Anomalous dimensions of octet baryonic currents in two-loop approximation

A calculation of the two-loop anomalous dimensions of the octet baryonic currents is presented. The anomalous dimension of the proton current is small enough and its influence on the analysis of the QCD sum rules for the proton turns out to be numerically insignificant.

Order-αs corrections to heavy-meson semi-leptonic decay form factors

We calculate the velocity-dependent two-loop anomalous dimension of weak currents and the first-order coefficient function in an effective field theory with two heavy quarks. Using these, we find the complete order- α s corrections to the semi-leptonic decay form factors of heavy mesons. The result is presented with the example of B→Dℓ ν ℓ decay.

Sub-leading logarithmic mass-dependence in heavy-meson form-factors

We calculate the two-loop anomalous dimension and the first-order coefficient function of weak-interaction currents in the heavy-quark effective field theory. Together with the two-loop QCD β-function, these quantities form the complete sub-leading logarithmic corrections to the mass-factorization of weak form factors.

QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes

We calculate next-to-leading QCD corrections to the effective hamiltonian for weak decays in the limit of massless quarks using three regularization schemes with different treatment of γ5: (i) dimensional regularization (anticommuting γ5 in D ≠ 4), (ii) 't Hooft-Veltman scheme (non-anticommuting γ5 in D ≠ 4) and (iii) dimensional reduction (γ5 in D = 4). The main part of the calculation is the evaluation of the two-loop anomalous dimensions of relevant four-quark operators. Although all three schemes give rather different results at the intermediate stages of the calculation, the final result for the complete next-to-leading order corrections turns out to be the same in all schemes considered and to be equal to the one of Altarelli et al. obtained previously in the dimensional reduction scheme. This result follows after a subtle analysis of operator mixing.

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3) c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν e ). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν e). It turns out that the result is sensitive to the ratios x ( i) = M H ( i) / M X where M H( i) are the masses of the twelve superheavy Higgs scalars in the 24 multiplet which breaks SU(5) → SU(3)× SU(2)× U(1).

The renormalization of FF

A fairly complete study of the renormalization of F a μν F μνa is presented in the gauge in which it is simplest: the background field gauge. This gauge allows one to go to second-order perturbation theory without evaluating a single Feynman integral. The use of the equations of motion, the gauge invariance of a classically gauge-invariant renormalized operator and the renormalization group invariance are studied. Its two-loop anomalous dimension is given and its relation to the trace anomaly obtained.

Two-Loop Anomalous Dimensions of Timelike Cut Vertices and Scaling Violation of Fragmentation Functions in QCD

Two-Loop Anomalous Dimensions of Timelike Cut Vertices and Scaling Violation of Fragmentation Functions in QCD

Higher order QCD corrections to an exclusive two-photon process

We calculate the next-to-leading order QCD corrections in the MS scheme to the coefficient functions in an operator product expansion of the amplitude T( q 2, p 2) for the process γ ∗(q) + γ ∗(p) → helicity-zero , flavour non-singlet meson in which − q 2 is large and − p 2 ⩾ 0. For an asymptotic wave function the complete O( α s) correction for a pseudoscalar meson is about 16% for p 2 = 0 and α s = 0.3; most of this correction can be removed by using a modified evolution equation for the wave function, leaving a correction of about 7%. For large p 2 the complete O( α s) correction for a pseudoscalar meson is about 10%. We discuss how our results can be combined with similar calculations for the pion form factor F π ( Q 2) to give a prediction: F π ( Q 2) = Aα s( Q 2) T π 2( q 2, 0)(1 + Bα s) that is independent of the as yet unknown two-loop anomalous dimension matrix.

QCD non-leading corrections to weak decays as an application of regularization by dimensional reduction

We compute in QCD with massless quarks the two-loop anomalous dimensions of the four-fermion operators relevant to weak non-leptonic amplitudes and discuss the physical implications for strange and charm particle decays. Our main goal was to derive the complete order α corrections to the inclusive decay width of a charm (or heavier) quark. We find that the correction terms in the effective hamiltonian show the same enhancement-suppression pattern as the leading terms. Also, for a free c quark, the non-leptonic decay width is further increased (and the semileptonic branching ratio further depleted) with respect to the leading approximation. Implications for D (especially D +) decays are discussed. The calculation was completely done by a recently proposed variant of dimensional regularization called dimensional reduction. Much of this paper is devoted to exposing and resolving (within two loops) the field theoretic subtleties associated with this method which was particularly suited to this computation.

Quantum-chromodynamic predictions for direct photons ine+e−collisions

We analyze the direct photon production in e/sup +/e/sup -/ collisions in quantum chromodynamics using the cut-vertex formalism and the renormalization-group method. The two-loop anomalous dimensions of timelike cut vertices are calculated from the two-loop parton decay probability functions. The moments of the transverse structure function W-bar/sup ..gamma..//sub T/ are calculated up to the next-to-leading order. The nonleading corrections to W-bar/sup ..gamma..//sub T/ turn out to be large, and even larger than those to the photon structure function F/sup ..gamma..//sub 2/ in photon-photon scattering. Also, the moments of the longitudinal structure function W-bar/sup ..gamma..//sub L/ are calculated in the leading order. The corrections are found to be small.

Two-loop anomalous dimensions of timelike cut vertices in QCD

Abstract The two-loop corrections to the anomalous dimensions of timelike cut vertices in QCD are presented for the non-singlet case. We check that cut vertices are renormalizable to two-loop order.

Weak non-leptonic decays beyond leading logarithms in QCD

We compute the two-loop anomalous dimensions of the four-fermion operators relevant to weak non-leptonic decays and discuss the physical implications for strange and charm particle decays. In particular, we derive the complete order α S corrections to the inclusive decay width of a heavy quark.

Space- and time-like cut vertices in QCD beyond the leading order—The singlet sector

The analytic continuation relation found in the non-singlet structure of the processes e +h→e −X and e −e +→hX up to the next-to-the-leading-logarithm approximation, is shown to be true also for the singlet case. This relation is used to find the two-loop anomalous dimensions for the singlet time-like cut vertices from the anomalous dimension of the singlet space-like cut vertices. We give also the singlet time-like coefficient functions.

Full estimate of the higher-order corrections to the Drell-Yan process in quantum chromodynamics

The complete formula up to the next-to-leading order in quantum chromodynamics is derived for the Drell-Yan cross section: The two-loop anomalous dimension is included in the parton distribution functions and the one-loop finite part is taken into account in the parton hard scattering. It is found that the famous scheme dependence of the running coupling constant disputed in deep-inelastic scattering also shows up here in the Drell-Yan process and influences the magnitude of the next-to-leading-order corrections. The quantum-chromodynamics correction to the parton-model sum rule in the Drell-Yan process is also discussed and found to be large.