Next-to-leading order perturbative QCD corrections to baryon correlators in matter (original) (raw)
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Physical Review D, 1996
We analyse the possible existence of non-perturbative contributions in heavȳ QQ systems (Q and Q need not have the same flavour) which cannot be expressed in terms of local condensates. Starting from QCD, with well defined approximations and splitting properly the fields into large and small momentum components, we derive an effective lagrangian where hard gluons (in the non-relativistic aproximation) have been integrated out. The large momentum contributions (which are dominant) are calculated using Coulomb type states. Besides the usual condensate corrections, we see the possibility of new nonperturbative contributions. We parametrize them in terms of two low momentum correlators with Coulomb bound state energy insertions E n . We realize that the Heavy Quark Effective lagrangian can be used in these correlators. We calculate the corrections that they give rise to in the decay constant, the bound state energy and the matrix elements of bilinear currents at zero recoil. We study the cut-off dependence of the new contributions and we see that it matches perfectly
Analytical calculation of heavy baryon correlators in NLO of perturbative QCD
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Higher Order QCD Corrections to Timelike Processes
1997
Samenvatting Curriculum vitae List of publications In the two decades after the second world war an enormous amount of particles was discovered, in particular hadrons. Cosmic ray experiments found the mesons π, K, and the hyperons Λ, Σ and Ξ. In particular, when the particle accelerators came into operation in the fifties, many new hadrons were discovered. During this period their decay rates and masses were experimentally well measured but one was unable to make any quantitative or qualitative predictions about these quantities. This unlike in Quantum Electrodynamics (QED), where for example the anomalous magnetic moment of the electron was calculated with high precision (for a review see [1]). In 1961 Gell-Mann [2] and independently Ne'eman [3] shed new light on the mass spectrum of the hadrons by classifying them according to the higher irreducible representations, like the octet 8 and decuplet 10, of the flavour symmetry group SU (3) F. In view of the mass differences between the hadrons within a multiplet the flavour symmetry is a, medium strong, broken symmetry. The Gell-Mann-Okubo mass formula [4] provided a very good description of this symmetry breaking. In 1961 the decuplet had one vacancy. The mass of this missing particle, called Ω − , could be predicted rather accurately using the Gell-Mann-Okubo mass formula. The discovery [5] of this particle in 1964 with the correct predicted mass was a great success putting the SU (3) F symmetry of Gell-Mann and Ne'eman on a firm footing. Since the higher SU (3) representations can be obtained from the fundamental representation 3, it lead to a model in which all hadrons can be described in terms of only two (mesons) or three (baryons) constituents. This so-called quark model, proposed by Gell-Mann [6] and independently by Zweig [7] needed three quarks ("up", "down", and "strange") as the constituents to build all known hadrons. However, in spite of this success, there still remained many unsolved technical difficulties. One of them was that e.g. the delta resonance ∆(1236) (consisting of three S-wave up quarks) which has a spin equal to 3/2 was described by a symmetric wave function in spite of the fact that it is a fermion. According to the Pauli-principle its wave function should be totally anti-symmetric in contrast to what follows from the quark model. This led to the introduction [8] of an additional symmetry group given by SU (3) C where the quarks are put in the fundamental representation of the group. This implies that the quarks are coming out in three species distinguished by a new quantum number called colours. These colours predicted the correct decay rate of the neutral pion to two photons and the correct ratio of the cross sections of the This breaking of scaling could be explained by QCD because in this theory the partons, which are represented by the quarks and gluons, no longer behave as free particles but interact with each other. Because QCD possesses the property of asymptotic freedom the strong coupling constant α s vanishes as the energy scale increases. This implies that at large momentum transfer the partons are almost free particles, explaining why just a small breaking of scaling is observed. Due to the smallness of α s at large scales it is possible to make a series expansion in α s for the structure functions. In such an expansion the results of the scaling parton model of Feynman just represents the lowest order term. If the higher order corrections are included one can then speak about the QCD improved parton model. In the calculation of the higher order QCD corrections to the Drell-Yan cross sections above (see [21, 22, 23]) one has taken all quark masses equal to zero. This approximation is correct for the light quarks but is in general wrong for the heavy quarks like charm, bottom or top. For instance in the case of vector boson (γ, Z, W ±) production via the Drell-Yan process one cannot neglect the masses of the bottom and top quark anymore except for the charm which can be treated as massless. Therefore in this thesis we study the effect of the heavy quark mass for the computation of dσ/dQ where Q denotes the di-lepton pair mass and compare it with
2014
Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current, which can be related to the electric dipole moments in the continuum, in the framework of chiral perturbation theory up to next-to-leading order taking into account the breaking of Lorentz symmetry. A chiral extrapolation of the recent lattice results of both the neutron and proton electric dipole moments is performed, which results in d n = (−2.7 ± 1.2) × 10 −16 e θ 0 cm and d p = (2.1 ± 1.2) × 10 −16 e θ 0 cm.
Physics Letters B, 1994
The coefficient functions of the gluon condensate <G2><G^2><G2>, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z=q2/4m2z=q^2/4m^2z=q2/4m2. In the limiting cases zto0z\to0zto0, zto1z\to1zto1, and zto−inftyz\to-\inftyzto−infty, comparisons are made with previous partial 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 {\em single} moment, combined with only the {\em leading} threshold and asymptotic behaviours, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields <fracalpharmspiG2>approx0.021<\frac{\alpha_{\rm s}}{\pi}G^2>\approx0.021<fracalpharmspiG2>approx0.021 GeV$^4$.
We compute the next-to-leading order (NLO) perturbative QCD corrections to the correlators of nucleon interpolating currents in relativistic nuclear matter. The main new result is the calculation of the O(α s) perturbative corrections to the coefficient functions of the vector quark condensate in matter. This condensate appears in matter due to the violation of Lorentz invariance. The NLO perturbative QCD corrections turn out to be large which implies that the NLO corrections must be included in a sum rule analysis of the properties of both bound nucleons and relativistic nuclear matter.