One-loop Self Research Articles

GKZ-hypergeometric systems for Feynman integrals

Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how to perform triangulation and how to construct canonical series solutions in the corresponding convergent regions. The series solutions constructed for these hypergeometric systems recover the well known results in literature.

Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.

On the chiral expansion of vector meson masses

We study the chiral expansion of meson masses and decay constants using a chiral Lagrangian that was constructed previously based on the hadrogenesis conjecture. The one-loop self energies of the Goldstone bosons and vector mesons are evaluated. It is illustrated that a renormalizeable effective field theory arises once specific conditions on the low-energy constants are imposed. For the case where the hadrogenesis mass gap scale Lambda_{HG} is substantially larger than the chiral symmetry breaking scale Lambda_chi a partial summation scheme is required. All terms proportional to (M/\Lambda_\chi)^n can be summed by a suitable renormalization, where M is the chiral and large-N_c limit of the vector meson masses in QCD. The size of loop effects from vector meson degrees of freedom is illustrated for physical quarks masses. Naturally sized effects are observed that have significant impact on the chiral structure of low-energy QCD with three light flavours.

Krein regularization of λϕ3 theory

In this paper, the one-loop self energy of λϕ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λϕ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of “Krein Regularization”.

Oblique Corrections in the MSSM at One-Loop—Part I: Scalars

This paper is devoted to reconsider the one-loop oblique corrections arising from the scalar superpartners in the MSSM, that is, the squarks, the sleptons, and the scalars in Higgs sector. We explicitly present the complete one-loop forms of self-energy corrections to the gauge bosons of SM electroweak gauge groups, as well as their descendants theS,T, andUparameters, which can be directly applied to constrain the parameter space of the MSSM. Our results about one-loop self energies are found to agree with Drees et al. (1992) and Pierce et al. (1997). Nevertheless, theS,T, andUparameters are not in agreement with Dobado et al. (1999).

Four-momentum boosted fermion fields

A formulation of the fermion action is discussed which includes an explicit four momentum boost on the field prior to discretisation. This is used to shift the zero of lattice momentum to lie near one of the on-shell quark poles. The positive pole is selected if we wish to describe a valence quark, and negative pole for a valence antiquark. Like NRQCD, the typical lattice momenta involved in hadronic correlation functions can be kept small: of order O(αΛQCD), rather than O(amQ) even when describing heavy quarks. If we expand around the particle pole, the anti-particle correlator will be poorly described for large amQ. However, in that case the anti-particle will be far off shell and will only affect unphysical, renormalization factors. The formulation produces the correct continuum limit, and preliminary results have been obtained (for an unimproved action) of both the one-loop self energy and a non-perturbative correlation function.

One-Loop Self Energies at Finite Temperature

The complete one-loop self energies (real and imaginary parts) for photons, gluons, electrons, and quarks at finite temperature are calculated numerically and compared to the results of the hard thermal loop (HTL) approximation used for the resummation technique of Braaten and Pisarski. In this way some light is shed on the validity of the weak coupling limit assumption (g⪡1) or equivalently the high temperature assumption, on which the HTL approximation is based. Furthermore, the gauge dependence of the fermion self energy beyond the HTL approximation is considered. Finally the dispersion relations following from the real part of the self energies are compared to the HTL results.

The Lamb shift of excited S-levels in hydrogen and deuterium atoms

A specific combination of $s$-state Lamb shift $\Delta E_L(1s_{1/2}) - n^3 \Delta E_L(ns_{1/2})$ is considered. Its value is calculated both in the hydrogen and deuterium atoms for $n$ up to 12. The result inludes all correction which can contribute $1 kHz$ and particulary: one-loop self energy and vacuum polarization, two-loop contribution. Nuclear finite-size corrections for the isotopic difference of the combination are also evaluated.

Higher-order binding corrections to the Lamb shift of 2P states.

We present an improved calculation of higher-order corrections to the one-loop self energy of 2P states in hydrogen-like systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon energy into a high- and a low-energy part. The high-energy part is calculated by an expansion of the electron propagator in powers of the Coulomb field. The low-energy part is simplified by the application of a Foldy-Wouthuysen transformation. This transformation leads to a clear separation of the leading contribution from the relativistic corrections and removes higher order terms. The method is applied to the 2P_{1/2} and 2P_{3/2} states in atomic hydrogen. The results lead to new theoretical values for the Lamb shifts and the fine structure splitting.

Field theoretic effects in highly charged ions

It is argued that the study of the spectroscopy of highly charged few-electron ions provides a uniquely powerful probe of our understanding of the relativistic many-body problem and its basis in quantum field theory. The use of S-matrix techniques is shown to lead to energy shifts defined in terms of a set of Feynman diagrams. Numerical issues involved in the evaluation of the one-loop self energy graph, which contributes to the Lamb shift, are discussed. Two-photon exchange graphs are shown to contribute simultaneously to correlation and to screening of the Lamb shift for two-electron ions. Particular emphasis is made on distinguishing field-theoretic effects from effects already contained in Hamiltonian formalisms.