Photon Self-energy Research Articles

Corrected calculation for the non-local solution to the g − 2 anomaly and novel results in non-local QED

We provide the corrected calculation of the (g − 2)μ in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F1(q2) and F2(q2) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 105−1010 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.

Enhancement of dilepton production rate and electric conductivity around the QCD critical point

Abstract We investigate whether the soft mode that becomes massless at the QCD critical point (CP) causes an enhancement of the dilepton production rate (DPR) and electric conductivity around the CP through modification of the photon self-energy using the two-flavor Nambu–Jona-Lasinio model. The modification is described by the so-called Aslamazov–Larkin, Maki–Thompson, and density of states terms, which have been taken into account in our previous study on the DPR near the color-superconducting phase transition, with a replacement of the diquark modes with the soft mode of the QCD CP. We show that the coupling of photons with the soft modes brings about an enhancement of the DPR in the low-invariant-mass region and the conductivity near the CP, which would be observable in relativistic heavy-ion collisions.

Soft photon propagation in a hot and dense medium to next-to-leading order

We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in QED. The calculation is performed within the real-time formalism utilizing dimensional regularization in $4\ensuremath{-}2ϵ$ dimensions, while the result is reported including explicit $O(ϵ)$ terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a companion paper. These results pave the way for a similar future calculation in quantum chromodynamics.

Degenerate fermionic matter at N3LO : Quantum electrodynamics

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N$^3$LO) in the fine-structure constant $\alpha_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O(\alpha_e^3 \ln \alpha_e^{ })$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N$^3$LO calculation for cold and dense quark matter.

Anomalous enhancement of dilepton production due to soft modes in dense quark matter

We explore how the dilepton production rate is modified near the critical temperature of color superconductivity and QCD critical point by the soft modes inherently associated with the phase transitions of second-order. It is shown that the soft modes affect the photon self-energy significantly through so called the Aslamasov-Larkin, Maki-Thompson and density of states terms, which are known responsible for the paraconductivity in the metalic superconductivity, and cause an anomalous enhancement of the production rate in the low energy/momemtum region.

Anomalous enhancement of dilepton production as a precursor of color superconductivity

Abstract We compute the modification of the photon self-energy due to dynamical diquark fluctuations developed near the critical temperature of two-flavor superconductivity, which is one of the color superconducting phases, through the Aslamasov–Larkin, Maki–Thompson, and density of states terms, which are responsible for the paraconductivity in metals at vanishing energy and momentum. The analysis is performed through an investigation of the diquark fluctuations within the normal phase determined by the mean-field approximation in the massless two-flavor Nambu–Jona-Lasinio model. It is shown that the rate has a significant enhancement in low-invariant-mass regions over a rather wide range of temperatures in the normal phase. This enhancement is worth exploring in the relativistic heavy-ion collisions, which may thereby reveal the significance of the diquark fluctuations in dense quark matter.

Electromagnetic spectral functions in hot and dense chirally imbalanced quark matter

The photon self-energy from chirally imbalanced quark matter is evaluated at finite temperature and density using the real time formulation of thermal field theory. The analytic structure is explored in detail exposing the cut structure which corresponds to a variety of physical scattering and decay processes in the medium and their thresholds. The mass of the quarks in the chiral symmetry broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio model. It is found that, in presence of finite chiral chemical potential, the chiral condensate tends to get stronger at low temperatures while the opposite is observed at high temperature values. A continuous spectrum is obtained for the electromagnetic spectral function and this is purely a finite chiral chemical potential effect.

Real time thermal photon–photon interactions in the mixed space

Using the effective Lagrangian for the low energy/temperature of photon–photon interaction and the lowest-order photon self-energy is calculated in the Real-Time Formalism (RTF) for an arbitrary path specified by the [Formula: see text]-parameter within the new basis. The causal Green’s functions (without chemical potential) for the scalar field are evaluated to derive the usual thermal propagators in the mixed space. It is shown that the symmetric propagator does not depend on [Formula: see text]-parameter. Furthermore, the photon self-energy is used to calculate some electromagnetic properties, such as dielectric tensor and velocity of light from photon self-energy in the mixed space that greatly simplifies calculations in RTF. Their time dependence is investigated, and a comparison between our results and those obtained by other models is discussed.

Critical fluctuations of QCD phase transitions and their related observables

We study how the dilepton production rate and the electric conductivity are affected by the soft modes inherently associated with the second-order phase transitions at the critical temperature of color superconductivity and QCD critical point. It is shown that the soft modes modify the photon self-energy significantly through the so called Aslamasov-Larkin, Maki-Thompson and density of states terms, which are known responsible for the paraconductivity in the metallic superconductivity, and they lead to an anomalous enhancement of the production rate in the low energy/momemtum region and the divergence of conductivity at the critical temperature.

Two-loop photon self-energy in pseudoquantum electrodynamics in the presence of a conducting surface

In the present paper, we investigate the influence of a grounded perfectly conducting surface on the photon self-energy of a $2+1\mathrm{D}$ system of massless Dirac fermions, whose electron interaction is described by pseudoquantum electrodynamics. We calculate the temporal component of the polarization tensor up to 2-loop perturbation order in the presence of the conducting surface and, applying the Kubo formula, we obtain the longitudinal and optical conductivities of such system. When the distance between the system and the plate tends to infinity, we recover the correspondent results found in the literature. Since pseudoquantum electrodynamics proved to give a good description of the transport properties of graphene, our results can be useful as an alternative way to control the longitudinal and optical conductivities of this material.

Photon self-energy in a magnetized chiral plasma from kinetic theory

We study the photon self-energy in magnetized chiral plasma by solving the response of electromagnetic field perturbations in chiral kinetic theory with Landau level states. With lowest Landau level approximation and in collisionless limit, we find solutions for three particular perturbations: parallel electric field, static perpendicular electric and magnetic field, corresponding to chiral magnetic wave, drift state and tilted state, from which we extract components of photon self-energy in different kinematics. We show no solution is possible for more general field perturbations. We argue this is an artifact of the collisionless limit: while static solution corresponding to drift state and tilted state can be found, they cannot be realized dynamically without interaction between Landau levels. We also discuss possible manifestation of side-jump effect due to both boost and rotation, with the latter due to the presence of background magnetic field.

Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium

We consider weakly magnetized hot QED plasma comprising electrons and positrons. There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Considering the resummed fermion propagator in a weakly magnetized medium for the soft fermion and the Schwinger propagator for hard fermion, we calculate the soft contribution to the damping rate of hard photon. In weak field approximation the thermal and thermo-magnetic contributions to damping rate get separated out for each transverse dispersive mode. The total damping rate for each dispersive mode in presence of magnetic field is found to be reduced than that of the thermal one. This formalism can easily be extended to QCD plasma.

Implications of extra dimensions on the effective charge and the beta function in quantum electrodynamics

A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories, characterized by an infinite number of Kaluza-Klein fields, one-loop amplitudes involve discrete as well as continuous sums, $\sum^\infty_{n=1}\int d^4k$, that could diverge. Using dimensional regularization, we express such sums as products of gamma and Epstein functions, both defined on the complex plane, with divergences arising from poles of these functions in the limit as $ D \to 4$. Using the analytical properties of the Epstein function, we show that the ultraviolet divergences generated by the Kaluza-Klein sums can be consistently renormalized, which means that the corresponding renormalized quantities reduce to the usual ones of QED at the limit of a very large compactification scale $R^{-1}$. The main features of QED at the one-loop level were studied. We use the mass-dependent $\mu$-scheme to calculate, in QED with an arbitrary number $n$ of extra dimensions, a beta function fulfilling all desirable physical requirements. We argue that in this type of theories, with a large mass spectrum covering a wide energy range, beta functions should not be calculated by using mass-independent renormalization schemes. We show that the beta function is finite for any energy $\mu$. In particular, it reduces to the usual QED result $e^3/12\pi^2$ for $m\ll \mu \ll R^{-1}$ and vanishes for $m\gg \mu$, with $m$ the usual fermion mass. Throughout the work, the decoupling nature of all our results obtained from the analytical properties of the Epstein function is stressed.

The HTL Lagrangian at NLO: The photon case

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta. This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order. This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma. We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation. In the limit of soft photon momenta, our result is finite. It not only provides an O(α) correction to the Debye mass, but also a new non-local structure. A consistent regularization of radial and angular integrals is crucial to get this new structure. As an application we calculate the plasmon dispersion relations at NLO.

Hard dilepton production from a weakly magnetized hot QCD medium

We have computed the hard dilepton production rate from a weakly magnetized deconfined QCD medium within one-loop photon self-energy by considering one hard and one thermomagnetic resummed quark propagator in the loop. In the presence of the magnetic field, the resummed propagator leads to four quasiparticle modes. The production of hard dileptons consists of rates when all four quasiquarks originating from the poles of the propagator individually annihilate with a hard quark coming from a bare propagator in the loop. Besides these, there are also contributions from a mixture of pole and Landau cut part. In weak field approximation, the magnetic field appears as a perturbative correction to the thermal contribution. Since the calculation is very involved, for a first effort as well as for simplicity, we obtained the rate up to first order in the magnetic field, i.e., ${\cal O}[(eB)]$, which causes a marginal improvement over that in the absence of magnetic field.

One-loop corrections in the z=3 Lifshitz extension of QED

In this work we study a z=3 Horava-Lifshitz-like extension of QED in (3+1) dimensions. We calculate the one-loop radiative corrections to the two and three-point functions of the gauge and fermion fields. Such corrections were achieved using the perturbative approach and a dimensional regularization was performed only in the spatial sector. Renormalization was required to eliminate the divergent contributions emergent from the photon and electron self-energies and from the three-point function. We verify that the one-loop vertex functions satisfy the usual Ward identities and using renormalization group methods we show that the model is asymptotically free.

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.

Remarks on the Chern-Simons photon term in the QED description of graphene

We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this non-local but still gauge invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz non-invariant case due to the Fermi velocity $v_F<c$. This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of $(2+1)$-dimensional planar reduced QED.

Strong, random field behavior of the Euclidean Dirac propagator

The one-loop effective action of quantum electrodynamics in four dimensions is shown to be controlled by the Euclidean Dirac propagator $G$ in a background potential. After separating the photon self-energy and photon-photon scattering graphs from the effective action the remainder is known to be the logarithm of an entire function of the electric charge of order 4 under mild regularity assumptions on the potential. This input together with QED's lack of an ultrastable vacuum constrain the strong field behavior of $G$. It is shown that $G$ vanishes in the strong field limit. The relevance of this result to the decoupling of QED from the remainder of the electroweak model for large amplitude variations of the Maxwell field is discussed.

Photon production spectrum above Tc with a lattice quark propagator

The photon production rate from the deconfined medium is analyzed with the photon self-energy constructed from the quark propagator obtained by numerical simulation on the quenched lattice for two values of temperature, |$T=1.5T_{\rm c}$| and |$3T_{\rm c}$|⁠, above the critical temperature |$T_{\rm c}$|⁠. The photon self-energy is calculated by the Schwinger–Dyson equation with the lattice quark propagator and a vertex function determined so as to satisfy the Ward–Takahashi identity. The obtained photon production rate exhibits a similar behavior to the perturbative results for photon energies larger than |$0.5$| GeV.