We calculate the electron self-energy in a magnetized QED plasma to the leading perturbative order in the coupling constant and to the linear order in an external magnetic field. We find that the chiral asymmetry of the normal ground state of the system is characterized by two new Dirac structures. One of them is the familiar chiral shift previously discussed in the Nambu--Jona-Lasinio model. The other structure is new. It formally looks like that of the chiral chemical potential but is an odd function of the longitudinal component of the momentum, directed along the magnetic field. The origin of this new parity-even chiral structure is directly connected with the long-range character of the QED interaction. The form of the Fermi surface in the weak magnetic field is determined.
The interaction induced chiral asymmetry is calculated in cold QED plasma beyond the weak-field approximation. By making use of the recently developed Landau-level representation for the fermion self-energy, the chiral shift and the parity-even chiral chemical potential function are obtained with the help of numerical methods. The results are used to quantify the chiral asymmetry of the Fermi surface in dense QED matter. Because of the weakness of the QED interactions, the value of the asymmetry appears to be rather small even in the strongest magnetic fields and at the highest stellar densiti…
We calculate the leading radiative corrections to the axial current in the chiral separation effect in dense QED in a magnetic field. Contrary to the conventional wisdom suggesting that the axial current should be exactly fixed by the chiral anomaly relation and is described by the topological contribution on the lowest Landau level in the free theory, we find in fact that the axial current receives nontrivial radiative corrections. The direct calculations performed to the linear order in the external magnetic field show that the nontrivial radiative corrections to the axial current are provid…
The fermion self-energy is calculated for a cold QED plasma with chiral chemical potential in a magnetic field. It is found that a momentum shift parameter dynamically generated in such a plasma leads to a modification of the chiral magnetic effect current. It is argued that the momentum shift parameter can be relevant for the evolution of magnetic field in the chirally asymmetric primordial plasma in the early Universe.
In a previous paper we have shown how the Wilsonian renormalization group naturally leads to the equivalence of the standard QED with a matter-only theory. In this paper we give an improved explanation of the equivalence and discuss, as an example, the equivalence of a chiral QED in the Higgs phase with a matter-only theory. Ignoring the contributions suppressed by the negative powers of a UV cutoff, the matter-only theory is equivalent to the perturbatively renormalizable chiral QED with two complex Higgs fields. In the matter-only theory chiral anomaly arises without elementary gauge fields.
The catalysis of chiral symmetry breaking in the massless weakly coupled QED in a magnetic field at finite temperature is studied. The temperature of the symmetry restoration is estimated analytically as $T_c\simeq m_{dyn}$, where $m_{dyn}$ is the dynamical mass of a fermion at zero temperature.
A recent result of Gusynin, Miransky and Shovkovy concerning chiral symmetry breaking by a constant external magnetic field in parity-invariant three-dimensional QED is generalised to the case of inhomogeneous fields by relating the phenomenon to the zero modes of the Dirac equation. Virtual photon radiative corrections and four-dimensional QED are briefly discussed.
We compute a full set of the first order QED corrections to the parity-violating observables in polarized Moller scattering. We employ a covariant method of removing infrared divergences, computing corrections without introducing any unphysical parameters. When applied to the kinematics of the SLAC E158 experiment, the QED corrections reduce the parity violating asymmetry by 4.5%. We combine our results with the previous calculations of the first-order electroweak corrections and obtain the complete O(alpha) prescription for relating the experimental asymmetry A_LR to the low-energy value of t…
The theory of the magnetic catalysis of chiral symmetry breaking in QED is developed. An approximation for the Schwinger-Dyson equations describing reliably this phenomenon is established, i.e., it is shown that there exists a consistent truncation of those equations in this problem. The equations are solved both analytically and numerically, and the dynamical mass of fermions is determined.
We describe a (first, to the best of our knowledge) essentially soluble example of dynamical symmetry breaking phenomenon in a 3+1 dimensional gauge theory without fundamental scalar fields: QED in a constant magnetic field.
We study the chiral critical behaviors of QED by using Non-Perturbative Renormalization Group (NPRG). Taking account of the non-ladder contributions, our flow equations are free from the gauge parameter ($α$) dependence. We clarify the chiral phase structure, and calculate the anomalous dimension of $\barψψ$, which is enhanced compared to the ladder approximation. We find that the cutoff scheme dependence of the physical results is very small.
Parametrizing the possible underlying theory or new physics' decoupling effects in the most general way we reexamined the validity of canonical trace relation and chiral symmetry in certain one-loop two-point functions. The anomalies and the relation between chiral and trace Ward identities are investigated and interpreted in the perspective of a complete underlying theory or new physics instead of regularization, with some new phenomena found as by-products.
We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and o…
It is shown that the chiral symmetry is spontaneously broken by a constant magnetic field in QED. The dynamical mass of fermions (energy gap in the fermion spectrum) is $m_{dyn}\simeq C\sqrt{eB}\exp\left[-\left(π/α\right) ^{1/2}\right]$, where $B$ is the magnetic field, the constant $C$ is of order one and $α=e^2/4π$ is the renormalized coupling constant. Possible applications of this effect are discussed.
Reduced gauge theories are theories in which while gauge fields propagate in a bulk, fermion fields are localized on a brane. We study dynamical chiral symmetry breaking on a 2-brane and a 1-brane in reduced QED_{3+1}, and on a 1-brane in reduced QED_{2+1}. Since, unlike higher dimensional gauge theories, QED_{3+1} and QED_{2+1} are well defined, their reduced versions can serve as a laboratory for studying dynamics in a higher dimensional brane world. The analysis of the Schwinger-Dyson (SD) equations in these theories reveals rich and quite nontrivial dynamics in which the conformal symmetry…
The coupled system of renormalized Dyson-Schwinger equations for the electron self-energy and the photon propagator are supplied with the tree level vertex as Ansatz for the renormalized three point function. The system is investigated numerically. In the case of a massive electron, the theory is ``weakly renormalizable'', i.e.\ cutoff independent for values of the cutoff below an upper limit. In this regime of cutoff independence, the quenched approximation yields good results for the electron self-energy. In the chiral limit, a logarithmic cutoff dependence of the electron self-energy is fou…
Inspired by recent discussions of inverse magnetic catalysis in the literature, we examine the effects of a uniform external magnetic field on the chiral phase transition in quenched ladder QED at nonzero chemical potential. In particular, we study the behaviour of the effective potential as the strength of the magnetic field is varied while the chemical potential is held constant. For a certain range of the magnetic field, the effective potential develops a local maximum. Inverse magnetic catalysis is observed at this maximum, whereas the usual magnetic catalysis is observed at the true minim…
The electron structure function method is applied to calculate model-independent radiative corrections to an asymmetry of electron-proton scattering. The representations for both spin-independent and spin-dependent parts of the cross-section are derived. Master formulae take into account the leading corrections in all orders and the main contribution of the second order next-to-leading ones and have accuracy at the level of one per mille. Numerical calculations illustrate our analytical results for both elastic and deep inelastic events.
The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow γ^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(α^6 L^6)$ extending the known corrections up to $O(α^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical results are presented for various energies around the $Z$-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC$\_$ee.
Chiral phase transition in (2+1)-dimensional quantum electrodynamics (QED$_3$) at finite temperature is investigated in the framework of truncated Dyson-Schwinger equations (DSEs). We go beyond the widely used instantaneous approximation and adopt a method that retains the full frequency dependence of the fermion self-energy. We also take further step to include the effects of wave-function renormalizations and introduce a minimal dressing of the bare vertex. Finally, with the more complete solutions of the truncated DSEs, we revisit the study of chiral phase transition in finite-temperature Q…
Scalar QED with fermions is investigated in an expansion in powers of the inverse gauge coupling constant. The fermion mass generation is studied in next to leading order of the strong coupling expansion for the Higgs-phase of the model. Chiral symmetry breaking is discussed. Our approach supports from a strong coupling point of view the results obtained earlier by Miransky, Bardeen and Kondo.
We extend a previous Landau-gauge study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex proposed by Curtis and Pennington with an additional correction term included to compensate for the small gauge-dependence induced by the ultraviolet regulator. We discuss the chiral limit and the onset of dynamical chiral symmetry breaking in the presence of nonperturbative renormalization. We extract the critical coupling in several different gauges and find evi…
The ${\cal O}(α)$ radiative corrections to the process $p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$} \rightarrow γ^*, \, Z \rightarrow \ell^+ \ell^-$ ($\ell=e,\,μ$) are calculated. Factorizing the collinear singularity associated with initial state photon bremsstrahlung into the parton distribution functions, we find that initial state corrections have a much smaller effect than final state radiative corrections. Due to mass singular logarithmic terms associated with photons emitted collinear with one of the final state leptons, QED radiative corrections strongly affect the shape of the di-lepton inva…
The electromagnetic field inside an isotropic optically active medium is quantized on the base of Fedorov's model for optical activity. The modified photon propagator is derived. Using this result it is shown that the QED correction to the electron mass contains chiral terms which nevertheless are parity invariant. The spontaneous emission rate of a two-level atom is shown to increase in the medium. The spontaneously emitted radiation is partially polarized.
In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. In D < 4 dimensions the theory has solutions which exhibit chiral symmetry breaking for all values of the coupling. To begin with, we study this phenomenon both numerically and, with some approximations, analytically within the rainbow approximation in the Landau gauge. In particular, we discuss how to extract the critical coupling alpha_c = pi/3 relevant in four dimensions from the D dimensional theory. We further present analytic results for the…
We study the connection of the chiral dynamics in QED and QCD in a strong magnetic field with noncommutative field theories (NCFT). It is shown that these dynamics determine complicated nonlocal NCFT. In particular, although the interaction vertices for electrically neutral composites in these gauge models can be represented in the space with noncommutative spatial coordinates, there is no field transformation that could put the vertices in the conventional form considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model in a magnetic field where such a field transformation c…
Based on the feature of chiral susceptibility and thermal susceptibility at finite temperature, the nature of chiral phase transition around the critical number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a fixed fermion flavors number in massless QED$_3$ are investigated. It is showed that, at finite temperature the system exhibits a second-order phase transition at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1, while it reveals a higher-order continuous phase transition around $N_c$ at zero temperature.
We study in this paper the radiative corrections to chiral magnetic current at both zero and nonzero temperature. Our motivation is a radiative correction to the matrix element of the anomalous Ward identity in massless QED stemming from a three-loop diagram where the two photons coming from the one-loop anomalous triangle are re-scattered. Through the interplay between the Ward identity and the infrared subtlety of the fermion loop integral, we are able to reproduce the corrections known in literature in a simpler approach and obtain its contribution to the chiral magnetic current at zero tem…
We propose a novel lattice calculation of spontaneous chiral symmetry breaking in QED model with 2+1 dimensional fermion brane. Considering the relativistic action with gauge symmetry we rigorously carry out path integral in Monte-Carlo simulation with Fermi-velocity relevant to effective coupling constant. We numerically show the evidence of spontaneous chiral symmetry breaking in strong coupling region with chiral condensate, low-lying mode distribution and Nambu-Goldstone boson spectrum in bare Fermi-velocty $v=0.1$. This is a feasible study to investigate the phase structure of Graphene.
The catalysis of chiral symmetry breaking by a magnetic field in the massless weak-coupling phase of QED is studied. The dynamical mass of a fermion (energy gap in the fermion spectrum) is shown to depend essentially nonanalytically on the renormalized coupling constant $α$ in a strong magnetic field. The temperature of the symmetry restoration is calculated analytically as $T_c\approx m_{dyn}$, where $m_{dyn}$ is the dynamical mass of a fermion at zero temperature.
Employing the Schwinger's proper-time method, we calculate the $<\barψ ψ>$-condensate for massive Dirac fermions of charge $e$ interacting with a uniform magnetic field in a heat bath. We present general results for arbitrary hierarchy of the energy scales involved, namely, the fermion mass $m$, the magnetic field strength $\sqrt{eB}$ and temperature $T$. Moreover, we study particular regimes in detail and reproduce some of the results calculated or anticipated earlier in the literature. We also discuss possible applications of our findings.
We study QED corrections to chiral symmetry breaking in the Nambu--Jona-Lasinio (NJL) model with two flavors of quarks. In this model, the isospin symmetry is broken by the differences between the current quark masses and the electromagnetic charges of the up and down quarks. To leading order in the 1/N expansion, we calculate the effective potential of the model with one-loop QED corrections at finite temperature. Evaluating the effective potential, we study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass plays an essential…
In quenched QED we construct a non-perturbative fermion-boson vertex that ensures the fermion propagator satisfies the Ward-Takahashi identity, is multiplicatively renormalizable, agrees with perturbation theory for weak couplings and has a critical coupling for dynamical mass generation that is strictly gauge independent. This is in marked contrast to the rainbow approximation in which the critical coupling changes by 50% just between the Landau and Feynman gauges. The use of such a vertex should lead to a more believable study of mass generation.
Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and $\textit{d}$-wave superconducting ($\textit{d}$SC) phases, the influences of gauge boson mass $m_{a}$ on chiral symmetry restoration and deconfinement phase transitions in QED$_{3}$ are investigated simultaneously within a unified framework, i.e., Dyson-Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass $m_{a}$ is a typical second-order phase transition; the chiral symmetry restoration and deconfinement p…
We present a first principles study of chiral plasma instabilities and the onset of chiral turbulence in QED plasmas far from equilibrium. By performing classical-statistical lattice simulations of the microscopic theory, we show that the generation of strong helical magnetic fields from a helicity imbalance in the fermion sector proceeds via three distinct phases. During the initial linear instability regime the helicity imbalance of the fermion sector causes an exponential growth(damping) of magnetic field modes with right(left) handed polarization, for which we extract the characteristic gr…
We present results from a study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in massive strong-coupling quenched QED$_4$. Results are compared for three different fermion-photon proper vertex {\it Ansätze\/}: bare $γ^μ$, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used and it should prove useful in future DSE studies, whenever renormalization is required in numerical work.
Through more detailed calculations on QED$_{1+1}$ and QED$_{3+1}$ emplying a new treatment of Feynman Amplitudes, we attribute the regularization independent and hence definite origin of chiral anomaly in perturbation theory to an unambiguous term which is a rational function in momentum space. Some relevant remarks are presented.
We have studied the chiral phase transition in three-dimensional QED in the presence of a Chern--Simons term for the gauge field. There exists a phase where the chiral symmetry is broken dynamically and we have determined the critical line for this symmetry breaking as a function of the effective coupling and the strength of the additional Chern--Simons term. In the presence of a Chern--Simons term, the chiral phase transition turns out to be first order, in sharp contrast to the phase transition in pure three-dimensional QED.
We report the generation of a pseudovector electric current having imbalanced chirality in an electron-positron strongly magnetized gas in QED. It propagates along the external applied magnetic field B as a chiral magnetic effect in QED. It is triggered by a perturbative electric field parallel to B, associated to a pseudovector longitudinal mode propagating along B. An electromagnetic chemical potential was introduced, but our results remain valid even for vanishing chemical potential. A nonzero fermion mass was assumed, which is usually considered vanishing in the literature. In the quantum …
It has been shown recently that a neutron placed in an external quasistatic electric field develops an induced electric dipole moment $\mathbf{p}_{\mathrm{IND}}$ due to quantum fluctuations in the QED vacuum. A feasible experiment which could detect such an effect is proposed and described here. It is shown that the peculiar angular dependence of $\mathbf{p}_{\mathrm{IND}}$ on the orientation of the neutron spin leads to a characteristic asymmetry in polarized neutron scattering by heavy nuclei. This asymmetry can be of the order of $10^{-3}$ for neutrons with epithermal energies. For thermali…
The catalysis of chiral symmetry breaking in the massless weakly coupled QED in a magnetic field is studied. It is shown that the effect is due to the dimensional reduction $D\to D-2$ in the dynamics of fermion pairing in a magnetic field. The dynamical mass of fermions (energy gap in the fermion spectrum) is determined. The temperature of the symmetry restoration is estimated analytically.
We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors above which chiral symmetry is restored. This effect is in diametrical op…
In three-dimensional QED with a Chern--Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger--Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger--Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absence of the Chern--Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place …
Compact lattice Quantum Electrodynamics (QED) with four species of fermions is simulated with massless quarks by using the $χ$QED scheme of adding a four-fermi interaction to the action. Simulations directly in the chiral limit of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices, and the phase diagram, parameterized by the gauge and the four-fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration. The simulation results indicate that the monopole condensation transition is first order whil…
The measurement of the charge asymmetry $A_{FB}(e^-e^+\to μ^-μ^+)$ will play an important role at the high-luminosity circular electron-positron collider FCCee considered for construction at CERN. In particular, near the Z resonance, $\sqrt{s} \simeq M_Z \pm 3.5$ GeV, $A_{FB}$ will provide a very precise value of the pure electromagnetic coupling constant $α_{QED}(M_Z)$, which is vitally important for overall tests of the Standard Model. For this purpose, $A_{FB}$ will be measured at the FCCee with an experimental error better than $δA_{FB} \simeq 3\cdot 10^{-5},$ at least a factor 100 more pr…
At zero temperature and density, the nature of the chiral phase transition in QED$_3$ with $\textit{N}_{f}$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors $\textit{N}_{f}$ reaches the critical number $\textit{N}_{f,…
Previous analytical studies of quantum electrodynamics in $2+1$ dimensions (QED3) have shown the existence of a critical number of fermions for onset of chiral symmetry breaking, the most known being the value $N_c\approx3.28$ obtained by Nash to $1/N^2$ order in the $1/N$ expansion [16]. This analysis is reconsidered by solving the Dyson-Schwinger equations for the fermion propagator and the vertex to show that the more accurate gauge independent value is $N_c\approx2.85$, and for $N<N_c$ the chiral symmetry is dynamically broken. An estimate for the value of chiral condensate $\langle\barψψ\…
Chiral magnetic effect (CME) has been suggested to take place during peripheral relativistic heavy ion collisions. However, signals of its realization are not yet independent of ambiguities and thus probing the non-trivial topological vacua of quantum chromodynamics (QCD) is still an open issue. Weyl materials, particularly graphene, on the other hand, are effectively described at low energies by the degrees of freedom of quantum electrodynamics in two spatial dimensions, QED3. This theory shares with QCD some interesting features, like confinement and chiral symmetry breaking and also possess…
The dressed-electron eigenstate of Feynman-gauge QED is computed in light-front quantization with a Fock-space truncation to include at most the one-photon/one-electron sector. The theory is regulated by the inclusion of three massive Pauli-Villars (PV) particles, one PV electron and two PV photons. In particular, the chiral limit is investigated, and the correct limit is found to require two PV photons, not just one as previously thought. The renormalization and covariance of the electron current are also analyzed. We find that the plus component is well behaved and use its spin-flip matrix e…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal…
We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically gener…
We perform a general chiral symmetry and unitarity based analysis of a local process of the fermion-antifermion creation from the vacuum by a high-energy photon as well as an explicit partial wave analysis of the vector current in QED and QCD. It turns out that such a local process proceeds necessarily via a certain superposition of the $S$- and $D$-wave contributions. These constraints from chiral symmetry and unitarity are confronted then with the well-known theoretical and experimental results on $e^+e^-\toγ\to e^+e^-$, $e^+e^-\toγ\to μ^+μ^-$, and $e^+e^-\toγ\to q\bar{q}$ in the ultrarelati…
We show that the chiral-symmetry-broken phase of massless QED in the presence of a magnetic field exhibits strong paraelectricity. A large anisotropic electric susceptibility develops in the infrared region, where most of the fermions are confined to their lowest Landau level, and dynamical mass and anomalous magnetic moment are generated via the magnetic catalysis mechanism. The nonperturbative nature of this effect is reflected in the dependence of the electric susceptibility on the fine-structure constant. The strong paraelectricity is linked to the electric dipole moments of the particle/a…
We study chiral symmetry breaking in quenched strong-coupling QED$_4$ in arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A recently developed numerical renormalization program is fully implemented. Results are compared for three different fermion-photon proper vertex {\it Ansätze\/}: bare $γ^μ$, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. We discuss the chiral limit and observe that in this limit the renormalized axial current is conserved. A detailed study of residual gauge dependence due to the verte…
In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta m…
We study QED corrections to the chiral symmetry breaking in Nambu-Jona-Lasinio (NJL) model with two flavors of quarks. In the model the isospin symmetry is broken by differences of the current quark masses and the electromagnetic charges between up and down quarks. In the leading order of the 1/N expansion we calculate the effective potential of the model with one-loop QED corrections. Evaluating the effective potential, we study an influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass has an important contribution for the orientation…
Experiment E158 at SLAC can measure an azimuthal asymmetry in single-spin, transversely polarized Moller scattering, e^{-\uparrow} e^- -> e^- e^-, which arises from a QED rescattering phase. We recompute the leading-order (one-loop) asymmetry, confirming previous results, and calculate the leading logarithmic QED corrections due to initial-state radiation from the beam and target electrons, and due to final-state radiation. The size of these radiative corrections is quite sensitive to experimental details, such as the acceptance in energy and in polar angle of the scattered electron. For E158,…
