Two-photon Vertex Research Articles

Dominant role of two-photon vertex in nonlinear response in two-dimensional Dirac systems

We show that the standard concepts of nonlinear response to electromagnetic fields break down in two-dimensional Dirac systems, like graphene, in the quantum regime close to the Dirac point. We present a compelling many-body theory for nonlinear transport focusing on disorder scattering as a benchmark example. We show that, although the diamagnetic two-photon vertex is absent at the non-interacting level, disorder effects give rise to a self-generation of such two-photon vertex surviving even in the clean limit. We predict that the two-photon vertex self-generation is present only in two dimensions. The impact of such a striking scenario on the nonlinear quantum transport is discussed, predicting a huge enhancement of third-order dc conductivity comparing to the common models.

Nucleon Compton scattering in the Dyson-Schwinger approach

We analyze the nucleon's Compton scattering amplitude in the Dyson-Schwinger/Faddeev approach. We calculate a subset of diagrams that implements the nonperturbative handbag contribution as well as all $t$-channel resonances. At the quark level, these ingredients are represented by the quark Compton vertex whose analytic properties we study in detail. We derive a general form for a fermion two-photon vertex that is consistent with its Ward-Takahashi identities and free of kinematic singularities, and we relate its transverse part to the on-shell nucleon Compton amplitude. We solve an inhomogeneous Bethe-Salpeter equation for the quark Compton vertex in rainbow-ladder truncation and implement it in the nucleon Compton scattering amplitude. The remaining ingredients are the dressed quark propagator and the nucleon's bound-state amplitude which are consistently solved from Dyson-Schwinger and covariant Faddeev equations. We verify numerically that the resulting quark Compton vertex and nucleon Compton amplitude both reproduce the $\ensuremath{\pi}\ensuremath{\gamma}\ensuremath{\gamma}$ transition form factor when the pion pole in the $t$ channel is approached.

Detecting Axionlike Particles with Gamma Ray Telescopes

We propose that axionlike particles (ALPs) with a two-photon vertex, consistent with all astrophysical and laboratory bounds, may lead to a detectable signature in the spectra of high-energy gamma-ray sources. This occurs as a result of gamma rays being converted into ALPs in the magnetic fields of efficient astrophysical accelerators according to the "Hillas criterion", such as jets of active galactic nuclei or hot spots of radio galaxies. The discovery of such an effect is possible by GLAST in the 1-100 GeV range and by ground-based gamma-ray telescopes in the TeV range.

Signatures of axionlike particles in the spectra of TeV gamma-ray sources

One interpretation of the unexplained signature observed in the PVLAS experiment invokes a new axionlike particle (ALP) with a two-photon vertex, allowing for photon-ALP oscillations in the presence of magnetic fields. In the range of masses and couplings suggested by PVLAS, the same effect would lead to a peculiar dimming of high-energy photon sources. For typical parameters of the turbulent magnetic field in the galaxy, the effect sets in at ${E}_{\ensuremath{\gamma}}\ensuremath{\gtrsim}10\text{ }\text{ }\mathrm{TeV}$, providing an ALP signature in the spectra of TeV gamma sources that can be probed with Cherenkov telescopes. A dedicated search will be strongly motivated if the ongoing photon regeneration experiments confirm the PVLAS particle interpretation.

Induced magnetic moment in noncommutative Chern–Simons scalar QED

We compute the one loop, $O(\th)$ correction to the vertex in the noncommutative Chern-Simons theory with scalar fields in the fundamental representation. Emphasis is placed on the parity odd part of the vertex, since the same leads to the magnetic moment structure. We find that, apart from the commutative term, a $\th$-dependent magnetic moment type structure is induced. In addition to the usual commutative graph, cubic photon vertices also give a finite $\th$ dependent contribution. Furthermore, the two two-photon vertex diagrams, that give zero in the commutative case yield finite $\th$ dependent terms to the vertex function.

Pions versus magnons: from QCD to antiferromagnets and quantum Hall ferromagnets

The low-energy dynamics of pions and magnons—the Goldstone bosons of the strong interactions and of magnetism—are analogous in many ways. The electroweak interactions of pions result from gauging an SU(2) L ⊗ U(1) Y symmetry which then breaks to the U(1) em gauge symmetry of electromagnetism. The electromagnetic interactions of magnons arise from gauging not only U(1) em but also the SU(2) s spin rotational symmetry, with the electromagnetic fields E → and B → appearing as non-Abelian vector potentials. Pions couple to electromagnetism through a Goldstone–Wilczek current that represents the baryon number of Skyrmions and gives rise to the decay π 0→ γγ. Similarly, magnons may couple to an analogue of the Goldstone–Wilczek current for baby-Skyrmions which induces a magnon–two-photon vertex. The corresponding analogue of photon–axion conversion is photon–magnon conversion in an external magnetic field. The baryon number violating decay of Skyrmions can be catalyzed by a magnetic monopole via the Callan–Rubakov effect. Similarly, baby-Skyrmion decay can be catalyzed by a charged wire. For more than two flavors, the Wess–Zumino–Witten term enters the low-energy pion theory with a quantized prefactor N c —the number of quark colors. The magnon analogue of this prefactor is the anyon statistics angle θ which need not be quantized.

Photon mixing in universes with large extra dimensions

In presence of a magnetic field, photons can mix with any particle having a two-photon vertex. In theories with large compact extra-dimensions, there exists a hierachy of massive Kaluza-Klein gravitons that couple to any photon entering a magnetic field. We study this mixing and show that, in comparison with the four dimensional situation where the photon couples only to the massless graviton, the oscillation effect may be enhanced due to the existence of a large number of Kaluza-Klein modes. We give the conditions for such an enhancement and then investigate the cosmological and astrophysical consequences of this phenomenon; we also discuss some laboratory experiments. Axions also couple to photons in the same way; we discuss the effect of the existence of bulk axions in universes with large extra-dimensions. The results can also be applied to neutrino physics with extra-dimensions.

Feynman Rules for Magnetised Spin-O Bosons

Solutions of the Klein-Gordon equation are given in the Landau and cylindrical gauges and these are used to calculate explicit forms of the vertex function. From an S-matrix expansion analogous to the spin-i case we obtain the Feynman rules for magnetised spin-O particles: the major differences between the spin-i and spin-O cases are the explicit forms of the respective vertex functions and the addition of a two-photon vertex in the spin-O case. This additional vertex makes possible a whole new class of Feynman diagrams.

Mixing of the photon with low-mass particles.

Photons can mix with low-mass bosons in the presence of external electromagnetic fields if these particles---not necessarily of spin 1---couple by a two-photon vertex. Important examples are the hypothetical axion (spin 0) and graviton (spin 2). We develop a formalism which is adapted to study the evolution of a photon (axion, graviton) beam in the presence of external fields. We apply our results to discuss the possibility of detecting axions by a measurement of the magnetically induced birefringence of the vacuum. We also discuss photon-axion (graviton) transitions in pulsar magnetic fields. The QED-induced nonlinearity of Maxwell's equations causes magnetic birefringence effects which are much stronger than the axion-induced effects in the range of axion parameters allowed by astrophysical constraints. Also, this QED effect induces an index of refraction for photons in vacuum which is so large near pulsars that photon-axion (graviton) transitions are strongly suppressed. However, this QED effect can be canceled by plasma refractive effects, leading to degeneracy between photons and axions so that resonant transitions can occur in analogy with the Mikheyev-Smirnov-Wolfenstein effect. The adiabatic condition can be met only in spatially extended systems, possibly in the magnetosphere of magnetic white dwarfs. Our conclusions differ substantially from several recent discussions of various aspects of these mixing phenomena.

EXCLUSIVE HADRON PRODUCTION IN TWO-PHOTON REACTIONS

This paper summarizes experimental results on exclusive hadron production in two-photon collisions at electron-positron storage rings and attempts some interpretation. Experimental know-how is described and new suggestions are made for future analyses. New model calculations on resonance form factors and pair production amplitudes are presented. The two-photon vertex is decomposed such that experiments can be parameterized with the minimal number of free parameters. Selection rules for off-shell photon collisions are given in addition to Yang’s theorems. [Formula: see text]

Pseudoscalar electromagnetic vertex function: Quark-hadron duality.

A double-dispersion-relation model for the neutral-pseudoscalar-meson--two-photon vertex function is proposed. Several spectral-function sum rules are derived. Quark-hadron duality is established in the model, so that the low-energy behavior of the vertex function is dominated by vector-meson resonances, and the high-energy behavior of the vertex function is determined by QCD dynamics and light-cone algebra. The vertex function is then applied to study the decay processes ${\ensuremath{\pi}}^{0}$(${\ensuremath{\eta}}^{0}$)\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}, ${\ensuremath{\pi}}^{0}$(${\ensuremath{\eta}}^{0}$)\ensuremath{\rightarrow}${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$(${\ensuremath{\mu}}^{+}$\ensuremath{\mu} $^{\mathrm{\ensuremath{-}}}$), ${\ensuremath{\pi}}^{0}$(${\ensuremath{\eta}}^{0}$)\ensuremath{\rightarrow}${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$(${\ensuremath{\mu}}^{+}$\ensuremath{\mu} $^{\mathrm{\ensuremath{-}}}$)\ensuremath{\gamma}, and the scattering process ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$(${\ensuremath{\eta}}^{0}$)\ensuremath{\gamma}.

Cross-section for annihilation of a pair in two photons with gauge-invariant modification of the electron propagator

We will calculate the cross-section for annihilation in two photons of an electron-positon pair with a simple modification of the electronic propagator. In order to conserve the gauge invariance, besides the modification of the vertex prescribed by the Ward-Takahashi identity and proposed by McClure and Drell, also the intervention of a two-photon vertex is considered. First the problem of the general construction of such vertex is dealt with; afterwards, we apply this result, in the simplest form, to compute differential and total cross-sections. The calculation is done in view of the experiments of pair annihilation planned in order to test in this way the validity of quantum electrodynamics.

Electromagnetic Meson Mass Differences

It is shown that if the pi and K meson electromagnetic mass differences are calculated in the finite electromagnetic gage, the two-photon vertex term becomes finite in the pole approximation to the dispersion relation and a satisfactory quantum theory of both pi and K meson mass splitting is obtained. An equation is derived for the mass difference between pi /sup +/+ and pi /sup 0/ mesons, which gives a result agreeing with experiment; and the equation for K/sup +/ and K/sup 0/ mesons gives a mass difference of -3.5 Mev, corresponding to a K meson model of a positively charged cloud of radius approximately 0.5 x 10/sup -13/ cm with a negatively charged core of radius approximately O.2 x 10/sup -13/ cm. (D.L.C.)