Soft Photon Energy Research Articles

Universal lepton universality violation in exclusive processes

In high energy exclusive processes involving leptons, QED corrections can be sensitive to infrared scales like the lepton mass and the soft photon energy cut, resulting in large logarithms that need to be resummed to all order in $\ensuremath{\alpha}$. When considering the ratio of the exclusive processes between two different lepton flavors, the ratio $R$ can be expressed in terms of factorized functions in the decoupled leptonic sectors. While some of the functional terms cancel, there remain the large logarithms due to the lepton mass difference and the energy cut. This factorization process can be universally applied to the exclusive processes such as $Z\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{l}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{l}$, where the resummed result in the ratio gives significant deviations from the naive expectation from lepton universality.

Bhabha scattering at NNLO with next-to-soft stabilisation

A critical subject in fully differential QED calculations originates from numerical instabilities due to small fermion masses that act as regulators of collinear singularities. At next-to-next-to-leading order (NNLO) a major challenge is therefore to find a stable implementation of numerically delicate real-virtual matrix elements. In the case of Bhabha scattering this has so far prevented the development of a fixed-order Monte Carlo at NNLO accuracy. In this paper we present a new method for stabilising the real-virtual matrix element. It is based on the expansion for soft photon energies including the non-universal subleading term calculated with the method of regions. We have applied this method to Bhabha scattering to obtain a stable and efficient implementation within the McMule framework. We therefore present for the first time fully differential results for the photonic NNLO corrections to Bhabha scattering.

Black hole discharge: Very-high-energy gamma rays from black hole-neutron star mergers

With mass ratio larger than $\sim 5$ (which depends on the black hole spin and the star radius), star disruption is not expected for a black hole merging with a neutron star during the final plunge phase. In the late inspiral stage, the black hole is likely charged as it cuts through the magnetic field carried by the neutron star, leaving a temporarily charged black hole after merger. The unstable charged state of the remnant black hole rapidly neutralizes by interacting with the surrounding plasma and photons, which we investigate in first principle by numerically solving a coupled set of Boltzmann equations of 1+1 form for non-spinning BH background. The resulting basic picture is as follows. Electrons and positrons are accelerated in the BH electric field, which then lose energy to surrounding soft photons via Compton scattering; more electrons and positrons will be created from pair production as the hard photons colliding with soft photons, or through the Schwinger process in strong electromagnetic fields. The cascade stops when the charged black hole accretes enough opposite charges and becomes neutralized. We find that $\sim 10\%$ (which depends on the soft photon energy and number density) of the total electric energy is carried away to infinity in a time interval $\sim 1$ ms by very-high-energy ($>50$ GeV, the low energy detection threshold of the MAGIC telescope) gamma rays whose spectrum is approximately a power law with spectral index $\sim -2.3$. We expect the discharge picture to be true for spinning charged BHs as well.

Soft-Photon Corrections to B[over ¯]→Dτ^{-}ν[over ¯]_{τ} Relative to B[over ¯]→Dμ^{-}ν[over ¯]_{μ}.

We evaluate long-distance electromagnetic (QED) contributions to B[over ¯]^{0}→D^{+}τ^{-}ν[over ¯]_{τ} and B^{-}→D^{0}τ^{-}ν[over ¯]_{τ} relative to B[over ¯]^{0}→D^{+}μ^{-}ν[over ¯]_{μ} and B^{-}→D^{0}μ^{-}ν[over ¯]_{μ}, respectively, in the standard model. We point out that the QED corrections to the ratios R(D^{+}) and R(D^{0}) are not negligible, contrary to the expectation that radiative corrections are almost canceled out in the ratio of the two branching fractions. The reason is that long-distance QED corrections depend on the masses and relative velocities of the daughter particles. We find that theoretical predictions for R(D^{+})^{τ/μ} and R(D^{0})^{τ/μ} can be amplified by ∼4% and ∼3%, respectively, for the soft-photon energy cut in the range 20-40MeV.

Relativistic theory for radiative forward electron emission in heavy ion-atom encounters

The forward electron emission with simultaneous photon production during the scattering of relativistic, highly stripped projectiles from light target atoms is calculated within the Dirac theory. The method of calculation is a simplification of the impulse approximation and is based on the relation of the cross section for radiative capture to continuum of loosely bound electrons to the frame-transformed electron bremsstrahlung cross section. It is demonstrated that such an approximation is well justified in a large region of energies and photon emission angles, with the exception of the extreme forward and backward emission and the soft-photon energy limit. The cusp spectrum and the corresponding angular distribution are compared to recent experimental data for the collision system 90.38 MeV/amu U88+ + N2.

Demonstration of multilayer reflective optics at photon energies above 0.6 MeV.

Focusing optics operating in the soft gamma-ray photon energy range can advance a range of scientific and technological applications that benefit from the large improvements in sensitivity and resolution that true imaging provides. An enabling technology to this end is multilayer coatings. We show that very short period multilayer coatings deposited on super-polished substrates operate efficiently above 0.6 MeV. These experiments demonstrate that Bragg scattering theory established for multilayer applications as low as 1 eV continues to work well into the gamma-ray band.

DIRECT MEASUREMENT OF THE X-RAY TIME-DELAY TRANSFER FUNCTION IN ACTIVE GALACTIC NUCLEI

The origin of the observed time lags, in nearby active galactic nuclei (AGN), between hard and soft X-ray photons is investigated using new XMM-Newton data for the narrow-line Seyfert I galaxy Ark 564 and existing data for 1H0707-495 and NGC 4051. These AGN have highly variable X-ray light curves that contain frequent, high peaks of emission. The averaged light curve of the peaks is directly measured from the time series, and it is shown that (i) peaks occur at the same time, within the measurement uncertainties, at all X-ray energies, and (ii) there exists a substantial tail of excess emission at hard X-ray energies, which is delayed with respect to the time of the main peak, and is particularly prominent in Ark 564. Observation (i) rules out that the observed lags are caused by Comptonization time delays and disfavors a simple model of propagating fluctuations on the accretion disk. Observation (ii) is consistent with time lags caused by Compton-scattering reverberation from material a few thousand light-seconds from the primary X-ray source. The power spectral density and the frequency-dependent phase lags of the peak light curves are consistent with those of the full time series. There is evidence for non-stationarity in the Ark 564 time series in both the Fourier and peaks analyses. A sharp `negative' lag (variations at hard photon energies lead soft photon energies) observed in Ark 564 appears to be generated by the shape of the hard-band transfer function and does not arise from soft-band reflection of X-rays. These results reinforce the evidence for the existence of X-ray reverberation in type I AGN, which requires that these AGN are significantly affected by scattering from circumnuclear material a few tens or hundreds of gravitational radii in extent.

THE ORIGIN OF GAMMA RAYS FROM GLOBULAR CLUSTERS

Fermi has detected gamma-ray emission from eight globular clusters. We suggest that the gamma-ray emission from globular clusters may result from the inverse Compton scattering between relativistic electrons/positrons in the pulsar wind of MSPs in the globular clusters and background soft photons including cosmic microwave/relic photons, background star lights in the clusters, the galactic infrared photons and the galactic star lights. We show that the gamma-ray spectrum from 47 Tuc can be explained equally well by upward scattering of either the relic photons, the galactic infrared photons or the galactic star lights whereas the gamma-ray spectra from other seven globular clusters are best fitted by the upward scattering of either the galactic infrared photons or the galactic star lights. We also find that the observed gamma-ray luminosity is correlated better with the combined factor of the encounter rate and the background soft photon energy density. Therefore the inverse Compton scattering may also contribute to the observed gamma-ray emission from globular clusters detected by Fermi in addition to the standard curvature radiation process. Furthermore, we find that the emission region of high energy photons from globular cluster produced by inverse Compton scattering is substantially larger than the core of globular cluster with a radius >10pc. The diffuse radio and X-rays emitted from globular clusters can also be produced by synchrotron radiation and inverse Compton scattering respectively. We suggest that future observations including radio, X-rays, and gamma-rays with energy higher than 10 GeV and better angular resolution can provide better constraints for the models.

Soft-photon corrections in multi-body meson decays

The effects due to soft-photon emission (and the related virtual corrections) in multi-body decays of B, D, and K mesons are analyzed. We present analytic expressions for the universal \(\mathcal{O}(\alpha)\) correction factors which can be applied to all multi-body decay modes where a tight soft-photon energy cut in the decaying-particle rest frame is applied. All-order resummations valid in the limit of small and large velocities of the final-state particles are also discussed. The phenomenological implications of these correction factors in the distortion of Dalitz plot distributions of K→3π decays are briefly analyzed.

The phase-resolved high energy spectrum of the crab pulsar

We present a modified outer gap model to study the phase-resolved spectra of the Crab pulsar. A theoretical double peak profile of the light curve containing the whole phase is shown to be consistent with the observed light curve of the Crab pulsar by shifting the inner boundary of the outer gap inwardly to ∼10 stellar radii above the neutron star surface. In this model, the radial distances of the photons corresponding to different phases can be determined in the numerical calculation. Also the local electrodynamics, such as the accelerating electric field, the curvature radius of the magnetic field line and the soft photon energy, are sensitive to the radial distances to the neutron star. Using a synchrotron self-Compton mechanism, the phase-resolved spectra with the energy range from 100 eV to 3 GeV of the Crab pulsar can also be explained.

A Test of External Compton Models for Gamma‐Ray Active Galactic Nuclei

There is clear evidence that the gamma-ray emission from active galactic nuclei (AGNs) can be attributed to inverse Compton scatterings in the relativistic blobs near the massive black holes. If the soft seed photons are from the regions outside the blobs, a linear relation between (vF(v,gamma)/vF(v,syn)u(*))(1/(1+alpha)) and the Doppler factor delta is expected, where vF(v,gamma) and vF(v,syn) are monochromatic gamma-ray and synchrotron fluxes, respectively, and u(*) is the energy density of soft seed photons. We estimate the soft photon energy density in the relativistic blobs contributed by the broadline regions (BLRs) in these gamma-ray AGNs using their broad-line emission data. The Doppler factors delta are derived from their radio core and X-ray emission data, based on the assumption that the X-ray emission is produced through synchrotron self-Compton (SSC) scatterings. We find two nearly linear correlations: (vF(v,gamma)/vF(opt)u(*))1/(1+alpha) proportional to delta(1.09) and (vF(v,gamma)/vF(IR)u(*))(1/(1+alpha)) proportional to delta(1.20), which are roughly consistent with the linear correlation predicted by the theoretical model for external Compton scatterings. Our results imply that the soft seed photons are predominantly from the BLRs in these gamma-ray AGNs.

Compton Scattering in the Klein‐Nishina Regime Revisited

In blazars such as 3C 279, GeV gamma rays are thought to be produced by inverse Compton scattering of soft photons injected from external sources into the jet. Because of the large bulk Lorentz factor of the jet, the energy of soft photons is Doppler shifted in the comoving frame of the jet, and the scattering is likely to occur in the Klein-Nishina regime. Although the Klein-Nishina effects are well known, the properties of the electron and emission spectra have not been studied in detail in the environment of blazars. We solve the kinetic equation of electrons with the spatial escape term of the electrons to obtain the electron energy spectrum in the jet and calculate the observed emission spectrum. In calculations of the Compton losses in the Klein-Nishina regime, we use the discrete loss formalism to take into account the significant energy loss in a single scattering. Although the scattering cross section decreases because of the Klein-Nishina effects, ample gamma rays are emitted by inverse Compton scattering. When the injection spectrum of electrons obeys a power law, the electron spectrum does not follow a broken power law, as a result of the Klein-Nishina effects, and a large number of high-energy electrons remain in the emitting region.

Coulomb Focusing Effects on Bremsstrahlung Spectrum from ECR Plasmas

The Coulomb focusing effects are investigated on electron-ion bremsstrahlung emission rate from magnetized electron cyclotron resonance (ECR) plasmas. The bremsstrahlung emission rate is obtained for both the soft and hard photon energies. The result shows that the Coulomb focusing effects in Maxwellian distribution plasmas are found to be more significant than those in non-Maxwellian plasmas. It is also found that the Coulomb focusing effects on the bremsstrahlung spectrum significantly decrease with increasing non-Maxwellian character. The Coulomb focusing effects also decrease with increasing perpendicular temperature (T⊥).

Timing and Spectral Properties of X-Ray Emission from the Converging Flows onto a Black Hole: Monte Carlo Simulations

We demonstrate that an X-ray spectrum of a converging inflow (CI) onto a black hole is the sum of a thermal (disk) component and the convolution of some fraction of this component with the Comptonization spread (Green's) function. The latter component is seen as an extended power law at energies much higher than the characteristic energy of the soft photons. We show that the high-energy photon production (source function) in the CI atmosphere is distributed with the characteristic maximum at about the photon bending radius, 1.5rS, independently of the seed (soft) photon distribution. We show that high-frequency oscillations of the soft photon source in this region leads to the oscillations of the high-energy part of the spectrum but not of the thermal component. The high-frequency oscillations of the inner region are not significant in the thermal component of the spectrum. We further demonstrate that Doppler and recoil effects (which are responsible for the formation of the CI spectrum) are related to the hard (positive) and soft (negative) time lags between the soft and hard photon energy channels, respectively.

Radiative leptonicBcdecays in effective field theory

The recent discovery of the B_c meson by the CDF collaboration and proposed new experiments at Fermilab and CERN motivate new theoretical studies of the B_c system. Here we investigate the radiative leptonic decay B_c -> gamma l nu. This process is an important background to the annihilation process B_c -> l nu, which will be used to extract the B_c decay constant. We perform a model-independent calculation, based on QCD, of the partial width and various kinematic distributions. We also examine the decay within the framework of NRQCD, an effective field theory of nonrelativistic quarks, generalizing the NRQCD Lagrangian to include external sources for the weak and electromagnetic currents. Finally, we comment on the role of the B_c* intermediate state for very soft photon energies.

QED radiative corrections to neutrino counting reaction [formula omitted

We calculate the QED one-loop corrections to the reaction e + e − → ν νγ mediated by the Z-boson. The full expressions for virtual corrections are analytically presented. The virtual corrections with the soft photon emission correction give negative values of around several tens of percent in the range of total energy 100–130 GeV when the cut on soft photon energy is set to 0.2 GeV. Also taken into account are the effects due to the hard collinear photon and to the two parallel photons not discriminated from a single photon. Various distributions are given around the Z-boson peak. It is pointed out that there the sum of QED corrections is fairly small and the reactions can be really used for the deduction of the number of massless neutrinos.

Is the remnant of SN1006 composed of iron?

The remnant of the supernova explosion of AD 1006 (the brightest in recorded history) has a shell-like appearance at both radio and X-ray wavelengths. Einstein X-ray observations by Pye et al.1 show a soft (photon energy e ≲ ¼ keV) filled interior surrounded by a harder (e ≳ 1 keV) unresolved ring of emission of radius ∼15 arc min. Superficially it appears to be similar to most supernova remnants for which many studies have shown that the X-ray emission is thermal radiation from gas shock-heated by high-velocity ejecta. The spectrum2 of parts of the edge of the remnant in the range 0.75 ≲ e ≲ 10 keV shows, however, no evidence for line emission. The spectral shape is consistent with a power-law perhaps due to a non-thermal mechanism. Moreover, the total mass of gas1 required exceeds ∼10M⊙ if it is of normal cosmic abundance. This is much greater than that expected for a remnant several hundred parsecs above the galactic plane. As no pulsar (or Crab-like morphology) is evident in the remnant of SN1006, Reynolds and Chevalier3 have proposed that relativistic particles are being efficiently accelerated in shocked gas, and provide the major source of X rays through synchrotron emission. SN1006 is then an important region for the study of such acceleration processes. Here we reinvestigate a thermal interpretation and show that the element abundances associated with a Type I supernova4–7 may provide an alternative explanation.