Soft Photon Emission Research Articles

Electromagnetic corrections to hadron-hadron scattering

We use S-matrix methods to determine the electromagnetic corrections to relativistic hadron scattering. The infrared divergences associated with soft photon emission and with the Coulomb interaction are removed to give a finite scattering amplitude which obeys crossing and has the usual analytic structure. An approximate calculation of the electromagnetic correction to the phase of the πN P 33 amplitude is given.

Radiative Corrections top+p→l++l−+``Anything''and Application to Muon-Electron Symmetry

Radiative corrections, to order $\ensuremath{\alpha}$, are carried out to the lepton lines in the process $p+p\ensuremath{\rightarrow}{l}^{+}+{l}^{\ensuremath{-}}+``\mathrm{anything}''$. Expressions are derived which relate the radiative corrections, due to the emission of soft photons, and of hard photons from the lepton lines, to the observed cross section for production of electron or muon pairs. These expressions are used to predict the difference, based purely on electromagnetic interactions, between the cross sections for production of electron and muon pairs. As a specific example, computations are done using the BNL data for production of lepton pairs in hadron-hadron collisions.

Photon retinue and infra-red divergence problem in quantum electrodynamics

This paper is a careful study of the infra-red divergence problem in quantum electrodynamics. It is found that the conventional treatments of this problem are not consistent with the concept of the photon as a real physical object and it is held here that the problem is a physical one rather than merely one of computational technique. By taking into account the cohesive photon retinue induced by the electron, it is shown that, for any definite number of soft-photon emissions, the cross-sections are always divergence-free. The precise physical significance of the photon retinue in connection with experimental measurement is also discussed.

Infra-red divergence and incident photons

Similar to the usual infra-red divergence corresponding to the emission of soft photons, there is an increasing behaviour of the probability amplitudes for processes including incident photons with lower and lower energies. We show that such a behaviour is only apparent: it vanishes already in a first-order perturbation theory. This cancellation occurs when all the experimentally indistinguishable processes are taken into account, in a way quite different however from the well-known infra-red compensation between radiated and virtual soft photons.

Exchange Currents and Soft Photons

We verify the validity of the low-energy theorem for emission of soft photons in the case of two particles which interact via an exchange potential. To lowest order in $K$, the photon momentum, we define the amplitude for emission from exchange currents, and show that it cancels part of the amplitude arising from internal nucleon lines. Comparison is made with the definition of exchange currents made by other authors.

On the Low-Burnett-Kroll theorem for soft-photon emission

On the Low-Burnett-Kroll theorem for soft-photon emission

Coulomb Interference in High-Energy Scattering

The relativistic Coulomb interference problem is carefully examined in order to evaluate critically the equations used in analyzing experiments designed to test the forward $\ensuremath{\pi}\ensuremath{-}N$ dispersion relations. We show that with a suitable interpretation the nonrelativistic Bethe formula for the phase difference $\ensuremath{\varphi}$ between the strong and electromagnetic contributions is valid. However, for high energy near forward scattering there are unknown contributions which can change this phase by $O(\ensuremath{\alpha})$ rad; this is to be compared with a magnitude of $\ensuremath{\varphi}$ of $\ensuremath{\sim}2\ensuremath{\alpha}$ rad. We further show that two previous relativistic calculations of $\ensuremath{\varphi}$ are incomplete. The effects of calculable radiative corrections such as soft photon emission or vacuum polarization are examined. For the former it is found that although their magnitude is relatively large, they can, in general, be neglected. The reason for this is that by folding an accurate measurement of the total cross section into the data analysis a compensation of errors is induced. No such compensation takes place for the case of vacuum polarization, and its contribution could be important. Finally, we investigate the effects of small admixtures to the strong interactions which are not of the form ${e}^{a+{b}^{2}t}$. We find that they are unlikely to be of significance here provided they can be assumed to be $\ensuremath{\lesssim}20%$ of the complete amplitude.

A soft-photon emission approach to [formula omitted] with SU(3)-symmetry breaking

Using the technique of soft-photon emission and the partial conservation of the tensor currents, the branching ratio Γ(η → 2γ) Γ(π o → 2γ) has been calculated including the first-order SU(3)-symmetry breaking of the decay constants, and found to be consistent with the recent measurements.

Soft-photon emission and some radiative decays of the η and χ0 mesons

Soft-photon emission and some radiative decays of the η and χ0 mesons

Partial summation of the perturbation expansion in high-energy quantum electrodynamics

The renormalization group method is applied to the perturbation expansion of electromagnetic scattering cross-sections at high momentum transfer. It is shown that the limit of vanishing electron mass exists for high momentum transfer and high normalization momentum. In this limit the functional equations of the renormalization group provide a means to sum over «maximally logarithmic terms» to all orders starting only from the knowledge of the lowest order radiative corrections. The summation over soft particle emission which is included here, contains not only soft photons but also soft electron pairs. The summation over the soft photon emission is performed with an accuracy somewhat better than that provided by the renormalization group method. The terms that remain after the summation over «maximally logarithmic terms» and soft particle emission are of the relative order (α/π)2 ln (q2/m2) and (α/π) ΔE/q, wherem is the electron mass,q is the momentum transfer and ΔE is the experimental energy resolution. It is also found that in high-energy scattering the one-photon exchange strongly dominates over the exchange of several photons except for nearly forward or backward scattering in the c.m. system.

Range Distribution ofμ-Mesons fromπ-Meson Decay in Photographic Emulsion

The lengths of $\ensuremath{\mu}$-meson tracks from 1000 $\ensuremath{\pi}$-meson decays have been measured in two Ilford C-2 200-micron thick emulsions, which had been exposed by R. Sagane in a spiral orbit spectrometer to the Berkeley cyclotron. Shrinkage factors obtained from this analysis were used to calculate the true ranges of the $\ensuremath{\mu}$-meson tracks. The distribution of true ranges meets statistical tests for a Gaussian distribution; it has a mean of 597\ifmmode\pm\else\textpm\fi{}1 microns and a standard deviation of 29.1\ifmmode\pm\else\textpm\fi{}0.7 microns. Since decay in flight and soft photon emission accompanying decay have negligible effects in this study, the straggling parameter for 4.1 Mev $\ensuremath{\mu}$-mesons in photographic emulsion can be obtained; it is 4.86\ifmmode\pm\else\textpm\fi{}0.12 percent. The effect of experimental uncertainties on these values can be about 0.1 percent, which is slightly less than the statistical limits imposed by the finite number of events.

On Soft Photon Emission in Radiation Processes

On Soft Photon Emission in Radiation Processes