High-energy $\pi \pi$ scattering without and with photon radiation

Abstract

We discuss the processes $\pi \pi \to \pi \pi$ and $\pi \pi \to \pi \pi \gamma$ from a general quantum field theory (QFT) point of view. We study the soft-photon limit where the photon energy $\omega \to 0$ and where we have the theorems due to F.E. Low and S. Weinberg. We consider for the radiative amplitude the Laurent expansion in $\omega$ and calculate the terms of order ${\omega }^{-1}$ and ${\omega }^0$. The pole term $\propto {\omega }^{-1}$ is given by Weinberg's soft-photon theorem. Then we calculate the amplitudes for the above reactions for high center-of-mass energies and small momentum transfers, that is, in the soft-diffraction regime using the tensor-pomeron model. We identify places where "anomalous" soft photons could come from. Three soft-photon approximations (SPAs) are introduced. The corresponding SPA results are compared to those obtained from the full tensor-pomeron model for center-of-mass energies $\sqrt{s}=10$ GeV and 100 GeV. The kinematic regions where the SPAs are a good representation of the full amplitude are determined. Finally we make some remarks on the type of fundamental information one could obtain from high-energy exclusive hadronic reactions without and with soft photon radiation.

57 pages, 20 figures, v3 is a final version including corrections from the published Erratum

References in corpus (15)

• Low's Subleading Soft Theorem as a Symmetry of QED
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• Single Spin Asymmetry $A_N$ in Polarized Proton-Proton Elastic Scattering at $\sqrt{s}=200$ GeV
• Low-Energy Thermal Photons from Meson-Meson Bremsstrahlung
• Evidence for an Excess of Soft Photons in Hadronic Decays of Z^0
• Helicity in Proton-Proton Elastic Scattering and the Spin Structure of the Pomeron
• Photoproduction of pi+ pi- pairs in a model with tensor-pomeron and vector-odderon exchange
• The ${\rho }^0$ and Drell-Söding contributions to central exclusive production of ${\pi }^{+}{\pi }^{-}$ pairs in proton-proton collisions at high energies
• Central exclusive diffractive production of $K^{+}{K}^{-}{K}^{+}{K}^{-}$ via the intermediate $\varphi \varphi$ state in proton-proton collisions
• A next-generation LHC heavy-ion experiment
• Observation of the Muon Inner Bremsstrahlung at LEP1
• Forward Physics at the LHC, Detecting Elastic pp Scattering by Radiative Photons
• Study of the exclusive reaction $pp\to pp{K}^{\ast 0}{\bar{K}}^{\ast 0}$: $f_2(1950)$ resonance versus diffractive continuum
• Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering
• Deeply virtual Compton scattering in the tensor-pomeron approach

Cited by in corpus (8)

• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Soft-photon radiation in high-energy proton-proton collisions within the tensor-Pomeron approach: Bremsstrahlung
• Linear power corrections to top quark pair production in hadron collisions
• Central exclusive diffractive production of a single photon in high-energy proton-proton collisions within the tensor-Pomeron approach
• Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering
• Deeply virtual Compton scattering in the tensor-pomeron approach
• Exclusive diffractive bremsstrahlung of one and two photons at forward rapidities: Possibilities for experimental studies in $pp$ collisions at the LHC
• Soft-photon theorem for pion-proton elastic scattering revisited