Medium-induced photon bremsstrahlung in neutrino-nucleus, antineutrino-nucleus, and electron-nucleus scattering from multiple QED interactions

Interactions of charged leptons with nuclei and the naive tree-level kinematics of these processes are affected by radiation of photons induced by the QED nuclear medium. We evaluate cross section modifications at leading orders of the number of correlated interactions inside the nucleus, known as the opacity expansion. We derive results for soft and collinear types of the bremsstrahlung at the first three orders in opacity and generalize them to higher orders. We present the leading in opacity energy spectra of soft and collinear photons and radiative energy loss inside the nucleus for experiments with lepton kinematics in the GeV energy range. At leading power of the Glauber soft-collinear effective field theory, the soft radiation is further resummed to all orders both in opacity and in the electromagnetic coupling constant. We find that the soft and collinear medium-induced radiation is vacuumlike, and additional corrections are power suppressed. Despite the negligible modification to the induced photon spectra, the nuclear medium-induced radiation sizably affects the broadening of charged leptons in the direction orthogonal to their propagation.

Figure 1

Diagrams for the one-Glauber exchange amplitude with one radiated photon in the charged-current (anti)neutrino-nucleus scattering.

Figure 2

Soft-photon corrections in the elastic electron-, electron flavor neutrino-, and antineutrino-nucleus scattering are shown as a function of the squared momentum transfer for an incoming beam energy $E_{\mathrm{beam}}=2\mathrm{GeV}$ and the soft-photon energy cutoff $\mathrm{\Delta }E=10\mathrm{MeV}$. Contributions from the one-photon soft functions in electron-, neutrino-, and antineutrino-nucleus scattering $S_{1\gamma }^e$, $S_{1\gamma }^{\nu }$, and $S_{1\gamma }^{\overline{\nu }}$, respectively, are compared to the exponentiated results $S^e$, $S^{\nu }$, and $S^{\overline{\nu }}$.

Figure 3

The energy spectrum of QED nuclear medium-induced collinear photons is compared to the collinear radiation in vacuum for the charged-current elastic neutrino scattering process. The absolute value for the distribution corresponds to the negative contribution of the QED nuclear medium-induced bremsstrahlung to the total photon energy spectrum. The incoming muon neutrino energy is $E_{{\nu }_{\mu }}=2\mathrm{GeV}$ and the squared momentum transfer is $Q^2=0.05{\mathrm{GeV}}^2$. The relative QED nuclear medium-induced correction does not depend on $x$.

Figure 4

Same as Fig. 3, but for the squared momentum transfer $Q^2=0.3{\mathrm{GeV}}^2$.

Figure 5

Same as Fig. 3, but for the antineutrino scattering. We do not indicate the absolute value for positive contributions to the photon energy spectrum.

Figure 6

Same as Fig. 4, but for the antineutrino scattering.

Figure 7

Same as Fig. 3, but for the electron scattering. Initial- and final-state photon energy spectra are shown.

Figure 8

Same as Fig. 4, but for the electron scattering. Initial- and final-state photon energy spectra are shown.