Longitudinal spin polarization in multiphoton Bethe-Heitler pair production

Helicity transfer in electron-positron pair production by a relativistic proton colliding with an intense laser beam of circular polarization is studied. The pairs are produced nonlinearly via absorption of few laser photons. Our approach relies on the laser-dressed description of the leptons by relativistic Volkov states and the spin-projection formalism. We calculate spin-resolved production rates, differential in the energy and emission angle of one of the created leptons. The degree of longitudinal polarization is shown to depend on the number of laser photons involved, even when the total energy and momentum absorbed from the laser field is kept constant.

Figure 1

Energy-dependent degree of longitudinal polarization of a lepton beam produced via the linear Bethe-Heitler process with 20-MeV photons. The gray solid line represents the analytical result from Eq. (31), whereas the blue dashed line shows the numerical result obtained from the present approach.

Figure 2

Energy-dependent degree of longitudinal polarization of one of the leptons produced via the reaction $p+n\omega \to p+e^{+}{e}^{-}$ for $n=1,2,3,4$ as indicated. The total energy of the $n$ absorbed photons is kept at the constant value of $n\hslash {\omega }_{\mathrm{nuc}}=20\mathrm{MeV}$.

Figure 3

Color-coded degree of longitudinal polarization for the absorption of (a) one, (b) two and (c) three photons with a total energy of $n\hslash {\omega }_{\mathrm{nuc}}=1.5$ MeV as a function of the transversal and parallel momentum components of the lepton with respect to the laser beam. Negative degrees of polarization [red areas in the lower left of each panel] occur at large emission angles in the proton rest frame, while positive degrees of polarization [blue areas] arise at high energies and at small angles. Contours of the double-differential production rates are plotted as black lines at every fifth part of the corresponding maximum value [see Eqs. (33, 34, 35)].

Figure 4

Double-differential rates at fixed angle $\widehat{\theta }$ plotted against the created lepton's energy in the proton's rest frame for the absorption of (a) one, (b) two, and (c) three photons with a total energy of $n\hslash {\omega }_{\mathrm{nuc}}=1.5$ MeV. Each graph shows the total spin-summed rate (black solid line) together with the corresponding probability rates for measuring a right-handed (blue dashed line) or left-handed (red dotted line) lepton in the proton's rest frame. The rates are scaled to their corresponding maximum values [see Eqs. (33, 34, 35)].

Figure 5

Degree of longitudinal polarization at fixed angle $\theta =\pi /5$ plotted against the created lepton's energy in the proton's rest frame for the absorption of $n=1,2$, or 3 photons, as indicated. The total photon energy is $n\hslash {\omega }_{\mathrm{nuc}}=1.5$ MeV.

Figure 6

Double-differential pair-production rates in the laboratory frame at a fixed lepton energy ${\widehat{E}}_{\mathrm{lab}}$, plotted against the lepton emission angle with respect to the laser beam direction for the absorption of (a) one, (b) two, and (c) three photons with a total energy of $n\hslash {\omega }_{\mathrm{lab}}=7.5\mathrm{keV}$. The photons collide with a proton beam of 94-GeV energy ($\gamma =100$). Each graph shows the total spin-summed rate (black solid line) together with the corresponding probability rates for measuring a right-handed (blue dashed line) or left-handed (red dotted line) lepton in the laboratory frame. The rates are scaled to their corresponding maximum values.

Figure 7

The degree of longitudinal polarization is shown for a total amount of energy $n\hslash {\omega }_{\mathrm{nuc}}=1.5\mathrm{MeV}$ at an invariant intensity parameter of $\xi ={10}^{-2}$ for all possible different leading orders with the same combined energy, i.e., $n=1,2,3$. The proton is moving at a velocity of $\gamma =100$.