Polarization observables in lepton-deuteron elastic scattering including the lepton mass

Expressions for the unpolarized differential cross section and for various polarization observables in the lepton-deuteron elastic scattering, $\ell +D\to \ell +D,\ell =e,\mu ,\tau$, have been obtained in the one-photon-exchange approximation, taking into account the lepton mass. Polarization effects have been investigated for the case of a polarized lepton beam and polarized deuteron target which can have vector or tensor polarization. Numerical estimations of the lepton mass effects have been done for the unpolarized differential cross section and for some polarization observables and applied to the case of low-energy muon deuteron elastic scattering.

Figure 1

Effect of the lepton mass on the kinematics of the scattered lepton: (a) the relative difference in percent between the scattered lepton energy and (b) the momentum transfer squared taking and not taking into account, respectively, the lepton mass as a function of the scattering muon angle and of the incident energy.

Figure 2

Bidimensional plot of the ratio between the cross section taking and not taking into account the lepton mass as function of ${\varepsilon }_1$ and $\theta$.

Figure 3

Correlation coefficients $C_{xx}$ (top left), $C_{yy}$ (top right), $C_{zx}$ (bottom left), and $C_{xz}$ (bottom right) as functions of ${\varepsilon }_1$ and $\theta$.

Figure 4

Correlation coefficients $C_{zz}$ (top left) and $C_{zz}^{\left(0\right)}$ (top right) as functions of ${\varepsilon }_1$ and $\theta$. The ratio of the observables taking and not taking into account the lepton mass is shown for $C_{zz}$ (bottom left) and for $C_{xz}$ (bottom right), respectively.

Figure 5

Tensor asymmetries from left to right $A_{xx},A_{xz},A_{zz}$. From top to bottom, the first (second) row represents the observables taking (not taking) into account the lepton mass, respectively. The third row shows their difference.