Null-test signal for $T$-invariance violation in $pd$ scattering

The integrated proton-deuteron cross section $\tilde{\sigma }$ for the case of the incident proton vector polarization $p_y^p$ and tensor polarization $P_{xz}$ of the deuteron target provides a null-test signal for time-reversal invariance violating but $P$-parity conserving (TVPC) effects. We study the null-test observable $\tilde{\sigma }$ within the Glauber theory of the double-polarized $pd$ scattering. Full spin dependence of the ordinary strong $pN$ scattering amplitudes and different types of the hypothetical TVPC $pN$ amplitudes are taken into account. We show that the contribution from the exchange of the lowest-mass meson allowed in the TVPC interaction, i.e., the $\rho$ meson, to the null-test observable $\tilde{\sigma }$ is zero. The axial $h_1$ meson exchange makes a nonzero contribution. We find that inclusion of the Coulomb interaction does not lead to divergence of the cross section $\tilde{\sigma }$ and we calculate its energy dependence at the proton beam energy 100–1000 MeV.

Figure 1

Double-scattering mechanism with TVPC (black circle) and $T$-even $P$-even (open circle) charge-exchange $pn$ interaction.

Figure 2

Results of our calculation [14] of the spin observables $C_{xz,y}$ (a), $C_{z,x}$ (b), $C_{y,y}$ (c), and $C_{x,z}$ (d) for the $pd$ elastic scattering in comparison with the data [16] at 135 MeV: without (dashed line) and with the Coulomb interaction included (full).

Figure 3

The calculated energy dependence of the TVPC cross section $|\tilde{\sigma }|$ for the $h$ term in units of the constant ${\varphi }_h={\overline{G}}_h/G_h$ for $m_h=1.17$ GeV, $\mathrm{\Lambda }=2$ GeV in $h_N$ by Eq. (24) with the Coulomb interaction included (dashed line) and excluded (full). The dot-dashed curve is obtained at $\mathrm{\Lambda }\to \infty ,m_h^2+{\mathbf{q}}^2\to m_h^2$ without accounting for the Coulomb effects.