Factorization breaking of $A_d^T$ for polarized deuteron targets in a relativistic framework

We discuss the possible factorization of the tensor asymmetry $A_d^T$ measured for polarized deuteron targets within a relativistic framework. We define a reduced asymmetry and find that factorization holds only in plane wave impulse approximation and if $p$ waves are neglected. Our numerical results show a strong factorization breaking once final state interactions are included. We also compare the $d$-wave content of the wave functions with the size of the factored, reduced asymmetry and find that there is no systematic relationship of this quantity to the $d$-wave probability of the various wave functions.

Figure 1

Coordinate systems for the ${}^2\mathrm{H}(e,e^{\prime }p)$ reaction. $k$ and $k^{\prime }$ are the initial and final electron four-momenta, $q$ is the four-momentum of the virtual photon, and $p$ is the four-momentum of the final-state proton.

Figure 2

Feynman diagrams for the impulse approximation.

Figure 3

Feynman diagram representing the half-off-shell vertex function.

Figure 4

The factored, reduced asymmetry $a_d^T$ calculated for the eight different wave functions used in our calculations.

Figure 5

The ratio $u\left(p\right)/w\left(p\right)$ calculated for the eight different wave functions used in our calculations.

Figure 6

The envelopes of the reduced asymmetry $a_d^T$ calculated in PWBA and with FSI, for $x=1.00, Q^2=2.4{\mathrm{GeV}}^2, \varepsilon =8.3\mathrm{GeV}$, and $\varphi ={165}^{\circ }$. The horizontal dashed lines indicate the limits required by Eqs. (73) and (74).

Figure 7

The envelopes of the reduced asymmetry $a_d^T$ calculated in PWBA and with FSI, for $x=1.35, Q^2=4.25{\mathrm{GeV}}^2, \varepsilon =11\mathrm{GeV}$, and $\varphi ={165}^{\circ }$. The horizontal dashed lines indicate the limits required by Eqs. (73) and (74).