Deep inelastic scattering (DIS) and handbag diagram

Here, in page 11, you can see the so-called ‘handbag’ diagram that explains how a virtual photon emitted in a deep inelastic scattering (DIS) process interacts with a parton.

I’m going to use this diagram to compute the amplitude of the process $gamma P rightarrow X$, with $P$ the proton and $X$ a set of undetermined particles. So taking into account that the scattering matrix can be expanded in Taylor series as $S = 1 + A$, when wrting $A$ to first order you find that

$$
sum_X int frac{d^3 vec{p}_X}{(2pi)^3 2E_X} |A(gamma(q, Lambda) P rightarrow X)|^2 = 4pi VT epsilon^mu_{qLambda} epsilon^{nu *}_{qLambda} W_{nu mu}
$$

where the spacetime volume is $VT = (2pi)^4 delta(0)$, $W_{nu mu}$ is the hadronic tensor given as

$$
W_{nu mu} = frac{1}{4pi} int d^4 z e^{iqz} langle P| j_nu^dagger (z) j_mu(0) |Prangle, quad j_alpha = sum_q e_qbar{q}gamma_alpha q
$$

and $q$ is the quark field with electric charge $e_q$.

If $S = 1 + A$ then the optical theorem reads

$$
sum_X int frac{d^3 vec{p}_X}{(2pi)^3 2E_X} |A(gamma(q, Lambda) P rightarrow X)|^2 = -2Re [A(gamma P rightarrow gamma P)]
tag1$$

RHS represents (-2 times) the real part of the handbag diagram depicted above (we should include the diagram with the photons exchanged) and can be written as

$$
-2Re [A(gamma P rightarrow gamma P)] = 2VT Re left( sum_q e_q^2 int frac{d^4 k}{(2pi^4)} left[ gamma_nu left{ frac{i(not{k} + not{q})}{(k + q)^2 + i0} + frac{i(not{k} – not{q})}{(k – q)^2 + i0} right} gamma_mu right]_{ij} [f(p, k)]_{ji} epsilon^{nu *}_{qLambda} epsilon^{mu}_{qLambda} right)
$$

$VT = (2pi)^4 delta(0)$, i.e., the spacetime volume, a quantity that cancels out in the equality (1). $sum_{i, j}$ implicit and we have consider the approximation $m_q ll k, q$ with $m_q$ the quark mass.

Now my problem is how to compute the real part ($Re$) in the last formula since we know nothing about $f(p, k)$ and in principle the product of the polarization vectors is not necessarily real.