[ee] proposal abstract

[Pawel Nadel-Turonski]

Hello Everyone,

I started looking at the text of the new proposal, but before we discuss 
it in detail, I thought that for the discussion tomorrow it could be 
good to focus on the abstract. I include a draft below to serve as a 
starting point for how we should adjust the emphasis for the SoLID 
proposal. Once we have this in place I hope that updating the rest will 
go relatively quickly.

Cheers,

     Pawel

Abstract draft:
We propose to measure exclusive $e^+e^-$ production with SoLID using an 
11 GeV polarized beam and a $LH_2$ target to study the reaction $\gamma 
p \to \gamma^* p^\prime \to e^+ e^- p^\prime$, known as Timelike Compton 
Scattering (TCS), which is the timelike equivalent of (spacelike) DVCS. 
Both the differential cross section and moments of the weighted cross 
section will be measured as a function of the four-momentum transfer 
$-t$, the outgoing photon virtuality $Q^{\prime 2}$ (up to 9 GeV$^2$), 
and the skewness $\eta$. The latter reflects the difference between the 
initial and final momentum fraction carried by the struck quark, and 
corresponds to $\xi$ in DVCS. A first measurement of TCS at 12 GeV will 
be performed as part of the approved CLAS12 experiemnt E12-12-001. This 
proposed SoLID measurement will add two essential features. First, the 
different acceptance of the SoLID detector, which is more uniform in the 
azimuthal angle $\varphi$, will provide an important experimental cross 
check, resulting in reduced systematic uncertainties on, for instance, 
the real part of the Compton form factor $\mathcal{H}$, to which TCS 
provides a straightforward access. The higher luminosity of SoLID will 
also allow collecting an order of magnitude more statistics in the 
region of large $Q^{\prime 2}$ and $\eta$, making it possible to study 
the dependence on these variables in sufficiently narrow bins, which is 
important for understanding the effects of higher-twist and NLO 
corrections (in $\alpha_s$). Recent calculations suggest that the latter 
may be sizeable, and larger for TCS than DVCS, but are expected to be 
small at larger values of $\eta$ (above 0.3-0.4), and increase rapidly 
as $\eta$ approaches 0.1. Since $\eta = \tau / (2 - \tau) = Q^{\prime 2} 
/ (4ME_\gamma - Q^{\prime 2})$, where $\tau$ is the TCS equivalent of 
Bjorken $x$, $M$ is the proton mass, and $E_\gamma$ is the photon 
energy, the region of high $Q^{\prime 2}$, where both higher-twist and 
NLO corrections are expected to be small, provides a natural reference 
point - but one that requires a high luminosity for precision studies. 
On the other hand, the NLO corrections are almost entirely due to 
gluons. Once they are understood, this sensitivity at lower values of 
$\eta$ could provide a new tool for studying gluons at 12 GeV.