[ee] TCS meeting on Wednesday

[Pawel Nadel-Turonski]

Hello Everyone,

Our next TCS meeting will be on Wednesday, April 3 at 9:00 - 10:30 am 
EDT in F228. Finally back to our usual time!

The main focus of this meeting will be to discuss progress on the 
proposal writing. I attach four sections that I have updated so far. I 
also know that Jakub started writing the NLO section, and Vadim has 
promised to look at updates to the motivation section, including the 
higher-twist as we discussed at our last meeting. We should set up a 
plan for the remaining parts (mostly the experimental ones, including 
projections). Zhiwen may also want to say a few words about progress on 
binning and simulations. See you all tomorrow!

Best Regards,

         Pawel

CALL-IN INFORMATION
The international toll free number can be obtained from
http://www.readytalk.com/intl
The US toll free number is 1-866-740-1260.
The Participant Code for both is 9304543

-------------- next part --------------
\begin{figure}[t]
\includegraphics[scale=0.45]{R_dep_theta_var_6GeV.eps}
\caption{\small{The cosine moment of the weighted cross section, $R'$, in
the CLAS acceptance compared to GPD model calculations based on the dual
parametrization
\cite{Polyakov:2002wz,Guzey:2006xi,Guzey:2008ys,Polyakov:2008aa}
(upper, green curve), and the double distribution
\cite{Radyushkin:1998es} (lower, blue curves) for three weights applied
to the $D$-term. The BH-contribution is shown in red.}}
\label{fig:R_dep_theta_var_6GeV}
\end{figure}

Our proposed SoLID experiment builds upon experience gained from the analysis
of CLAS 6 GeV data, which has established the technique for carrying
out exclusive photoproduction experiments with quasi-real photons that we
propose for this experiment with SoLID. As will be discussed in Sec.
\ref{sec:tcs_selection}, this requires the detection of all final-state
particles except the scattered electron, for which the missing mass and
missing transverse momentum are constrained to be very small.
More specifically, this technique has also been successfully applied to pilot
measurements of timelike Compton scattering using the CLAS e1-6 and e1f data
sets. The results from this CLAS Approved Analysis (CAA-DP09-01) have been
documented in Ref.~\cite{Rafael:2010}. It demonstrated an impressive pion
pair rejection of factor of $2.07 \times 10^{-7}$. Measuring the $\phi$ cross
section in parallel with TCS showed that the flux of quasi-real photons is
well understood.
The results from the above analysis could also be compared with an TCS
analysis using the g12 data set, which was the only high-energy CLAS data set
with tagged real photons (up to 5.7 GeV) that utilized the Cherenkov counters.
These had been made ready specifically for TCS and other $e^+e^-$ physics. The
analysis of the g12 data is still ongoing, but preliminary results seems to be
in line with what was obtained with the quasi-real photon technique.
The tagged-photon beam will also make it possible to do an independent
determination of the photon flux, and offer an opportunity to explore event
topologies with only two out of the three final-state particles detected.

In addition to demonstrating the feasibility of the proposed measurement, the
pilot experiments at 6 GeV stimulated the development of new analysis methods.
An example of this was the introduction of the cosine moment $R'$, evaluated
within the acceptance of the detector in the $\varphi_{CM}-\theta_{CM}$ plane
(the lepton c.m. angles $\varphi$ and $\theta$ are defined in
Fig.~\ref{fig:Angle}). Whereas the original definition of $R$ implies using
the integration ranges shown in Eqs.(\ref{eq:S}) and (\ref{eq:R}), $R'$ adds
an function $a(\theta_{CM},\varphi_{CM})$ corresponding to the detector
acceptance for a given kinematic bin. Utilizing the same acceptance function
for both the experimental and theoretical evaluations allows a straightforward
comparison between data and predictions based on various GPD models. The
difference between $R'$ and $R$ is discussed in more detail in
Sec. \ref{sec:tcsrate} together with the projected results.

Fig.~\ref{fig:R_dep_theta_var_6GeV} shows $R'$ extracted from the combined
e1-6 and e1f data sets for four bins in $-t$, compared with two GPD model
calculations based on the dual parametrization
\cite{Polyakov:2002wz,Guzey:2006xi,Guzey:2008ys,Polyakov:2008aa} and double
distribution \cite{Radyushkin:1998es}, respectively. Results from the latter
are shown with three weights for the contribution from the $D$-term (0, 1, and
2). Both the experimental and theoretical points shown here were evaluated at
the average value for the bin, but an event-by-event approach will be adopted
in the future.

\begin{figure}[t]
\includegraphics[scale=0.45]{TCS407.eps}
\caption{\small{$e^+e^-$ invariant mass vs. quasi-real photon energy for the
e1-6 (left) and e1f (right) data sets. Only events with $M_{ee}$ above the
$\phi$ mass were used for TCS analysis at 6 GeV.}}
\label{fig:TCS6}
\end{figure}

However, despite the usefulness of the 6 GeV data for developing the TCS
program, only the 12 GeV era will provide the required luminosity and
kinematic coverage. In particular, the higher beam energy will make it
possible to study a range of invariant lepton pair masses where there are no
meson resonances that complicate the interpretation of the measurement. As
shown in Fig.~\ref{fig:TCS6}, only data above the $\phi$ mass were used for
TCS analysis at 6 GeV, but at 12 GeV it will be possible to move this range
above the mass of the $\rho^{\prime}$.
%as shown in Fig. \ref{fig:ee_to_hadrons}.
-------------- next part --------------
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. The high
luminosity of SoLID will make it possible to perform a detailed mapping
of the $Q^{\prime 2}$- and $\eta$-dependence, which will be essential for
understanding factorization, higher-twist effects, and NLO corrections.
This proposed experiment is complementary to the approved CLAS12 experiment
E12-12-001, which will focus on measuring the $t$-dependence in wider bins of
$Q^{\prime 2}$ and $\eta$. Experimentally, the SoLID and CLAS12 detectors also
offer complementary capabilities. Performing this new kind of measurement
using two detector setups, each with a different acceptance, will not only
provide an essential cross check, but could result in reduced overall
systematic uncertainties on, for instance, the real part of the Compton form
factor $\mathcal{H}$, to which TCS provides a straightforward access.
-------------- next part --------------
We request 60 PAC days with longitudinally polarized (80\%) 11 GeV beam and
an unpolarized proton target in the SoLID detector. For photoproduction using
quasi-real photons, the detector will have to incorporate time-of-flight
detectors covering a range comparable to that of the calorimeter. Alos,
the trigger cannot contain more than two leptons (\textit{i.e.}, a
coincidence between the Cherenkov and calorimeter), but could include an
additional track (the proton) that gives a signal in the time-of-flight
instead of the Cherenkov), to reduce the data rate. With the conditions
above, the requested beam-time can be shared with already approved experiments.
-------------- next part --------------
Understanding the structure and interactions of hadrons on the basis of
Quantum Chromodynamics (QCD) is one of the main objectives of nuclear physics.
The combination of fundamental properties of QCD as a quantum field theory,
such as relativity and causality, with factorization theorems allows us to
systematically explore the partonic structure of hadrons through various
processes using different probes. In this context, the correspondence between
spacelike and timelike processes plays a unique role. 
First, let us consider the Drell-Yan process, $h{\bar h} \to \gamma^{\ast}X$,
where $\gamma^{\ast}$ has a timelike virtuality ($Q^2 > 0$) and $h$
(${\bar h}$) denotes a baryon (antibaryon), which provided important
information on (anti)quark distributions. The same distributions are probed in
inclusive deep inelastic scattering (DIS), $\gamma^{\ast}h \to X$, mediated by
a spacelike virtual photon ($Q^2 < 0$). A comparison of the Drell-Yan and DIS
results thus convincingly demonstrated the universality of parton distribution
functions (PDFs).
In this proposal we focus on the correspondence between timelike and spacelike
deeply virtual Compton scattering (DVCS), where the former is also known as
timelike Compton scattering (TCS), and the universality of generalized parton
distributions (GPDs), measured in hard exclusive processes.

In the last 15 years, hard exclusive processes have emerged as a class of
reactions providing novel information on the quark and gluon distributions
in hadrons. This information is more complete than what can be obtained
from inclusive and elastic scattering alone; for reviews, see
Refs.~\cite{Goeke:2001tz,Diehl:2003ny,Belitsky:2005qn}.
QCD factorization theorems \cite{Collins:1996fb,Collins:1998be} make it
possible to express amplitudes of hard exclusive processes in terms of GPDs,
which are expected to provide a universal (process-independent) description
of the nucleon, and have a known QCD ($Q^2$) evolution. GPDs are hybrid
distributions that combine aspects of the usual collinear PDFs and elastic
form factors. As such, GPDs simultaneously encode information on parton
distributions and correlations in both momentum (in the longitudinal
direction) and coordinate (in the transverse direction) spaces.
Another interesting aspect of GPDs is their connection to the form factors
of the energy-momentum tensor, which, among other things, establishes the
decomposition of the proton spin in terms of the quark and gluon
contributions to the total orbital momentum~\cite{Ji:1996ek}.

The best studied hard exclusive process is DVCS,
$\gamma^{\ast}p \to \gamma p$, where the initial-state virtual photon is
spacelike ($Q^2 < 0$), and the final-state photon is real. From a theoretical
point of view, it is the simplest and cleanest way to access GPDs.
The leading-twist formalism is well established for DVCS at the leading and
next-to-leading orders in the strong coupling constant, and power-suppressed
corrections have been analyzed and estimated. On the experimental side, early
data have demonstrated the feasibility of DVCS measurements, established the
reaction mechanism based on the leading-twist approach (the handbag
mechanism), and provided first glimpses of the Compton form factors (CFFs)
and the related GPDs. The goal of determining the valence quark GPDs in the
nucleon through measurements of DVCS and other hard exclusive processes is
now a cornerstone of the 12 GeV program at Jefferson Lab.

Recently, a promising opportunity has emerged for extending our understanding
of GPDs by studying the timelike equivalent of traditional, spacelike DVCS.
The process, $\gamma p \to \gamma^{\ast} p$, is known as timelike Compton
scattering (TCS). Here, the timelike final-state photon immediately decays
into a lepton pair, the invariant mass of which is a measure of the photon
virtuality ($Q^{\prime 2} > 0$), and provides the hard scale for the reaction.
The leading-twist formalism for TCS~\cite{Berger:2001xd} (the factorization
theorem, the handbag reaction mechanism, etc) is as well established as that
for DVCS. However, as also shown in Ref.~\cite{Berger:2001xd}, the
phenomenology of TCS is quite different from DVCS. With an unpolarized photon
beam, TCS offers straightforward access to the real part of the CFFs through
the interference between the Compton and Bethe-Heitler (BH) amplitudes, which
can be extracted in a model-independent way from the azimuthal angular
distribution of the lepton pair into which the timelike photon decays.
Circular photon polarization also gives access to the imaginary part of CFFs.

In summary, the main motivation to study TCS includes:
\begin{itemize}
\item
A measurement of TCS will make it possible to test the universality of GPDs
implied by factorization through the timelike-spacelike correspondence with
DVCS.
\item
The straightforward access in TCS to, in particular, the real part of the
CFFs impacts models and parametrizations of GPDs in a broad range of
kinematics (light-cone fractions $\tau$ and $\eta$, which are the equivalent
of $x$ and $\xi$ in DVCS).
\item
The differential cross section (for TCS and its interference with BH) can
provide important input for global fits of CFFs \cite{Guidal:2008ie}.
\end{itemize}  

However, a solid interpretation of the results from the TCS program, will also
require understanding of higher-twist and NLO corrections (in $\alpha_s$).
If one wants to study factorization and effects related to higher-twist
(\textit{e.g.}, contributions from terms behaving like $|t|/Q^{\prime 2}$),
it is crucial to be able to map out the full range in $Q^{\prime 2}$ with
sufficient statistics for the highest points.
Recent calculations ~\cite{Moutarde:2013qs} suggest that the NLO corrections
may be sizeable, and larger for TCS than DVCS. They are, however, expected to
be small at large values of the skewness $\eta$ (\textit{i.e.}, above values
of 0.3-0.4), corresponding to a large difference between the initial and final
momentum fraction carried by the struck quark. They then increase rapidly as
$\eta$ approaches 0.1, which is at the lower limit of the reach of 12 GeV
kinematics. Since
\begin{equation}
\eta = \frac{\tau}{2 - \tau} = \frac{Q^{\prime 2}}{4ME_\gamma - Q^{\prime 2}},
\label{eq:etatauQ2}
\end{equation}
where $\tau$ is the TCS equivalent of Bjorken $x$, $M$ is the proton mass, and
$E_\gamma$ is the incident photon energy, large values of $\eta$ naturally
correspond to the region of large $Q^{\prime 2}$. To do the mapping in $\eta$,
it is thus necessary to have sufficient statistics at high values of
$Q^{\prime 2}$, where the cross section is small, and small bins in the
transition to lower values of $\eta$, where the change in the magnitude of
the NLO corrections is expected to be rapid. Thus, in 12 GeV kinematics the
region of high $Q^{\prime 2}$, where both higher-twist and NLO corrections
are expected to be small, provides a natural reference point.
On the other hand, the NLO corrections are almost entirely due to gluons. If
they turn out to be significant at lower values of $\eta$, and since they are
predicted to be larger in TCS than DVCS, TCS could become a very interesting
new tool for studying gluons at 12 GeV.

The primary goal of this proposed experiment for SoLID is to make a precision
study of the $Q^{\prime 2}$- and $\eta$-dependence of the differential cross
section and moments of the weighted cross section up to the highest values of
$Q^{\prime 2}$, for which a high luminosity is essential. This proposal is
thus complementary to the approved CLAS12 experiment the E12-12-001, which
will focus on studying the $t$-dependence in larger bins of $Q^{\prime 2}$
and $\eta$.
Experimentally, the two detectors also offer complementary capabilities. In
particular, the SoLID detector, being based on a solenoidal magnets, has a
more uniform acceptance in the azimuthal angle $\varphi$ than CLAS12, but
has a gap in the $\vartheta$-coverage between the inner (forward) and outer
detectors. The CLAS12 polar angle coverage is also generally somewhat better,
which is especially important for the recoil protons. Performing this new kind
of measurement using two setups, each with a different acceptance, will not
only provide an essential cross check, but could result in reduced overall
systematic uncertainties on, for instance, the real part of the Compton form
factor $\mathcal{H}$.

The feasibility of the experimental techniques involved in the measurement,
including the use of quasi-real photons (with $Q^2 < 0.1$ GeV$^2$) tagged by
detecting the complete final state except for the beam electron, have been
demonstrated in the analysis of CLAS 6 GeV data, which include pilot studies
of TCS. In terms of experimental requirements, photoproduction measurements in
SoLID will require time-of-flight detectors covering both the inner (forward)
as well as the outer calorimeter. The trigger for the reaction will have to
include at least two leptons and could require an additional track using the
time-of-flight rather than Cherenkov detector.
We thus propose to measure exclusive $e^+e^-$ production using the SoLID
detector and an 11 GeV linearly polarized electron beam and a $LH_2$ target
to study TCS over a wide range of $Q^{\prime 2}$, $\eta$, and $t$. Both the
differential cross section and the cosine and sine moments of the weighted
cross section will be measured.