11institutetext:  Thomas Jefferson National Accelerator Facility, 12000
Jefferson Avenue, Newport News, VA 23606, USA22institutetext: Université
Paris-Saclay, CNRS/IN2P3, IJCLab Orsay, France33institutetext: Faculté des
Sciences de Monastir, Tunisia44institutetext: The Catholic University of
America, Washington, DC 20064, USA55institutetext: A. Alikhanyan National
Laboratory, Yerevan Physics Institute, Yerevan 375036, Armenia66institutetext:
Old Dominion University, Norfolk, VA 23529, USA77institutetext: Ohio
University, Athens, OH 45701, USA88institutetext: Florida International
University, Miami, FL 33199, USA99institutetext: The George Washington
University, Washington, DC 20052, USA1010institutetext: University of New
Hampshire, Durham, NH 03824, USA1111institutetext: Idaho State University,
Pocatello, ID 83209, USA1212institutetext: University of Glasgow, Glasgow G12
8QQ, United Kingdom1313institutetext: University of Virginia, Charlottesville,
VA 22904, USA1414institutetext: Universität Gießen Luwigstraße 23, 35390
Gießen, Deutschland1515institutetext: Facility for Rare Isotope Beams,
Michigan State University, 640 South Shaw Lane, East Lansing, MI 48824,
USA1616institutetext: Istituto Nazionale di Fisica Nucleare, Sezione di
Catania, 95123 Catania, Italy1717institutetext: Mississippi State University,
MS 39762, USA1818institutetext: University of Colorado, Boulder, CO 80309,
USA1919institutetext: Stony Brook University, Stony Brook, NY 11794,
USA2020institutetext: James Madison University, Harrisonburg, VA 22807,
USA2121institutetext: Faculty of Mathematics and Physics, University of
Ljubljana, 1000 Ljubljana, Slovenia2222institutetext: Akdeniz Üniversitesi,
07070 Konyaalti, Antalya, Turkey2323institutetext: Hampton University Hampton,
VA 23668, USA2424institutetext: Commissariat à l’Energie Atomique, 91191 Gif-
sur-Yvette, France

# Deeply virtual Compton scattering using a positron beam in Hall-C at
Jefferson Lab

A. Afanasev 99 I. Albayrak 2222 S. Ali 44 M. Amaryan 66 J. R. M. Annand 1212
A. Asaturyan 55 V. Bellini 1616 V. V. Berdnikov 44 M. Boer 1010 K. Brinkmann
1414 W. J. Briscoe 99 A. Camsonne 11 M. Caudron 22 L. Causse 22 M. Carmignotto
11 D. Day 1313 M. Defurne 2424 S. Diehl 1414 R. Ent 11 P. Chatagnon 22 R.
Dupré 22 D. Dutta 1717 M. Ehrhart 22 M. A. I. Fernando 2323 T. Forest 1111 M.
Guidal 22 J. Grames 11 P. Gueye 1515 S. Habet 22 D. J. Hamilton 1212 A. Hobart
22 T. Horn 44 C. Hyde 66 G. Kalicy 44 D. Keller 1313 C. Keppel 11 M. Kerver 66
E. Kinney 1818 H.-S. Ko 22 D. Marchand 22 P. Markowitze 88 M. Mazouz 33 M.
McCaughan 11 B. McKinnon 1212 A. Mkrtchyan 55 H. Mkrtchyan 55 M. Muhoza 44 C.
Muñoz Camacho Contact person<EMAIL_ADDRESS>J. Murphy 77 P. Nadel-
Turonski 1919 S. Niccolai 22 G. Niculescu 2020 R. Novotny 1414 R. Paremuzyan
1010 I. Pegg 44 K. Price 22 H. Rashad 66 J. Roche 77 R. Rondon 1313 B.
Sawatzky 11 V. Sergeyeva 22 S. Širca 2121 A. Somov 11 I. Strakovsky 99 V.
Tadevosyan 55 R. Trotta 44 H. Voskanyan 55 E. Voutier 22 B. Wojtsekhowski 11
S. Wood 11 S. Zhamkochyan 55 J. Zhang 1313 S. Zhao 22 C. Zorn 11

(Received: date / Revised version: date)

###### Abstract

We propose to use the High Momentum Spectrometer of Hall C combined with the
Neutral Particle Spectrometer (NPS) to perform high precision measurements of
the Deeply Virtual Compton Scattering (DVCS) cross section using a beam of
positrons. The combination of measurements with oppositely charged incident
beams is the only unambiguous way to disentangle the contribution of the DVCS2
term in the photon electroproduction cross section from its interference with
the Bethe-Heitler amplitude. This provides a stronger way to constrain the
Generalized Parton Distributions of the nucleon. A wide range of kinematics
accessible with an 11 GeV beam off an unpolarized proton target will be
covered. The $Q^{2}-$dependence of each contribution will be measured
independently.

###### pacs:

PACS-keydiscribing text of that key and PACS-keydiscribing text of that key

##  1 Executive summary

An exciting scientific frontier is the 3-dimensional exploration of nucleon
(and nuclear) structure – nuclear femtography. Jefferson Lab with its high
luminosity and expanded kinematic reach at 12-GeV will allow the detailed
investigation of position and momentum distributions of partons inside protons
and neutrons in the valence-quark region. The study of the Generalized Parton
Distributions (GPDs) captures the images of the transverse position
distributions of fast-moving quarks. The cleanest reaction to access GPDs is
Deeply Virtual Compton Scattering (DVCS): $\gamma^{*}p\to\gamma p$.

A factorization theorem has been proven for DVCS in the Bjorken limit
Collins:1998be ; Ji:1998xh . It allows one to compute the DVCS amplitude as
the product of some GPDs and a coefficient function that can be calculated
perturbatively. GPDs are thus in very solid theoretical footing: at leading-
twist level, all-order QCD-factorization theorems directly relate the GPDs to
particular hard exclusive scattering processes. Therefore, GPDs are process-
independent, universal quantities.

DVCS interferes with the so-called Bethe-Heitler (BH) process, where the
lepton scatters elastically off the nucleon and emits a high energy photon
before or after the interaction (see Fig. 1). The BH amplitude
$\mathcal{T}^{BH}$ is electron charge even. On the other hand, the DVCS
amplitude $\mathcal{T}^{DVCS}$ is electric charge odd, i.e. its contribution
has different sign for electron vs. positron scattering. DVCS and BH are
indistinguishable and the photon electroproduction amplitude squared that we
can measure is therefore decomposed as:

$|\mathcal{T}(\pm ep\to\pm
ep\gamma)|^{2}=|\mathcal{T}^{BH}|^{2}+|\mathcal{T}^{DVCS}|^{2}\mp\mathcal{I}\,,$
(1)

where the $\pm$ signs correspond to the charge of the incident beam. The
$\mathcal{T}^{BH}$ amplitude is written in terms of the nucleon form factors,
and is real at the leading order in QED. The $|\mathcal{T}^{DVCS}|^{2}$
contribution is closest to a direct Compton scattering cross section and as
such gives direct information on nucleon structure – it depends on bilinear
combinations of GPDs.

Figure 1: Illustration of the DVCS (a) and Bethe-Heitler (b and c) processes.

Equation 1 shows how combining DVCS measurements with electrons and positrons
not only can cleanly isolate the $|\mathcal{T}^{DVCS}|^{2}$ term but also the
interference term $\mathcal{I}$. This interference term gives direct linear
access to DVCS at the amplitude level, thanks to its interference with the
known Bethe-Heitler amplitude. Similar as in spin-dependent scattering, such
interferences can lead to extremely rich angular structure:
$\mathcal{I}=2\mathcal{T}^{BH}\mathcal{R}e(\mathcal{T}^{DVCS})$.

The availability of positron beams thus can lead to direct access to nucleon
structure carried in the DVCS amplitude, and in addition a cleaner access to
the $|\mathcal{T}^{DVCS}|^{2}$ term.

##  2 Introduction

Deeply Virtual Compton Scattering (DVCS) refers to the reaction
$\gamma^{*}(q)P(p)\rightarrow P(p^{\prime})\gamma(q^{\prime})$ in the Bjorken
limit of Deep Inelastic Scattering (DIS). Experimentally, we can access DVCS
through electroproduction of real photons $e(k)P(p)\to
e(k^{\prime})P(p^{\prime})\gamma(q^{\prime})$, where the DVCS amplitude
interferes with the so-called Bethe-Heitler (BH) process. The BH contribution
is calculable in QED since it corresponds to the emission of the photon by the
incoming or the outgoing electron.

DVCS is the simplest probe of a new class of light-cone (quark) matrix
elements, called Generalized Parton Distributions (GPDs) Ji:1996ek . The GPDs
offer the exciting possibility of the first ever spatial images of the quark
waves inside the proton, as a function of their wavelength Mueller:1998fv ;
Ji:1996nm ; Ji:1996ek ; Ji:1997gm ; Radyushkin:1997ki ; Radyushkin:1996nd .
The correlation of transverse spatial and longitudinal momentum information
contained in the GPDs provides a new tool to evaluate the contribution of
quark orbital angular momentum to the proton spin.

GPDs enter the DVCS cross section through integrals over the quark momentum
fraction $x$, called Compton Form Factors (CFFs). CFFs are defined in terms of
the vector GPDs $H$ and $E$, and the axial vector GPDs $\widetilde{H}$ and
$\widetilde{E}$ Ji:1996ek . For example ($f\in\\{u,d,s\\}$) Belitsky:2001ns :

${\mathcal{H}}(\xi,t)=\sum_{f}\left[\frac{e_{f}}{e}\right]^{2}\Biggl{\\{}i\pi\left[H_{f}(\xi,\xi,t)-H_{f}(-\xi,\xi,t)\right]\\\
+{\mathcal{P}}\int_{-1}^{+1}dx\left[\frac{1}{\xi-x}-\frac{1}{\xi+x}\right]H_{f}(x,\xi,t)\Biggr{\\}},$
(2)

where $t=(p-p^{\prime})^{2}$ is the momentum transfer to the nucleon and
skewness variable $\xi$ is defined as
$\xi=-\overline{q}^{2}/(\overline{q}\cdot\overline{p})\approx x_{\rm
B}/(2-x_{\rm B})$, with $\overline{q}=(q+q^{\prime})/2$ and
$\overline{p}=p+p^{\prime}$.

Thus, the imaginary part accesses GPDs along the line $x=\pm\xi$, whereas the
real part probes GPD integrals over $x$. The ‘diagonal’ GPD,
$H(\xi,\xi,t=\Delta^{2})$ is not a positive-definite probability density,
however it is a transition density with the momentum transfer $\Delta_{\perp}$
Fourier-conjugate to the transverse distance $r$ between the active parton and
the center-of-momentum of the spectator partons in the target Burkardt:2007sc
. Furthermore, the real part of the Compton Form Factor is determined by a
dispersion integral over the diagonal $x=\pm\xi$ plus the $D$-term
Teryaev:2005uj ; Anikin:2007yh ; Anikin:2007tx ; Diehl:2007ru :

$\Re\text{e}\left[\mathcal{H}(\xi,t)\right]=\int_{-1}^{1}dx\left\\{\left[H(x,x,t)+H(-x,x,t)\right]\left[\frac{1}{\xi-x}-\frac{1}{\xi+x}\right]+2\frac{D(x,t)}{1-x}\right\\}$
(3)

The $D$-term Polyakov:1999gs  only has support in the region $|x|<\xi$ in
which the GPD is determined by $q\overline{q}$ exchange in the $t$-channel.

##  3 Physics goals

In this experiment we propose to exploit the charge dependence provided by the
use of a positron beam in order to cleanly separate the DVCS2 term from the
DVCS-BH interference in the photon electroproduction cross section.

Figure 2: Lowest order QED amplitude for the $ep\rightarrow ep\gamma$
reaction. The momentum four-vectors of all external particles are labeled at
left. The net four-momentum transfer to the proton is
$\Delta_{\mu}=(q-q^{\prime})_{\mu}=(p^{\prime}-p)_{\mu}$. In the virtual
Compton scattering (VCS) amplitude, the (spacelike) virtuality of the incident
photon is $Q^{2}=-q^{2}=-(k-k^{\prime})^{2}$. In the Bethe-Heitler (BH)
amplitude, the virtuality of the incident photon is $-\Delta^{2}=-t$. Standard
$(e,e^{\prime})$ invariants are $s_{e}=(k+p)^{2}$, $x_{B}=Q^{2}/(2q\cdot p)$
and $W^{2}=(q+p)^{2}$.

The photon electroproduction cross section of a polarized lepton beam of
energy $E_{b}$ off an unpolarized target of mass $M$ is sensitive to the
coherent interference of the DVCS amplitude with the Bethe-Heitler amplitude
(see Fig. 2). It was derived in Ji:1996nm  and can be written as:

$\frac{d^{5}\sigma(\lambda,\pm
e)}{d^{5}\Phi}=\frac{d\sigma_{0}}{dQ^{2}dx_{B}}\left|\mathcal{T}^{BH}(\lambda)\pm\mathcal{T}^{DVCS}(\lambda)\right|^{2}/|e|^{6}\\\
=\frac{d\sigma_{0}}{dQ^{2}dx_{B}}\left[\left|\mathcal{T}^{BH}(\lambda)\right|^{2}+\left|\mathcal{T}^{DVCS}(\lambda)\right|^{2}\mp\mathcal{I}(\lambda)\right]\frac{1}{e^{6}}$
(4) $\displaystyle\frac{d\sigma_{0}}{dQ^{2}dx_{B}}$ $\displaystyle=$
$\displaystyle\frac{\alpha_{\rm
QED}^{3}}{16\pi^{2}(s_{e}-M^{2})^{2}x_{B}}\frac{1}{\sqrt{1+\epsilon^{2}}}$ (5)
$\displaystyle\epsilon^{2}$ $\displaystyle=$ $\displaystyle
4M^{2}x_{B}^{2}/Q^{2}$ $\displaystyle s_{e}$ $\displaystyle=$ $\displaystyle
2ME_{b}+M^{2}$

where $d^{5}\Phi=dQ^{2}dx_{B}d\phi_{e}dtd\phi_{\gamma\gamma}$, $\lambda$ is
the electron helicity and the $+$($-$) stands for the sign of the charge of
the lepton beam. The BH contribution is calculable in QED, given our $\approx
1\%$ knowledge of the proton elastic form factors at small momentum transfer.
The other two contributions to the cross section, the interference and the
DVCS2 terms, provide complementary information on GPDs. It is possible to
exploit the structure of the cross section as a function of the angle
$\phi_{\gamma\gamma}$ between the leptonic and hadronic plane to separate up
to a certain degree the different contributions to the total cross section
Diehl:1997bu . The angular separation can be supplemented by an beam energy
separation. The energy separation has been successfully used in previous
experiments Defurne:2017paw  at 6 GeV and is the goal of already approved
experiment at 12 GeV E12-13-010 .

The $|\mathcal{T}^{BH}|^{2}$ term is given in Belitsky:2001ns , Eq. (25), and
only its general form is reproduced here:

$|\mathcal{T}^{BH}|^{2}=\frac{e^{6}}{x_{B}^{2}ty^{2}(1+\epsilon^{2})^{2}\mathcal{P}_{1}(\phi_{\gamma\gamma})\mathcal{P}_{2}(\phi_{\gamma\gamma})}\\\
\sum_{n=0}^{2}c_{n}^{BH}\cos(n\phi_{\gamma\gamma})\,.$ (6)

The harmonic terms $c_{n}^{BH}$ depend upon bilinear combinations of the
ordinary elastic form factors $F_{1}(t)$ and $F_{2}(t)$ of the proton. The
factors $\mathcal{P}_{i}$ are the electron propagators in the BH amplitude
Belitsky:2001ns .

The interference term in Eq. (4) is a linear combination of GPDs, whereas the
DVCS2 term is a bilinear combination of GPDs. These terms have the following
harmonic structure:

$\displaystyle\mathcal{I}$ $\displaystyle=$
$\displaystyle\frac{e^{6}}{x_{B}y^{3}\mathcal{P}_{1}(\phi_{\gamma\gamma})\mathcal{P}_{2}(\phi_{\gamma\gamma})t}\left\\{c_{0}^{\mathcal{I}}+\sum_{n=1}^{3}\left[c_{n}^{\mathcal{I}}\cos(n\phi_{\gamma\gamma})+\lambda
s_{n}^{\mathcal{I}}\sin(n\phi_{\gamma\gamma})\right]\right\\}$ (7)
$\displaystyle\left|\mathcal{T}^{DVCS}(\lambda)\right|^{2}$ $\displaystyle=$
$\displaystyle\frac{e^{6}}{y^{2}Q^{2}}\left\\{c_{0}^{DVCS}+\sum_{n=1}^{2}\left[c_{n}^{DVCS}\cos(n\phi_{\gamma\gamma})-\lambda
s_{1}^{DVCS}\sin(\phi_{\gamma\gamma})\right]\right\\}$ (8)

The $c_{0}^{DVCS,\mathcal{I}}$, and $(c,s)_{1}^{\mathcal{I}}$ harmonics are
dominated by twist-two GPD terms, although they do have twist-three admixtures
that must be quantified by the $Q^{2}$-dependence of each harmonic. The
$(c,s)_{1}^{DVCS}$ and $(c,s)_{2}^{\mathcal{I}}$ harmonics are dominated by
twist-three matrix elements, although the same twist-two GPD terms also
contribute (but with smaller kinematic coefficients than in the lower Fourier
terms). The $(c,s)_{2}^{DVCS}$ and $(c,s)_{3}^{\mathcal{I}}$ harmonics stem
from twist-two double helicity-flip gluonic GPDs alone. They are formally
suppressed by $\alpha_{s}$ and will be neglected here. They do not mix,
however, with the twist-two quark amplitudes. The exact expressions of these
harmonics in terms of the quark Compton Form Factors (CFFs) of the nucleon are
given in Belitsky:2010jw .

Equation (4) shows how a positron beam, together with measurements with
electrons, provides a way to separate without any assumptions the DVCS2 and
BH-DVCS interference contributions to the cross section. With electrons alone,
the only approach to this separation is to use the different beam energy
dependence of the DVCS2 and BH-DVCS interference. This is the strategy that
will be used in approved experiment E12-13-010. However, as recent results
have shown Defurne:2017paw  this technique has limitations due to the need to
include power corrections to fully describe the precise azimuthal dependence
of the DVCS cross sections.

A positron beam, on the other hand, will be able to pin down each individual
term. The $Q^{2}-$dependence of each of them can later be used to study the
nature of the higher twist contributions by comparing it to the predictions of
the leading twist diagram.

A positron beam can also be used to measure the corresponding beam charge
asymmetry defined as:

$A_{C}(\phi_{\gamma\gamma})=\frac{d\sigma^{+}(\phi_{\gamma\gamma})-d\sigma^{-}(\phi_{\gamma\gamma})}{d\sigma^{+}(\phi_{\gamma\gamma})+d\sigma^{-}(\phi_{\gamma\gamma})}\,,$
(9)

which is easier experimentally. This measurement was pioneered by the HERMES
collaboration Airapetian:2006zr . A drawback, however, is that it depends non-
linearly on the DVCS amplitudes because of the denominator. One can further
project the beam charge asymmetry on the various harmonics:

$A_{C}^{\cos{(n\phi)}}=\frac{2-\delta_{n0}}{2\pi}\int^{\pi}_{-\pi}d\phi_{\gamma\gamma}\cos{(n\phi_{\gamma\gamma})}A_{C}(\phi_{\gamma\gamma})\,,$
(10)

The $A_{C}^{\cos{(n\phi)}}$ is governed by the $c^{\mathcal{I}}_{n}$ of Eq.
(7). Nonetheless, because of the $\phi_{\gamma\gamma}$-dependent denominator
in (9), it is contaminated by all other harmonics as well Braun:2014sta .
Absolute cross-section measurements are thus needed to cleanly measure the
interference term without any contamination.

GPDs appear in the DVCS cross section under convolution integrals, usually
called Compton Form Factors (CFFs): $\mathcal{F}_{\mu\nu}$, where $\mu$ and
$\nu$ are the helicity states of the virtual photon and the outgoing real
photon, respectively. The interference between BH and DVCS provides a way to
independently access the real and imaginary parts of CFFs. At leading-order,
the imaginary part of the helicity-conserving $\mathcal{F}_{++}$ is directly
related to the corresponding GPD at $x=\xi$:

$\displaystyle\mathcal{R}\text{e}\,\mathcal{F}_{++}$ $\displaystyle=$
$\displaystyle\mathcal{P}\int_{-1}^{1}dx\left[\frac{1}{x-\xi}-\kappa\frac{1}{x+\xi}\right]F(x,\xi,t)\;,$
$\displaystyle\mathcal{I}\text{m}\,\mathcal{F}_{++}$ $\displaystyle=$
$\displaystyle-\pi\left[F(\xi,\xi,t)+\kappa F(-\xi,\xi,t)\right]\;,$ (11)

where $\kappa=-1$ if $F\in\\{H,E\\}$ and $1$ if
$F\in\\{\widetilde{H},\widetilde{E}\\}$. Recent phenomenology uses the
leading-twist (LT) and leading-order (LO) approximation in order to extract or
parametrize GPDs, which translates into neglecting $\mathcal{F}_{0+}$ and
$\mathcal{F}_{-+}$ and using the relations of Eq. 11 Kumericki:2009uq ;
Kumericki:2016ehc ; Dupre:2016mai .

The scattering amplitude is a Lorentz invariant quantity, but the deeply
virtual scattering process nonetheless defines a preferred axis (light-cone
axis) for describing the scattering process. At finite $Q^{2}$ and non-zero
$t$, there is an ambiguity in defining this axis, though all definitions
converge as $Q^{2}\to\infty$ at fixed $t$. Belitsky et al. Belitsky:2012ch
decompose the DVCS amplitude in terms of photon-helicity states where the
light-cone axis is defined in the plane of the four-vectors $q$ and $P$. This
leads to the CFFs defined previously. Recently, Braun _et al._ Braun:2014sta
proposed an alternative decomposition which defines the light cone axis in the
plane formed by $q$ and $q^{\prime}$ and argue that this is more convenient to
account for kinematical power corrections of $\mathcal{O}(t/Q^{2})$ and
$\mathcal{O}(M^{2}/Q^{2})$. The bulk of these corrections can be included by
rewriting the CFFs $\mathcal{F}_{\mu\nu}$ in terms of $\mathbb{F}_{\mu\nu}$
using the following map Braun:2014sta :

$\displaystyle\mathcal{F}_{++}=$
$\displaystyle\mathbb{F}_{++}+\frac{\chi}{2}\left[\mathbb{F}_{++}+\mathbb{F}_{-+}\right]-\chi_{0}\mathbb{F}_{0+}\;,$
(12) $\displaystyle\mathcal{F}_{-+}=$
$\displaystyle\mathbb{F}_{-+}+\frac{\chi}{2}\left[\mathbb{F}_{++}+\mathbb{F}_{-+}\right]-\chi_{0}\mathbb{F}_{0+}\;,$
(13) $\displaystyle\mathcal{F}_{0+}=$
$\displaystyle-(1+\chi)\mathbb{F}_{0+}+\chi_{0}\left[\mathbb{F}_{++}+\mathbb{F}_{-+}\right]\;,$
(14)

where kinematic parameters $\chi_{0}$ and $\chi$ are defined as follows (Eq.
48 of Ref Braun:2014sta ):

$\displaystyle\chi_{0}=$
$\displaystyle\displaystyle\frac{\sqrt{2}Q\widetilde{K}}{\sqrt{1+\epsilon^{2}}(Q^{2}+t)}$
$\displaystyle\propto\frac{\sqrt{t_{min}-t}}{Q}\;,$ (15) $\displaystyle\chi=$
$\displaystyle\displaystyle\frac{Q^{2}-t+2x_{B}t}{\sqrt{1+\epsilon^{2}}(Q^{2}+t)}-1$
$\displaystyle\propto\frac{t_{min}-t}{Q^{2}}\;.$ (16)

Within the $\mathbb{F}_{\mu\nu}$-parametrization, the leading-twist and
leading-order approximation consists in keeping $\mathbb{F}_{++}$ and
neglecting both $\mathbb{F}_{0+}$ and $\mathbb{F}_{-+}$. Nevertheless, as a
consequence of Eq. (13) and (14), $\mathcal{F}_{0+}$ and $\mathcal{F}_{-+}$
are no longer equal to zero since proportional to $\mathbb{F}_{++}$. The
functions that can be extracted from data to describe the three dimensional
structure of the nucleon become:

$\mathcal{F}_{++}=(1+\frac{\chi}{2})\mathbb{F}_{++},\,\mathcal{F}_{0+}=\chi_{0}\mathbb{F}_{++},\,\mathcal{F}_{-+}=\frac{\chi}{2}\mathbb{F}_{++}.$
(17)

A numerical application gives $\chi_{0}=$0.25 and $\chi=$0.06 for $Q^{2}$=2
GeV2, xB=0.36 and $t=-0.24$ GeV2. Considering the large size of the parameters
$\chi_{0}$ and $\chi$, these kinematical power corrections cannot be neglected
in precision DVCS phenomenology, in particular in order to unambiguously
extract the CFFs. Indeed, when the beam energy changes, not only do the
contributions of the DVCS-BH interference and DVCS2 terms change but also the
polarization of the virtual photon changes, thereby modifying the weight of
the different helicity amplitudes.

The calculation of power corrections to DVCS is one of the most important
theory advances in DVCS in recent years. BMP Braun:2014sta  have convincingly
shown that in JLab kinematics target mass corrections can be sizeable and
cannot be neglected.

##  4 Experimental setup

We propose to make a precision coincidence setup measuring charged particles
(scattered positrons) with the existing HMS and photons using the Neutral
Particle Spectrometer (NPS), currently under construction. The NPS facility
consists of a PbWO4 crystal calorimeter and a sweeping magnet in order to
reduce electromagnetic backgrounds. A high luminosity spectrometer and
calorimeter (HMS+PbWO4) combination proposed in Hall C is ideally suited for
such measurements.

The sweeping magnet will allow to achieve low-angle photon detection. Detailed
background simulations show that this setup allows for $\geq 10\mu A$ beam
current on a 10 cm long cryogenic LH2 target at the very smallest NPS angles,
and much higher luminosities at larger $\gamma,\pi^{0}$ angles E12-13-010 .

###  4.1 High Momentum Spectrometer

The magnetic spectrometers benefit from relatively small point-to-point
uncertainties, which are crucial for absolute cross section measurements. In
particular, the optics properties and the acceptance of the HMS have been
studied extensively and are well understood in the kinematic e between 0.5 and
5 GeV, as evidenced by more than 200 L/T separations ($\sim$1000 kinematics)
Liang:2004tj . The position of the elastic peak has been shown to be stable to
better than 1 MeV, and the precision rail system and rigid pivot connection
have provided reproducible spectrometer pointing for about a decade.

###  4.2 Photon detection: the neutral particle spectrometer (NPS)

We will use the general-purpose and remotely rotatable NPS system for Hall C.
A layout of NPS standing in the SHMS carriage is shown in Fig. 3(a). The NPS
system consists of the following elements:

  * •

A sweeping magnet providing 0.3 Tm field strength.

  * •

A neutral particle detector consisting of 1080 PbWO4 crystals in a temperature
controlled frame, comprising a 25 msr device at a distance of 4 meters.

  * •

Essentially deadtime-less digitizing electronics to independently sample the
entire pulse form for each crystal allowing for background subtraction and
identification of pile-up in each signal.

  * •

A new set of high-voltage distribution bases with built-in amplifiers for
operation in high-rate environments.

  * •

Cantilevered platforms on the SHMS carriage, to allow for precise and remote
rotation around the Hall C pivot of the full photon detection system, over an
angle range between 6 and 30 degrees.

  * •

A dedicated beam pipe with as large critical angle as possible to reduce
backgrounds beyond the sweeping magnet.

(a) (b)

(c)

Figure 3:  (a) The DVCS detector in Hall C. The cylinder in the left is the (1
m diameter) vacuum chamber containing the 10-cm long liquid-hydrogen target.
The NPS sweeping magnet and calorimeter are standing on the yellow platform of
the SHMS, which will be used as carriage to support them. The HMS (not shown)
placed on the other side of the beam line will be used to detect the scattered
positrons. (b) Front view of the NPS calorimeter showing the PbWO4 crystal
array. (c) Back view of the calorimeter showing the PMT voltage dividers and
the vertical PCB distribution boards which bring HV and transfer the PMT
signal to the read-out electronics.

#### The PbWO4 electromagnetic calorimeter

The energy resolution of the photon detection is the limiting factor of the
experiment. Exclusivity of the reaction is ensured by the missing mass
technique (see section 4.3) and the missing-mass resolution is dominated by
the energy resolution of the calorimeter.

We plan to use a PbWO4 calorimeter 56 cm wide and 68 cm high. This corresponds
to 28 by 34 PbWO4 crystals of 2.05 by 2.05 cm2 (each 20.0 cm long). We have
added one crystal on each side to properly capture showers, and thus designed
our PbWO4 calorimeter to consist of 30 by 36 PbWO4 crystals, or 60 by 72 cm2.
This amounts to a requirement of 1080 PbWO4 crystals.

To reject very low-energy background, a thin absorber could be installed in
front of the PbWO4 detector. The space between the sweeper magnet and the
proximity of the PbWO4 detector will be enclosed within a vacuum channel (with
a thin exit window, further reducing low-energy background) to minimize the
decay photon conversion in air.

Given the temperature sensitivity of the scintillation light output of the
PbWO4 crystals, the entire calorimeter must be kept at a constant temperature,
to within $0.1^{\circ}$ to guarantee 0.5% energy stability for absolute
calibration and resolution. The high-voltage dividers on the PMTs may
dissipate up to several hundred Watts, and this power similarly must not
create temperature gradients or instabilities in the calorimeter. The
calorimeter will thus be thermally isolated and be surrounded on all four
sides by water-cooled copper plates.

At the anticipated background rates, pile-up and the associated baseline
shifts can adversely affect the calorimeter resolution, thereby constituting
the limiting factor for the beam current. The solution is to read out a
sampled signal, and perform offline shape analysis using a flash ADC (fADC)
system. New HV distribution bases with built-in pre-amplifiers will allow for
operating the PMTs at lower voltage and lower anode currents, and thus protect
the photocathodes or dynodes from damage.

The PbWO4 crystals are 2.05 x 2.05 cm2. The typical position resolution is 2-3
mm. Each crystal covers 5 mrad, and the expected angular resolution is
0.5-0.75 mrad, which is comparable with the resolutions of the HMS and SOS,
routinely used for Rosenbluth separations in Hall C.

To take full advantage of the high-resolution crystals while operating in a
high-background environment, modern flash ADCs will be used to digitize the
signal. They continuously sample the signal every 4 ns, storing the
information in an internal FPGA memory. When a trigger is received, the
samples in a programmable window around the threshold crossing are read out
for each crystal that fired. Since the readout of the FPGA does not interfere
with the digitizations, the process is essentially deadtime free.

###  4.3 Exclusivity of the DVCS reaction

The exclusivity of the DVCS reaction will be based on the missing mass
technique, successfully used during Hall A experiments E00-110 and E07-007
with a PbF2 calorimeter. Fig. 4 presents the missing mass squared obtained in
E00-110 for H$(e,e^{\prime}\gamma)X$ events, with coincident electron-photon
detection.

Figure 4: Left: Missing mass squared in E00-110 for H$(e,e^{\prime}\gamma)X$
events (green curve) at $Q^{2}=2.3$ GeV2 and $-t\in[0.12,0.4]$ GeV2,
integrated over the azimuthal angle of the photon $\phi_{\gamma\gamma}$. The
black curve shows the data once the H$(e,e^{\prime}\gamma)\gamma X^{\prime}$
events have been subtracted. The other curves are described in the text.
Right: Projected missing mass resolution for a similar kinematic setting
($E_{b}=6.6$ GeV, $Q^{2}=3$ GeV2, $x_{B}=0.36$). By using PbWO4 instead of
PbF2, the missing mass resolution will be considerably improved. Values are
given in Tab. 2 and are to be compared to the the value
$\sigma(M_{X}^{2})=0.2$ GeV2 obtained in previous experiments in Hall A and
showed in this figure (left).

After subtraction of an accidental coincidence sample, our data is essentially
background free: we have negligible contamination of non-electromagnetic
events in the HRS and PbF2 spectra. However, in addition to
H$(e,e^{\prime}\gamma)p$, we do have the following competing channels:
H$(e,e^{\prime}\gamma)p\gamma$ from $ep\rightarrow e\pi^{0}p$, $ep\rightarrow
e\pi^{0}N\pi$, $ep\rightarrow e\gamma N\pi$, $ep\rightarrow e\gamma
N\pi\pi\ldots$. From symmetric (lab-frame) $\pi^{0}$-decay, we obtain a high
statistics sample of H$(e,e^{\prime}\pi^{0})X^{\prime}$ events, with two
photon clusters in the PbF2 calorimeter. From these events, we determine the
statistical sample of [asymmetric] H$(e,e^{\prime}\gamma)\gamma X^{\prime}$
events that must be present in our H$(e,e^{\prime}\gamma)X$ data. The
$M_{X}^{2}$ spectrum displayed in black in Fig. 4 was obtained after
subtracting this $\pi^{0}$ yield from the total (green) distribution. This is
a $14\%$ average subtraction in the exclusive window defined by ’$M_{X}^{2}$
cut’ in Fig. 4. Depending on the bin in $\phi_{\gamma\gamma}$ and $t$, this
subtraction varies from 6% to 29%. After our $\pi^{0}$ subtraction, the only
remaining channels, of type H$(e,e^{\prime}\gamma)N\pi$, $N\pi\pi$, etc. are
kinematically constrained to $M_{X}^{2}>(M+m_{\pi})^{2}$. This is the value
(’$M_{X}^{2}$ cut’ in Fig. 4) we chose for truncating our integration.
Resolution effects can cause the inclusive channels to contribute below this
cut. To evaluate this possible contamination, during E00-110 we used an
additional proton array (PA) of 100 plastic scintillators. The PA subtended a
solid angle (relative to the nominal direction of the q-vector) of
$18^{\circ}<\theta_{\gamma p}<38^{\circ}$ and $45^{\circ}<\phi_{\gamma
p}=180^{\circ}-\phi_{\gamma\gamma}<315^{\circ}$, arranged in 5 rings of 20
detectors. For H$(e,e^{\prime}\gamma)X$ events near the exclusive region, we
can predict which block in the PA should have a signal from a proton from an
exclusive H$(e,e^{\prime}\gamma p)$ event. The red histogram is the $X=(p+y)$
missing mass squared distribution for H$(e,e^{\prime}\gamma p)y$ events in the
predicted PA block, with a signal above an effective threshold $30$ MeV
(electron equivalent). The blue curve shows our inclusive yield, obtained by
subtracting the normalized triple coincidence yield from the
H$(e,e^{\prime}\gamma)X$ yield. The (smooth) violet curve shows our simulated
H$(e,e^{\prime}\gamma)p$ spectrum, including radiative and resolution effects,
normalized to fit the data for $M_{X}^{2}\leq M^{2}$. The cyan curve is the
estimated inclusive yield obtained by subtracting the simulation from the
data. The blue and cyan curves are in good agreement, and show that our
exclusive yield has less than $2\%$ contamination from inclusive processes.

In this proposed experiment we plan to use a PbWO4 calorimeter with a
resolution more than twice better than the PbF2 calorimeter used in E00-110.
While the missing mass resolution will be slightly worse at some high beam
energy, low $x_{B}$ kinematics, the better energy resolution of the crystals
will largely compensate for it, and the missing mass resolution in this
experiment will be significantly better than ever before. Fig. 4 (right) shows
the missing mass resolution for PbF2 and PbWO4 for a kinematic setting similar
to the one measured in Hall A. Tab. 2 shows the missing mass resolution
projected for each of the settings using the proposed PbWO4 calorimeter.

###  4.4 Systematics uncertainties

Source | pt-to-pt | scale
---|---|---
| (%) | (%)
Acceptance | 0.4 | 1.0
Electron/positron PID |  $<$0.1 |  $<$0.1
Efficiency | 0.5 | 1.0
Electron/positron tracking efficiency | 0.1 | 0.5
Charge | 0.5 | 2.0
Target thickness | 0.2 | 0.5
Kinematics | 0.4 |  $<$0.1
Exclusivity | 1.0 | 2.0
$\pi^{0}$ subtraction | 0.5 | 1.0
Radiative corrections | 1.2 | 2.0
Total | 1.8–1.9 | 3.8–3.9
Table 1: Estimated systematic uncertainties for the proposed experiment based
on previous Hall C experiments.

The HMS is a very well understood magnetic spectrometer which will be used
here with modest requirements (beyond the momentum), defining the
($x_{B},Q^{2}$) kinematics well. Tab. 1 shows the estimated systematic
uncertainties for the proposed experiment based on previous experience from
Hall C equipment and Hall A experiments.

##  5 Proposed kinematics and projections

Table 2 details the kinematics and beam time used in the projection. $Q^{2}$
scans at 4 different values of $x_{B}$ were chosen in kinematics with already
approved electron data E12-13-010 . The positron beam current assumed is 5
$\mu A$ (unpolarized beam) and is currently the limiting factor driving the
beam time needs. Considering a 1 $mA$ initial electron beam, 5 $\mu A$ of
positrons corresponds to the maximum positron to electron ratio produced by
123 MeV electrons Cardman:2018svy . This also corresponds to the lowest
polarization transfer to the positrons, which will be considered unpolarized
in our projections. Beam time in Table 2 is calculated in order collect
positron data corresponding to $\sim$25% of the approved electron data.

$x_{\text{Bj}}$ | 0.2 | 0.36 | 0.5 | 0.6
---|---|---|---|---
$Q^{2}\,\text{(GeV)}^{2}$ | 2.0 | 3.0 | 3.0 | 4.0 | 5.5 | 3.4 | 4.8 | 5.1 | 6.0
$E_{b}\ \text{(GeV)}$ | 6.6 | 8.8 | 11 | 6.6 | 8.8 | 11 | 8.8 | 11 | 8.8 | 11 | 6.6 | 8.8 | 11
$k^{\prime}\ \text{(GeV)}$ | 1.3 | 3.5 | 5.7 | 3.0 | 2.2 | 4.4 | 6.6 | 2.9 | 5.1 | 2.9 | 5.2 | 7.4 | 5.9 | 2.1 | 4.3 | 6.5 | 5.7
$\theta_{\text{Calo}}\,\text{(deg)}$ | 6.3 | 9.2 | 10.6 | 6.3 | 11.7 | 14.7 | 16.2 | 10.3 | 12.4 | 7.9 | 20.2 | 21.7 | 16.6 | 13.8 | 17.8 | 19.8 | 17.2
$D_{\text{Calo}}$ (m) | 6 | 4 | 6 | 3 | 4 | 3 | 4 | 3
$\sigma_{M_{X}^{2}}$(GeV2) | 0.17 | 0.22 | 0.13 | 0.12 | 0.15 | 0.19 | 0.09 | 0.11 | 0.09
$I_{\text{beam}}$ ($\mu$A) | 5
Days | 1 | 1 | 3 | 1 | 2 | 3 | 2 | 3 | 4 | 13 | 4 | 3 | 7 | 7 | 2 | 7 | 14
Table 2: DVCS kinematics with positrons in Hall C. The incident and scattered
beam energies are $k$ and $k^{\prime}$, respectively. The calorimeter is
centered at the angle $\theta_{\text{Calo}}$, which is set equal to the
nominal virtual-photon direction. The front face of the calorimeter is at a
distance $D_{\text{Calo}}$ from the center of the target, and is adjusted to
optimize multiple parameters: First to maximize acceptance, second to ensure
sufficient separation of the two clusters from symmetric
$\pi^{0}\rightarrow\gamma\gamma$ decays, and third to ensure that the edge of
the calorimeter is never at an angle less than $3.2^{\circ}$ from the beam
line. The maximum expected positron beam current (5 $\mu$A) will be used for
all kinematics settings. The total amount of beam time needed is 77 days.

The different kinematics settings are represented in Fig. 5 in the
$Q^{2}$–$x_{B}$ plane. The area below the straight line
$Q^{2}=(2M_{p}E_{b})x_{B}$ corresponds to the physical region for a maximum
beam energy $E_{b}=11$ GeV. Also plotted is the resonance region $W<2$ GeV.

Figure 5:  Display of different kinematic setting proposed. The $Q^{2}-x_{B}$
settings correspond to the ones approved in experiment E12-13-010, which will
measure DVCS cross sections using an electron beam. Shaded areas show the
resonance region $W<2$ GeV and the line $Q^{2}=(2M_{p}E_{b})x_{B}$ limits the
physical region for a maximum beam energy $E_{b}=11$ GeV.

We have performed detailed Monte Carlo simulation of the experimental setup
and evaluated counting rates for each of the settings. In order to do this, we
have used a recent global fit of world data with LO sea evolution by D. Müller
and K. Kumerički DMweb . This fit reproduces the magnitude of the DVCS cross
section measured in Hall A at $x_{B}=0.36$ and is available up to values of
$x_{B}\leq 0.5$. For our high $x_{B}$ settings we used a GPD parametrization
by P. Kroll, H. Moutarde and F. Sabatié Kroll:2012sm  fitted to Deeply Virtual
Meson Production data, together with a code to compute DVCS cross sections,
provided by H. Moutarde HerveTGV ; TGGuichon . Notice that for DVCS, counting
rates and statistical uncertainties will be driven at first order by the
Bethe-Heitler (BH) cross section, which is well-known.

Fig. 6 shows the projected results for 3 selected settings at different values
of $x_{B}=0.2,0.36,0.5$. Statistical uncertainties are shown by error bars and
systematic uncertainties are represented by the cyan bands.

Figure 6: Experimental projections for 3 different of the settings proposed:
$x_{B}=0.2$, $Q^{2}=2.0$ GeV2 (top), $x_{B}=0.36$, $Q^{2}=4.0$ GeV2 (middle)
and $x_{B}=0.5$, $Q^{2}=3.4$ GeV2 (bottom). Red points show the projected
positron cross sections with statistical uncertainties. Electron cross
sections that will be measured in experiment E12-13-010 are shown in magenta.
The combination of $e^{-}$ and $e^{+}$ cross sections allow the separation of
the DVCS2 contribution (blue) and the DVCS-BH interference (green). For
reference, the BH cross section is displayed in black. Systematic
uncertainties are shown by the cyan band.

The DVCS2 term (which is $\phi$ independent at leading twist) can be very
cleanly separated from the BH-DVCS interference contribution, and this without
any assumption regarding the leading-twist dominance. The $Q^{2}-$dependence
of each term will be measured (cf. Tab. 2) and its dependence compared to the
asymptotic prediction of QCD. The extremely high statistical and systematic
precision of the results illustrated in Fig. 6 will be crucial to disentangle
higher order effects (higher twist or next-to-leading order contributions) as
shown by recent results Defurne:2017paw .

##  6 Constraints on Compton Form Factors

In order to quantify the impact of the proposed experiment on the extraction
of the nucleon Compton Form Factors, we have simulated the extraction of the
proton CFFs by using only approved electron cross-section measurements (both
helicity-dependent and helicity-independent) from upcoming experiment
E12-13-010 and with the addition of the positron measurements proposed herein.
Measurements with an unpolarized target as proposed herein have little
sensitivity to GPDs $E$ and $\widetilde{E}$. Therefore, only the CFFs
corresponding to $H$ and $\widetilde{H}$ have been fitted. Prospects of
measurements with polarized targets would be, of course, extremely exciting
and complementary to these. Most importantly, as mentioned before, kinematics
corrections of $\mathcal{O}(t/Q^{2})$ and $\mathcal{O}(M^{2}/Q^{2})$ cannot be
neglected in JLab kinematics. Therefore, all CFFs $\mathbb{H}_{++}$,
$\mathbb{H}_{0+}$, $\mathbb{H}_{-+}$, $\widetilde{\mathbb{H}}_{++}$,
$\widetilde{\mathbb{H}}_{0+}$ and $\widetilde{\mathbb{H}}_{-+}$ have been
fitted.

First of all, the DVCS cross sections measured in Hall A with a 6 GeV beam
Defurne:2015kxq ; Defurne:2017paw  were fitted in order to extract some
realistic values of the CFFs. These values were then used to calculate
projected cross sections at the kinematics of Tab. 2. The CFFs are assumed
constant in $t$ for this exercise and equal to the average value of those
extracted from 6 GeV data. The projected electron and positron cross sections
are then fitted. In doing this, the statistical and systematic uncertainties
of the measurements were added quadratically. Fig. 7 shows the results for
kinematics with $x_{B}=0.36$. Each line shows the five kinematic settings in
$Q^{2}$, $E_{b}$ at constant $x_{B}$ and $t$, which are fitted simultaneously
neglecting the logarithmic $Q^{2}$-dependence of CFFs in the range of
$\sim$3–6 GeV2. In addition to the five independent terms on the azimuthal
angle ($\sim 1$, $\sim\cos{\phi}$, $\sim\cos{2\phi}$, $\sim\sin{\phi}$ and
$\sim\sin{2\phi}$), three different beam energies are fitted simultaneously.
Each column in Fig. 7 shows each of the 5 bins in $t$ where the data were
binned. The blue lines correspond to the fits of both the (approved) electron
data (helicity-dependent and helicity-independent) and the positron (proposed)
data (only helicity-independent). Notice that the NPS calorimeter acceptance
will allow a full coverage in $\phi$ for the bins in $t$ presented.

Figure 7: Fits of data with $x_{B}=0.36$. Each row shows five kinematic
settings in $Q^{2}$ at constant $x_{B}$ and $t$. Each column corresponds to 5
different bins in t. The blue lines are simultaneous fits of the (approved)
electron data, both the helicity-dependent (black squares) and helicity-
independent (black circles) cross sections, and the (proposed) positron data
(red points). Horizontal dashed lines in each panel indicate the origin of the
vertical axis: $d^{4}\sigma=0$.

Results of the CFFs extracted from the fits are shown in Fig. 8. The first
column in the left shows the results of the helicity-conserving CFFs when both
positron and electron data are used in the fit, and when only the electron
approved data are used. The second and third columns show the same information
for the helicity-flip CFFs. The solid horizontal lines in each panel indicate
the input values used to generate the cross-section data, which are then
accurately extracted by the fit. The ratio of the uncertainties between the
fit using both electron and positron data and the one using only electron data
is shown in the last column on the right. One can see the significant
improvement of positron data: a factor of 6 for
$\mathcal{R}e(\mathbb{H}_{++})$ and an average factor of 4 for
$\mathcal{R}e(\widetilde{\mathbb{H}}_{++})$. There is also a factor $\sim$2
improvement in the real part of most helicity-flip CFFs. The imaginary part of
CFFs are not impacted by these positron data – this is expected as no
helicity-dependent positron cross sections are used in the fits.

Figure 8: CFFs extracted from the fits in Fig. 7. Left: the first column in
the left shows the results of the helicity-conserving CFFs when both positron
and electron data are used in the fit (black), and when only the electron
approved data is used (grey). The second and third columns show the same
information for the helicity-flip CFFs. The solid horizontal lines indicate
the input values used to generate the cross-section data. Right: ratio of the
uncertainties between the fit using both electron and positron data and the
one using only electron data.

In addition to reducing the uncertainties of the fitted CFFs, positron data
also improves the correlation of the extracted parameters. Fig. 9 shows the
correlation coefficient between the different pairs of CFFs as extracted from
the electron data alone (left) and with the addition of positron data (right).
The correlation coefficient for each pair of extracted CFFs
$(\mathbb{F}_{i},\mathbb{F}_{j})$ is defined as
$\rho_{i,j}=\text{cov}[\mathbb{F}_{i},\mathbb{F}_{j}]/(\sigma_{i}\sigma_{j})$.
It varies from -1 to 1. and Fig. 9 reports its absolute value. One can notice,
in particular, that while the helicity-conserving real parts of
$\mathbb{H}_{+,+}$ and $\widetilde{\mathbb{H}}_{+,+}$ are very correlated in
the case of a fit with electron data only, the correlation is significantly
reduced when positron data are included. The improvement varies from $-98\%$
to $-54\%$ at the highest value of $|t|$ and from $-70\%$ to $-24\%$ at the
lowest $|t|$.

Figure 9: Magnitude of the correlation coefficients between the different CFFs
extracted from the fit of DVCS electron data (top) and from the combined fit
of DVCS electron and positron data (bottom). Plots correspond to bin
$x_{B}=0.36$ and $t=-0.26$ GeV2. The correlation between
$\mathcal{R}e(\mathbb{H}_{+,+})$ and
$\mathcal{R}e(\widetilde{\mathbb{H}}_{+,+})$ goes from $-94\%$ without
positrons to $-39\%$ when electron and positrons are combined.

##  7 Summary

We propose to measure the cross section of the DVCS reaction accurately using
positrons in the wide range of kinematics allowed by a set of beam energies up
to 11 GeV. We will exploit the beam charge dependence of the cross section to
separate the contribution of the BH-DVCS interference and the DVCS2 terms.

The $Q^{2}-$dependence of each individual term will be measured and compared
to the predictions of the handbag mechanism. This will provide a quantitative
estimate of higher-twist effects to the GPD formalism in JLab kinematics.

The combination of measurements with electrons and positrons allow to much
better constrain the Compton Form Factors measurements and reduce
significantly the correlations in the extracted values.

We plan to use Hall C High-Momentum Spectrometer, combined with a high
resolution PbWO4 electromagnetic calorimeter.

In order to complete this full mapping of the DVCS cross section with
positrons over a wide range of kinematics, we require 77 days of (unpolarized)
positron beam (I$>5\mu$A).

##  8 Acknowledgements

This material is based upon work supported by the U.S. Department of Energy,
Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177.

## References

  * [1] John C. Collins and Andreas Freund.  Proof of factorization for deeply virtual compton scattering in QCD.  Phys. Rev., D59:074009, 1999.
  * [2] Xiang-Dong Ji and Jonathan Osborne.  One-loop corrections and all order factorization in deeply virtual compton scattering.  Phys. Rev., D58:094018, 1998.
  * [3] Dieter Mueller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Horejsi.  Wave functions, evolution equations and evolution kernels from light-ray operators of QCD.  Fortschr. Phys., 42:101, 1994.
  * [4] Xiang-Dong Ji.  Deeply virtual Compton scattering.  Phys.Rev., D55:7114–7125, 1997.
  * [5] Xiang-Dong Ji.  Gauge invariant decomposition of nucleon spin.  Phys. Rev. Lett., 78:610–613, 1997.
  * [6] Xiang-Dong Ji, W. Melnitchouk, and X. Song.  A Study of off forward parton distributions.  Phys.Rev., D56:5511–5523, 1997.
  * [7] A. V. Radyushkin.  Nonforward parton distributions.  Phys. Rev., D56:5524–5557, 1997.
  * [8] A.V. Radyushkin.  Scaling limit of deeply virtual Compton scattering.  Phys.Lett., B380:417–425, 1996.
  * [9] Andrei V. Belitsky, Dieter Mueller, and A. Kirchner.  Theory of deeply virtual compton scattering on the nucleon.  Nucl. Phys., B629:323–392, 2002.
  * [10] Matthias Burkardt.  GPDs with zeta not equal 0.  2007\.
  * [11] O.V. Teryaev.  Analytic properties of hard exclusive amplitudes.  2005\.
  * [12] I.V. Anikin and O.V. Teryaev.  Dispersion relations and subtractions in hard exclusive processes.  Phys.Rev., D76:056007, 2007.
  * [13] I.V. Anikin and O.V. Teryaev.  Dispersion relations and QCD factorization in hard reactions.  Fizika, B17:151–158, 2008.
  * [14] M. Diehl and D. Yu. Ivanov.  Dispersion representations for hard exclusive reactions.  2007\.
  * [15] Maxim V. Polyakov and C. Weiss.  Skewed and double distributions in pion and nucleon.  Phys.Rev., D60:114017, 1999.
  * [16] Markus Diehl, Thierry Gousset, Bernard Pire, and John P. Ralston.  Testing the handbag contribution to exclusive virtual compton scattering.  Phys. Lett., B411:193–202, 1997.
  * [17] M. Defurne et al.  A glimpse of gluons through deeply virtual compton scattering on the proton.  Nature Commun., 8(1):1408, 2017.
  * [18] C. Muñoz Camacho, T. Horn, C. Hyde, R. Paremuzyan, J. Roche et al.  Hard.  experiment E12-13-010 (Hall C), 2010.
  * [19] A.V. Belitsky and D. Mueller.  Exclusive electroproduction revisited: treating kinematical effects.  Phys.Rev., D82:074010, 2010.
  * [20] A. Airapetian et al.  The Beam-charge azimuthal asymmetry and deeply virtual compton scattering.  Phys.Rev., D75:011103, 2007.
  * [21] Vladimir M. Braun, Alexander N. Manashov, Dieter Mueller, and Bjoern M. Pirnay.  Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections.  Phys. Rev., D89(7):074022, 2014.
  * [22] Kresimir Kumericki and Dieter Mueller.  Deeply virtual Compton scattering at small x(B) and the access to the GPD H.  Nucl.Phys., B841:1–58, 2010.
  * [23] Kresimir Kumericki, Simonetta Liuti, and Herve Moutarde.  GPD phenomenology and DVCS fitting.  Eur. Phys. J., A52(6):157, 2016.
  * [24] Raphael Dupre, Michel Guidal, and Marc Vanderhaeghen.  Tomographic image of the proton.  Phys. Rev., D95(1):011501, 2017.
  * [25] Andrei V. Belitsky, Dieter Mueller, and Yao Ji.  Compton scattering: from deeply virtual to quasi-real.  Nucl. Phys., B878:214–268, 2014.
  * [26] Y. Liang et al.  Measurement of R = sigma(L) / sigma(T) and the separated longitudinal and transverse structure functions in the nucleon resonance region.  2004\.
  * [27] Lawrence S. Cardman.  The PEPPo method for polarized positrons and PEPPo II.  AIP Conf. Proc., 1970(1):050001, 2018.
  * [28] D. Müller and K. Kumerički.  Model 3: http://calculon.phy.pmf.unizg.hr/gpd/.
  * [29] Peter Kroll, Herve Moutarde, and Franck Sabatie.  From hard exclusive meson electroproduction to deeply virtual Compton scattering.  Eur.Phys.J., C73:2278, 2013.
  * [30] H. Moutarde.  TGV code for fast calculation of DVCS cross sections from CFFs, private communication, 2013.
  * [31] P.A.M. Guichon and M. Vanderhaeghen.  Analytic $ee^{\prime}\gamma$ cross section, in Atelier DVCS, Laboratoire de Physique Corpusculaire, Clermont-Ferrand, June 30 - July 01, 2008.
  * [32] M. Defurne et al.  E00-110 experiment at Jefferson Lab Hall A: Deeply virtual Compton scattering off the proton at 6 GeV.  Phys. Rev., C92(5):055202, 2015.


# A Critical Look at the Current Usage of Foundation Model for Dense
Recognition Task

Shiqi Yang1,2, Atsushi Hashimoto3, Yoshitaka Ushiku3
1 Computer Vision Center, Bellaterra, Spain
2 Department of Computer Science, Universitat Autònoma de Barcelona,
Bellaterra, Spain
3 OMRON SINIC X, Tokyo, Japan
<EMAIL_ADDRESS>{atsushi.hashimoto<EMAIL_ADDRESS>Work is
done during intern at OMRON SINIC X.

###### Abstract

In recent years large model trained on huge amount of cross-modality data,
which is usually be termed as foundation model, achieves conspicuous
accomplishment in many fields, such as image recognition and generation.
Though achieving great success in their original application case, it is still
unclear whether those foundation models can be applied to other different
downstream tasks. In this paper, we conduct a short survey on the current
methods for discriminative dense recognition tasks, which are built on the
pretrained foundation model. And we also provide some preliminary experimental
analysis of an existing open-vocabulary segmentation method based on Stable
Diffusion, which indicates the current way of deploying diffusion model for
segmentation is not optimal. This aims to provide insights for future research
on adopting foundation model for downstream task.

##  1 Introduction

In the last decades, deep model trained with large amount of labeled data
succeeds to be top-rank in almost all computer vision tasks. Besides the
achievements in the supervised learning tasks, other research lines improve
the generalization and universality ability, such as self-supervised learning
[11, 9, 3] which empowers the model with strong representation feature
learning capacity with only unlabeled data, open-set or open-world learning
which endows the model with the ability to either reject [22, 38, 33] or
distinguish [2, 26, 32, 15] novel categories, and domain generalization [10,
18, 27] or domain adaptation [30, 20, 36] which improves model’s
generalization to test data of different distributions, to name a few.

More recently, the training of models with abundant cross modality data is
becoming more popular. For example, CLIP [25] is a visual-language model
trained with huge amount of image and text pairing data, via a contrastive
learning objective. Due to the learned image-language pairing representation,
with the provided text prompts during inference time, the model excels at
zero-shot recognition. SAM [16] is a general category-agnostic
segmentation/localization solution which supports several types of prompts, it
is capable of segmenting whole objects or object parts of any shape. ImageBind
[8] learns a joint embedding space across six different modalities, with
visual space as the intermedia embedding space, and it is a strong pipeline
for cross-modality recognition tasks.

Figure 1: Grad-CAM visualization of pretrained CLIP visual encoder. Only four
classes (used for text prompt) are considered: car, building, windows and
trees/palms.  Figure 2: Adopting binary threshold on the Grad-CAM.

Besides large model for discriminative tasks, diffusion based111In this
report, we regard (text-to-image) diffusion model also as a kind of foundation
model. image generation is another emerging hot research topic. Stable
Diffusion [28] is one of the most popular methods in both academic and non-
academic communities. The pretrained Stable Diffusion could be easily adapted
to the personalized data, for both image generation or editing, by fine-tuning
part of the model [29, 13] or conducting some processing in the fixed model
[12, 7]. Originally designed for text-to-image generation task, it can be
easily extended to other conditional image generation task [39], such as
depth-to-image and sketch-to-image generation/translation.

With the popularity of those foundation models, a natural question arises: can
those pretrained models, which are originally for image recognition or
generation, be applied to other downstream tasks? As these models are trained
with huge amounts of data and possess strong zero-shot recognition ability or
good feature representation, the learned knowledge is expected to also
facilitate other downstream tasks. This provides the possibility of using a
unified model for different tasks, which could have high practical value in
real-world applications. In this paper, we conduct a short survey on utilizing
pretrained foundation model for downstream tasks. We mainly focus on the
segmentation task, since segmentation information is also useful for other
tasks such as detection and localization.

Figure 3: Visualization of cross attention (for token ’horse’ with the text
prompt ’a horse on the grass’). The upper part is the cross attention in the
last timestep during generation stage. Then just like ODISE, we sent the
generated image back to diffusion model with adding one noise, the
visualization is shown in the lower part. In each case, the first row shows
the attention map from different layer in the output block and the second row
shows the average of those attention maps of different sizes. Figure 4:
K-means clustering visualization on UNet features of real image. The image is
directly fed into the diffusion model with adding noise once. We use the
average feature across the last 6 blocks for visualization.

##  2 Utilizing Foundation Model for Downstream Task

In the first part, we will focus on the typical discriminative foundation
model for downstream task. In the second part, we will exploit some current
methods utilizing Stable Diffusion for downstream discriminative task.

###  2.1 Visual-Language Model

Large vision-language model, such as CLIP [25] and ALIGN [14], are trained
with image-language pairs via contrastive learning, due to its strong zero-
shot image recognition performance, there is a new research line dubbed as
open-vocabulary objection/segmentation, aiming to introduce the open category
recognition ability into the objection or segmentation tasks. Early works on
open-vocabulary segmentation such as LSeg [1] directly transform the vision-
language model classification model to segmentation pipeline. More
specifically LSeg directly predicts the category of the pixel embedding with
the text embedding, without introducing any extra mask generator module.
MaskCLIP [41] first shows that the value (V) embedding output by the CLIP
visual part could be used as mask proposal for segmentation, together with the
text embedding as the classifier weight the CLIP pipeline could directly
output segmentation mask, then it further introduces Mask2Former [4] to
improve the results, which is trained in a self training manner with the
predicted segmentation masks. The recent works [24, 19] follow the similar
pipeline, which typically has two parts: the first part is transformer based
mask proposal network and the second part is the CLIP which is to provide
open-vocabulary prediction. There are also a few methods elegantly unifying
these two parts, for example, ZegCLIP [42] and SAN [35] directly adopt CLIP as
the main backbone (feature extractor part) and add a lightweight mask
generator which takes input feature from CLIP. Since the pipeline with
Mask2Former usually takes longer training time, the methods including MaskCLIP
(the one without extra mask generator) have fewer parameters and also could
achieve better performance, which could be a baseline for future research.

###  2.2 Text-to-image Diffusion Model

Diffusion models are another research hotspot in recent years. The most
successful application is text-to-image generation, by fine-tuning or directly
utilizing the pretrain diffusion model, where Stable Diffusion [28] is one of
the most popular deployed diffusion model. Since the text-to-image generation
model222If not specified, the (text-to-image) diffusion model refers to Stable
Diffusion in the subsequent sections. such as Stable Diffusion is trained with
large amount of image-text pairs just like CLIP, a natural question is that
whether those cross-modality generative models could be applied to
discriminative task? As some pioneer works [12] show that the features inside
the diffusion model already have rich semantic and localization information,
the pretrained diffusion model has potential to be extended to other
discriminative tasks.

There are already a few works trying to utilize the text-to-image diffusion
model for downstream tasks. Some methods [5, 17] transform the text-to-image
diffusion model to a zero-shot classification model which is competitive to
CLIP, by obtaining the posterior classification scores based on the predicted
noise during the denoising process. And other methods like OIDSE [34] and VPN
[40] utilize the UNet features in the diffusion model for downstream tasks
such as segmentation and depth estimation. In the following texts we focus on
the segmentation task.

In ODISE and VPN, the diffusion model is only to provide features, which will
be the input to the subsequent mask generator network such as Mask2Former [4]
or LAVT [37], both methods only adopt one time step for the diffusion model,
and VPN does not add the noise to the latent vector while ODISE does. In
ODISE, an extra learnable module called implicit captioner is proposed to
provide the textual embedding to UNet. VPN also utilizes a similar module
denoted as text adapter, as well as cross attention maps to be combined with
multi-level UNet features. Although these methods achieve good performance in
the downstream tasks, we question the efficiency of this naive way of directly
using UNet features with one time step. And actually, the ablation study in
VPN already shows that there is limited improvement by using the extra text
adapter and cross attention features, which indicates that this naive way is
not totally efficient to fully exploit the diffusion model for segmentation.
This conclusion also holds for the implicit captioner in ODISE.

Method | Architecture | PAS-21 | A-847 | PC-459 | A-150 | PC-59 | COCO
---|---|---|---|---|---|---|---
MaskCLIP [6] | CLIP + Mask2Former | - | 8.2 | 10.0 | 23.7 | 45.9 | -
ODISE [34] | CLIP + SD + Mask2Former | 84.4 | 11.1 | 14.5 | 29.9 | 57.3 | 65.2
ODISE w/o IC | CLIP + SD + Mask2Former | 82.4 | 10.3 | 12.4 | 28.3 | 54.3 | 61.6
ODISE w/o (IC & UNet) | CLIP + SD + Mask2Former | 76.6 | 10.1 | 12.4 | 27.2 | 51.7 | 56.3
ODISE * w/o (IC & VQGAN) | CLIP + SD + Mask2Former | 80.1 | 10.2 | 13.2 | 28.6 | 52.5 | 61.2
SAN [35] | CLIP + light decoder | 94.6 | 12.4 | 15.7 | 32.1 | 57.7 | -

Table 1: Detailed ablation study on ODISE, where the model is trained with
train set from COCO and the evaluated on other datasets. ’w/o IC’ denotes not
using implicit captioner and instead only adopting null text embedding, UNet
denotes using features from UNet, and * denotes without adding noise to the
output of encoder. We directly use the official ODISE code, due to the limited
computation resource, for the three ablation studies we only train 66999,
81999 and 48999 iterations out of the whole 92188 iterations, with 16 A100
GPUs.

##  3 Experimental Analysis

In this section, we will first show that the pretrained visual-language model,
more specifically the CLIP, has the potential to be directly extended to other
downstream tasks. Then, we will show the current methods using text-to-image
diffusion model are not efficient with the naive way of deploying pretrained
diffusion model as the feature extractor.

###  3.1 Visual-Language Model

We choose the widely used visual-language model CLIP for analysis. We
visualize the CLIP visual features under the weakly supervised segmentation
task [21], where every image is provided with its ground-truth class labels.
We adopt the Grad-CAM [31] for visualization333We follow CLIP-ES [21] to use
the features before the last attention layer to compute CAM.. For text prompt
input to the CLIP language part, we only use 4 classes here: trees/palms, car,
building and windows. The format of text prompt is ”a photo of classname”. The
visualization is shown in Fig. 1, it indicates that directly using CLIP
features is enough to achieve good localization or segmentation, and also the
prompt engineering, i.e., the choice of text prompt, is also important to
achieve better results. In Fig. 2, we further show that simply adopting the
binary threshold on the Grad-CAM could lead to refined segmentation. Those
findings that CLIP visual features already have localization and semantic
information show the potential of the extensibility to other discriminative
task. Fully investigating such localization ability of CLIP for segmentation
or other tasks is still not widely studied yet in the community.

###  3.2 Text-to-image Diffusion Model

Here we do a detailed analysis for ODISE, which is an open-vocabulary
segmentation method based on Stable Diffusion. In ODISE, the image will be fed
into the diffusion model with adding noise once, and the features from
encoder-decoder in the VQGAN along with the features from the UNet will be
used for the subsequent Mask2Former for mask proposal. Unlike the original
diffusion model achieving image generation through the denoising of multiple
time steps, the UNet feature (with one time step) from the ODISE may have poor
quality regarding the semantic and localization information, as a recent
method [23] hypothesizes that the denoising process is a coarse-to-fine
synthesis with multiple time steps. To verify it, we visualize the cross
attention in different scenarios as shown in Fig. 3. In Fig. 3, we first
deploy the Stable Diffusion for the normal text-to-image generation with the
text prompt ’a horse on the grass’, we visualize the cross attention
corresponding to the token ’horse’ in the last time step, we find these
attentions are basically accurate localizing the object. Then we send the
generated image back to the diffusion model with adding noise once just like
ODISE does, and we also visualize the cross attention of token ’horse’. It
turns out that the resulting attention maps become blurry and less accurate
for localization, compared to the ones during the generation process. This
attention degradation phenomenon may be even more severe if using real image
as in the ODISE. Since the UNet features used by ODISE, which will be used by
Mask2Former for mask proposal, are directly related to cross attention, the
attention degradation may deteriorate the segmentation performance. We also
directly visualize the UNet features by k-means clustering in Fig. 4, it shows
in some case the UNet feature indeed has poor semantic and localization
information, as shown in Fig. 4 (right). The finding indicates the necessity
of denoising process to get high quality features containing better semantic
and localization information.

We also conduct ablation study of ODISE. In ODISE, there are a diffusion model
(with adding noise once) and an implicit caption module, the output of which
will be utilized as textual/conditional embedding and will be combined with
null text embedding via summation. The features from encoder-decoder in VQGAN
inside the diffusion model, as well as the features from UNet will be sent to
Mask2Former for mask proposal. In Tab. 1, we ablate several modules in ODISE,
and it turns out that directly using UNet features with null text embedding
(ODISE w/o IC) already achieves decent performance, and the performance gain
from implicit captioner is relatively limited. Note that not using implicit
captioner means only having null text embedding in UNet (unconditional
embedding), which is not the right usage way of text-to-image diffusion with
conditional and unconditional embeddings, it has not explored the language
related information in Stable Diffusion. And in Tab. 1, ODISE, which utilizes
CLIP, diffusion model and Mask2Former, is still inferior to SAN, which only
uses CLIP and a lightweight decoder network. This indicates the current way
using diffusion model in ODISE is relatively naive, and has further space to
be improved.

##  4 Conclusion

In this paper, we investigate some recent works on using foundation models for
downstream tasks. Features from both discriminative model CLIP and generative
model Stable Diffusion, which are trained with large amount of cross-modality
data pairs, already contain semantic and localization information, and could
be deployed for other discriminative tasks. Although achieving great
performance, the current way using diffusion model for downstream tasks is not
efficient. We hope this report could provide some insights for the future
research.

##  5 Acknowledgement

We thank the GPUs support from Stability AI.

## References

  * [1] Dmitry Baranchuk, Ivan Rubachev, Andrey Voynov, Valentin Khrulkov, and Artem Babenko.  Label-efficient semantic segmentation with diffusion models.  arXiv preprint arXiv:2112.03126, 2021.
  * [2] Kaidi Cao, Maria Brbic, and Jure Leskovec.  Open-world semi-supervised learning.  arXiv preprint arXiv:2102.03526, 2021.
  * [3] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton.  A simple framework for contrastive learning of visual representations.  In International conference on machine learning, pages 1597–1607. PMLR, 2020.
  * [4] Bowen Cheng, Ishan Misra, Alexander G Schwing, Alexander Kirillov, and Rohit Girdhar.  Masked-attention mask transformer for universal image segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1290–1299, 2022.
  * [5] Kevin Clark and Priyank Jaini.  Text-to-image diffusion models are zero-shot classifiers.  arXiv preprint arXiv:2303.15233, 2023.
  * [6] Zheng Ding, Jieke Wang, and Zhuowen Tu.  Open-vocabulary panoptic segmentation with maskclip.  arXiv preprint arXiv:2208.08984, 2022.
  * [7] Rinon Gal, Yuval Alaluf, Yuval Atzmon, Or Patashnik, Amit H Bermano, Gal Chechik, and Daniel Cohen-Or.  An image is worth one word: Personalizing text-to-image generation using textual inversion.  arXiv preprint arXiv:2208.01618, 2022.
  * [8] Rohit Girdhar, Alaaeldin El-Nouby, Zhuang Liu, Mannat Singh, Kalyan Vasudev Alwala, Armand Joulin, and Ishan Misra.  Imagebind: One embedding space to bind them all.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15180–15190, 2023.
  * [9] Jean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre Richemond, Elena Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar, et al.  Bootstrap your own latent-a new approach to self-supervised learning.  Advances in neural information processing systems, 33:21271–21284, 2020.
  * [10] Ishaan Gulrajani and David Lopez-Paz.  In search of lost domain generalization.  arXiv preprint arXiv:2007.01434, 2020.
  * [11] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick.  Momentum contrast for unsupervised visual representation learning.  In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9729–9738, 2020.
  * [12] Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or.  Prompt-to-prompt image editing with cross attention control.  arXiv preprint arXiv:2208.01626, 2022.
  * [13] Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen.  Lora: Low-rank adaptation of large language models.  arXiv preprint arXiv:2106.09685, 2021.
  * [14] Chao Jia, Yinfei Yang, Ye Xia, Yi-Ting Chen, Zarana Parekh, Hieu Pham, Quoc Le, Yun-Hsuan Sung, Zhen Li, and Tom Duerig.  Scaling up visual and vision-language representation learning with noisy text supervision.  In International Conference on Machine Learning, pages 4904–4916. PMLR, 2021.
  * [15] Xuhui Jia, Kai Han, Yukun Zhu, and Bradley Green.  Joint representation learning and novel category discovery on single-and multi-modal data.  In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 610–619, 2021.
  * [16] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al.  Segment anything.  arXiv preprint arXiv:2304.02643, 2023.
  * [17] Alexander C Li, Mihir Prabhudesai, Shivam Duggal, Ellis Brown, and Deepak Pathak.  Your diffusion model is secretly a zero-shot classifier.  arXiv preprint arXiv:2303.16203, 2023.
  * [18] Haoliang Li, Sinno Jialin Pan, Shiqi Wang, and Alex C Kot.  Domain generalization with adversarial feature learning.  In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5400–5409, 2018.
  * [19] Feng Liang, Bichen Wu, Xiaoliang Dai, Kunpeng Li, Yinan Zhao, Hang Zhang, Peizhao Zhang, Peter Vajda, and Diana Marculescu.  Open-vocabulary semantic segmentation with mask-adapted clip.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7061–7070, 2023.
  * [20] Jian Liang, Dapeng Hu, and Jiashi Feng.  Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation.  In International Conference on Machine Learning, pages 6028–6039. PMLR, 2020.
  * [21] Yuqi Lin, Minghao Chen, Wenxiao Wang, Boxi Wu, Ke Li, Binbin Lin, Haifeng Liu, and Xiaofei He.  Clip is also an efficient segmenter: A text-driven approach for weakly supervised semantic segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15305–15314, 2023.
  * [22] Poojan Oza and Vishal M Patel.  C2ae: Class conditioned auto-encoder for open-set recognition.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2307–2316, 2019.
  * [23] Or Patashnik, Daniel Garibi, Idan Azuri, Hadar Averbuch-Elor, and Daniel Cohen-Or.  Localizing object-level shape variations with text-to-image diffusion models.  arXiv preprint arXiv:2303.11306, 2023.
  * [24] Jie Qin, Jie Wu, Pengxiang Yan, Ming Li, Ren Yuxi, Xuefeng Xiao, Yitong Wang, Rui Wang, Shilei Wen, Xin Pan, et al.  Freeseg: Unified, universal and open-vocabulary image segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 19446–19455, 2023.
  * [25] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al.  Learning transferable visual models from natural language supervision.  In International conference on machine learning, pages 8748–8763. PMLR, 2021.
  * [26] Mamshad Nayeem Rizve, Navid Kardan, Salman Khan, Fahad Shahbaz Khan, and Mubarak Shah.  Openldn: Learning to discover novel classes for open-world semi-supervised learning.  In Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXXI, pages 382–401. Springer, 2022.
  * [27] Alexander Robey, George J Pappas, and Hamed Hassani.  Model-based domain generalization.  Advances in Neural Information Processing Systems, 34:20210–20229, 2021.
  * [28] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer.  High-resolution image synthesis with latent diffusion models.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10684–10695, 2022.
  * [29] Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yael Pritch, Michael Rubinstein, and Kfir Aberman.  Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22500–22510, 2023.
  * [30] Kuniaki Saito, Kohei Watanabe, Yoshitaka Ushiku, and Tatsuya Harada.  Maximum classifier discrepancy for unsupervised domain adaptation.  In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3723–3732, 2018.
  * [31] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra.  Grad-cam: Visual explanations from deep networks via gradient-based localization.  In Proceedings of the IEEE international conference on computer vision, pages 618–626, 2017.
  * [32] Sagar Vaze, Kai Han, Andrea Vedaldi, and Andrew Zisserman.  Generalized category discovery.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7492–7501, 2022.
  * [33] Sagar Vaze, Kai Han, Andrea Vedaldi, and Andrew Zisserman.  Open-set recognition: A good closed-set classifier is all you need.  In International Conference on Learning Representations, 2022.
  * [34] Jiarui Xu, Sifei Liu, Arash Vahdat, Wonmin Byeon, Xiaolong Wang, and Shalini De Mello.  Open-vocabulary panoptic segmentation with text-to-image diffusion models.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2955–2966, 2023.
  * [35] Mengde Xu, Zheng Zhang, Fangyun Wei, Han Hu, and Xiang Bai.  Side adapter network for open-vocabulary semantic segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2945–2954, 2023.
  * [36] Shiqi Yang, Yaxing Wang, Joost Van De Weijer, Luis Herranz, and Shangling Jui.  Generalized source-free domain adaptation.  In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8978–8987, 2021.
  * [37] Zhao Yang, Jiaqi Wang, Yansong Tang, Kai Chen, Hengshuang Zhao, and Philip HS Torr.  Lavt: Language-aware vision transformer for referring image segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18155–18165, 2022.
  * [38] Ryota Yoshihashi, Wen Shao, Rei Kawakami, Shaodi You, Makoto Iida, and Takeshi Naemura.  Classification-reconstruction learning for open-set recognition.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4016–4025, 2019.
  * [39] Lvmin Zhang and Maneesh Agrawala.  Adding conditional control to text-to-image diffusion models.  arXiv preprint arXiv:2302.05543, 2023.
  * [40] Wenliang Zhao, Yongming Rao, Zuyan Liu, Benlin Liu, Jie Zhou, and Jiwen Lu.  Unleashing text-to-image diffusion models for visual perception.  arXiv preprint arXiv:2303.02153, 2023.
  * [41] Chong Zhou, Chen Change Loy, and Bo Dai.  Extract free dense labels from clip.  In Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXVIII, pages 696–712. Springer, 2022.
  * [42] Ziqin Zhou, Yinjie Lei, Bowen Zhang, Lingqiao Liu, and Yifan Liu.  Zegclip: Towards adapting clip for zero-shot semantic segmentation.  In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11175–11185, 2023.