Single and double spin asymmetries for deeply virtual Compton scattering measured with CLAS and a longitudinally polarized proton target

3.5 MB·English

by  S. Pisano

Single and double spin asymmetries for deeply virtual Compton scattering measured
with CLAS and a longitudinally polarized proton target
S. Pisano,1,2,∗ A. Biselli,3 S. Niccolai,2 E. Seder,4,5 M. Guidal,2 M. Mirazita,1 K.P. Adhikari,6 D. Adikaram,6
M.J. Amaryan,6 M.D. Anderson,7 S. Anefalos Pereira,1 H. Avakian,8 J. Ball,5 M. Battaglieri,9 V. Batourine,8
I. Bedlinskiy,10 P. Bosted,8,11 B. Briscoe,12 J. Brock,8 W.K. Brooks,13 V.D. Burkert,8 C. Carlin,8 D.S. Carman,8
A. Celentano,9 S. Chandavar,14 G. Charles,2 L. Colaneri,15,16 P.L. Cole,17 N. Compton,14 M. Contalbrigo,18
O. Cortes,17 D.G. Crabb,19 V. Crede,20 A. D’Angelo,15,16 R. De Vita,9 E. De Sanctis,1 A. Deur,8
C. Djalali,21 R. Dupre,2,22 H. Egiyan,8 A. El Alaoui,13,22,23 L. El Fassi,6,† L. Elouadrhiri,8 P. Eugenio,20
G. Fedotov,21,24 S. Fegan,7,9 A. Filippi,25 J.A. Fleming,26 A. Fradi,2 B. Garillon,2 M. Gar¸con,5 Y. Ghandilyan,27
G.P. Gilfoyle,28 K.L. Giovanetti,29 F.X. Girod,8 J.T. Goetz,14 W. Gohn,4,‡ E. Golovatch,24 R.W. Gothe,21
K.A. Griffioen,11 L. Guo,8,30 K. Hafidi,22 C. Hanretty,19,20,§ M. Hattawy,2 K. Hicks,14 M. Holtrop,31
S.M. Hughes,26 Y. Ilieva,21 D.G. Ireland,7 B.S. Ishkhanov,24 D. Jenkins,32 X. Jiang,33 H.S. Jo,2 K. Joo,4
5 S. Joosten,34 C.D. Keith,8 D. Keller,19,14 A. Kim,35,¶ W. Kim,35 F.J. Klein,36 V. Kubarovsky,8 S.E. Kuhn,6
1
P. Lenisa,18 K. Livingston,7 H.Y. Lu,21 M. MacCormick,2 I .J .D. MacGregor,7 M. Mayer,6 B. McKinnon,7
0
D.G. Meekins,8 C.A. Meyer,37 V. Mokeev,8,24 R.A. Montgomery,1 C.I. Moody,22 C. Munoz Camacho,2
2
P. Nadel-Turonski,8,36 M. Osipenko,9 A.I. Ostrovidov,20 K. Park,8,21,∗∗ W. Phelps,30 J.J. Phillips,7 O. Pogorelko,10
n
J.W. Price,38 S. Procureur,5 Y. Prok,6,19 A.J.R. Puckett,4 M. Ripani,9 A. Rizzo,15,16 G. Rosner,7 P. Rossi,8,1
a
J P. Roy,20 F. Sabati´e,5 C. Salgado,39 D. Schott,12,30 R.A. Schumacher,37 I. Skorodumina,21,24 G.D. Smith,26

8 D.I. Sober,36 D. Sokhan,7,26 N. Sparveris,34 S. Stepanyan,8 P. Stoler,40 S. Strauch,21 V. Sytnik,13 Ye Tian,21
2 S. Tkachenko,19,6 M. Turisini,18 M. Ungaro,4,8 E. Voutier,23 N.K. Walford,36 D.P. Watts,26 X. Wei,8

L.B. Weinstein,6 M.H. Wood,41,21 N. Zachariou,21 L. Zana,26,31 J. Zhang,8,6 Z.W. Zhao,6,21,8 and I. Zonta15,16
]
x (The CLAS Collaboration)
e
- 1INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy
p 2Institut de Physique Nucl´eaire Orsay, 91406 Orsay, France
e 3Fairfield University, Fairfield, Connecticut 06824
h
4University of Connecticut, Storrs, Connecticut 06269
[
5CEA, Centre de Saclay, Irfu/Service de Physique Nucl´eaire, 91191 Gif-sur-Yvette, France
1 6Old Dominion University, Norfolk, Virginia 23529
v 7University of Glasgow, Glasgow G12 8QQ, United Kingdom
2 8Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
5 9INFN, Sezione di Genova, 16146 Genova, Italy
0 10Institute of Theoretical and Experimental Physics, Moscow, 117259, Russia
7 11College of William and Mary, Williamsburg, Virginia 23187-8795
0 12The George Washington University, Washington, D.C. 20052
1. 13Universidad T´ecnica Federico Santa Mar´ıa, Casilla 110-V Valpara´ıso, Chile
0 14Ohio University, Athens, Ohio 45701
5 15INFN, Sezione di Roma Tor Vergata, 00133 Roma, Italy
1 16Universita` di Roma Tor Vergata, 00133 Roma, Italy
: 17Idaho State University, Pocatello, Idaho 83209
v
18INFN, Sezione di Ferrara, 44100 Ferrara, Italy
i
X 19University of Virginia, Charlottesville, Virginia 22901
r 20Florida State University, Tallahassee, Florida 32306
a 21University of South Carolina, Columbia, South Carolina 29208
22Argonne National Laboratory, Argonne, Illinois 60439
23LPSC, Universit´e Grenoble-Alps, CNRS/IN2P3, Grenoble, France
24Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia
25INFN, Sezione di Torino, 10125 Torino, Italy
26Edinburgh University, Edinburgh EH9 3JZ, United Kingdom
27Yerevan Physics Institute, 375036 Yerevan, Armenia
28University of Richmond, Richmond, Virginia 23173
29James Madison University, Harrisonburg, Virginia 22807
30Florida International University, Miami, Florida 33199
31University of New Hampshire, Durham, New Hampshire 03824-3568
32Virginia Tech, Blacksburg, Virginia 24061-0435
33Los Alamos National Laboratory, Los Alamos, NM 87545
34Temple University, Philadelphia, Pennsylvania 19122
35Kyungpook National University, Daegu 702-701, Republic of Korea
36Catholic University of America, Washington, D.C. 20064
37Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
2
38California State University, Dominguez Hills, Carson, California 90747
39Norfolk State University, Norfolk, Virginia 23504
40Rensselaer Polytechnic Institute, Troy, New York 12180-3590
41Canisius College, Buffalo, New York 14208
(Dated: January 29, 2015)
Single-beam, single-target, and double-spin asymmetries for hard exclusive photon production on
the proton (cid:126)ep(cid:126) → e(cid:48)p(cid:48)γ are presented. The data were taken at Jefferson Lab using the CLAS
detectorandalongitudinallypolarized14NH target. Thethreeasymmetriesweremeasuredin165
3
4-dimensionalkinematicbins,coveringthewidestkinematicrangeeverexploredsimultaneouslyfor
beamandtarget-polarizationobservablesinthevalencequarkregion. Thekinematicdependencesof
the obtained asymmetries are discussed and compared to the predictions of models of Generalized
Parton Distributions. The measurement of three DVCS spin observables at the same kinematic
pointsallowsaquasi-model-independentextractionoftheimaginarypartsoftheH andH˜ Compton
Form Factors, which give insight into the electric and axial charge distributions of valence quarks
in the proton.
I. GENERALIZED PARTON DISTRIBUTIONS Q2 of the photon exchanged with the nucleon by the ini-
AND DEEPLY VIRTUAL COMPTON tial lepton, defined as
SCATTERING
Q2 =−(k−k(cid:48))2, (1)
It is well known that the fundamental particles that
where k and k(cid:48) are the four momenta of, respectively,
form hadronic matter are the quarks and the gluons,
the incoming (e) and scattered electron (e(cid:48)), must be
whose interactions are described by the Lagrangian of
sufficiently large for the reaction to happen at the quark
Quantum Chromo-Dynamics (QCD). However, exact
level. Figure 1 illustrates the leading-twist [8] process
QCD-based calculations cannot yet be performed to ex-
for DVCS, also called the “handbag mechanism”, on a
plain the properties of hadrons in terms of their con-
proton target. The virtual photon interacts with one of
stituents. One has to resort to phenomenological func-
the quarks of the proton, which propagates radiating a
tionstointerpretexperimentalmeasurementsinorderto
real photon.
understand how QCD works at the “long distances” at
play when partons are confined in nucleons. Typical ex- t=(p−p(cid:48))2 (2)
amplesofsuchfunctionsincludeformfactorsandparton
distributions. GeneralizedPartonDistributions(GPDs), is the squared four-momentum transfer between the ini-
which unify and extend the information carried by both tial(p)andfinalproton(p(cid:48)). x+ξ andx−ξ arethelon-
form factors and parton distributions, are nowadays the gitudinal momentum fractions of the quark before and
object of an intense effort of research, for a more com- after radiating the real photon, respectively. ξ is defined
plete understanding of the structure of the nucleon. The as [9]:
GPDs describe the correlations between the longitudinal
momentumandthetransversepositionofthepartonsin- 1+ t
side the nucleon, they give access to the contribution of ξ =xB2−x +Qx2 t , (3)
theorbitalmomentumofthequarkstothenucleonspin, B BQ2
and they are sensitive to the correlated qq¯components.
which at leading twist (−t<<Q2) becomes
The original articles, general reviews on GPDs and de-
tails on the formalism can be found in Refs. [1–7]. x
ξ (cid:39) B , (4)
The GPDs are universal nucleon-structure functions, 2−x
B
which can be accessed experimentally via the exclu-
sive leptoproduction of a photon (DVCS, deeply virtual where xB is the Bjorken scaling variable
Compton scattering) or of a meson from the nucleon at
Q2
high momentum transfer. More precisely, the virtuality x = , (5)
B 2Mν
M is the proton mass, and
∗ contactauthor: [email protected]
† Current address:Mississippi State University, Mississippi State, ν =Ee−Ee(cid:48). (6)
MS39762
‡ Current address:University of Kentucky, Lexington, Kentucky IntheBjorkenlimit,definedbyhighQ2,highν andfixed
40506 x , the DVCS process can be factorized into a hard-
B
§ Currentaddress:ThomasJeffersonNationalAcceleratorFacility, scattering part (γ∗q → γq(cid:48)) that can be treated pertur-
NewportNews,Virginia23606
batively, and a soft nucleon-structure part, described by
¶ Current address:University of Connecticut, Storrs, Connecticut
the GPDs. At leading-order QCD and at leading twist,
06269
∗∗ Current address:Old Dominion University, Norfolk, Virginia consideringonlyquark-helicityconservingquantitiesand
23529 the quark sector, the DVCS process is described by four
3
data at a given (ξ,t) point depends on the observable
involved. When measuring observables sensitive to the
real part of the DVCS amplitude, such as double-spin
asymmetries, beam-charge asymmetries or unpolarized
crosssections,therealpartoftheCFF,(cid:60)eF,isaccessed.
When measuring observables sensitive to the imaginary
part of the DVCS amplitude, such as single-spin asym-
metries or cross-section differences, the imaginary part
of the CFF, (cid:61)mF, can be obtained. However, knowing
the CFFs does not define the GPDs uniquely. A model
input is necessary to deconvolute their x dependence.
The DVCS process is accompanied by the Bethe-
Heitler (BH) process, in which the final-state photon is
FIG. 1. (Color online) The handbag diagram for the DVCS radiated by the incoming or scattered electron and not
process on the proton ep→e(cid:48)p(cid:48)γ(cid:48). by the nucleon itself. The BH process, which is not sen-
sitive to the GPDs, is experimentally indistinguishable
from DVCS and interferes with it. However, considering
that the nucleon form factors are well known at small t,
the BH process is precisely calculable.
GPDs,H,H˜,E,E˜,whichaccountforthepossiblecombi-
It is clearly a non-trivial task to measure the GPDs.
nationsofrelativeorientationsofnucleonspinandquark
Itcallsforalong-termexperimentalprogramcomprising
helicity between the initial and final state.
the measurement of different observables. Such a dedi-
The GPDs depend upon the variables x, ξ and t. The
cated experimental program, concentrating on a proton
Fouriertransform,atξ =0,ofthetdependenceofaGPD
target, has started worldwide in the past few years. Jef-
provides the spatial distribution in the transverse plane
ferson Lab (JLab) has provided the first measurement,
for partons having a longitudinal momentum fraction x
in the valence region, of beam-polarized and unpolar-
[10].
ized DVCS cross sections at Hall A [11], providing a
Model-independent sum rules link the first moment in
Q2-scaling test that supports the validity of the leading-
x of the GPDs to the elastic form factors (FFs) [2]:
order, leading-twist handbag mechanism starting at val-
(cid:90) 1 (cid:90) 1 ues of Q2 of 1-2 (GeV/c)2. Hall B provided pioneering
dxH(x,ξ,t)=F1(t); dxE(x,ξ,t)=F2(t) measurements of beam [12] and target [13] spin asym-
−1 −1 metries with the CLAS detector [14], and afterwards ob-
(cid:90) 1 (cid:90) 1
tained beam-spin asymmetries (BSA) over a large kine-
dxH(cid:101)(x,ξ,t)=GA(t); dxE(cid:101)(x,ξ,t)=GP(t),(7) matic range and with high statistics [15]. Beam-charge
−1 −1
asymmetries, longitudinally and transversely polarized
where F (t) and F (t) are the Dirac and Pauli FFs, and
1 2 target-spin asymmetries (TSAs), as well as double-spin
G (t) and G (t) are the axial and pseudoscalar FFs.
A P asymmetries (DSAs), have also been measured by the
Among the three variables x, ξ and t, which appear in
HERMES Collaboration [16].
the DVCS formalism, only two, ξ and t, are experimen-
Thispaperisfocusedontheextractionoflongitudinal
tally accessible, since x appears only in the quark loop
TSAs, BSAs and DSAs for proton DVCS over a wide
and is integrated over. Indeed, the DVCS amplitude is
phase space using dedicated data taken at Jefferson Lab
proportional to sums of integrals over x of the form:
with the CLAS detector.
(cid:90) 1 (cid:20) 1 1 (cid:21)
dxF(∓x,ξ,t) ± (8)
x−ξ+i(cid:15) x+ξ−i(cid:15)
−1 II. DVCS ON A LONGITUDINALLY
POLARIZED PROTON TARGET
where F represents a generic GPD and the top and bot-
tom signs apply, respectively, to the quark-helicity inde-
pendent,orunpolarized,GPDs(H,E)andtothequark- An analysis of DVCS observables, including the asym-
metries of interest in this work, in terms of Fourier mo-
helicity dependent, or polarized, GPDs (H(cid:101),E(cid:101)). Each of
ments with respect to the azimuthal angle, was carried
these4integrals,whicharecalledComptonFormFactors
out by Belitsky et al. [9], up to a twist-3 approxima-
(CFFs),canbedecomposedintotheirrealandimaginary
tion. These asymmetries allow one to extract separate
parts, as
componentsoftheangulardependenceoftheep→e(cid:48)p(cid:48)γ
(cid:90) 1 (cid:20) 1 1 (cid:21) crosssection,thatarerelatedtotheComptonFormFac-
(cid:60)eF =P dx ∓ F(x,ξ,t) (9)
tors, defined in Eq. (9). The five-fold cross section for
x−ξ x+ξ
−1
exclusive real photon electroproduction [9]
(cid:61)mF(ξ,t)=−π[F(ξ,ξ,t)∓F(−ξ,ξ,t)], (10)
where P is Cauchy’s principal value integral. The in- dσ = α3x√By (cid:12)(cid:12)(cid:12)T (cid:12)(cid:12)(cid:12)2 (11)
formation that can be extracted from the experimental dxBdydtdφdϕe 16π2Q2 1+(cid:15)2 (cid:12)e3(cid:12)
4
II.1. Target-spin asymmetry
g
f The use of a longitudinally polarized (LP) target al-
e’ lows the extraction of the target-spin asymmetry AUL,
where the first letter in the subscript refers to the beam
polarization(“Unpolarized”,inthiscase)andthesecond
p
e leptonic plane tothetargetpolarization(“Longitudinallypolarized”,in
p’ this case), and which is given at twist-2 by:
hadronic
plane sI sinφ
A (φ)∼ 1,LP ,
UL cBH +(cBH +cI +...)cosφ+...
0,unp 1,unp 1,unp
(17)
FIG. 2. Scheme to illustrate the definition of the angle φ,
where the ellipses in the denominator represent smaller,
formed by the leptonic and hadronic planes.
higher-twistterms,andtheunpsubscriptstandsfor“un-
polarized”. The sinφ coefficient s , originating from
1,LP
the DVCS/BH interference term, at leading twist is pro-
dependsonxB,t,theleptonenergyfractiony =p·q1/p· portional to a linear combination of the imaginary parts
k, with q1 = k −k(cid:48), (cid:15) = 2xBMQ, and, in general, two of the four CFFs (Eq. (9)),
hazeirmeudtohanloatndgelepsenφdanond ϕϕee., tThheeaozbimseurtvhaablleasnogfleinotfertehset s1,LP ∝(cid:61)m[F1H(cid:101)+ξ(F1+F2)(H+ x2BE)+
scattered electron in the laboratory frame. The angle φ x t
is formed by the leptonic and hadronic planes, as shown −ξ( 2BF1+ 4M2F2)E(cid:101)] . (18)
inFig.2. Thechargeoftheelectronisdenotedwitheand
Due to the relative values of the proton form factors F
α represents the fine-structure constant. The amplitude 1
and F , and given the typical JLab kinematics, the co-
T is the coherent sum of the DVCS and Bethe-Heitler 2
efficients in Eq. (18) enhance the contribution to A
amplitudes (T , T ): UL
DVCS BH
comingfrom(cid:61)mH(cid:101) overtheonesfromotherCFFs. How-
T2 =|T |2+|T |2+I, (12) ever, given that (cid:61)mH is expected to be about twice as
BH DVCS
with the interference term defined as big as (cid:61)mH(cid:101), AUL will also be sensitive to (cid:61)mH. In
thekinematicalrangeofthedatapresentedhere,higher-
I =T T∗ +T∗ T . (13) twist effects would appear in Eq. (17) as additional φ-
DVCS BH DVCS BH
dependent terms, the dominant of which is a sin2φ term
The azimuthal angular dependence of each of the three
in the numerator [9].
terms in Eq. (12) is given by [9]:
e6
|TBH|2 = x2y2(1+(cid:15)2)2tP (φ)P (φ)[cB0H+ II.2. Beam-spin asymmetry
B 1 2
2
+ (cid:88)cBH cosnφ+sBH sinφ], (14) Theexpressionattwist-twoofthebeam-spinasymme-
n 1 try is
n=1
sI sinφ
|T |2 = e6 {cDVCS+(cid:88)2 [cDVCScosnφ+ ALU(φ)∼ cB0,Hunp+(cB1,Hun1p,u+npcI1,unp+...)cosφ... ,(19)
DVCS y2Q2 0 n
n=1 where
+sDVCSsinnφ]}, (15) t
n sI1,unp ∝(cid:61)m[F1H+ξ(F1+F2)H(cid:101)− 4M2F2E]. (20)
I = e6 {cI +(cid:88)3 [cIcosnφ+ Thus, the beam-spin asymmetry for DVCS on a proton
x y3tP (φ)P (φ) 0 n target is particularly sensitive to the imaginary part of
B 1 2
n=1
the CFF of the unpolarized GPD H. As for the TSA,
+sIsinnφ]}, (16)
n moretermsmustbeaddedifonegoesbeyondtheleading-
whereP andP areintermediateleptonpropagators(for twist approximation, the larger of which is a sin2φ term
1 2
moredetailsanddefinitions, see[9]). AmongtheFourier in the numerator. As mentioned in Section I, the slope
coefficients cP, sP appearing in the previous expansions, in t of the GPDs is related via a Fourier transform to
i i
the ones appearing in |T |2 (P = BH) depend on the the transverse position of the struck parton. Therefore,
BH
well-known electromagnetic FFs, while the ones appear- ameasurementof(cid:61)mH(cid:101) and(cid:61)mHprovides,respectively,
ing in |T |2 (P = DVCS) and I (P = I) depend on informationontheaxialandelectricchargedistributions
DVCS
the Compton Form Factors, the latter linearly. In the in the nucleon as a function of x (see Eq. (7)). A mea-
B
next sections, the sensitivity to the various CFFs of the surement of both the TSA and BSA at the same kine-
DVCS spin observables presented in this paper will be matics is needed to truly distinguish between the two
outlined. contributions.
5
II.3. Double-spin asymmetry segments were individually instrumented to form six in-
dependent magnetic spectrometers with a common tar-
get, trigger, and data-acquisition system. An additional
Theuseofapolarizedelectronbeamalongwithalon-
detector, the Inner Calorimeter, constructed for a pre-
gitudinally polarized target allows also the determina-
vious DVCS-dedicated experiment [15] to complete the
tionofthedouble-spinasymmetryA . UnlikeA ,the
LL UL
photon acceptance at low polar angles (from 4o to 15o),
Bethe-Heitler process alone can generate a double-spin
was placed at the center of CLAS. Figure 3 shows the
asymmetry. At twist-2 level, this observable takes the
whole setup, including the polarized target, CLAS and
form:
the IC. A totally absorbing Faraday cup (FC), down-
stream of CLAS, was used to determine the integrated
cBH +cI +(cBH +cI )cosφ beam charge passing through the target.
A (φ)∼ 0,LP 0,LP 1,LP 1,LP , (21)
LL cBH +(cBH +cI +...)cosφ... Thedatapresentedherecomefromthefirsttwoofthe
0,unp 1,unp 1,unp
threepartsinwhichtheexperimentwasdivided, andfor
with which a 14NH3 target was used. The main differences
between these two parts (referred to as A and B) were
x
cI0,LP,cI1,LP ∝(cid:60)e[F1H(cid:101)+ξ(F1+F2)(H+ 2BE)+ the target position with respect to the center of CLAS
(z = −57.95 cm for part A and z = −67.97 cm for part
x t
−ξ( 2BF1+ 4M2F2)E(cid:101)], (22) B)andtheelectron-beamenergy(E =5.886±0.005GeV
for part A and E =5.952±0.005 GeV for part B). The
where terms depending on powers of t were neglected. beamenergyvalueswereobtainedfromelastic-scattering
Q2 analysis on these data, using the 14NH target.
In this expression, the interference terms, related to the 3
GPDs, are expected to be smaller than the known BH The beam was rastered over the target in a spiral mo-
terms [9]. Moreover, both the constant and the cosφ- tion in order to assure a homogeneous depolarization
dependenttermscontaincontributionsfrombothBHand over the whole volume of the target. The beam po-
the DVCS/BH interference. Nonetheless, given the fast larization was frequently monitored in Møller runs, via
variation of BH depending on the kinematics, it is im- the measurement of the asymmetry of elastic electron-
portant to sample A over a wide phase space to find electron scattering. The target polarization was con-
LL
possible regions of sensitivity to (cid:60)eH and (cid:60)eH(cid:101), which tinuously monitored by a Nuclear Magnetic Resonance
dominate in Eq. (22). (NMR) system. Runs on a carbon target were taken
periodically throughout the duration of the experiment
for unpolarized-background studies. The selection of the
data to be analyzed was done by monitoring the stabil-
III. THE EXPERIMENT
ityovertimeofFaraday-cupnormalizedyieldspersector.
Fortheresultspresentedhere,runstakenwiththe14NH
The data were taken in Hall B at Jefferson Lab from 3
and carbon targets from parts A and B were used. The
February to September 2009, for a total of 129 days. A
two parts were analyzed separately and the final results
continuous polarized electron beam was delivered by the
were found by combining the results from the two parts,
CEBAF accelerator onto a solid ammonia target, polar-
as will be described in Section V.9.
ized along the beam direction. Frozen beads of param-
agnetically doped 14NH , kept at temperatures of about
3
1K and in a 5T magnetic field, were dynamically po-
larized by microwave irradiation [17]. The target was IV. DEFINITIONS OF THE ASYMMETRIES
1.45 cm long and 1.5 cm in diameter. The target system
included a 4He evaporation refrigerator and a supercon-
This paper reports on the extraction of three kinds of
ducting split-coil magnet. The magnet, which provided
asymmetries, the experimental definitions of which are
a uniform polarizing field (∆B/B = 10−4) and at the
given here. In all of the formulae below, the first sign in
same time focused the low-energy Møller electrons to-
the superscript on the number of normalized DVCS/BH
ward the beam line, was inserted in the center of the
events N is the beam helicity (b) and the second sign
CLAS detector [14]. CLAS was a spectrometer, based
is the target polarization (t). N is obtained from epγ
on a toroidal magnetic field, providing a wide accep-
events(N ),normalizedbythecorrespondingFaraday-
tance. The CLAS magnetic field was generated by six epγ
cupcharge(FCbt)aftersubtractionoftheπ0background
superconducting coils arranged around the beamline to
as follows:
produce a field pointing primarily in the azimuthal di-
rection. The particle detection system consisted of drift
Nbt
chambers(DC)todeterminethetrajectoriesandthemo- Nbt =(1−Bbt)· epγ, (23)
menta of charged particles curved by the magnetic field, π0 FCbt
gas Cˇerenkov counters (CC) for electron identification,
scintillation counters for measuring time-of-flight (TOF) where Bπ0 is the relative π0 contamination, outlined
and electromagnetic calorimeters (EC) to detect shower- in Section V.7.
ing particles (electrons and photons) and neutrons. The The beam-spin asymmetry is calculated as:
6
Electromagnetic
Calorimeters
Inner
Calorimeter
Polarized Target
Beam
Pipe
Beam Position
Monitor
Region 1, 2, and 3
Drift Chambers
Beam Direction
Cerenkov
Counters
TOF Scintillators
0 1 2 3 4
METERS
FIG.3. Drawingof theexperimentalsetup, includingtheCLASdetectorwithitscomponents(DC,EC,CC,TOF),theInner
Calorimeter and the polarized target.
The double (beam-target) spin asymmetry is obtained
as:
P−(N++−N−+)+P+(N+−−N−−)
A = t t ,
LU P (P−(N+++N−+)+P+(N+−+N−−))
b t t
(24)
where P is the polarization of the beam and P+(−) are
b t
the values of the polarization of the target for its two A =Alab+c , (27)
polarities. LL LL ALT
The target-spin asymmetry is computed as:
A =Alab+c , (25) where
UL UL AUT
where
N+++N−+−N+−−N−− N+++N−−−N+−−N−+
Alab = . Alab =
UL D (P−(N+++N−+)+P+(N+−+N−−)) LL P ·D (P−(N+++N−+)+P+(N+−+N−−))
f t t b f t t
(26) (28)
D is the dilution factor to account for the contribution and c is the analog of c for the double-spin asym-
f ALT AUT
of the unpolarized background (Section V.5) and c metry (Section V.10).
AUT
represents a correction applied to define the target-spin In thefollowing, thesteps leading to theextraction from
asymmetry with respect to the virtual-photon direction the data of all the terms composing these asymmetries
(Section V.10). will be presented.
7
V. DATA ANALYSIS ) 0.5 negative particles
c
V.1. Particle identification p ( 104
E / 0.45
The final state was selected requiring the detection of 0.4 103
exactly one electron and one proton, and at least one
0.35
photon.
The electrons were selected among all the negative 0.3 102
tracks with momenta above 0.8 GeV/c, but requiring
0.25
that their energy deposited in the inner layers of the EC 10
[18] be greater than 0.06 GeV, in order to reject nega- 0.2
tive pions, and that their hits in the CC and in the SC
0.15
1
be matched in time. Fiducial cuts were also applied to
electrons
eliminate the events at the edges of the EC (where the 0.5
104
energyofaparticlecannotbecorrectlyreconstructedbe-
0.45
cause a large part of the induced electromagnetic shower
is lost), and to remove the “shadow” of the IC, which 0.4 103
limits the CLAS acceptance for charged particles. The 0.35
effect of these cuts on the distribution of the total en- 0.3 102
ergy deposited in the EC divided by the momentum is
0.25
shown as a function of the momentum in Fig. 4. The 10
comparison of the top and middle plots of Fig. 5 shows 0.2
theeffectofthesesamecutsonthenumberofCCphoto- 0.15
1
electrons. Most of the events in the single-photoelectron 1 1.5 2 2.5 3 3.5 4 4.5 5
p (GeV/c)
peak, which come from either pions or electronic noise
in the PMTs, are removed by our particle identification
FIG. 4. (Color online) Total energy deposited in the EC (in-
(PID) cuts for electrons. The rest of the background is
ner+outer layers), E, divided by the particle momentum p
eliminated by the exclusivity cuts applied afterwards as
as a function of p for all the negative tracks. Top: nega-
explained in Section V.3 (Fig. 5, bottom).
tive charged particles, before cuts. Bottom: after minimum-
Theprotonswereselectedfromthecorrelationbetween
momentum, EC , fiducial and timing cuts.
in
their velocity, deduced from the time-of-flight measure-
ment using the SC, and the proton momentum as mea-
suredbytheDCs(Fig.6). Fiducialcutsonθ andφwere
also applied in order to remove the shadow of the IC. • optimizationoftheDVCSandepπ0exclusivitycuts
For the photons, two different sets of cuts were (Sections V.3 and V.7, respectively);
adopted, dependingonwhetherthephotonwasdetected
• evaluation of the epπ0 contamination in the epγ
in the IC or in the EC. For the IC case, a low-energy
event sample (Section V.7).
thresholdof0.25GeVandacutonθversusE toremove
γ
the background coming from Møller electrons (Fig. 7) The two sets of generated events, DVCS/BH and epπ0
were applied, as well as fiducial cuts on x and y, to re-
(Section V.2.1 and V.2.2), were fed to the CLAS
move the outer and inner edges of the detector, where
GEANT3-based simulation package (GSIM) to simulate
clusters could not be fully reconstructed. For the EC
theresponseoftheCLASdetector. TheoutputofGSIM
case, all neutrals passing a low-energy threshold of 0.25
wasthenfedtoapost-processingcode(GPP)thatsimu-
GeV and having β > 0.92 (Fig. 8) to select the in-time
latesdeadorinefficientDCwiresandsmearstheDCand
photons were retained. Fiducial cuts as for the electrons
TOF resolutions to more closely agree with the experi-
were also adopted to remove the edges of the detector
ment. TheoutputofGPPwasfinallyfedtotheCLASre-
and IC-frame cuts were applied to remove the shadow of
construction package, and reduced ntuples and root files
the IC over the EC.
were obtained from the reconstructed files in the same
way as was done in the data processing.
V.2. Monte-Carlo simulations
V.2.1. DVCS/BH simulation
Monte-Carlo simulations were used in this analysis for
the three following tasks:
A DVCS/BH event-generator code, which produced
• determination of angular and momentum correc- epγ events according to the formalism of Belitsky et al.
tions for electrons and protons to compensate for [9], was used for the Monte-Carlo simulation. Figure
multiple scattering and energy losses in the target 9 shows a comparison of the distributions of the rele-
and detector materials, as well as for imperfections vant kinematic variables for the data (black lines) and
in the trajectory reconstruction; the Monte-Carlo simulation (shaded areas). Here, PID
8
×10
-6unts x10 3305 θ (deg)b 111231 110045
o a 10
C 25 L
9 103
20 8
15 7 102
6
10 5 10
5 4
×10 3 1 2 3 4 5 6 1
-30 2.5 Energy (GeV)
1
x
nts 2 FIG. 7. (Color online) Polar angle θ as a function of the
u reconstructedenergyforIChits,showingthecutonthemin-
o
C imum energy at 0.25 GeV, as well as the “triangular” cut to
1.5
remove the low-energy/low-θ accidental background, applied
to select photons.
1
0.5 1.2
β
1.1 104
×10
3 1
-0 1.6
1 0.9 103
x
s 1.4 0.8
nt
ou 1.2 0.7 102
C
1 0.6
0.5
0.8 10
0.4
0.6
0.3
1
0.4 0.5 1 1.5 2 2.5 3
Energy (GeV)
0.2
0 FIG.8. (Coloronline)Distributionofβvsenergyforneutrals
50 100 150 200 250
measured by time-of-flight with EC. The events for which
N x10
phe β >0.92 (black line) were retained as photon candidates.
FIG. 5. Number of CC photoelectrons (times 10) for all neg-
ativetracks(top),afterapplyingallPIDandfiducialcutsfor
electrons (middle), and after epγ exclusivity cuts. and epγ exclusivity cuts, which will be described in Sec-
tion V.3, were included for both the data and the Monte
Carlo. The agreement between data and simulation is
quite good, especially given the purposes of the simula-
1.2
β tions in these analyses: they are not used for absolute
acceptance corrections, but only to help in the deter-
1 104
mination of cut widths and for background subtraction.
Slight differences between data and MC, especially visi-
0.8 103
ble in the high-t and central-φ region, are coming from
events in the EC topology. This is probably due to the
0.6 102
fact that the data, unlike the MC, are not only pure
epγ events, butarecontaminatedbyexclusiveπ0 events.
0.4
10 Thefactthattheepπ0 contaminationislargerintheEC
topology,aswillbereiteratedinSectionV.3,canexplain
0.2
0.5 1 1.5 2 2.5 3 1 the data/MC discrepancies.
p (GeV/c)
FIG. 6. (Color online) β as a function of p for positively V.2.2. Exclusive π0 simulation
charged particles. The black lines represent the cut applied
to select protons.
Exclusive epπ0 events were generated using a code for
mesonelectroproductionthatincludedaparametrization
9
s1600 s s s 450
nt nt7000 nt nt
u1400 u u 500 u 400
Co1200 Co6000 Co Co 350
5000 400 300
1000
800 4000 300 250
200
600 3000 200 150
400 2000 100
100
200 1000 50
0 0 0 0
1 2 3 4 5 6 0 1 2 3 4 1 2 3 4 5 6 0 0.5 1 1.5 2
Q2 (GeV2/c2) -t (GeV2/c2) Q2 (GeV2/c2) -t (GeV2/c2)
nts2500 nts1000 nts nts
u u u 700 u 250
o o o o
C2000 C 800 C 600 C
200
500
1500 600
400 150
1000 400 300 100
200
500 200 50
100
0 0 0 0
0.2 0.4 0.6 0 100 200 300 0.2 0.4 0.6 0 100 200 300
x φ (deg) x φ (deg)
B B
FIG.9. DVCSchannel. Comparisonofdata(blacklines)and FIG. 10. Exclusive π0 channel. Comparison of data (black
Monte-Carlo simulation (shaded areas). From the top left, lines) and Monte-Carlo simulation (shaded areas). Starting
Q2,−t,x andφareplotted. Thehistogramsarenormalized from the top left, Q2, −t, x and φ are plotted. The his-
B B
to each other via the ratio of their integrals. tograms are normalized to each other via the ratio of their
integrals.
of the epπ0 differential cross sections that have recently
beenmeasuredbyCLAS[19]. Figure10showsacompar- and proton together with ep→e(cid:48)p(cid:48)X kinematics;
ison of the distributions of the relevant kinematic vari-
• ∆φ, the difference between two ways to compute
ables for the data (black) and the Monte-Carlo simula-
the angle φ between the leptonic and the hadronic
tion(shadedareas). Here,PIDandepπ0-exclusivitycuts,
plane. The two ways concern the definition of the
which will be described in Section V.7, were included for
normalvectortothehadronicplane: oneisviathe
both the data and the Monte Carlo. The agreement be-
crossproductofthemomentumvectorsofthepro-
tween data and simulation is quite good.
tonandtherealphoton,andtheotheroneisviathe
crossproductofthemomentumvectorsofthepro-
tonandthevirtualphoton. Fortheepγ finalstate,
V.3. DVCS channel selection
∆φ should be distributed as a gaussian centered at
zero, with width determined by the experimental
After selecting events with exactly one electron and resolution;
one proton, and at least one photon, and having ap-
plied the momentum corrections, further cuts need to be • pperp, the transverse component of the missing
applied to ensure the exclusivity of the epγ final state. momentum of the reaction ep → e(cid:48)p(cid:48)γX, given
(cid:112)
Two kinds of backgrounds need to be minimized: the by pperp = px(X)2+py(X)2, in the laboratory
nuclear background coming from scattering off the ni- frame.
trogen of the 14NH target, and the background coming
3 The definition of the exclusivity cuts is quite a delicate
fromotherchannelscontaininganelectron,aprotonand
step in the DVCS analysis. It is important that the cuts
at least one photon in the final state. Having measured
are determined in a consistent way for the data and for
the four-momenta of the three final-state particles, one
the Monte-Carlo simulation, because the latter will be
can construct several observables, hereafter referred to
used to evaluate the π0 background contamination. In
as “exclusivity variables”, on which cuts can be applied
this analysis it was chosen to define each exclusivity cut
to select the epγ channel. Here, the following quantities
byfittingthecorrespondingvariablewithagaussianand
were studied:
cutting at ±3σ around the fitted mean. This procedure
• the squared missing mass of the ep system, was done separately for the data and for the simulation.
MM2(ep); This way, the same fraction of events was kept, for both
data and simulation. The exclusivity variables to be fit-
• the angle θ between the measured photon and ted were plotted after applying preliminary cuts that in-
γX
the calculated photon, using the detected electron cluded:
10
• Kinematic cuts to be above the region of the nu- Bin xB bin θe bin (cid:104)xB(cid:105) (cid:104)Q2(cid:105) ((GeV/c)2)
cleon resonances and to approach the regime of 1 0.1<xB <0.2 15o <θe <48o 0.179 1.52
applicability of the leading-twist GPD formalism: 2 0.2<xB <0.3 15o <θe <34o 0.255 1.97
Q2 > 1 (GeV/c)2, −t < Q2, and W > 2 GeV/c2; 3 0.2<xB <0.3 34o <θe <48o 0.255 2.41
(where W =(cid:112)M2+2Mν−Q2) 45 0.3x<x>B0<.40.4 1155oo <<θθe <<4455oo 00..344553 23..6301
B e
TABLE I. Definition of the bins in x and θ (Q2), and av-
B e
• Eγ >1 GeV, since the real photons of interest are erage kinematics for xB and Q2 ((GeV/c)2) for each bin.
expected to have high energy;
• 3σ cut around the mean of MM2(ep) to eliminate V.4. Four-dimensional binning and central
kinematics
from the experimental data the background from
channels other than epγ or epπ0 (visible in the top
leftplotofFigs.11and12,wherepeaksfromη and
The DVCS reaction can be described by four indepen-
ω/ρ are evident).
dent kinematic variables. The typical variables used to
interpret the results in terms of Generalized Parton Dis-
tributions are Q2, x , −t and φ. In accordance with the
In order to eliminate broadening on the widths of the B
choicemadeinpreviousDVCSanalyses[15],thebinning
peaks due to events from electron scattering on the ni-
of the data in the Q2-x plane was done making 5 slices
trogen, the fits to the exclusivity variables were done on B
inthepolarangleθ oftheelectronandinx . Thelimits
the spectra obtained after subtracting carbon data from e B
of the slices are given in Table I, as well as the bin aver-
the 14NH data. The two datasets were normalized to
3 agesforQ2 andx ,definedastheweightedaverageover
eachotherviatheratiooftheirFaraday-cupcountsmul- B
the distribution of events in each bin. The size of the
tiplied by a constant that accounts for different densities
bins was optimized to have comparable statistics. The
of materials for the two target types (see Section V.5).
top plot of Fig. 13 shows the chosen grid in the Q2-x
B
The method to define the cuts described above was plane. Tenequallyspacedbinsinφand4binsin−twere
adopted for the topology where the photon was detected adopted. The bin limits and data-averaged bin centers
intheIC,sincethecomparisonwithMonteCarloshowed are summarized in Table II. The bottom plot of Fig. 13
thatthesedataarestronglydominatedbytheDVCS/BH shows the binning in the t-x plane.
B
channel. Figure11shows,fortheICtopology,theeffects
of the exclusivity cuts, which appear successful both in
extracting quite a clean epγ final state (shaded areas) Bin −t range (GeV/c)2 (cid:104)−t(cid:105) (GeV/c)2
and in minimizing the background originating from the 1 0.08<−t<0.18 0.137
nitrogen part of the target (black areas). 2 0.18<−t<0.3 0.234
3 0.3<−t<0.7 0.467
A different strategy was found to be necessary for the
4 0.7<−t<2.0 1.175
EC case, which displayed, before cuts, a larger contri-
bution from epπ0 events. The peaks in the exclusivity
TABLEII.Definitionofthebinsin−tandaveragekinematics
variables for the data in this topology are very broad,
for each bin.
whenvisible,andnotnecessarilyproducedbyDVCS/BH
candidates. In the first plot of Fig. 12, for example, the
distributionofthesquaredmissingmassoftheepsystem
Thecentralkinematicsinthisanalysisweredefinedas
is shown for the EC case. As is clearly visible, the peak
theaveragevaluefromthedataofeachofthe4kinematic
ofthedistributionisnotcenteredatzerobutaroundthe
variablesforeachbin. Infact,atfirstordertheuncertain-
squared π0 mass, indicating a significant contamination
tiesonanasymmetryinducedbytakingbinsoffinitesize
fromtheexclusiveπ0 eventsthatwillbesubtractedlater
areminimizedwhenthecentralkinematicsarechosento
through the procedure described in Section V.7.
be the weighted average over the distribution of events
Thus it was decided, for the EC topology, not to fit inthatbin. Theproceduretocomputesecond-orderbin-
the distributions of the exclusivity variables to extract centering corrections is reported in Section V.11. The
cut means and widths. Instead it was chosen to fit only grid of bins was applied to both parts A and B of the
thepeaksoftheDVCS/BHMonte-Carlosimulations. To experiment. In order to establish whether the asymme-
correct for the discrepancies in resolutions between data tries obtained from the two sets of data could eventually
andsimulation,thewidthsofthevariousexclusivityvari- be combined, the central values of the various bins into
ables obtained from the fits were then multiplied by ap- which the available phase space was divided were com-
propriate scaling factors. These factors were obtained puted, and compared for the two parts. For each bin in
from the comparisons of data/MC for the epπ0 channel Q2 (θ )-x and −t, the central kinematics for parts A
e B
in the EC-EC topology. The cuts and their effects are and B were found compatible well within their standard
shown in Fig. 12. deviations.