A precision measurement of the $p$($e,e^\prime p\,$)$\pi^0$ reaction at threshold

0.27 MB·English

by  K. Chirapatpimol

A precision measurement of the p(e,e′p)π0 reaction near threshold
K. Chirapatpimol,1,2 M.H. Shabestari,1,3 R.A. Lindgren,1 L.C. Smith,1 J.R.M. Annand,4 D.W. Higinbotham,5
B. Moffit,5 V. Nelyubin,1 B.E. Norum,1 K. Allada,6 K. Aniol,7 K. Ardashev,1 D.S. Armstrong,8 R.A. Arndt‡,9
F. Benmokhtar,10 A.M. Bernstein,6 W. Bertozzi,6 W.J. Briscoe,9 L. Bimbot,11 A. Camsonne,5 J.-P. Chen,5
S. Choi,12 E. Chudakov,5 E. Cisbani,13 F. Cusanno,13 M.M. Dalton,5 C. Dutta,14 K. Egiyan‡,15
C. Ferna`ndez-Ram`ırez,5 R. Feuerbach,5 K.G. Fissum,16 S. Frullani,13 F. Garibaldi,13 O. Gayou,6 R. Gilman,17
S. Gilad,6 J. Goity,18 J. Gomez,5 B. Hahn,8 D. Hamilton,4 J.-O. Hansen,5 J. Huang,6 R. Igarashi,19 D. Ireland,4
C.W. de Jager,5,1 X. Jin,1 X. Jiang,17 T. Jinasundera,1 J. Kellie,4 C.E. Keppel,18 N. Kolb,19 J. LeRose,5
5 N. Liyanage,1 K. Livingston,4 D. McNulty,20,21 L. Mercado,20 R. Michaels,5 M. Mihoviloviˇc,22 S. Qian,6
1 X. Qian,23 S. Mailyan,15 V. Mamyan,24 S. Marrone,13 P. Monaghan,6 S. Nanda,5 C.F. Perdrisat,8
0
E. Piasetzky,25 D. Protopopescu,4 V. Punjabi,26 Y. Qiang,6 I.A. Rachek,27 A. Rakhman,28 G. Ron,29,30
2
G. Rosner,4 A. Saha‡,5 B. Sawatzky,31,5 A. Shahinyan,15 S. Sˇirca,32,22 N. Sparveris,6,31 R.R. Subedi,33
r
p R. Suleiman,6 I. Strakovsky,9 V. Sulkosky,6,5 J. Moinelo,34 H. Voskanyan,15 K. Wang,1 Y. Wang,17
A J. Watson,33 D. Watts,35 B. Wojtsekhowski,5 R.L. Workman,9 H. Yao,31 X. Zhan,6 and Y. Zhang6

0 (The Hall A Collaboration)
1 1University of Virginia, Charlottesville, VA 22904
2Chiang Mai University, Chiang Mai, Thailand 50200
]
x 3Mississipi State University, Starkville, MS 39762
e 4University of Glasgow, Glasgow, G12 8QQ Scotland UK
- 5Thomas Jefferson National Accelerator Facility, Newport News, VA 23606
cl 6Massachusetts Institute of Technology, Cambridge, MA 02139
u 7California State University, Los Angeles, Los Angeles, CA 90032
n 8College of William and Mary, Williamsburg, VA 23187
[ 9The George Washington University, Washington, D.C. 20052

10Duquesne University, Pittsburgh, PA 15282
3
11Institut de Physique Nucleaire, F-91406 Orsay Cedex, France
v
7 12Seoul National University, Seoul 151-747, Korea
0 13Istituto Nazionale di Fisica Nucleare, Sezione Sanit`a, I-00161 Rome, Italy
6 14University of Kentucky, Lexington, KY 40506
5 15Yerevan Physics Institute, Yerevan, 0036 Armenia
0 16University of Lund, Box 118, SE-221 00 Lund, Sweden
. 17Rutgers University, New Brunswick, NJ 08903
1
18Hampton University, Hampton, VA 23668
0
19University of Saskatchewan, Saskatoon, Canada S7N 0W0
5
1 20University of Massachusetts, Amherst, MA 01003
: 21Idaho State University, Pocatello, ID, 83209
v 22Joˇzef Stefan Institute, SI-1000 Ljubljana, Slovenia
Xi 23Duke University, Durham, NC 27708
24Carnegie Mellon University, Pittsburgh, PA 15213
ar 25Tel Aviv University, Tel Aviv 69978, Israel
26Norfolk State University, Norfolk, VA 23504
27Budker Institute, 630090 Novosibirsk, Russia
28Syracuse University, Syracuse, NY 13244
29Lawrence Berkeley National Lab, Berkeley, CA 94720
30Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel 91904
31Temple University, Philadelphia, PA 19122
32University of Ljubljana, 1000 Ljubljana, Slovenia
33Kent State University, Kent, OH 44242
34Universidad Complutense de Madrid, Madrid, 98040 Spain
35University of Edinburgh, Edinburgh, EH8 9YL Scotland, UK
(Dated: April14, 2015)
New results are reported from a measurement of π0 electroproduction near threshold using the
p(e,e′p)π0 reaction. The experiment was designed to determine precisely the energy dependence
of s− and p−wave electromagnetic multipoles as a stringent test of the predictions of Chiral Per-
turbation Theory (ChPT). The data were taken with an electron beam energy of 1192 MeV using
a two-spectrometer setup in Hall A at Jefferson Lab. For the first time, complete coverage of the
2
φ∗ and θ∗ angles in the pπ0 center-of-mass was obtained for invariant energies above threshold
π π
from 0.5 MeV up to 15 MeV. The 4-momentum transfer Q2 coverage ranges from 0.05 to 0.155
(GeV/c)2 in finesteps. A simple phenomenological analysis of our datashows strong disagreement
with p−wave predictions from ChPT for Q2 >0.07 (GeV/c)2, while the s−wave predictions are in
reasonable agreement.
PACSnumbers: 25.30.Rw,13.60.Le,12.39.Fe
Neutral pion production from the proton vanishes in TheJLAB/HallAexperimentreportedhereprovidesthe
the chiral limit of zero quark masses and pion momenta mostextensive(Q2,W)coverageofπ0 electroproduction
p → 0. As a result, the reaction at threshold is partic- to date for testing theories of chiral dynamics substan-
π
ularly sensitive to non-perturbative mechanisms within tially above threshold.
QCDwhichbreakchiralsymmetry. Itisalsoexperimen- Under the one-photon-exchange approximation, the
tallythemostchallengingtostudy. Pionphoto-andelec- p(e,e′p)π0 cross section factorizes as follows:
troproductionexperimentsarenowproducingdataofun-
precedentedprecisiontotestChiralPerturbationTheory d3σ dσ
=JΓ (1)
(ChPT),thelow-energyeffectivefieldtheoryofQCD[1]. dQ2dWdΩ∗ v dΩ∗
π π
ChPT treats the spontaneous and explicit chiral sym-
where Γ is the virtual photon flux and the Jacobian
metry breaking in terms of a perturbative expansion in v
smallmomentaandquarkmasses,andmakespredictions J = ∂(Q2,W)/∂(Ee′,cosθe′) relates the differential vol-
ume element of data binned in dQ2dW to the scattered
for the s− and p−wavemultipoles for the γN →πN re-
action in the near-threshold region. Within ChPT, the electron kinematics dEe′dcosθe′. The pπ0 center-of-
mass (C.M.) differential cross section, dσ/dΩ∗, depends
internal structure of the pion and nucleon is systemat- π
onthetransverseǫandlongitudinalǫ polarizationofthe
ically parameterized by Low Energy Constants (LEC), L
virtual photon through the response functions R ,R
while the long-range external πN dynamics are fixed by T L
and their interference terms R and R :
the underlying chiral symmetry. Once the LECs are de- LT TT
termined by experiment near threshold, the convergence dσ p∗
of the chiral expansion can be tested by comparing pre- dΩ∗ = kπ∗(RT +ǫLRL+ǫRTT cos2φ∗π
π γ
dictions with data taken at energies above threshold.
+p2ǫ (ǫ+1)R cosφ∗). (2)
Recently π0 photoproduction cross-section and po- L LT π
larized photon beam-asymmetry (Σ) data from the The response functions depend implicitly on Q2,W and
MAMI A2/CB-TAPS experiment [2] were used to test θ∗, the π0 C.M. angle, while the angle φ∗ defines the
π π
two versions of ChPT. The relativistic ChPT calcula- rotation of the pπ0 plane with respect to the electron
tion (RChPT/χMAID) [3–5] has been carried out to scattering plane (e,e′). Other definitions are ǫ =
L
(cOBa(lKcpuπ4Ml)a,0t1iwo)nh[i6(l]eHbBtuhCtehonPnoTlny)-roiefslaOotfi(vpOiπ3s(t)picπf4o)Hrfepoa−rvwyphaBovteaosrpyironondeluCecchttPirooTn- mJ(Qe=2n/tπ|akW∗o|f/2E)tǫhe,eEvΓe′ivmrtup=.alFpαinhEaoeltl′oyknγ∗|Wka∗n/|d2aπnp2dioEnpe∗πmreapsrQpee2tc(ht1eiv−Cel.yMǫ,)w.mahniolde-
production (BKM96) [7]. Both the BKM01 and RChPT k∗ =(W2−m2)/2W istherealphotonequivalentenergy.
γ p
calculations, after fits of LECs to the data, were com- The p(e,e′p)π0 experiment was performed in Hall A
patible with the experimental multipoles E0+,E1+,M1+ at Jefferson Lab using the Left High Resolution Spec-
and M within an incident photon energy rangeof 7 to
1− trometer (LHRS) [14] to detect the scattered electron
25 MeV above threshold [3, 8].
and the BigBite Spectrometer [15] to detect the coinci-
The pionelectroproductionreactionγ∗p→pπ0 allows dent proton. The CEBAF beam was energy-locked to
amorestringenttestofChPT,sincethefour-momentum 1192 MeV and delivered to a 6-cm long, 2.54-cm wide
transfer Q2 and invariant energy W can be varied in- cylindrical liquid hydrogen (LH ) target. Beam cur-
2
dependently. Chiral πN dynamics naturally involve the rents below 5 µA were used to limit the singles rates in
massscaleQ2/m2,whiletheLECsfittedinphotoproduc- both spectrometers. Four angular settings for the LHRS
π
tion encapsulate higher order processes, involving pos- (θe′ =12.5◦,14.5◦,16.5◦ and20.5◦)coveredanearlycon-
sibly N∆ or ρ,ω degrees of freedom. The Q2 depen- tinuous Q2 range of 0.05−0.155 (GeV/c)2 using a 4.4
dencenearthresholdmayrevealtheonsetoftheseshort- msr acceptance cut. The LHRS momentum acceptance
ranged mechanisms. Until now, only limited kinematic wascenteredonthe pπ0 thresholdandcoveredthe range
coveragefrom γ∗p→pπ0 threshold experiments is avail- −3%<δp/p<+5%.
able [9–12]. Several older MAMI experiments showed Three angular settings of the BigBite were used
a Q2 dependence of the total cross section near thresh- (θ =43.5◦,48◦ and 54◦) which provided full coverage
p
oldincompatiblewith HBChPT[11,12], althoughanew (Fig. 1) of the proton cone up to an invariant energy
MAMI re-measurement has superceded those data [13]. above threshold of ∆W=15 MeV (at the largest Q2).
3
FIG. 2. Left: Coincidence timing between the LHRS and
BigBite. Eventsbelonging to the true coincidence peak were
selected using cuts indicated by the vertical lines, while ran-
domcoincidenceswereselectedfromtheregionhighlightedin
FIG. 1. Left: Overlap between three BigBite Spectrom-
red. Right: Missing mass distribution at Q2=0.15 (GeV/c)2
eter proton laboratory angle settings (colored boxes) and
pπ0 center-of-massbinsatQ2=0.135(GeV/c)2 and∆W=9.5 fortheinvariantmassrange0<∆W <10MeV.Background
∗ ∗ events from random coincidences (red) and target cell win-
MeV.Radialandconcentriclinesseparatebinsofφ andθ ,
π π
∗ dows (blue) were subtracted from the raw distribution, leav-
respectively. Only 5 out of 9 θ bins are shown. The blue
line shows φ∗=180. Right: Radiπal and concentric lines sepa- ing theπ0 missing mass peak shown in gray.
π
∗
rate bins of θ and ∆W, respectively, projected onto proton
π
lab momentum pp and θp. Bins to the(left,right) of the blue
∗ ◦ ∗ ◦
line correspond to (φ =180 , φ =0 ). The innermost circle
π π
represents ∆W = 0.5 MeV. inFig.2beforeandaftersubtractionofbothrandomco-
incidences and target-window contributions. The latter
background was estimated using cuts on ∆W below the
The BigBite momentum acceptance covered the range π0 threshold.
(0.25<p <0.5GeV/c),limitedbythetargetenergyloss Before binning the data, both incident and scattered
p
atlowmomentumandthethresholdsontheE−∆Escin- electron energies were corrected for ionization losses in
tillatorcountersathighmomentum. Thelowmomentum the LH2 and target windows, using the calculated en-
cutoff was achievedusing a thin (25 µm) Ti exit window trance and exit paths with respect to the measured tar-
in the target scattering chamber and a helium bag for get interaction vertex. Proton transport energy losses
transportuptoandbetweenthe BigBitedrift chambers. through the target, Ti window and BigBite were also
Absolute normalization,energyandanglecalibrationsin corrected for each event. Acceptance corrections were
both spectrometers were checked at each kinematic set- derivedfromaMonte-Carlosimulationofbothspectrom-
tingusingelasticscatteringrunswithLH andthinsolid eters, using the Dubna-Mainz-Taipei (DMT) model [18]
2
targets. as a physics event generator. Special care was taken to
Scintillator hodoscopes provided the primary triggers incorporate into the simulation radiative correction and
for both spectrometers. A gas threshold Cˇerenkov de- straggling losses, a fine-mesh magnetic field map for the
tector in the LHRS provided electron identification with BigBite,andthemeasuredenergyandangularresolution
99% efficiency. Signals from either E or ∆E scintillator andenergycalibrationdeterminedfromelasticscattering
planesattherearofBigBitewereusedinthecoincidence runs,inordertoproperlyaccountfortheirsystematicef-
trigger, while signal thresholds in both the hodoscopes fectsnearthreshold. Thedominantsourcesofsystematic
andmulti-wire drift chamberswereset to suppressmini- uncertainty are target window background subtraction,
mum ionizing tracks from pions. Final proton identifica- accidentalcoincidencecorrectionsandLHRScentralmo-
tionwasmadeusingE−∆Ecutsonthehighlysegmented mentum calibration, which combined contribute to the
scintillators. The path-lengthcorrectedcoincidencetime overallnormalization error of 20% near threshold at low
distribution between the LHRS and BigBite is shown in Q2 decreasing to 7% for data above threshold at higher
Fig. 2. A 10 ns wide cut centered on the peak was used Q2.
to select true coincidences, while a 30 ns cut (excluding Events were accumulated using (12,30,18,9) bins for
the peak) selected random coincidences for subtraction. (Q2,∆W,φ∗,θ∗) respectively,with a cut of±10MeVon
π π
Selection of the pπ0 final state required calculation of the missing-mass peak. The ∆W bin width was 1 MeV
the missing-mass M after reconstruction of the detected andtheLHRSacceptanceextendedupto∆W=30MeV,
particle’s 3-momenta: although with reduced C.M. coverage. The average Q2
binwidthwas0.01(GeV/c)2. Figure3showstypicaldif-
M2 =(E+mp−Ee′ −Ep)2−(p~e−p~e′ −p~p)2 (3) ferentialcrosssectionsforeachφ∗ andθ∗ binobtainedat
π π
Theexperimentalmissing-massdistributionisalsoshown Q2=0.135 (GeV/c)2 and ∆W = 9.5 MeV. The curve la-
4
FIG. 3. Differential cross sections for p(e,e′p)π0 from this
experiment at Q2 = 0.135 (GeV/c)2 and ∆W = 9.5 MeV FIG.4. Totalcrosssection forp(e,e′p)π0 asafunctionofQ2
binned in pπ0 center-of-mass angles φ∗ and and cos θ∗. See fordifferentbinsin∆W (invariantmassabovethreshold)for
π π ((cid:3)) this experiment and (△) MAMI [13]. Units of ∆W are
text for description of curves. Units are µb/sr. Errors are
MeV. Errors are statistical only.
statistical only.
beledBKM96istheHBChPTpredictionfromBernardet
al. [7], which uses LECs fitted to older photoproduction
data from MAMI and electroproduction data at Q2=0.1
(GeV/c)2 from MAMI and NIKHEF. The other curve is
an empirical fit to the data which we use to obtain the
totalcrosssectionσ . Theempiricalfitusestheformin
tot
Eq.(2)andexpandstheresponsefunctionswithLegendre
polynomials P(x), where x=cosθ∗,
l π
R +ǫ R =AT+L+AT+LP (x)+AT+LP (x)(4)
T L L 0 1 1 2 2
R =ATT (1−x2) (5)
TT 0
R =(ALT +ALT P (x))(1−x2)1/2. (6)
LT 0 1 1
The total cross section σ is given by 4πp∗π AT+L.
tot k∗ 0
γ
The Q2 dependence of σtot is shown in Fig. 4 for dif- FIG.5. TheQ2dependenceofa0(left)andb(right)fromthe
ferent ∆W bins starting 0.5 MeV above threshold. Two fits of Eq. 7 to the Legendre coefficient AT+L. The theory
0
ChPT calculations are shown (BKM96 [7], χMAID [4]), curves are calculated for the beam energy of our experiment
along with the SAID08 solution [16] and phenomeno- (1192 MeV). For the curve labeled REFIT the BKM96 LEC
logical models (DMT [18], MAID [17]) which have been bP has been lowered from 13 to 9.3 (GeV)−3 (see text and
Fig. 6). Errors are statistical only.
fitted to the world data on pion photo- and electropro-
duction. Compared to the linear Q2 dependence of the
HBChPT/BKM96 curve, our σ measurement shows a
tot
bending over at higher Q2 similar to the phenomenolog- The b coefficient parameterizes the contribution of
ical models and the RChPT/χMAID theory. At lower p−wave multipoles arising from their intrinsic p∗π de-
Q2,bothChPTcalculationsareconsistentwithourdata pendence near threshold, while a0 fits the combination
over the entire ∆W range shown here. Note that two |E0+|2+ǫL|L0+|2 of s−wave multipoles extrapolated to
of the RChPT LECs were fitted to a new MAMI re- threshold. The L0+ multipole dominates a0 over our Q2
measurement [13] (triangles in Fig. 4) of earlier Q2 > 0 range due to a large ǫL factor. The extraction of a0 and
experiments,whiletheremainingLECswerefittedtothe b from fitting our data up to ∆W = 9.5 MeV is shown
Q2 =0 A2/CB-TAPS data [2]. in Fig. 5, along with fits to the newest MAMI data [13]
Near threshold, the s− and p−wave decomposition of up to ∆W = 3.5 MeV (the limit of their measurement)
σ can be obtained by fitting the p∗ dependence of andpreviousresultsfromNIKHEF[9,10]. Thereisgood
tot π
AT+L according to agreement of both a0 and b with the chiral model pre-
0
dictions for our lowest Q2 points. For higher Q2, the
AT+L =a +b|p∗|2. (7) HBChPT curve describes a better than RChPT. How-
0 0 π 0
5
by the REFIT b curve in Fig. 5. Moreover, a different
adjustment of b is required to match our measurement
P
of AT+L.
2
The O(p4) RChPT calculation [4] predicts a nearly
identical Q2 dependence for the b curve in Fig. 5 as the
O(p3) HBChPT theory. At leading-order and next-to-
leading order, P is controlled by a single O(p3) LEC
3
d , similarly to HBChPT [3]. However d is highly con-
9 9
strained by the Q2=0 photoproduction fits, and there
is almost no room for adjustment. Other O(p4) LECs,
which explicitly control Q2 dependent terms, either do
not appreciably affect the p−wave multipoles, or effect
the same Q2 response as b .
P
Despite the very different LEC composition of
HBChPTandRChPT,itappearsneithercalculationcan
be adjusted to agree with the Q2 trend of our p−wave
data. Furthermore this discrepancy occurs well within
the ∆W range where photoproduction p−waves are well
described at O(p4) [8]. Our data therefore suggest that
FIG. 6. The ∆W dependence of Legendre coefficients from higher powers of Q2 are needed in the ChPT formalism,
fits to our data at Q2 = 0.135 (GeV/c)2. Note that the while the onset of disagreement (Q2 >0.07) implies a
∆W=9.5 MeV bin corresponds to the Legendre fit shown in
t−channelenergyscaleabovethepionmass. Similardis-
Fig. 3. Errors are statistical only.
crepancies in ChPT calculations of nucleon form factors
were removed by including vector mesons as dynamical
degrees of freedom [21]. Our data could provide strong
everthestrongdisagreementofourbcoefficientwithboth
constraints to analogous extensions of pion electropro-
chiral curves for Q2 > 0.07 GeV2 suggests at least one
duction calculations.
of the p−wave multipoles is described incorrectly in the
calculations. The Q2 dependence of b from fitting the Insummary,aJLAB/HallAexperimenthasmeasured
for the first time both the Q2 and extended ∆W depen-
MAMI dataisqualitativelysimilar,althoughwithlarger
denceofthe thresholdp(e,e′p)π0 reactionwithfullC.M.
errors,due to the smaller ∆W range of their data.
coverage and fine binning. Our phenomenological fit of
Further insight can be obtained from the ∆W de-
the data shows reasonable agreement with two leading
pendence of the Legendre coefficients in the Q2 >
ChPT theories for s−waves, while chiral predictions of
0.07 (GeV/c)2 region. This is shown in Fig. 6 at
p−wavecontributions strongly divergefromour data for
Q2=0.135(GeV/c)2. Whileallmodelsareingoodagree-
Q2 > 0.07 (GeV/c)2. We use a Legendre decomposition
ment with our data near threshold, the theory curves
of our cross sections to show there is insufficient flexibil-
for AT+L, AT+L and ATT show large variations above
0 2 0 ity in the low energy constants available for p−waves to
∆W=3MeV.Thesecoefficientsareparticularlysensitive
account for the Q2 discrepancy.
tothep−wavemultipolecombinationsP =2M +M
3 1+ 1−
The collaboration wishes to acknowledge the Hall A
andP =3E −M +M ,whileATT isalsosensitive
2 1+ 1+ 1− 0
to the combination ∆P2 = (P2−P2)/2. Our fit result technicalstaffandtheJeffersonLabAcceleratorDivision
23 2 3
fortheir support. Specialthanks goesto Ulf-G. Meiβner
for ATT is close to zero over the ∆W range of our data,
0
which implies P2 ≈ P2 or M /M ≈ −2 (neglecting for his support in the early phases of this experiment.
2 3 1+ 1−
Thisworkwassupportedbythe U.S.DepartmentofEn-
the weak electric quadrupole E ).
1+
ergy and the U.S. National Science Foundation and in
Only the DMT model predicts ATT ≈ 0 for ∆W <
0 particularDOE contractDE-FG02-97ER41025andNSF
15MeV,largelyduetotheircalculationoftheM mul-
1− MRI Award No. 021635. Jefferson Science Associates
tipole[19],thevalueofwhichissubstantiallylargerthan
operates the Thomas Jefferson National Accelerator Fa-
predicted by ChPT. A similar result was obtained from
cility under DOE contract DE-AC05-06OR23177.
disperson relations [20]. In the BKM96 theory, which
usesaO(p3)p−waveexpansion,itisnotpossibletosep- ‡ Deceased.
arately adjust M and M , since only P is controlled
1+ 1− 3
by a single LEC b . By reducing b in the calculation
P P
from 13.0 to 9.3 (GeV)−3, we can improve agreement
with both AT+L and ATT as shown in Fig. 6 by the
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