Measurement of the LT-asymmetry in π^0 electroproduction at the energy of the Δ(1232) resonance

0.48 MB·English

by  D. Elsner

EPJ manuscript No.
(will be inserted by the editor)
π0
Measurement of the LT-asymmetry in electroproduction at
∆
the energy of the (1232) resonance
6 D. Elsner1 a, A. Su¨le1 b, P. Barneo2, P. Bartsch3, D. Baumann3, J. Bermuth3, R. B¨ohm3 D. Bosnar3 c, M. Ding3, M.
0 Distler3, D. Drechsel3, I. Ewald3, J. Friedrich3, J.M. Friedrich3 d, S. Gr¨ozinger3 e, P. Jennewein3, S. Kamalov3, F. H.
0 Klein1, M. Kohl4 f, K.W. Krygier3, H. Merkel3, P. Merle3, U. Mu¨ller3, R. Neuhausen3, Th. Pospischil3, M. Potokar5,
2 G. Rosner3 g, H. Schmieden1, M. Seimetz3 h, O. Stra¨hle3, L. Tiator3 Th. Walcher3, M. Weis3

n
1 Physikalisches Institut,Rheinische Friedrich-Wilhelms-Universit¨at, D-53115 Bonn, Germany
a
J 2 NIKHEF,Amsterdam, The Netherlands
3 Institut fu¨r Kernphysik,Johannes Gutenberg–Universit¨at, D-55099 Mainz, Germany
8
4 Institut fu¨r Kernphysik,Technische Universit¨at Darmstadt, D-64289 Darmstadt, Germany
2
5 Institut Joˇzef Stefan, University of Ljubljana, SI-1001 Ljubljana, Slovenia

2
v Received: date/ Revised version: date
4
1 Abstract. The reaction p(e,e′p)π0 has been studied at Q2=0.2 (GeV/c)2 in the region of W=1232 MeV.
0
7 From measurements left and right of q, cross section asymmetries ρLT have been obtained in forward
0 kinematics ρLT(θπcm0 =20◦)=(−11.68±2.36stat±2.36sys) and backward kinematics ρLT(θπcm0 =160◦)=
5 (12.18±0.27stat ±0.82sys) π0. Multipole ratios ℜ{S1∗+M1+}/|M1+|2 and ℜ{S0∗+M1+}/|M1+|2 were de-
termined in the framework of the MAID2003 model. The results are in agreement with older data. The
0
/ unusally strong negative ℜ{S0∗+M1+}/|M1+|2 required to bring also the result of Kalleicher et al. in ac-
x cordance with the rest of thedata is almost excluded.
e
-
l PACS. 13.60.Le Mesonproduction–13.40.-f Electromagneticprocessesandproperties–14.20.Gk Baryon
c
resonances with S=0
u
n
:
v 1 Introduction 3/2 ∆(1232) excitation. Within constituent quark mod-
i els those components originate from tensor forces gen-
X
The nucleon ground- and excited state properties pres- erated by a color hyperfine interaction [1,2,3,4]. Larger
r
a ently elude a consistent description in terms of QCD as quadrupolestrengthsareexpectedfrommodelsemphasiz-
the basic theory of strong interaction, due to the non– ing the particular role of pions via exchange currents [5]
linear, non–perturbative interaction of quarks and glu- orthe ‘pioncloud’[6,7,8,9,10],andalsoinfirstquenched
ons. Over the last years, considerable efforts aimed at a LatticeQCDcalculations[14].Dynamicalapproaches[11,
better understanding of this complicated structure, both 12,13] enable a decomposition into the “bare” contribu-
theoretically and experimentally. One important issue is tions,asdescribedinquarkmodels,andthe“dressing”by
the understanding of the ‘shape’ of the nucleon. Despite the pion cloud.
its spin of 1/2 and, in consequence, the vanishing spec- The quadrupole strength is usually characterized by
troscopic quadrupole moment, the nucleon wave function the ratios REM = E1+/M1+ and RSM = S1+/M1+ of
mighthavequadrupolecomponentswhichareexpectedto the πN multipoles in the ∆(1232) → Nπ decay1, which
exhibit in the transition of the ground state to the spin are uniquely related to the photon multipoles of electro-
magnetic excitation [17,18]. Hence, these ratios can be
a corresponding author, email: [email protected] measured in photo- and electroproduction of pions in the
b email: [email protected] energy region of the ∆(1232) resonance. Since unwanted
c permanent address: Department of Physics, University of non–resonantcontributionsarestronglysuppressedinthe
Zagreb, Croatia π0channelcomparedtothechargedpionproduction,most
d present address: Physik Department E18, TU Mu¨nchen, measurements focused on the γ(∗)p→pπ0 reaction.
Germany A number of studies pursued at the laboratories pro-
e present address: GSI, Darmstadt, Germany vidingcw electronbeamsyieldedprecisecoincidencedata
f present address: MIT/Bates, Massachusetts, USA based on high luminosity beams and high resolution de-
g present address: Dept. of Physics and Astronomy, Univer-
sity of Glasgow, UK 1 Exact definition and aspects of isospin separation see [15,
h present address: DAPNIA/SPhN,CEA Saclay, France 16].
2 D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232)
tectors with large angular coverage. Partially single or The partial differential cross sections, for which we use
double polarizationobservableshave been measured.The the short-hand notation σ , describe the response of the
i
evolution of R and R with negative squared four– hadronic system to the polarization of the photon field,
EM SM
momentumtransfer,Q2,hasbeeninvestigatedoveralarge characterizedbythedegreesoftransverse(T)andlongitu-
rangeinQ2upto4(GeV/c)2[19,20,21].Theextractionof dinal (L) polarization,ǫ and ǫ = Q2 ǫ, respectively. The
the quadrupole ratios from the measuredcross sections is L ωc2m
angleφisthetiltinganglebetweentheelectronscattering
non-trivial.FortheRSM discussedhere,itismorereliable plane and the reaction plane. At φ = 0◦ and 180◦ (φ =
at lower Q2 where M1+ dominance is more pronounced 90◦and270◦)pionsareejectedin(perpendicularlyto)the
than at higher Q2 and single [22,23] and double polar-
scattering plane.
izationresults [24,25,26] are alreadyavailablein addition
to unpolarized recent measurements [20,21,27,28,29,30].
The low Q2 results are almost all compatible with each
3 Method
other,yieldingR ≃−6%,cf.fig.5.The onlyexception
SM
is the result of Kalleicher et al. [27]. However, due to the
Thepartialcrosssectionσ issensitiveto bothS and
particular kinematics it could be interpreted in line with LT 0+
S .Itcanbedeterminedfromafitoftheφ-dependenceof
the other results,ifthe ratioS /M ≃−10%[16].S 1+
0+ 1+ 0+
thecrosssectionofeq.(3).Tothisend,twomeasurements
isrelatedtothespin1/2→1/2transition.Thisamplitude
left (φ = 0◦) and right (φ = 180◦) of the q direction are
wasneglectedinthe analysisof[27]. Bothmagnitude and
sufficient, which allow to form the asymmetry
sign of such an S are however unexpected from mod-
0+
els, e.g. MAID2003 [18], but not excluded by older mea- ◦ ◦
σ (φ=0 )−σ (φ=180 )
surements with large errors [31,32] which yielded slightly ρ (θcm):= v v (4)
LT π0 σ (φ=0◦)+σ (φ=180◦)
positive values with errors of the order 10% absolute. v v
In order to investigate this issue, measurements of π0
as a function of the π0 center-of-mass polar angle, θcm.
electroproductioninforwardandbackwarddirectionhave π0
According to eq. (3), it is related to the partial cross sec-
beenperformed,whicharereportedinthispaper.Itisor-
tions via
ganized as follows: In the next section the cross section
formalism is briefly summarized and the method is moti-
vated. The description of the experiment is then followed ρ (θcm)= p2ǫL(ǫ+1)σLT . (5)
LT π0 σ +ǫ σ +ǫσ
by a discussionofthe data analysis,systematic errorcon- T L L TT
tributions and the results in sections 5, 6 and 7.
ThesensitivitytoS andS isshownbyapartialwave
0+ 1+
decomposition of eq. (5), where only the leading multi-
poles areretained.At the ∆(1232)resonancepositionthe
2 Cross section of pion electroproduction
asymmetry
Inone-photon-exchangeapproximationthe fivefolddiffer- ℜ{(S∗ +6S∗ cosθcm)M }
ential cross section of pion electroproduction ρ (θcm)≃f(θcm)· 0+ 1+ π0 1+ (6)
LT π0 π0 |M |2
1+
d5σ d2σ
v
=Γ (1)
dE dΩ dΩcm dΩcm is obtained. Thus measurements of ρLT in the forward
e e π π
(θ ) and backward cm-hemisphere (θ = π - θ ) allow the
1 2 1
factorizes into the virtual photon flux extraction of S /M and S /M :
1+ 1+ 0+ 1+
′
Γ = 2απ2EE Qkγ21−1 ǫ (2) ℜ{|SM1∗+M|21+} =f1(θ1,2)·[ρLT(θ1)−ρLT(θ2)]+C1 (7)
1+
aHnedretαhedevniorttuesalthpehfiontoenstcrmuctucrroescsonsesctatinotn, kdγ2σ=v/(dWΩ2πcm−. ℜ{|SM0∗+M|21+} =f0(θ1,2)·[ρLT(θ1)+ρLT(θ2)]+C0. (8)
m2)/2m the laboratory energy of a real photon for the 1+
p p
excitationofthetargetwithmassm tothecmenergyW,
p Thefunctionsf (θ )andf (θ )denotekinematicalfac-
andǫ=[1+(2|q|2/Q2)tan2 ϑe]−1thephotonpolarization tors, C and C0 c1o,n2tain co1ntr1i,b2utions of multipoles be-
2 0 1
parameter. Q2 = |q|2 −ω2 is the negative squared four- yond the approximation.
momentum transfer, q and ω are the three-momentum
′
and energy transfers, respectively, and E, E and ϑ the
e
incoming and outgoing electron energy and the electron 4 Experiment
scattering angle in the laboratory frame.
Theunpolarizedcrosssectionforpionproductionwith The p(e,e′p)π0 experiment was performed at the Mainz
virtual photons is given by [17,18]
Microtron MAMI [33] using a beam energy of 855 MeV
d2σ and currents of ∼ 33 µA which were measured with high
v
dΩcm =:σv =σT +ǫLσL precision by a F¨orster probe in the recirculation path of
π the 3rd microtron stage. The beam hit a liquid hydro-
+p2ǫ (1+ǫ)σ cosφ+ǫσ cos2φ. (3) gen target. Specifically designed for this experiment, the
L LT TT
D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232) 3
Fig. 1. Typical coincidence-time (a,b,c) and missing-mass (a′,b′,c′) spectra for Kin. I, II and IIa. Light spectra result from
standard cuts without phase-space restrictions. Shaded time spectra (FWHM peaks: (a) 0.8 ns, (b) 2.7 ns, (c) 3.0 ns) result
from missing-mass cuts (dashed vertical lines in the missing-mass plots) around the π0 mass; in Kin. I and Ia (not shown)
the cut eleminates the π−-time peak and at Kin. II and IIa the prompt time peak becomes symmetric (see text). The shaded
missing-mass spectra result similarly from the indicated cuts around the coincidence-time peak.
∅ 1 cm cylindrical target cell with 6.25 µm Havar walls possibly caused by inefficiencies of the focal plane detec-
[34] enabled the detection of very low-energetic protons. tors in the proton arm, Spectrometer B was displaced by
◦
The scattered electrons were detected at a central angle 1 against the nominal setting for part of the measure-
ofθlab=44.45◦ andcentralmomentum ofp=408.7MeV/c ments.
in Sep−ectrometer A of the Three-Spectrometer setup of The π0-data were supplemented by elastic p(e,e′p) mea-
the A1-collaboration [35]. It consists of a QSDD mag-
netic system and is equipped with two double planes of
vertical drift chambers for measurement of particle tra- Table 2. Elastic scattering kinematics.
jectories inthe focal plane.During the courseof the mea-
Spec. A (electron) Spec. B (proton) Beam
surements presented here, the standardCherenkov detec-
− − θ (◦) p (MeV/c) θ (◦) p (MeV/c) E (MeV)
tor for π /e -discrimination was not available, since it
55.5 612.0 43.6 - 46.0 704.4 855.0
was replaced by a focal-plane proton polarimeter [36] for
46.5 314.6 58.4, 59.4 251.0 351.3
other experiments [24,37]. In coincidence with the scat-
tered electron, the recoil protons of the p(e,e′p)π0 re-
action were detected in Spectrometer B with a similar
surements (table 2) to monitor the overall experimental
focal-plane instrumentation. The smallest possible angle
consistencywithhighprecision.Theoverdeterminedkine-
◦
betweenSpectrometerBandtheexitbeam-pipeis9 and
maticsallowscomparisonofeverymeasuredvariablewith
the momentum-threshold for the proton-detection is 250
the values calculated from the other measured variables.
MeV/c.HenceQ2=0.2(GeV/c)2 wastheminimumpossi-
Correctionsof0.5MeV/cforthecentralmomentumofthe
blemomentumtransferthatcouldbereachedatW=1232 ◦
electron-spectrometerand0.1 forthe angleofthe proton
MeV. The four different kinematic settings are summa-
spectrometer were determined. The probable origin is a
very slight mismatch between hardware (detector angle,
field integral) and the track reconstruction.
Table 1. Proton kinematics. Precise measurements of electron beam current and
Kin. θcm (◦) φ (◦) plab (MeV/c) θlab (◦) deadtime allowedan accuratedetermination of the effec-
π0 p p
tive luminosity.
I 160 0 741.7 33.0/32.0
Ia 180 20.9/21.9
II 20 0 265.02 44.2/43.7
IIa 180 9.8/10.3 5 Data analysis
Typical coincidence-time and missing-mass spectra are
rized in table 1. In order to check for false asymmetries, shown in fig. 1. The overdetermined kinematics allows
4 D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232)
”nominal kinematics”. For this projection we made use
ofthe MAID2000parametrisation.The projectionfactors
are obtained as the calculated ratios of differential cross
sections. In order to minimise the projection error, only
dataareusedwithintheθcm–Woverlapregionofthe two
π0
acceptance bands in fig. 2. Remaining uncertainties are
included in the systematic error.
The appropriately normalised and projected numbers
of events left (l) and right (r) of q are determined by
nl(φ=0◦),r(φ=180◦) = PBins(Nl,r/LPl,r)·MAIDcl,orrr. (9)
l,r
Fig. 2. Spectrometer acceptances for left (θlab=33◦ ) and
p
right (θplab=20◦ ) settings of kinematics I. W is limited by the Here Nl,r denotes the number of counts after cuts, which
electron-spectrometer(A)acceptance.Theangularacceptance has to be divided by the relative phase-space acceptance
of the proton-spectrometer (B) determinesthe width in θcm. P . MAIDcorr is the projection factor and L repre-
π0 l,r l,r l,r
sents the relative luminosity.The asymmetry is then sim-
ply given by
the reconstruction of the unobserved π0 by its missing
cmoainssc,idmenπmc0ies-st.imBeasiccutbsacakngdrosuunbdtrraecdtuiocntioonfirsaonbdtoaminecdoibny- ρLT(θπcm0 )= nnll+−nnrr. (10)
cidences via sidebands. In addition to the almost back-
′
ground-free e-p coincidence peak, the time spectrum for
the high proton-momentum kinematics shows a smaller 6 Systematic errors
secondpeakat∼-2.2ns(Kin.I,cf.fig.1a).Itiscausedby
negative pions, predominantly from π+π− reactions, the
− ThesystematicerrorhasbeenestimatedforKin.I/Iafrom
π ofwhicharedetectedintheelectronspectrometerafter
thedatathemselvesbyvariationofallkinematiccuts.For
a longer flight time compared to electrons. These events
thedatawithlowproton-momentum(Kin.II/IIa)suchan
can be eliminated by the coincidence-time cut indicated
analysis is limited by the available statistics and experi-
infig.1a.However,forKin.II andIIa,theunwantedneg-
mentalresolution.TheslidingcutsinthevariablesWand
ativepionscannolongerbeseparatedbycoicidencetime,
mπ0 resulted in non-negligible systematic errors (table
duetoinsufficienttimeresolutioncausedbymultiplescat- miss
tering at the low proton-momentum. Instead, additional 3a,3b).Theslidingcutinmπ0 setsalimitonremaining
miss
missing-mass cuts are used to suppress these events. As radiativeeffects beyondthoseincludedinthephase-space
alsoillustratedinfig.1,withacut aroundm (a′,b′,c′) simulation. The spectrometer correction, which was de-
π0
theπ−peakvanishesinKin.I(shadedareaoffig.1a).Un- termined by elastic measurements, has been taken into
der the conditions of Kin. II/IIa the resulting coincident- accountboth in analysis (trackreconstruction)andsimu-
time peakbecomessymmetric afterthe missing-masscut. lation. The value given in table 3c results from the varia-
◦
Standardcutsensurevalidtrackreconstructioninboth tionoftheangleofSpectrometerBby±0.1 .Potentialer-
spectrometers.Notarget-vertexcutswereappliedinorder ror contributions of the MAID-projection were estimated
to avoid artificial ρLT-asymmetries from the very differ- through relative variation of M1+ by ±5% and, simulta-
entvertex-resolutionalongthebeam-directionforthe dif- neously, of S1+ and S0+ by ± 50% in the full MAID2000
ferentsettings.Spectrometeracceptanceswerenormalised calculation.Thelargestdeviationisgivenintable3d.Ad-
with standard Monte-Carlo phase-space simulations, ditionalerrorsfortheluminositydeterminationarenotre-
which also include the radiative corrections [39]. quired. The maximum variations of 2%-relative were cor-
rected, and the remaining effect is negligible. All kine-
The limited spectrometer acceptances cause different
correlations between W,Q2,ǫ,θcm and φ for the settings matic settings were measured repeatedly to avoid time-
leftandrightofq,asillustratedπin0 fig.2.Duetothesecor- dependent effects, e.g. efficiency variations. These data
sub-sets werecombined for the left- andright-kinematics.
relations,equalbinninginthevariablesneverthelessleads
tounequaldistributionsleftandrightofq.Thusartificial
ρ -asymmetries can be generated, if the mean values of
LT
the kinematic variablesdiffer betweenleft andright.This
isobvious,e.g.,foracasewhereW =1232MeV−δand Table 3. Absolute systematic errors (∆ρLT) of high proton-
left momentum kinematics
W = 1232MeV +δ, since the trivial W dependence
right
of the cross section produces a ρ 6=0. a) W cut 0.29 %
LT
It is extremely important to base the experimental b) mπm0iss cut 0.23 %
asymmetriesonleft-rightbins with the samemean values c) Spectrometer corrections 0.57 %
ofthe variablesW,Q2,θcm andφ. This is ensuredby pro- d) MAID2000 projection 0.46 %
π0
jection of the numbers measured in each bin to the same
D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232) 5
Fig. 3. ThemeasuredρLT asymmetriescomparedwithmodel Fig. 4. Results for ρLT′ from reference [23] with model
predictions from MAID2003 [18] (dotted), DMT2001 [11,12] predictions from MAID2003 [18] (dotted), DMT2001 [11,12]
(dashed),Sato/Lee [13](dasheddotted).Thefullcurverepre- (dashed),Sato/Lee[13](dashed dotted).Thefullcurverepre-
sentstheMAID2003re-fitreportedinthispaper.Thedepicted sents the MAID2003 re-fit. The depicted errors are only sta-
errors represent the statistical (inner bars) and the quadratic tistical.
sum of the statistical and systematical errors (outer bars) as
discussed in thetext.
From our MAID re-fit we extract the results given in
the first rowin table 4.The denotederrorsaredue to the
7 Results and discussion
re-fitofS andS withintheMAID2003analysistaking
1+ 0+
into account the statistical and systematical errors. The
modeldependenceoftheextractioncanbeestimatedfrom
From eq. 10 the asymmetries
the truncated multipole result given in the second row in
table4.Intheframeworkofthisapproximationweextract
ρ (θcm =160◦)=(12.18±0.27 ±0.82 )%
LT π0 stat sys from the measured ρLT asymmetries the multipole ratios
ρLT(θπcm0 =20◦)=(−11.68±2.36stat±2.36sys)% viaeqs.(7and8)withonlyleadingtermsinS1+,S0+ and
M .Thelasttwolinesintable4containstandardmodel
1+
are determined. The total systematic erroris obtainedby values without re-fit to our data.
quadraticsummationoftheindividualcontributionsinta- Figure 5 shows our full MAID2003 result for R .
SM
ble 3. For the forward measurement a systematic error of Within the errors, our extracted value is in accordance
the same size as its statistical one is assumed as a worst withmeasurementsatthesameQ2[28]andmeasurements
case estimate. Using these new data in conjunction with at adjacent Q2 [21,24]. The negative-slope tendency of
the previous measurement of the ρLT′ asymmetry (fifth the CLAS-data [21] seems to be further supported by our
structure function) of Bartsch et al. [23], we performed a R value at smaller Q2. Provided there is no sharp Q2-
SM
re-fitoftheMAID2003parameters.We obtainedsensitiv- dependence in R , we can rule out the result of Kalle-
SM
ity to real and imaginary parts of the S1+ and S0+ am- icher et al. [27] at Q2=0.127 (GeV/c)2. This has been
plitudes in the pπ0 channel. The results for ρLT and ρLT′ argued before from measurements in backward kinemat-
are depicted in fig. 3 and 4 which, for comparison, also ics [29] where an S contribution can not be excluded.
0+
showsthestandardMAID2003andthecalculationwithin In contrast, our conclusion comes from forward kinemat-
the dynamical models of Kamalov/Yang(DMT2001) [11, ics as also exploited by [27]. This is illustrated in in fig.
12] and Sato/ Lee [13]. 6. On a different scale it shows the same ρ -asymmetry
LT
as fig. 3, the Maid2003 re-fit and a full MAID2003 calcu-
lation using the multipole ratios S /M and S /M
0+ 1+ 1+ 1+
Table 4. Comparison of multipole ratios from data and cal- of Kalleicheret al.. In addition, a full MAID2003 calcula-
culations, as discussed in thetext. tion using S0+/M1+ ≃ −10%, which could reconcile the
ℜ{|SM1∗+1+M|21+} (%) ℜ{|SM0∗+1+M|21+} (%) Kisacllleeaicrhlyerexrcelsuudltedwbityhooutrhemrsea[1su6r],emisesnhtoawtnθ.πcHm0o=we2v0e◦r,wthitihs
MAID2003 re-fit -5.45±0.42 2.56±2.25 a 4σ significance.
from eqs. (7,8) -4.78±0.69 0.56±3.89 OurS /M ratio,extractedfromtheMAID2003re-
0+ 1+
MAID2003 -6.65 7.98 fit, is plotted in fig. 7.Within the errors it agrees with
Sato/Lee -4.74 5.14 older data at slightly larger Q2 [31,32]. Although a little
lower, it is also compatible with the Sato/Lee, DMT2001
6 D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232)
Fig. 5. Result for ℜ{S1∗+M1+}/|M1+|2 with statistical and
systematical errors as extracted from this experiment using
Fig. 6. The plot shows, at smaller scale, the MAID2003
the MAID2003 re-fit (full cross), compared to measurements.
re-fit (solid) in comparison to the full MAID2003 calcula-
Data where only statistical errors are given: DESY [31] (open
tion with modified ℑ{S1+} and ℑ{S0+} for two situations:
square),NINA[32](opencircles),Bonnsynchrotron[40](open
S1+/M1+ = −12.5%, S0+/M1+ = 0.0% (dashed dottet), i.e.
triangle tip up) and ELSA [27] (full triangle tip down). Data,
the result of [27], and S1+/M1+ = −10%, S0+/M1+ = −14%
where statistical and systematical errors are given: ELSA [28]
(dottet),whichwouldbring[27]inaccordancewithothermea-
(fullcircle,toimprovethepresentationshiftetfrom Q2=0.201
surements[16].
(GeV/c)2 to Q2=0.221 (GeV/c)2), MAMI [24] (open dia-
mond), CLAS [21] (full triangles) and BATES [29,30] (full
square). The curves show model calculations MAID2003 [18]
(solid),DMT2001[12](dashed)andSato/Lee[13](dasheddot-
ted).
andstandardMAID2003parametrisations.In view ofthe
quite large experimental errorsit is not yet clear whether
thisratiodiffersfromzero.Butwecannotsupportalarge
negative S /M ratio.
0+ 1+
A sensitive access to the ratio S /S is providedby
0+ 1+
aprecisemeasurementofthezero-crossingofρ orσ .
LT LT
By now it is possible to extract this ratio from available
dataclosetothezerocrossingatQ2=0.127(GeV/c)2 [30],
with the result compatible to the MAID2003 parametri-
sation.Otherexistingdata[21]coverthefullrangeofθcm
π0
at Q2=0.4-1.8 (GeV/c)2. However, at higher Q2 the S
0+
extraction seems to be affected more strongly by higher
partial waves than expected in the paper by Joo et al. Fig. 7. Result for ℜ{S0∗+M1+}/|M1+|2 with statistical and
[21]. This might be resolved by very recent polarisation systematical errors as extracted from this experiment using
data [41,42]. the MAID2003 re-fit (full cross); compared to measurements
In future experiments at MAMI-C a more accurate de- fromDESY[31](opensquare),NINA[32](opencircles),where
terminationof S at low Q2 is feasible,using the Three- only statistical errors are indicated. The curves show model
0+
calculations MAID2003 [18] (solid), DMT2001 [12] (dashed)
SpectrometersetupoftheA1-collaborationcomplemented
and Sato/Lee [13] (dashed dotted).
by the KaoS-spectrometer [43].
8 Summary
proximation or, alternatively, using the full MAID2003
parametrisation without any truncation. Our results for
We have measured the ρLT asymmetry in forward S1+/M1+ and S0+/M1+ are in agreement with existing
(θcm=20◦) and backward (θcm=160◦) kinematics of π0 measurements and calculations. Our result removes a re-
π0 π0
electroproduction off the proton at Q2=0.2 (GeV/c)2 mainingpossibilitytoreconcilethedatumofKalleicheret
aroundW=1232MeV.The measurementofthe twokine- al. [27] for the ratio S /M with other measurements
1+ 1+
matic settings allows the extraction of S and S in a through a large negative S /M .
1+ 0+ 0+ 1+
very transparent way within a simple s- and p-wave ap- We thank T.-S.H. Lee and T.Sato for providing their cal-
D. Elsner, A.Su¨le et al.: Measurement of theLT-asymmetry in π0 electroproduction at the energy of the∆(1232) 7
culations. This work was supported by the Deutsche 40. K. B¨atzner et al., Nulc.Phys. B 76, (1974) 1
Forschungsgemeinschaft(SFB 443). 41. J. J. Kelly et al.,Phys. Rev.Lett. 95, (2005) 102001
42. J. J. Kelly et al.,nucl-ex/0509004
43. P. Senger, Nucl. Instr.and Meth. A327, (1993) 393-411
References
1. A. de Ru´jula, H. Georgi, S.L. Glashow, Phys. Rev. D 12,
(1975) 147
2. N.Isgur,G.Karl,andR.Koniuk,Phys.Rev.D 25,(1982)
2394
3. S.S. Gershtein and G.V. Dzhikiya, Sov. J. Nucl. Phys. 34,
(1982) 870
4. D. Drechsel and M.M. Giannini, Phys. Lett. 143B, (1984)
329
5. A.J. Buchmann et al.,Phys. Rev.C 58, (1998) 2478
6. K. Bermuth et al., Phys.Rev.D 37, (1988) 89
7. H. Walliser and G. Holzwarth, Z. Phys. A357, (1997) 317
8. G.C. Gellas et al.,Phys. Rev.D 60, (1999) 054022
9. A. Silvaet al., Nucl.Phys. A 675, (2000) 637
10. L. Amoreira, P. Alberto, and M. Fiolhais, Phys. Rev. C
62, (2000) 045202
11. S.S.Kamalov and S.N. Yang,Phys. Rev.Lett. 83, (1999)
4494
12. S.S.Kamalov,S.N.Yang,D.DrechselandL.Tiator,Phys.
Rev.C 64, (2001) 032201
13. T.Satoand T.-S.H.Lee,Phys.Rev.C 63, (2001) 055201
14. C. Alexandrou,Phys. Rev.Lett. 94, (2005) 021601
15. H.Schmieden Eur. Phys.J. A 1, (1998) 427-433
16. H. Schmieden, Proceedings of NSTAR2001, edited by D.
Drechsel and L. Tiator, World Scientific(2001), p.27
17. D.Drechsel and L. Tiator, J. Phys. G 18, (1992) 449
18. D. Drechsel, O. Hanstein, S.S. Kamalov and
L. Tiator, Nucl. Phys. A 645, (1999) 145 and
http://www.kph.uni-mainz.de/MAID/maid2000/
19. V.V.Frolov et al.,Phys. Rev.Lett. 82, (1999) 45
20. R.W.Gothe, Prog. Part. Nucl. Phys. 44, (2000) 185
21. K.Joo et al., Phys.Rev.Lett. 88, (2002) 122001
22. G. Warren et al., Phys.Rev.C 58, 1998) 3722
23. P.Bartsch et al.,Phys. Rev.Lett. 88, (2002) 142001
24. Th. Pospischil et al.,Phys. Rev.Lett. 86, (2001) 2959
25. L.D.vanBuurenetal.,Phys.Rev.Lett.89,(2002)012001
26. A.Biselli et al.,Phys. Rev.C 68, (2003) 35202
27. F. Kalleicher et al.,Z. Phys.A359, (1997) 201
28. D.Wacker, Ph.D. thesis. Institut fu¨r Strahlen- und Kern-
physik, University Bonn (1998)
29. C. Mertz et al., Phys.Rev.Lett. 86, (2001) 2963
30. N.F. Sparveriset al., Phys.Rev.Lett. 94, (2005) 022003
31. R.Siddle et al.,Nucl. Phys.B 35, (1971) 93
32. J.C. Alder et al., Nucl.Phys. B 46, (1972) 573
33. H.Herminghaus,Proceedings of the 1990 Linear Accelera-
tor Conference, Albuquerque, 1990, p.362
34. D.Elsner,diplomathesis,Institutfu¨r Kernphysik,Univer-
sity Mainz (2000)
35. K. I. Blomqvist et al., Nucl. Instr. and Meth. A 403,
(1998) 263-301
36. Th.Pospischiletal.,Nucl.Instr.andMeth.A483,(2002)
713-725
37. Th. Pospischil et al., Eur. Phys. J. A 12, (2001) 125-127
38. Th.Pospischil,Ph.D.thesis.Institutfu¨rKernphysik,Uni-
versity Mainz (2000)
39. M.O.Distler,H.Merkel,M.Weis,Proceedings ofthe 12th
IEEEReal TimeCongress on Nuclear and Plasma Sciences,
Valencia (2001)