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Measurement of the recoil polarization in the p(e, e′ p )π 0 reaction at the ?(1232) resonance

Th. Pospischil1? , P. Bartsch1 , D. Baumann1 , J. Bermuth2 , R. B¨hm1 , K. Bohinc1,3 , S. D

erber1 , M. Ding1 , M. o Distler1 , D. Drechsel1 , D. Elsner1 , I. Ewald1 , J. Friedrich1 , J.M. Friedrich1? , R. Geiges1 , S. Hedicke1 , P. Jennewein1 , M. Kahrau1 , S.S. Kamalov1? , F. Klein1 , K.W. Krygier1, J.Lac4 , A. Liesenfeld1 , J. McIntyre4 , H. Merkel1 , P. Merle1 , U. M¨ ller1 , R. Neuhausen1 , M. Potokar3, R.D. Ransome4 , D. Rohe2,5 , G. Rosner1§ , H. Schmieden1?? , M. Seimetz1 , u ˇ S. Sirca3?? , I. Sick5 , A. S¨ le1 , L.Tiator1 , A. Wagner1 , Th. Walcher1 , G.A. Warren5 , and M. Weis1 u

Institut f¨r Kernphysik, Universit¨t Mainz, D-55099 Mainz, Germany u a 2 Institut f¨r Physik, Universit¨t Mainz, D-55099 Mainz, Germany u a 3 Institut Joˇef Stefan, University of Ljubljana, SI-1001 Ljubljana, Slovenia z 4 Rutgers University, Piscataway, NJ, USA Dept. f¨r Physik und Astronomie, Universit¨t Basel, CH-4056 Basel, Switzerland u a (February 8, 2008)

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arXiv:nucl-ex/0010020v1 31 Oct 2000

The recoil proton polarization has been measured in the p(e, e′ p )π 0 reaction in parallel kinematics around W = 1232 MeV, Q2 = 0.121 (GeV/c)2 and ? = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components Px /Pe = (?11.4 ± 1.3 ± 1.4) %, Py = (?43.1 ± 1.3 ± 2.2) %, and Pz /Pe = (56.2 ± 1.5 ± 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (?6.4 ± 0.7stat ± 0.8syst ) % was determined from Px in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.

? ?

comprises part of doctoral thesis present address: Physik Department E18, TU M¨nchen, Germany u ? permanent address: Laboratory for Theoretical Physics, JINR Dubna, Russia § present address: Dept. of Physics and Astronomy, University of Glasgow, UK ?? corresponding author, email: hs@kph.uni-mainz.de ?? present address: Laboratory for Nuclear Science, MIT, Cambridge, MA, USA

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The interaction between the three constituent quarks in a nucleon is mediated by gluons and, at long range, pions. Both exchange bosons produce a tensor force and, consequently, the nucleon wave function might have a D-state admixture [1], as is the case for the deuteron. Such an admixture results in an intrinsic deformation of the nucleon [2]. However, the spectroscopic quadrupole moment of the nucleon must vanish due to its spin 1/2. In the case of the ?rst excited state ?(1232) with spin 3/2 the short life-time prohibits a direct measurement of the quadrupole moment. On the other hand, in the electromagnetic N → ?(1232) excitation a Dadmixture will be visible as small quadrupole admixtures to the dominating M1 transition. In the decay of the ?(1232) resonance into the N π channel, this quadrupole mixing is associated with non-zero electric quadrupole to magnetic dipole (EMR) and Coulomb quadrupole to magnetic dipole ratios (CMR). These can be de3/2 3/2 ?ned as EMR = ?m{E1+ }/?m{M1+ } and CMR = 3/2 3/2 ?m{S1+ }/?m{M1+ }, where the pion multipoles, AIπ ± , l are characterized through their magnetic, electric or longitudinal (scalar) nature, A = M, E, S, the isospin, I, and the pion-nucleon relative angular momentum, lπ , whose coupling with the nucleon spin is indicated by ±. Recently, the EMR was determined at squared 4momentum transfer Q2 = 0 with linearly polarized real photons in the reaction p(γ, p)π 0 [3]. The result is EMR = (?2.5 ± 0.2 ± 0.2)%, in agreement with the combined partial wave analysis from p(γ, p)π 0 and p(γ, π + )n which allows an isospin decomposition of the multipoles [4–6]. The determination of the longitudinal quadrupole mixing requires pion electroproduction experiments. In the one-photon exchange approximation the N (e, e′ π)N cross section can be split into photon ?ux and the virtual photon cross section. Without target or recoil polarization, the latter is given by [7] dσv = λ · [RT + ?L RL + d?π +?RT T cos 2Φ + Pe 2?L (1 + ?)RLT cos Φ 2?L (1 ? ?)RLT ′ sin Φ]. (1)

? ? ?e{E1+ M1+ } and ?e{S1+ M1+ } from the RT T and RLT structure functions [3,4,8–14]. The interference terms are closely related to the EMR and CMR, respectively. Due to the unavoidable non delta-resonant contributions in the structure functions, it is important to measure the resonant amplitudes in several di?erent combinations with the background amplitudes. This possibility is o?ered by double polarization observables [15,16], which furthermore bene?t from their insensitivity to experimental calibration uncertainties. The general cross section for the p(e, e′ p )π 0 reaction with longitudinally polarized electrons and measurement of the recoil proton polarization is composed of 18 structure functions [7,17]. In parallel kinematics, where the proton is detected along the direction of the momentum transfer, the three components of the proton polarization take the simple form [16] (here the notation of ref. [7] is used):

σ0 Px = λ · Pe · σ0 Py = λ · σ0 Pz = λ · Pe ·

t 2?L (1 ? ?)RLT ′ n ?)RLT

(2) (3) (4)

2?L (1 +

l 1 ? ?2 RT T ′ .

The proton polarization independent cross section σ0 is dominated by |M1+ |2 . The axes are de?ned by y = ki × ? kf /|ki × kf |, z = q/|q | and x = y × z , where ki and ? ? ? ? kf are the momenta of incoming and scattered electron, respectively. The structure functions of Eq. (2)-(4) can be decomposed into multipoles of the π 0 p ?nal state, which are 3/2 1/2 related to the isospin multipoles by Al± = Al± + 2 Al± . 3 Displaying only the leading resonance terms with the dominant M1+ amplitude, the polarization components simply read

? σ0 Px = λ · Pe · c? · η · ?e{4S1+ M1+ + n.l.o.} ? σ0 Py = ?λ · c+ · η · ?m{4S1+ M1+ + n.l.o.}

(5) (6) (7)

σ0 Pz = λ · Pe ·

1 ? ?2 |M1+ |2 + n.l.o.,

The structure functions, Ri , parameterize the response of the hadronic system to the various polarization states of the photon ?eld, which are described by the transverse and longitudinal polarization, ? and ?L , respectively, and by the longitudinal electron polarization, Pe . The ratio cm cm λ = |pπ |/kγ is determined by the pion cm momentum

cm cm pπ and kγ = 1 (W ? Wp ), which is the photon equiva2 lent energy for the excitation of the target with mass mp to the cm energy W . Φ denotes the tilt angle between electron scattering and reaction plane. 3/2 3/2 Due to the smallness of the E1+ and S1+ multipoles 3/2 compared to the dominating M1+ amplitude, all experimental information so far is based on the extraction of m2

where η = ωcm /|qcm | denotes the ratio of cm energy and momentum transfer and c± = 2?L (1 ± ?). As a con3/2 sequence of the M1+ dominance, ?e M1+ vanishes very close to the resonance position (W = 1232 MeV). In this case the non-leading order (n.l.o.) contributions to Px are mainly determined by interferences of imaginary parts of background amplitudes with ?m M1+ . Since the background is predominantly composed of almost purely real amplitudes, only small n.l.o. contributions to Px are expected. The situation is di?erent for Py , because here all Born multipoles contribute, including higher partial waves. The large Py ? 40% that has recently been measured at MIT-Bates [18] should, therefore, not a priori be interpreted as evidence for non-resonant (imaginary!) background amplitudes in Px . Eqs. (5) and (7) show that, in the pπ 0 channel, CMR = ? ?e{S1+ M1+ }/|M1+ |2 can be almost directly determined 2

through either Px or the polarization ratio Px /Pz [16]. Furthermore, the ratio RL /RT of longitudinal to transverse response is model-independently accessible without Rosenbluth-separation [19]. At the Mainz Microtron MAMI [20] a p(e, e′ p )π 0 experiment with longitudinally polarized electron beam and measurement of the recoil proton polarization has been performed. The polarized electrons were produced by photoemission from strained GaAsP crystals using circularly polarized laser light [21]. During the experiment the beam helicity was randomly ?ipped with a frequency of 1 Hz in order to eliminate instrumental asymmetries. Longitudinal polarization after acceleration was achieved by ?ne-tuning of the energy of the microtron to 854.4 MeV. A 5 cm thick liquid hydrogen target was used. Beam currents up to 15 ?A with an average polarization of Pe = 75 % were available. The scattered electrons were detected at θe = 32.4? in Spectrometer B of the three spectrometer setup of the A1-collaboration [22]. At Q2 = 0.121 (GeV/c)2 a range of invariant energies of W = 1200 to 1260 MeV was covered. The recoil protons were detected in Spectrometer A at an angle of θp = 27? with a coincidence time resolution of 1 ns. The unobserved π 0 was identi?ed with a resolution of 3.8 MeV (FWHM) via its missing mass. After all cuts, the experimental background was reduced to 0.4 % of the accepted π 0 events and thus neglected. The proton polarization was measured with a focal plane polarimeter using inclusive p?12 C scattering [23]. The detector package of Spectrometer A, consisting of two double planes of vertical drift chambers for particle tracking and two planes of scintillators for triggering purposes [22], was supplemented by a 7 cm thick carbon scatterer followed by two double planes of horizontal drift chambers. This setup allowed the eventwise reconstruction of the proton carbon scattering angles ΘC and ΦC with a resolution of 2 mrad. The proton polarization could be extracted from the azimuthal modulation of the cross section

f f σC = σC,0 1 + AC (Py p cos ΦC ? Px p sin ΦC ) .

given by electron kinematics and the proton elastic form factors. From these measurements also the absolute value of Pe was determined, because in this case the error of AC cancels out in the determination of the quantities Px /Pe and Pz /Pe . The spin-precession matrix was used for the extraction of the recoil proton polarization in the p(e, e′ p )π 0 experiment. In order to account for the ?nite acceptance around nominal parallel kinematics (W = 2 1232 MeV, Q2 = 0.121 (GeV/c) , ? = 0.718), averaged MAID ? polarizations Px,y,z were generated with the Mainz Unitary Isobar Model (MAID2000) [25] for the event population of the experiment. With the ratios of nominal to MAID ? MAID averaged polarization, ρx,y,z = Px,y,z /Px,y,z = 1.247, 1.238 and 0.946, respectively, the experimental polarizations were extrapolated to nominal parallel kinematics: ? Px,y,z = ρx,y,z · Px,y,z . An additional systematic error is assigned to the polarizations due to the model uncertainty in ρx,y,z . It is estimated by a ±5 % variation of the M1+ multipole and a ±50 % variation of the other multipoles in MAID. The results are summarized in Table 1 along with the statistical and systematical errors. Px and Pz are given normalized to the beam polarization. Under the assumptions that the n.l.o. corrections in Eqs. (5) and (7) as well as the isospin-1/2 contributions in CMR 1 can be neglected, the quantities S = 4ηc? Px /Pe and

/Pe 1?? R = 4ηc? Px /Pe of the last two columns can be idenPz ti?ed with the CMR. In contrast to the beam helicity independent Py , false systematic asymmetries and systematic errors of the analyzing power have no impact on Px /Pe and Pz /Pe . On the other hand, the error caused by drifts of the beam polarization only a?ects Px /Pe and Pz /Pe . The uncertainty of the spin tracing a?ects all three polarization components and remains the only experimental systematic error in the ratio R, where both the electron beam polarization and the analyzing power drop out. The results for the three polarization components are shown in Figure 1 along with MAID2000 calculations. The curves represent the calculations for four values of the CMR: 0, ?3.2 %, ?6.4 % and ?9.6 %. Px is most sensitive to the CMR and from this component CMR = (?6.4 ± 0.7stat ± 0.8syst ) % is extracted. The result for the MAID2000 analysis of the ratio Px /Pz is CMR = (?6.8 ± 0.7stat ± 0.8syst ) %. Both values agree very well and are also close to S and particularly to R. Apparently, the various interference terms in the n.l.o. corrections of Eqs. (5) and (7) are small or cancel to a large extent. From the variation of the multipoles in MAID2000 a model dependence of the order of 1 % absolute of the extracted CMR is estimated. The 20 % discrepancy between MAID and the measured Py is not expected to further a?ect the extracted CMR, because Py is more sensitive to interferences other than the CMR.

2

√

(8)

σC,0 denotes the polarization-independent part of the inclusive cross section and AC the analyzing power, which was parameterized according to [24] for ΘC < 18.5? and according to [23] for ΘC ≥ 18.5? . f f The two polarization components Px p and Py p are measured behind the spectrometer’s focal plane. It is possible to determine all three components at the electron scattering vertex due to the spin precession in the spectrometer and the additional information provided by the helicity ?ip of the electron beam. The spectrometer’s ‘polarization-optics’ is described by a 5-dimensional spin precession matrix [23]. It was checked through a series of measurements of the focal plane polarization of protons from elastic p(e, e′ p ) scattering where the polarization is 3

In order to compare our result to those from previous π 0 electroproduction experiments with unpolarized electrons, Figure 2 shows CMR instead of CMR. The MAID2000 analysis of Px yields CMR = (?6.6±0.7stat ± 0.8syst ) %. The fact that CMR and CMR agree so well demonstrates how accurately, at the resonance position, the pπ 0 channel yields the CMR which is de?ned in the isospin 3 channel. Our result agrees with older data 2 [8–10] and preliminary new Bonn results [14], but a recent ELSA result [11] seems to be incompatible with all other data. Whether this has experimental or statistical origin, or points to an unexpected ?mS0+ background contribution — which was neglected in [11] — is still undecided [26]. The ratio RL /RT of longitudinal to transverse response can be obtained in various ways from the socalled reduced polarizations (RPs) χx,y,z [19,27]. However, the results vary signi?cantly. The smallest value, RL /RT = (4.7 ± 0.4stat ± 0.6syst ) %, is extracted from the quadratic sum χ2 + χ2 of the transverse RPs and y x +1.7 the largest one, RL /RT = (12.2 ?1.6stat +2.9syst ) %, from ?2.7 χz alone. Despite the non-linear error propagation in RL /RT (χz ), the probability is only a few percent that this discrepancy has purely statistical origin. As a consequence, the consistency relation between the transverse and the longitudinal RPs derived in [19] seems to be violated. This presently prohibits a reliable extraction of RL /RT but stresses the importance of a simultaneous measurement of all polarization components with further improved accuracy. In summary, we have measured the recoil proton polarization in the reaction p(e, e′ p )π 0 at the energy of the ?(1232) resonance. Due to the spin precession in the magnetic spectrometer all three polarization components Px , Py and Pz were simultaneously accessible. From Px the Coulomb quadrupole to magnetic dipole ratio was determined in the framework of the Mainz Unitary Isobar Model as CMR(Q2 = 0.121 GeV2 ) = (?6.4 ± 0.7stat ± 0.8syst ) %, which is in good agreement with the result obtained from the polarization ratio Px /Pz . There is only a moderate model dependence expected to remain. However, the consistency relation among the polarization components seems to be violated. The excellent operation of the accelerator and the polarized source by K. Aulenbacher, H. Euteneuer, and K.H. Kaiser and their groups is gratefully acknowledged. We thank R. Beck for many discussions. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 443), the Schweizerische Nationalfonds and the U.S. National Science Foundation.

[1] A. de R?jula, H. Georgi, S.L. Glashow, Phys. Rev. D 12, u 147 (1975). [2] S.L. Glashow, Physica 96 A, 27 (1979) [3] R. Beck et al., Phys. Rev. Lett. 78, 606 (1997) [4] G. Blanpied et al., Phys. Rev. Lett. 79, 4337 (1997) [5] O. Hanstein, D. Drechsel and L. Tiator, Nucl. Phys. A632, 561 (1998) [6] R. Beck et al., Phys. Rev. C 61, 035204 (2000) [7] D. Drechsel and L. Tiator, J. Phys. G 18, 449 (1992) [8] R. Siddle et al., Nucl. Phys. B 35, 93 (1971) [9] J.C. Alder et al., Nucl. Phys. B 46, 573 (1972) [10] K. B¨tzner et al., Nucl. Phys. B 76, 1 (1974) a [11] F. Kalleicher et al., Z. Phys. A 359, 201 (1997) [12] V.V. Frolov et al., Phys. Rev. Lett. 82, 45 (1999) [13] C. Mertz et al., nucl-ex/9902012 [14] R.W. Gothe, Prog. Part. Nucl. Phys. 44, 185 (2000) [15] R. Lourie, Nucl. Phys. A 509, 653 (1990) [16] H. Schmieden, Eur. Phys. J. A 1, 427 (1998) [17] A.S. Raskin and T.W. Donnelly, Ann. of Phys. 191, 78 (1989) [18] G. Warren et al., Phys. Rev. C 58, 3722 (1998) [19] H. Schmieden and L. Tiator, Eur. Phys. J. A 8, 15 (2000) [20] H. Herminghaus, Proc. Linear Accelerator Conf., Albuquerque, USA (1990) [21] K. Aulenbacher et al., Nucl. Instr. Methods A 391, 498 (1997) [22] K.I. Blomqvist et al., Nucl. Instr. Methods A 403, 263 (1998) [23] Th. Pospischil, doctoral thesis, Mainz (2000) and Th. Pospischil et al., submitted to Nucl. Instr. Methods A [24] M.W. McNaughton et al., Nucl. Instr. Methods A 241, 435 (1985) [25] D. Drechsel, O. Hanstein, S.S. Kamalov and L. Tiator, Nucl. Phys. A 645, 145 (1999) and http://www.kph.unimainz.de/MAID/maid2000/ [26] H. Schmieden et al., approved MAMI proposal A1-3/98 [27] J.J. Kelly, Phys. Rev. C 60, 054611 (1999)

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Observable Px /Pe (%) Measurement –11.4 stat. error ±1.3 false asymm. – δPe ±0.45 δAC – spin precession ±1.05 δρ ±0.9 total systematic ±1.4

Py (%) Pz /Pe (%) –43.1 56.2 ±1.3 ±1.5 ±1.61 – – ±2.25 ±0.87 – ±0.45 ±0.81 ±1.2 ±1.0 ±2.2 ±2.6

S (%) –5.2 ±0.6 – ±0.21 – ±0.48 ±0.41 ±0.7

R (%) –6.4 ±0.7 – – – ±0.62 ±0.51 ±0.8

0 5 0 -5 -10 -15 -20 0.0 0.2 0.4 Px/ Pe (%) -10 -20 -30 -40 -50 -60 0.0 0.2

2

80 Py (%) 70 60 50 40 30 20 10 0.4

2

Pz/ Pe (%)

TABLE I. Results for the recoil proton polarization in nominal parallel kinematics. The quadratic sum of the systematic error contributions yields the total systematic error. The extrapolation to nominal parallel kinematics as well as the ratios S and R, which approximate the CMR, are explained in the text.

0.0

0.2

0.4

Q

2

(GeV / c )

FIG. 1. Measured polarization components in comparison with MAID2000 calculations. The dashed, dot-dashed, full and dotted curves correspond to CMR = 0, ?3.2, ?6.4, ?9.6 %, respectively. The MAMI data (full circles) are shown with statistical and systematical error. For the Bates Py (cross) only the statistical error is indicated, the value is rescaled in ? and, though measured at the same Q2 , slightly shifted for clarity.

0

(%) Re(S1+ M1+) / |M1+|

2 *

-2 -4 -6 -8 -10 -12 -14 -16 0.2 0.4 0.6

2 2

0.8

1.0

Q

2

(GeV / c )

? FIG. 2. Result for ?e{S1+ M1+ }/|M1+ |2 as extracted from Px /Pe of this experiment (full circle) with statistical and systematical error, compared to unpolarized measurements from DESY, NINA, the Bonn synchrotron [8–10] (open circles) and ELSA [11] (open square), where only the statistical errors are indicated.

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