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9

Electroproduction of the S11(1535) Resonance at High Momentum Transfer

C. S. Armstrong2∗, P. Stoler7, G. S. Adams7, A. Ahmidouch3,4, K. Assamagan3, S. Avery3, O. K. Baker3,8,P. Bosted1, V. Burkert8, R. Carlini8, J. Dunne8, T. Eden3, R. Ent8, V. V. Frolov7,†, D. Gaskell3, P. Gueye3,

W. Hinton3, C. Keppel3,8, W. Kim5, M. Klusman7, D. Koltenuk9, D. Mack8, R. Madey3,4, D. Meekins2,R. Minehart10, J. Mitchell8, H. Mkrtchyan11, J. Napolitano7, G. Niculescu3, I. Niculescu3, M. Nozar7,

J. W. Price7,‡, V. Tadevosyan11, L. Tang3,8, M. Witkowski7, S. Wood8

1Physics Department, American University, Washington D.C. 20016, USA2Department of Physics, College of William & Mary, Williamsburg, VA 23187, USA

3Physics Department, Hampton University, Hampton, VA 23668, USA4Physics Department, Kent State University, Kent, OH 44242, USA

5Physics Department, Kyungpook National University, Taegu, South Korea7Physics Department, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

8Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA9Physics Department, University of Pennsylvania, Philadelphia, PA 19104, USA10Physics Department, University of Virginia, Charlottesville, VA 22903, USA

11Yerevan Physics Institute, Yerevan, Armenia

(December 26, 2013)

The differential cross section for the process p(e, e′p)η hasbeen measured at Q2 = 2.4 and 3.6 (GeV/c)2 at center-of-mass energies encompassing the S11(1535) resonance. Thelatter point is the highest-Q2 exclusive measurement of thisprocess to date. The resonance width and the helicity-1/2transition amplitude are extracted from the data, and evi-dence for the possible onset of scaling in this reaction is shown.A lower bound of ≈ 0.45 is placed on the S11(1535) → p ηbranching fraction.

PACS Numbers: 13.60.Rj, 13.40.Gp, 13.60.Le, 14.20.Gk

I. INTRODUCTION

Baryon electroproduction allows the measurement oftransition form factors, which test models of hadronicstructure in ways that static baryon properties alonecannot. Recently much effort has gone into attemptsto reproduce observed transition form factors over alarge range of four-momentum transfer. At low four-momentum transfer, or Q2, the focus has been on in-corporating relativistic effects into the constituent quarkmodel (CQM) [1], using light-front [2–4] and other [5,6]approaches. At higher Q2, perturbative QCD (pQCD)sum rule calculations [7] and valence pQCD [8] have beenemployed. The applicable range in Q2 for these variousapproaches is not clear.

Among the most interesting of baryon case studiesis the S11(1535) resonance, which is one of the moststrongly excited states over all Q2, and which is eas-ily isolated because it is the only resonance that has alarge branching fraction to the η. The reproduction ofthe S11(1535) form factor has become a goal of manymodels, but the effort has been hampered by a lack ofprecise electroproduction data. In addition, the uncer-

tainty in the S11(1535) transition amplitude is limitedby knowledge of the full width and branching fraction tothe η. We report here on a measurement of the reactione + p → e′ + S11(1535) → e′ + p + η and an extractionof the helicity-conserving transition amplitude Ap

1/2at

Q2 = 2.4 and 3.6 (GeV/c)2. We also use a recent anal-ysis of inclusive (e, e′) data to put a lower bound on theS11(1535) → p η branching fraction.

II. THE EXPERIMENT

The experiment was performed in Hall C of theThomas Jefferson National Accelerator Facility (Jeffer-son Lab), shown in Figure 1. The Short Orbit Spectrom-eter (SOS), which is a resistive QDD device, was usedto detect electrons. The High Momentum Spectrometer(HMS), which is a superconducting QQQD spectrom-eter, was used to detect protons. Figure 2 shows theHMS detectors, which include drift chambers (DC1 andDC2) for determining track information, scintillator ar-rays (S1X/Y and S2X/Y) for triggering and time-of-flightmeasurement, and a threshold gas Cerenkov and elec-tromagnetic calorimeter for particle identification (PID).The SOS detectors are configured similarly.

The incident electrons had energies E = 3.245 and4.045 GeV for the Q2 = 2.4 and 3.6 (GeV/c)2 points,respectively. At each of the two Q2 points, the electronspectrometer was fixed in angle and momentum, thusdefining a central three-momentum transfer q and direc-tion of a boosted decay cone of protons. The protonspectrometer was stepped in angle and in momentum tocapture as much of this decay cone as possible. Datawere obtained at 33 (21) kinematic settings at the low(high) Q2 point.

Target protons were provided in the form of liquidhydrogen at 19 K flowing through a target of length

1

4.36 cm. The relative current of the electron beam wasmeasured by two resonant-cavity current monitors, whichwere calibrated periodically using the absolute beam cur-rent measurement of a parametric current transformer.The combined measurement had an absolute accuracy ofσ = 1.5%.

Electrons were identified in the SOS using theCerenkov detector and lead-glass calorimeter (see Fig-ure 3). In the HMS, protons were separated from pionsusing the time of flight measured between two pairs ofscintillator arrays (see Figure 4). In both spectrometers,tracking information was obtained from the drift cham-bers. Details of the experiment and analysis are given inRef. [9], and information on a simultaneous measurementof the ∆(1232) can be found in Ref. [10].

III. DATA ANALYSIS

The data were corrected for trigger and PID inefficien-cies (< 1%), track reconstruction inefficiencies (≈ 5%),computer and electronic dead times (< 5%), current-dependent target density changes (≈ 3%), and protonsundetected due to interactions in the detector stack(≈ 3%). The data were binned in W , cos θ∗η , φ∗

η , and

M2x (with 6, 10, 6, and 20 bins, respectively). Here W

is the invariant mass; θ∗η is the polar angle between thedirection of the η and the three-momentum transfer q

in the center-of-mass (c.m.) of the resonance; φ∗η is the

azimuthal angle of the η with respect to the electron scat-tering plane; and M2

x is the square of the missing massfor p(e, e′p)X . The η mesons were identified in the fi-nal state using M2

x . Figure 5 shows the missing massdistribution for a typical kinematic setting.

Modest backgrounds in M2x due to accidentals (≈ 2%,

shown in Figure 4) and protons penetrating the HMScollimator and magnet apertures (≈ 4%) were measuredand subtracted from the data. The remaining contin-uum background in missing mass was due to multi-pion(nπ) production (ranging from 30% to 50% of the reso-nance data) and a small (< 2%) contribution from target-window interactions. Two independent techniques wereused to subtract these remaining background events. Thefirst technique fitted a polynomial plus peak in M2

x to thedata in each (cos θ∗η, φ∗

η) bin (integrated over the W ac-ceptance for that kinematic setting), and then subtractedthe background contribution from each bin. The sec-ond technique scaled a Monte Carlo-generated nπ back-ground to match the data above and below the missing-mass peak and then subtracted this background fromeach (W , cos θ∗η, φ∗

η) bin.Three different models were used to simulate the nπ

background in the Monte Carlo: e p → e′ p π+ π−, e p →e′ ∆++ π− → e′ p π+ π−, and a crude approximation ofthree-body phase space. The Monte Carlo simulation wasalso used to simulate multiple scattering and ionizationenergy loss, and to correct for experimental acceptance

and the effect of radiative processes. Once the nπ back-ground was subtracted from both experimental and sim-ulated spectra, the experimental yields were corrected toaccount for finite Q2 acceptance. The differential crosssection was then given by the ratio of experimental tosimulated yield in each (W , cos θ∗η, φ∗

η) bin, normalizedby the simulation resonance cross section for that bin.

The cross sections obtained using the different nπ mod-els and the two background subtraction techniques allagreed within 2%; both the following figures and our fi-nal results were obtained using the first subtraction tech-nique together with a background generated by combin-ing two of the nπ models. Figure 6 shows data and fits forseveral typical (cos θ∗η , φ∗

η) bins of one kinematic setting.Figure 7 shows the result of fits for several kinematic set-tings, where for each setting we have integrated both thedata and their respective fits over the sixty individual(cos θ∗η , φ∗

η) bins.Using similar techniques we verified the well-known

1H(e, e′p) cross section [11] to within 2%.

IV. RESULTS

The five-fold differential cross section for the e p →e′p η process may be expressed as the product of thetransverse virtual photon flux Γ

T(Hand convention [12])

and the c.m. cross section for the electroproduction ofthe p η pair:

dσ

dΩedE′edΩ∗

η

= ΓT

dσ

dΩ∗η

(γv p → p η) . (1)

Previous data indicate that the c.m. γv p → p ηcross section is dominated by S-waves arising from theS11(1535) [13,14]. This dominance was confirmed by thepresent data, which showed that terms other than S-wavewere less than 7% and consistent with zero within the sta-tistical uncertainty of the data. Angular distributions forthe Q2 = 3.6 (GeV/c)2 data are shown in Figure 8.

From S-wave fits to the angular distributions, the to-tal cross section was calculated (at each Q2 point) as afunction of W :

σtot(W ) = 4πdσ

dΩ∗η

(γvp → pη) . (2)

This cross section, which consists of resonant and nonres-onant parts, was fitted with a relativistic Breit-Wignerplus nonresonant background curve,

σtot(W ) = σres(W ) + σnr(W )

= A2res

|p∗η|W

mp K

W 2R Γ2

R

(W 2 − W 2R)2 + W 2

R Γ2(W )

+ Bnr

√

W − Wthr , (3)

where WR is the resonance mass, ΓR is the full width,A2

res and Bnr are the Q2-dependent magnitudes of the

2

resonant and nonresonant terms, K is the equivalent realphoton energy [K = (W 2 − m2

p)/(2mp) ], and p∗η is the

three-momentum of the η in the c.m. of the p η system.The p η production threshold is at Wthr ≈ 1486 MeV(in the lowest W bin). At both values of Q2, thefitted value of the phenomenological nonresonant term(Bnr

√W − Wthr) was consistent with zero (with an un-

certainty of 1% of the resonant term).The energy-dependent resonance width Γ(W ) of Eq. 3

was parameterized in terms of the branching frac-tions bη (≡ Γη/ΓR at WR), bπ, and bππ according toWalker [15]. At present the Particle Data Group (PDG)gives an estimated range for the η branching fraction of0.30 ≤ bη ≤ 0.55 [16]. Therefore, fits to σres(W ) weremade assuming three sets of values for the branchingfractions (bη : bπ : bππ), which we define as Fits 1–3,respectively: (0.55 : 0.35 : 0.10), (0.45 : 0.45 : 0.10), and(0.35 : 0.55 : 0.10). A consequence of the p η thresholdis that the fit to σres(W ) cannot constrain the branchingfractions [9] (i.e., the three fits result in curves that arevirtually indistinguishable).

Based on a branching fraction constraint presented be-low, we consider Fit 1 (bη = 0.55) to σres(W ) to be thepreferred fit. The fits for both Q2 points are shown inFigure 9. With the Fit 1 branching fractions, we obtaina full width ΓR = (154 ± 20) MeV. This width changedless than 10 MeV over the range of branching fractionassumptions. The uncertainty is statistical added inquadrature with systematic. Our result agrees with thePDG estimate (≈ 150 MeV) [16], and appears lower thanthe recent Mainz measurement, ΓR = (203±35) MeV [13](see inset of Figure 9). These recent results disagreewith the value of ΓR = (68 ± 7) MeV obtained fromthe high-Q2 measurement of Ref. [14]. The form of theBreit-Wigner parameterization used by the three groupsis essentially the same, and so does not account for thedifferences in ΓR.

As noted above, the fit to σres(W ) cannot constrainthe branching fraction bη, but a comparison between thiswork and a recent fit to inclusive (e, e′) scattering [17]can. The fit by Keppel et al. models the inclusive crosssection in terms of transverse resonant (σTres

) and non-resonant (σTnr

) contributions using

dσ

dΩedE′e

= ΓT

[ σTnr(1 + ε Rnr) + σTres

] . (4)

In that work, the resonant contribution from each of thethree resonance regions (assumed to be entirely trans-verse) is fit using a Breit-Wigner form. The transversecomponent of the nonresonant contribution is fit usingthe phenomenological form

σ =

3∑

n=1

Cn(Q2) (W − Wthr)n− 1

2 , (5)

where the Cn(Q2) are fourth-order polynomials in Q2.The longitudinal component of the nonresonant cross sec-

tion, which enters through the longitudinal-to-transverseratio Rnr, is taken from a fit to deep inelastic data [18].

The resonant part of the second resonance region isdominated at low Q2 by the D13(1520). At higherQ2, however, the S11(1535) begins to dominate, and byQ2 = 4 (GeV/c)2 it is expected that the S11(1535) isresponsible for over 90% of the resonant cross section atW ≈ 1535 MeV [14]. Assuming that the resonant partof the inclusive cross section is the incoherent sum of theresonant contributions of the various decay channels, wecan use the inclusive and exclusive resonant cross sectionsto put a lower bound on bη [9]:

bη ≥ σres(S11 → p η)

σres(inclusive), (6)

where both cross sections are taken at W ≈ 1535 MeV. Avalue of bη = 0.55 results in good agreement between thehigh-Q2 point of this work and the inclusive fit; a valueof bη = 0.35, on the other hand, implies an inclusive crosssection 50% greater than the fit to the measured inclusivecross section, which is strong evidence that the branchingfraction is not this low. With the incoherent summationansatz given above, and assigning a 10% uncertainty tothe inclusive fit, we find a lower bound of bη = 0.45 with a95% confidence level. Assuming complete S11 dominanceat Q2 = 4.0 (GeV/c)2, we find a best fit of bη = 0.55.

Neglecting resonances other than the S11(1535), we re-late the amplitude Ap

1/2to σres by [13,19]

Ap1/2

(Q2) =

[

WR ΓR

2 mp bη

σres(Q2, WR)

1 + ε R

]1/2

. (7)

Here ε is the longitudinal polarization of the virtual pho-ton, and R = σ

L/σ

T. For R we assumed a parame-

terization based on a quark-model calculation [20]. Theexpected impact of the longitudinal-to-transverse ratio Ron the final physics result is small: a 100% error in theassumed value [≈ 4% at Q2 = 2.4 (GeV/c)2] correspondsto an uncertainty of less than 1% in the quoted value ofAp

1/2.

Table I gives final results for Fits 1–3. The uncertain-ties are systematic and statistical added in quadrature;for Ap

1/2we included estimates for the uncertainties from

ΓR and bη, which were obtained by varying these quanti-ties over reasonable ranges (150–200 MeV and 0.45–0.6,respectively) and studying the effect on the helicity am-plitude.

Table II lists the dominant sources of systematic un-certainty in the measurement and their impact on thedifferential cross section and on the helicity amplitude.

The uncertainty in d 2σdΩ∗

ηis given as a range, where the

largest uncertainties are for the highest W bins.Figure 10 shows the helicity amplitude results, along

with points calculated from previous e p → e′p η data andsome theoretical predictions. All data points in the figurewere calculated using Eq. 7 assuming ΓR = 154 MeV

3

TABLE I. Results. The uncertainties are systematic (in-

cluding estimated uncertainties in ΓR and bη for Ap1/2

) and

statistical added in quadrature. The top Ap1/2

result is for

Q2 = 2.4 (GeV/c)2, the bottom is for Q2 = 3.6 (GeV/c)2.Fit 1 is preferred for reasons discussed in the text. The ‘bestvalue’ for bη assumes S11 dominance at Q2 = 4 (GeV/c)2.

Quantity Fit 1 Fit 2 Fit 3

WR [MeV] 1532 ± 5 1527 ± 5 1521 ± 5ΓR [MeV] 154 ± 20 150 ± 19 147 ± 19

Ap1/2

[10−3 GeV−1/2] 50 ± 7 55 ± 8 63 ± 9

Ap1/2

[10−3 GeV−1/2] 35 ± 5 39 ± 6 44 ± 6

bη = Γη/ΓR > 0.45; best value ≈ 0.55

TABLE II. Dominant sources of systematic uncertainty,not including ΓR and bη (which affect Ap

1/2).

Fractional uncertainty (σ) in

Quantity d 2σdΩ∗

ηAp

1/2

Monte Carlo nπ model 1% to 7% 1%nπ subtraction 1% to 6% 1%Knowledge of E 1% to 10% 0.8%Knowledge of θe 0.2% to 11% 1%Experimental Acceptance 1% to 6% 1%

and bη = 0.55; if either assumption is wrong, all datapoints will scale together. Not included for any of thedata points in the figure are the uncertainties in ΓR andbη. Note the good agreement between the high-Q2 pointof the present work and the inclusive fit for bη = 0.55;assumption of a lower branching fraction shifts the dataup relative to the inclusive fit.

The present result differs from previous work in boththe strength and the slope of the S11(1535) form factor;most notably, we find a cross section 30% lower than thatof Ref. [14] [found by interpolating the results of this workto Q2 = 3 (GeV/c)2]. This difference is reduced in theamplitude by the square root relating Ap

1/2to the cross

section (Eq. 7). Although the present data were taken ata different value of ε than those of Ref. [14], a longitudinalcross section is not responsible for the difference betweenthe two measurements; a value of R ≈ 2.3 (which is ruledout at low Q2 [21,22]) would be necessary to account forthe discrepancy.

Of the various CQM curves shown in Figure 10, noneexhibit a slope as shallow as that of the data. Those thatindicate an amplitude at Q2 ∼ 3 (GeV/c)2 roughly con-sistent with experimental data also predict excess ampli-tude at lower Q2. Our data also have consequences for arecent coupled-channel model for the S11(1535) [27]; theproposed quasi-bound KΣ (five quark) state is expectedto have a form factor that decreases more rapidly than isobserved.

Figure 11 shows the quantity Q3Ap1/2

for the S11(1535),

which is predicted by pQCD to asymptotically approacha constant at high Q2 [7]. As has been pointed out else-

where [28], such scaling might be due to non-perturbativecontributions. While there is no strong scaling evidentin the figure, our data indicate that Q3Ap

1/2may be ap-

proaching a constant value by Q2 ∼ 5 (GeV/c)2.

V. CONCLUSIONS

We have presented the results of a precise, high statis-tics measurement of the e p → e′p η process at W ≈1535 MeV and at Q2 = 2.4 and 3.6 (GeV/c)2 [29]. Thecontribution of terms other than S-wave multipoles is ob-served to be less than 7%, which is consistent with previ-ous measurements. More importantly, the cross sectionobtained from the new data is about 30% lower and in-dicates a full width twice that of the only other exclusivemeasurement at comparable Q2 [14].

While the new data exhibit no strong perturbative sig-nature, they do have a Q2 dependence that is markedlydifferent than the older high-Q2 measurement. Evengiven the new (lower) cross section obtained from thismeasurement, however, relativized versions of the quarkmodel fail to reproduce the Q2 dependence seen experi-mentally.

A comparison of the new high-Q2 datum (the highestin existence) with a recent inclusive analysis indicates anS11(1535) → p η branching fraction of at least bη = 0.45 .Using bη = 0.55 we obtain ΓR = 154 MeV and a newmeasurement of Ap

1/2(Q2) (see Table I).

We wish to acknowledge the support of those in the Jef-ferson Lab accelerator division for their invaluable workduring the experiment. This work was supported in partby the U. S. Department of Energy and the National Sci-ence Foundation. CSA also thanks SURA and JeffersonLab for their support.

∗ Present address: Thomas Jefferson National Accelera-tor Facility, Newport News, VA 23606, USA. Email:csa@jlab.org.

† Present address: University of Minnesota, Minneapolis,MN, 55455.

‡ Present address: Physics Program, Louisiana Tech Uni-versity, Ruston, LA 71272.

[1] N. Isgur and G. Karl, Phys. Lett. 72B, 109 (1977);Phys. Lett. 74B, 353 (1978).

[2] S. Capstick and B. D. Keister, Phys. Rev. D 51, 3598(1995).

[3] This is a calculation in the light-front model of Ref. [2],which assumes pointlike quarks and simple wavefunc-tions, but (in contrast to the published work) uses thestandard convention for the normalization of states, anda different method for extraction of helicity amplitudes,along with numerical improvements. This effort is on-

4

going at the time of this writing. S. Capstick, personalcommunication (1998).

[4] R. Stanley and H. Weber, Phys. Rev. C 52, 435 (1995).[5] Z. Li and F. Close, Phys. Rev. D 42, 2207 (1990).[6] M. Warns et al., Z. Phys. C45, 613 (1990); Z. Phys. C45,

627 (1990); Phys. Rev. D 42, 2215 (1990).[7] C. E. Carlson and J. L. Poor, Phys. Rev. D 38, 2758

(1988).[8] D. B. Leinweber, T. Draper, and R. M. Woloshyn,

Phys. Rev. D 46, 3067 (1992).[9] C. S. Armstrong, Ph.D. dissertation, College of William

& Mary (unpublished) (1998).[10] V. V. Frolov et al., Phys. Rev. Lett. 82, 45 (1999);

V. V. Frolov, Ph.D. dissertation, Rensselaer PolytechnicInstitute (unpublished) (1998).

[11] The Monte Carlo simulation of 1H(e, e′p) used the dipoleform factor (1 + Q2/0.71)−2 for GEp , and the Gari-Krumpelmann parameterization for GMp [M. Gari andW. Krumpelmann, Z. Phys. A322, 689 (1985)].

[12] L. N. Hand, Phys. Rev. 129, 1834 (1963).[13] B. Krusche et al., Phys. Rev. Lett. 74, 3736 (1995).[14] F. Brasse et al., Z. Phys. C22, 33 (1984).[15] R. L. Walker, Phys. Rev. 182, 1729 (1969).[16] C. Caso et al., European Physical Journal C3, 1 (1998).[17] C. Keppel, Workshop on CEBAF at Higher Energies,

Newport News, 1994, edited by N. Isgur and P. Stoler,and C. Keppel, Ph.D. dissertation, The American Uni-versity (unpublished) (1994). This is a global fit to SLACresonance electroproduction data. It is similar to earlierwork done by Bodek [A. Bodek, Phys. Rev. D 20, 1471(1979)] and Stoler [P. Stoler, Phys. Rev. Lett. 66, 1003(1991); Phys. Rev. D 44, 73 (1991)]. A similar fit, butto a reduced data set, is found in L. M. Stuart, et al.,Phys. Rev. D58, 032003 (1998). In the kinematic regionof the present work, the Keppel and Stuart fits are inagreement at the 2% level.

[18] L. W. Whitlow et al., Phys. Lett. 250B, 193 (1990).[19] Particle Data Group, Rev. Mod. Phys. 48, S157 (1976).[20] F. Ravndal, Phys. Rev. D 4, 1466 (1971).[21] H. Breuker et al., Phys. Lett. 74B, 409 (1978).[22] F. Brasse et al., Nucl. Phys. B139, 37 (1978).[23] P. Kummer et al., Phys. Rev. Lett. 30, 873 (1973).[24] U. Beck et al., Phys. Lett. 51B, 103 (1974).[25] J. Alder et al., Nucl. Phys. B91, 386 (1975).[26] M. Aiello, M. M. Giannini, and E. Santopinto,

J. Phy. G24, 753 (1998). The curve shown is the cal-culation for ‘potential 1’ of that work.

[27] N. Kaiser et al., Phys. Lett. B362, 23 (1995);Nuc. Phys. A612, 297 (1997).

[28] N. Isgur and C. H. Llewellyn Smith, Phys. Rev. Lett. 52,1080 (1984); A. V. Radyushkin, Nucl. Phys. A527, 153c(1991).

[29] The angular distribution data are available upon request;please contact C. S. Armstrong.

FIG. 1. A plan view of the Hall C end station at JeffersonLab. The electron beam enters from the left, and the scatter-ing takes place in the cryogenic target placed in the beamline.In this experiment, outgoing particles were detected by twomagnetic spectrometers: the Short-Orbit Spectrometer (SOS)was used to detect electrons and the High-Momentum Spec-trometer (HMS) was used to detect protons.

FIG. 2. A side view of the HMS detector stack, as seenfrom the door of the detector hut. The detected particlestravel from left to right (along positive z).

FIG. 3. The response of the SOS calorimeter and Ceren-kov for events of a typical data run. The calorimeter responseEcal is the total energy deposited normalized to the particlemomentum, while the Cerenkov response Np.e. is the numberof photo-electrons detected. The events at Np.e. = 0 are π−

(note the peak at Ecal ≈ 0.25). The events at Np.e. > 0,Ecal > 0.7 are electrons. The events at Np.e. > 0, Ecal ≈ 0.3are caused by π− that produced knock-on electrons that trig-gered the Cerenkov. Note that the z axis is on a log scale.

FIG. 4. Velocity from time of flight (βHMS) and coincidencetime (the difference in time of arrival for the two spectrome-ters) for events of a typical data run. The band of events atβHMS ≈ 1 are π+, while those at βHMS ≈ 0.8 are protons. Thereal proton coincidences are at t = 0 ns, and the nominal 2 nsradio frequency structure of the beam is visible in the adja-cent accidental peaks. The low-βHMS tail emanating from thereal coincidence peak is most likely due to protons undergoinginteractions in the detectors after the drift chambers.

FIG. 5. A plot of M2x for one kinematic setting. The peak

at M2x ≈ 0.3 (GeV/c2)2 corresponds to undetected η mesons

in the final state (the peak at M2x ≈ 0.02 (GeV/c2)2 corre-

sponds to π0, the subject of Ref. [10]). Note the presenceof the multi-pion background as well as the radiative tail ex-tending to the right of the η peak.

FIG. 6. Fits to the M2x distribution for several typical

(cos θ∗η , φ∗

η) bins, one kinematic setting.

FIG. 7. Results of background fits for several typical kine-matic settings. Data are on the left and the correspondingMonte Carlo result is on the right. Each figure shows theintegration of sixty individual (cos θ∗

η , φ∗η) bins and their re-

spective fits (like those shown in Figure 6). The solid lineis the sum of the background and peak fits; the dashed lineshows the background only. The lines at the bottom of thedata plots show the small contribution from the accidentalcoincidence and HMS collimator backgrounds.

FIG. 8. Angular distributions for the Q2 = 3.6 (GeV/c)2

data. Each plot shows the cos θ∗η distribution for a single

(W , φ∗η) bin. The rows correspond to different bins in W ,

the columns to different bins in φ∗η . Data corresponding to

φ∗η = ±90 degrees are not shown; the out-of-plane experimen-

tal coverage was complete only for the lowest W bin (wherethe data looked similar to that in the φ∗

η bins shown here), andwas almost nonexistent at higher W . The lines are S-wavefits to the data.

5

FIG. 9. Fit 1 to σres(W ) for the two Q2 points of this work(errors on the data are statistical only). Note the presenceof the p η threshold. The inset shows the W -dependence ofthis cross section as measured by the present work (solid line,ΓR = 154 MeV), Ref. [13] (dashed line, ΓR = 203 MeV), andRef. [14] (dotted line, ΓR = 68 MeV). The curves in the insethave been normalized to the same magnitude.

FIG. 10. The helicity amplitude Ap1/2

(Q2) of the S11(1535),

measured via e p → e′p η, together with some theoretical pre-dictions. The data points ( [13,14,21–25] and the presentwork) were calculated using ΓR = 154 MeV, bη = 0.55, andthe parameterization of R referenced in the text. The errorsshown on previous data are statistical only. The errors shownfor the present work include both statistical and systematicuncertainties, with the exceptions noted in the text. The the-oretical curves of Refs. [3–6,26] are based on variants of theCQM. The curve from Ref. [7] is the result of a pQCD cal-culation. The curve from Ref. [17] is a fit to inclusive data.

FIG. 11. The quantity Q3Ap1/2

(Q2) for the S11(1535).The dot-dashed line is an exponential fit to the crosssection given by the two points of the present work(σres = 16.5 exp [−0.565 Q2] µb, where Q2 is in [(GeV/c)2]),and the solid line is a fit to inclusive data (as in Figure 10).The errors that are shown, and the assumed values for ΓR ,bη , and R, are the same as in Figure 10.

6

Cryogenictargets HMS

(protons)

SOS(electrons)

Beam

meters0 5 10

To BeamDump

Hall C

DC1

DC2S1X

S1Y

S2XS2Y

Pb-glassCalorimeter

x

zgas Cerenkov

SOS Particle ID

Cˇerenkov Np.e.

Cal. Ecal

010

2030

4050

600

0.2

0.4

0.6

0.8

1

1.2

1

10

10 2

10 3

HMS Particle ID and Coincidence Time

Coin time [ns]

βHMS

-20 -15 -10 -5 0 5 10 15 200.65

0.70.75

0.80.85

0.90.95

11.05

1.1

0

20

40

60

80

100

120

Mx2 [GeV2/c4]

π0

η

0

200

400

600

800

1000

0 0.1 0.2 0.3 0.4 0.5

0

25

50

75

100

0.25 0.3 0.35 0.40

20

40

60

0.25 0.3 0.35 0.4

0

10

20

30

40

0.25 0.3 0.35 0.40

25

50

75

100

0.25 0.3 0.35 0.4

M x2

M x2

M x2

M x2

Arb

. U

nit

s

M (data, setting 7) M (MC, setting 7)

M (data, setting 10) M (MC, setting 10)

M (data, setting 23) M (MC, setting 23)

0

1000

2000

3000

0.25 0.3 0.35 0.40

1000

2000

3000

0.25 0.3 0.35 0.4

0

500

1000

1500

2000

0.25 0.3 0.35 0.40

500

1000

1500

2000

0.25 0.3 0.35 0.4

0

500

1000

1500

2000

0.25 0.3 0.35 0.40

500

1000

1500

0.25 0.3 0.35 0.4

Q2 = 2.4 (GeV/c)

2A

rb. U

nit

s

2x

2x

2x

2x

2x

2x

0

0.1

0.2

0

0.1

0.2

0

0.1

0.2

0

0.1

0.2

0

0.1

0.2

-1 0 1 -1 0 1 -1 0 1

φη = -150 φη = -30 φη = 30 φη = 150

1.49

1.515

1.54

1.565

1.59

W[GeV]

cos θ*η

-1 0 1

dσ/

dΩ

*

[µb/s

r]

W [GeV]

σ res

[µb]

Q2 = 2.4 (GeV/c) 2

σ res

[µb]

Q2 = 3.6 (GeV/c) 2

0

1

2

3

4

5

6

1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66

00.20.40.60.8

1

1.5 1.55 1.6 1.65

NRCQM[3][4][5][6][26][7] (pQCD, high Q2)[17] (inc. fit, high Q2)

This work (TJNAF)[Q2 = 2.4, 3.6 (GeV/c)2]

[13][14][21][22][23][24][25]

Ap

1/2

[10-3

GeV

-1/2]

Q2 [(GeV/c)2]

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5 3 3.5 4

Previous ep → e’pη, W ≈ 1535 MeV dataThis work (TJNAF)Exponential fit to this work[7] (pQCD, high Q2)[17] (fit to inclusive)

Q3 A

p 1

/2 (S

11)

[G

eV5/

2 ]

bη = 0.55

Q2 [(GeV/c)2]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5