Bled Workshops in Physics Vol. 6, No. 1
A
Proceedings of the Mini-Workshop Exciting Hadrons (p. 78) Bled, Slovenia, July 11-18, 2005
Structure of the Roper resonance
from pion electro-production experiments
S. SircaQ'b
Q Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia bJoZef Stefan Institute, 1000 Ljubljana, Slovenia
Abstract. The Pu (1440) (Roper) resonance remains one of the least understood excited states of the nucleon. Relevant open issues of the theoretical and phenomenological analyses of the Roper are identified, and a proposal for a study of the Roper in a pion electro-production experiment with double-polarization observables is given.
1 Introduction
The Pn (1440) (Roper) resonance [1] is the lowest positive-parity N* state. It is visible only indirectly in partial-wave analyses of nN —> nN and nN —> nnN scattering as a shoulder around 1440 MeV with a large width. The Roper is buried underneath the Born backgrounds and merges with the tails of other neighbouring resonances (in particular the P33 (1232), Di3(1520), and Sn (1535)), and thus can not be resolved from the W-dependence of the cross-section alone. Furthermore, the methods by which the masses and widths of the Roper have been determined, differ significantly: from nN scattering, a Breit-Wigner mass of - 1470 MeV and width of - 350 MeV is extracted, while a speed-plot analysis (local maxima of |dT/dW|) yields - 1375 MeV and - 180 MeV, respectively [2]. In addition, due to its high inelasticity, the Roper resonance has a very atypical behaviour of ImTnN and exhibits multiple T-matrix poles in the complex energy plane on auxiliary Riemann sheets.
Although this four-star resonance is within the energy range of many modern facilities, the experimental analyses so far have not ventured far beyond the determination of its mass, widths, and photon decay amplitudes. Very little is known about its internal structure.
2 Two "standard" views of the Roper
The photo-couplings and helicity amplitudes of the Roper resonance have been computed in a multitude of approaches, and have yielded a set of predictions which at this stage can not be conclusively confirmed or ruled out by data. In the SU(6) quark model, the Roper can be understood as a radial excitation of the proton to the (1s)2 (2s)1 configuration. This excitation results in a "breathing
mode" of the proton, implying a sizable Coulomb monopole contribution (C0 or Si_). Some models describe the Roper as a gluonic partner of the proton, representing it as a (q3 g) hybrid baryon with three quarks oscillating against explicitly excited configurations of the gluon fields. In this picture, the CO strength should thus be highly suppressed, implying a predominantly magnetic dipole transition (M1 or Mi_), in contrast to the concept of "breathing". These two opposing concepts result in rather different predictions for the Q2-dependence of the transverse (Al/2) and scalar (S^/2) electro-production helicity amplitudes shown in Fig. 1. Of course, numerous other approaches have been suggested (see e.g. [3] for a review).
	• PDG (2004)
	■ DESY (1980)
	DESY (1986)
I	<:> CLAS prelim
f	□ Hall A prelim
ji............ i \.........	r _......
	............ (q3) radial exc
	...... (q g) hybrid
^ 50
> O
0.5 1 1.5 2 Q2 [ (GeV/c)2 ]
-50
-100
0.5
■ DESY (1980) DESY (1986) o CLAS prelim □ Hall A prelim
............... (q3) radial exc
1 E5 2 Q2 [ (GeV/c)2 ]
Fig. 1. Nucleon-Roper transverse (left) and scalar (right) helicity amplitudes for the charged (proton) state. The curves are for a Roper as a radially excited (q3) state or a (q3g) hybrid state.
3 Assessment of experimental situation
Experimentally, the Q2-dependence of the helicity amplitudes is not well known (see Fig. 1). A re-analysis of old DESY and NINA electro-production experiments yielded S^/2 consistent with zero, and gave contradictory results for the A^/2. The lack of (double)-polarized measurements is, to a great extent, responsible for such large uncertainties. Newer, polarized experiments at Jefferson Lab have yielded more precise values of S^/2 at Q2 = 0.4 and 0.65 (GeV/c)2. The A^/2 has also been extracted at Q2 = 0.4,0.65, and 1.0 (GeV/c)2. It appears to exhibit a zero-crossing in the vicinity of Q2 = 0.5 (GeV/c)2, although the situation remains unclear due to limited Q2-coverage and modest error-bars.
Kinematically most extensive data sets on single-pion electro-production in the Roper region come from Hall B of Jefferson Lab. Angular distributions and
W-dependence of the electron beam asymmetry ctlt ' have been measured for both channels in the P33(1232) region at Q2 = 0.4 and 0.65 (GeV/c)2 [4,5]. A complete angular coverage was achieved, and different non-resonant amplitudes were be separated in a partial-wave analysis. The Legendre moments D0, Dj, and D2 of the expansion were determined. The Dj appears to be sensitive to higher resonances, with contributions of about 15 — 20 % coming mainly from the Im(M|_S1 + ) interference, pointing to the relevance of the Roper.
Dispersion-relation techniques and unitary isobar models have been applied to analyze the CLAS ctlt' data at Q2 = 0.4 and 0.65 (GeV/c)2 spanning also the second resonance region, in order to extract the contributions of the P33 (1232), Pn (1440), Di3 (1520), and Sn (1535) resonances to single-pion production. Since both the pn0 and the nn+ channel were measured (facilitating isospin decomposition), the transverse helicity amplitude A1^ as well as the scalar Sp/2 could be extracted. The results show a rapid fall-off of Ap/2 and indicate its zero-crossing at Q2 ~ 0.5 — 0.6 (GeV/c)2 shown in Fig. 1. It was also shown that ctlt' is mainly sensitive to the imaginary part of P11 (1440), while the cross-section is sensitive to the real part of the P11 multipoles.
In Hall B, further experiments will be devoted to single-pion photo-production in both p(y, n+)n and p(y, p)n0 channels, with polarized beam and longitudinally as well as transversely polarized target using the CLAS detector. There is also a competing real-photon experiment of the A2 Collaboration at MAMI devoted to the measurement of polarized asymmetry G.
These uncertainties, in particular the location of the zero-crossing in Q2, are motivating the Hall A study of the Roper by means of double-polarization observables. A measurement over a broad range of W and Q2 would provide us with a rich data set on the transition amplitudes in electro-production.
4 Lessons learned from E91-011
Polarized electron beam and recoil-polarimetry capability of Hall A allow access to double-polarization observables in single-pion electro-production. Recoil-polarization observables are composed of different combinations of multipole amplitudes than observables accessible in the case of a polarized target. In the sense of experimental method, the measurements of Hall A would be complementary to the efforts with CLAS in Hall B.
A complete angular coverage of the outgoing hadrons to the extent of the CLAS detector in not possible in Hall A due to relatively small angular openings of the Hall A HRS spectrometers except at high Q2 where the Lorentz boost from the center-of-mass to lab frame focuses the reaction products into a cone narrow enough to provide a virtually complete out-of-plane acceptance. The E91-011 neutral-pion electro-production experiment in Hall A [6] was performed at sufficiently high Q2 = (1.0 ± 0.2) (GeV/c)2 and W = (1.23 ± 0.02) GeV to allow for a measurement of all accessible response functions, even those that vanish for coplanar kinematics. Two Rosenbluth combinations and 14 structure functions were separated, allowing for a restricted partial-wave analysis giving access to
all 1 < 1 multipole amplitudes relevant to the N —> A transition. Both extracted M-i_ and Si_ multipoles [6] in the pn° channel indicate a rising trend approaching the W - 1440 MeV region, pointing towards the Roper.
Unfortunately, the cross-sections at W - 1440 MeV (for any Q2) are about an order of magnitude smaller than in the A-peak. For high Q2 - 1 (GeV/c)2, where a large out-of-plane coverage would allow for a decent partial-wave analysis in Hall A, the cross-sections are even smaller. Furthermore, due to the zero-crossing uncertainty of the Mi _ multipole, it is not clear what value of Q2 to choose in order to have a prominent Ml signal. Furthermore, models indicate that the crucial features of the Roper multipoles (or helicity amplitudes) are visible at relatively small Q2 of a few 0.1 (GeV/c)2, nullifying the boost-advantage of the HRS.
We believe that a measurement in the spirit of the E91-011, attempting a precise extraction of the Roper multipoles from a complete partial-wave analysis at a single Q2-point, is not the most effective strategy at this moment. Instead, we believe that a precise measurement of a more restricted set of double-polarization observables, highly sensitive to the Roper multipoles, and spanning a broad range in Q2 and W, would yield a more rewarding and critical insight into the structure of the N R transition through comparison with models.
5 Options for a Roper experiment in Jefferson Lab Hall A
We believe that an attempt at a large-scale analysis of the Roper multipoles, aiming at a complete partial-wave analysis at a single Q2-point in the spirit of the N —> A experiment E91-011 [6], presently may not be the most effective approach to study the structure of the N R transition. We are working on designing an experiment that would measure recoil polarization components which exhibit high sensitivities to the Roper resonant multipoles and span a broad range in Q2 and W. It is this extended coverage that would allow for a more instructive study of the transition through comparison with models.
In anti-parallel kinematics for the p(e, e'p)n° process, the polarization components of the ejected proton P- and Py have the following multipole structure:
PxX - Rlt ' = Re {L°+E°+
+ (L°+ - 4L1+ - L1_)Mi_ + L1_(Mi+ - E°+ + 3Ei + ) - L°+(3Ei+ + Mi + )+ L1+(4Mi+ - E°+) + 12LJ + Ei + , (1) Py - RLt = -Im{•••}.	(2)
The L°+E°+ interference is relatively large and prominent in all kinematics. The combinations L|_(-E°+ + 3E1 +) and (-4L|+ - L|_)M1_ involving M1_ and/or Li _ are either relatively small or cancel substantially. The terms largest in magnitude and sensitivity are the L°+ M1_ and the L|_M1+ each involving one of the relevant Roper multipoles linearly. The contributions of the Mi _ and Si _ multi-poles to P-X and Py depend strongly on Q2 and W, so a measurement of P- and Py in a broad range of Q2 and W would allow us to quantify these dependencies.
We are considering performing two W-scans at fixed momentum transfers of Q2 of 0.13 and 0.33 (GeV/c)2 to explore the behaviour on and away from
the resonance position, and a more extensive Q2-scan at the resonance position W = 1440 MeV, with two overlapping settings. The W-scans could be performed at relatively small Q2 because the predicted asymmetries and their sensitivities to the relevant multipoles appear to be largest there. Two beam energies (2 and 3 GeV) could be used. The lower beam energy is needed in order to accommodate the low-Q2 end of the Q2-scan (and the corresponding W-scan) without running into the geometrical limits of the HRS spectrometers in Hall A. The proposed kinematics coverage is illustrated in Fig. 2.
> (D
- R
1400
o o1!
q7 This proposal
o9
o" o2'
-© o8
15

27
-e-
55
E91-011
A 1200
0	0.5	1
Q2 [ (GeV/c)2 ]
Fig. 2. The kinematic coverage in W and Q2 of the E91-011 experiment in Hall A (hatched area) and of the present proposal.
The sensitivity of Py to the resonant Roper multipoles Mi_ (proportional to the helicity coupling Ap/2) and Si_ (proportional to Sp/2) is different at low and high Q2, and varies through the W-range. At Q2 = 0.13 (GeV/c)2 (Fig. 3 left), the full prediction for Py at the resonance position is almost +100 %, with comparable Mi_ and Si_ contributions, while it is close to zero with the Roper switched off. At Q2 = 0.33 (GeV/c)2, Py drops to about +40 % (Fig. 3 right), dropping to about

40 % with the Roper switched off, with different roles of Mi_ and Si_ .At high Q2 = 0.73 (GeV/c)2 and above (not shown), the full Py is about -50 %, and only Si_ plays an appreciable role.
The role of the resonant multipoles changes very quickly, resulting in dramatic changes in the polarization components on a relatively narrow range in W (about ±60 MeV away from the resonance position to each side plus some additional coverage due to extended acceptance). The Py being so large (on the order of several tens of %), a measurement in a broad range of Q 2 and W would therefore enable us to study its dependencies quite precisely.
The W-dependencies of both PxX and become washed out at high Q 2. However, the large asymmetries persist in Py and, to some extent, also in the P^. A
measurement of the Q2-dependence of Py and PxX (see Fig. 4) therefore gives us yet another handle to quantify the role of the individual multipoles, and can be mapped onto the zero-crossing of the A^/2 helicity amplitude.
W[MeV]	W[MeV]
Fig.3. Sensitivity of Py to the resonant Roper multipoles Mi_ (helicity amplitude A1^) and Si _ (Sl/2), as a function of W at Q2 = 0.13 and 0.33 (GeV/c)2. The expected statistical uncertainties of the proposed measurement are also shown.
Fig.4. Sensitivity of the normal (induced) recoil polarization component Py and of the inplane component PxX/Pe to the resonant Roper multipoles M1- and Si_, as a function of Q2 at W = 1440 MeV.
References
1.	L. D. Roper, Phys. Rev. Lett. 12 (1964) 340.
2.	S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592 (2004) 1.
3.	O. Gayou, S. Gilad, S. Sirca, A. Sarty (co-spokespersons), Jefferson Lab Proposal PR05-010 (2005).
4.	K. Joo et al. (CLAS Collaboration), Phys. Rev. C 68 (2003) 032201(R).
5.	K. Joo et al. (CLAS Collaboration), Phys. Rev. C 70 (2004) 042201(R).
6.	J. J. Kelly et al. (Hall A Collaboration), Phys. Rev. Lett. 95 (2005) 102001.