Constraining N∗(1535) parameters from the eta photoproduction

3

April 1997

PHYSICS

ELSENER

LETTERS B

Physics LettersB 397 (1997) 171-176

Constraining N* ( 1535) parameters from the eta photoproduction B. Krusche a, Nimai C. Mukhopadhyay

b, J.-F. Zhang b, M. BenmerroucheC

a II. Physikalisches Institut, Universitiit Giessen, D-35392 Giessen, Germany b Department of Physics, Applied Physics and Astronomy Rensselaer Polytechnic Institute, Troy, NY 12180-3590, c Linear Accelerator Laboratory University of Saskatchewan Saskatoon, SK S7N 5C6, Canada

USA

Received 6 January 1997 Editor: R.H. Siemssen

Abstract

Current broad uncertainties on the position, total width and eta branching ratio for N*( 1535), reported in the 1996 Particle Data Tables, can be narrowed down considerably utilizing the precise Mainz and Bonn data on eta photoproduction. We obtain here a precise determination of the total width from such a study, fixing other parameters. We find the set of N* (1535) parameters, suggested by the Particle Data Group (PDG), to be inconsistent with the experimental results from q-photoproduction. In particular, values for the photon helicity coupling and/or the eta branching ratio of the resonance, required in order to fit the data, are larger than the PDG values. This result has important consequences for the interpretation of the resonance in the framework of different models, including some exotic possibilities. @ 1997 Published by Elsevier Science B.V. PACS: 13.6O.Le;

12.40.Aa; 25.10.+s; 25.2O.Lj

Determination of electrostrong properties of baryon resonances has recently emerged as a powerful tool in applying QCD to the baryon structure [ 11. On the theory side, this research has moved from the use of the so-called “QCD-inspired” models [ 21 to computing hadron properties on the lattice [ 11. On the experimental side, advent of high duty-factor electron facilities and laser-driven light sources is allowing us to study photo- and electroproduction of mesons off nucleons with relative ease [ 3,4]. One example of this development that we study here is the excitation of the state N* ( 1535), which is easily probed by its decay channel, NV [ 4,5]. Other baryon resonances below 2 GeV do not have a large branching ratio to decay in this channel [ 61, a fact noted very early in the development of the quark shell model [ 71. Despite this advantage, the state N* ( 1535) continues

to provoke many passionate theoretical debates as to its characteristic parameters [ 8,9]. Recent incarnations of the QCD inspired models [ 21 have not been able to describe the properties of N* ( 1535) very well. To take some examples, the quark model by Bijker et al. [ 21, emphasizing the dynamic U( 7) symmetry, is unable to generate the relatively large decay width of this state for the NT channel. In fact, almost all quark model descriptions fail to explain the large NT branching ratio and many predict values of the photon . . hehclty amplitude Ay,z which are significantly larger than the number extracted from pion photoproduction experiments. As a consequence, even the very nature of the N* ( 1535) as a nucleon resonance has been questioned. In a recent approach by Kaiser et al. [ lo], the N*( 1535) has been treated as a meson-baryon n-cluster. On the other hand, Bijker et al. [2] fail

0370.2693/97/$17.00 0 1997 Published by Elsevier Science B.V. All rights reserved. PIZ SO370-2693(97)00160-3

172

B. Krusche et al./Physics

to fit this resonance into their quark model and suggest a quasi-bound NT [penta-quark] state close to threshold as a possible explanation of their failure. If such suggestions are correct, an interesting question would be: where are the regular three-quark states of the 70, l- multiplet anticipated in the quark model [ 21 with the quantum numbers l/2-, l/2? The precise determination of properties of this state is essential to further our understanding of these vital issues. Of particular interest is the electromagnetic helicity coupling Af,2. For an extended KI: molecule one expects than for the Besides an point [ 151,

a much faster drop of the coupling with Q2 classical 3-quark picture of the resonance. acute shortage of strength at the photon the experimental values of Ab2 show a

Q2-dependence which is unlike any model prediction. We recall at the outset the most recent ranges of these parameters reported by the Particle Data Group (PDG) [6]: MR = 1520 to 1555 MeV, I? = 100 to 250 MeV, b, = 0.30 to 0.55, Ay,2 = ( 70 + 12) x 10 -3 (GeV)

-l/2

.

(1)

The PDG do not recommend any nominal value of b,, but suggest MR and I to be 1535 MeV and 150 MeV, respectively, as representative of the above range. The parameters given above are mainly determined from pion photoproduction experiments, where the N* ( 1535) contribution is hard to extract. Clearly photoproduction of g-mesons, which is dominated by this resonance, is a much better suited channel. It is important to note that all analyses of the recent precise cross-section measurements of Y+P+P+T

(2)

carried out in Mainz with the TAPS-detector [4], produce significantly larger values for A:,,. Different analyses generated values of 98 [ 51, 102 [ 161, 107 [17], 111 [18], and 125f25 [4] (all in units of 10m3 (GeV) -1/2). The discrepancy of these values with the results from pion photoproduction is even more severe if one takes into account that PDG average already includes the value from Ref. [ 51.

Letters% 397 (1997) 171-176

The analyses quoted above differ from one another in detail: e.g. in the treatment of possible nonN*( 1535) background terms, which are ignored in some [ 4,181, but included at different levels in the others. However, as it turns out, the crucial difference among them stems from the large uncertainties of the hadronic widths of the resonance. If the above values for AT,, are renormalized to the same hadronic widths, assuming a Breit-Wigner shape of the resonance, they all fall within a narrow range. For example, assuming I = 150 MeV and b, = 0.45, we obtain A; 2= 103 [5], 105 [16], 108 [17], 102 [18], and 10 d [4]. It is noteworthy that these values are still considerably higher than the PDG average for Ay,2, although the PDG values for the width and the branching ratio have been used. This long introduction brings us to our objective in this Letter: which is to show that the difserentiut and total cross-section measurements from Mainz [4], combined with the total cross section for velectroproduction close to the photon point recently measured at Bonn [ 111, allow us to narrow the value of the total decay width I of N* ( 1535) very significantly, given the position MR and the branching ratio b, for the decay of N*( 1535) into the Nr] channel. In particular, we find that the combined set of parameters ( MR = 1535 MeV, I = 150 MeV, and A’;‘,, = (70 f 12) x 10e3 (GeV)-‘/2) suggested by the PDG in [ 61 is inconsistent with the new v-photoproduction data. In the first step of our analysis we employ a simple Breit-Wigner (SW) fit to the combined data set using:

+$J)

_!a

=

2m,(A$2)2bqMRr

q;R k* (MS - W2)2 + M2,1Y2x2 ’

(3)

where x = bVz

q;

+ b,2

71

+ b,,

(4)

%r

with the notation as in [4]. Using 0.45 as the central value of the the range for the branching ratio b, given in [ 61 this fit gives us a narrow range for the N* ( 1535) parameters: MR = (1544~!~2.0&6) I’=(203f9&5)

MeV,

MeV,

B. Krusche et al. / Physics Letters B 397 (1997) 171-l 76

700

800

900

photon energy [MeVl Fig. 1. BW-fit of the phase-space reduced total cross section (effective 1E,+ 1amplitude) for the eta photoproduction as a function of the photon lab energy, E,. Data are from Mainz [4] (solid squares) and Bonn [ 1l] (open circles). The solid line shows the best BW-fit to the data up to 875 MeV. The dashed line shows a BW-curve corresponding to the parameters suggested by the PDG, the dashed-dotted line the BW-curve corresponding to the upper limits for b, and A’1/2 from the PDG compilation and the dotted curve the result of a fit with bv and A$ limited to the upper PDG limits and all other parameters fitted to the data.

A;,, = (124 1.3 & 15) x 1O-3 (GeV) -“*,

(5)

where the first error is from the fit and the second reflects the uncertainty of bq. The result of this fit is compared to the total cross sectioh data in Fig. 1. The electroproduction data at energies above 875 MeV are excluded from the fit. It is impossible to fit the entire range from threshold up to 900 MeV with one BW-curve. At the highest energies other contributions, presumably from higher lying resonances cannot be ignored anymore. The figure also shows that the BW-curve corresponding to the PDG parameters MR = 1535 MeV, l? = 150 MeV, ATi = 70 x and bq = 0.45 does not fit the data. low3 (GeV)-‘/* Even the curve corresponding to the upper PDG limits and b,, = 0.55 clearly of A$, = 82 x 10e3 (GeV)-l/* falls short of the data. Varying additionally position and width of the resonance does not help us either. The best fit obtained for AT,, 5 82 x lop3 (GeV) -‘/* and b, < 0.55, which is also shown in the figure, is excluded by 20 standard deviations. So far we have ignored non-N*( 1535) contributions to the cross section due to weakly contributing resonances like the N*( 1520) and from background contributions like the nucleon Born terms or vector

173

meson exchange [ 51. However, the measured differential cross sections [ 41 are not completely isotropic, indicating the presence of such terms. Their importance was investigated and emphasized in Ref. [ 51. Thus it is evident that the parameters given in Eq. (5) are subject to an additional uncertainty due to the background ambiguities. We now study these effects in the framework of the effective Lagrangian approach (ELA) developed in [ 51. Our theoretical procedure consists of using the standard ELA which has the nucleon s- and u-channel Born terms, t-channel p and w exchanges and sand u-channel nucleon resonances, N* ( 1535) and N* ( 1520). This is a truncated version of a fit that included more intermediate nucleon resonances [ 121. From our fits to the Mainz differential cross section data off protons from the eta production threshold to E, = 790 MeV, we fix the parameters of our ELA, as is discussed elsewhere in detail [ 51. In our ELA, various fitting strategies are possible. We adopt the following: we keep the rlpp coupling constant g7/ fixed, along with the parameters for the vector mesons. These are determined using theoretical inputs as well as exploratory fits [ 51. We then choose a value for MR for the N*( 1535) and allow the fit to yield a value of the width lY that produces the lowest x2 for such a fit, fixing the value of bv = 0.45. The outcome is illustrated in Fig. 2, where different (MR, IY) sets are shown yielding a minimum chi-square( x2), for a fixed set of background parameters. Thus, we cannot uniquely fix the values of MR and l?. This is not surprising, because the 1ELA has more parameters than the BW-fit and because differential cross sections are needed to fix the background parameters, we can .only fit up to 790 MeV, i.e. below the peak position of the N* ( 1535)) which introduces correlations between position and widths. Only when MR is also kept fixed, a uni’que value of r emerges. Thus, keeping the N*( 1535) resonance position MR fixed at the PDG nominal value of 1535 MeV, we get the following parameter values: I’ = 185 f 45 MeV, A:,, = 115 f 15 x low3 GeV’j2,

(6)

while keeping MR fixed at 1544 MeV, the value suggested by our BW-fits to the total cross section yields

B. Krusche et al./Physics

Fig. 2. The x2 profile for our sample ELA fits of the Mainz data [4] on the differential cross section for eta photoproduction. Background parameters for nucleon and vector meson Born terms are kept fixed. Various minima of x2 correspond to different MR values, showing the correlation of l? with MR. The dot-dashed line is for MR = 1539 MeV, the solid line, 1542; the dotted line, 1544; the long dashed line, 1546; the dashed line, 1549.

Letters B 397 (1997) 171-176

Fig. 3. Various ELA fits of the Maim differential eta photoproduction cross section data used as predictions for the reduced total cross section. Data points: circles are Mainz [ 41, stars are Bonn [ 111. Various ELA models, with b,, = 0.45, are as follows: the lower solid line, MR = 1535 MeV, r = 185 MeV, the dotted line: (1539, 203); the dashed line: (1542,212); the long dashed line: (1544, 212); the dot-dashed line: (1546, 220); the upper solid line: ( 1549, 230).

I=212&20MeV A;,2 = 120 & 11 x 10m3 GeV1/2

(7)

for the minimum x2 for our nominal values of other background parameters. It should be noted that again, even if the PDG resonance position is used, the value for AT,2 is significantly larger than the largest PDG value. On the other hand, the parameters extracted for the same resonance position from the ELA-fit (7) and the BW-fit (5) are consistent. We then use the fitted parameters to predict the total cross section (Fig. 3)) measured both at Mainz [ 41 and at Bonn [ 111. Agreement there is a check of our ELA, and an indication that the inference of the properties of the dominant resonance excitation, that of N* ( 1535) in the reaction (2), is quite reasonable. It is interesting to note that using the Mainz data set as a basis for the fit of our ELA parameters, up to photon energy E, = 790 MeV, allows us to predict the total cross section or the effective Eo+ amplitude in a region well beyond the Mainz data set [4]. This can now be tested, thanks to the new electroproduction data set from Bonn [ 111. The latter allows us to extract total eta photoproduction cross-section for E, between 800 and 900 MeV. Our ELA prediction agrees nicely with the Bonn data up to 875 MeV (Fig. 3). Beyond that, it breaks down in the same way as discussed above for

the BW-fits. The energy E, = 875 MeV corresponds to a cm energy of W = 1588 MeV, thereby showing that we have covered the N*( 1535) resonance quite adequately in this fit. The breakdown occurs when other nucleon resonances are excited. This is not surprising, given the change of dynamics that come into play from the onset [ 121 of excitation of the N*( 1650) and N* ( 1710) at higher energy, neglected in our low energy ELA fits. It is obvious from Fig. 3 that different fits are able to describe the total cross section data, although the fit using the PDG resonance position is somewhat worse than the fit using the resonance parameters extracted from the BW-fits. The additional uncertainty in the ELA fits as compared to the BW-fits is due to the small background contributions which are neglected in the latter. These contributions cannot be adequately tested by total cross section data, which are quite insensitive to them due to the strong dominance of the N* ( 1535). On the other hand, this insensitivity is the justification for fitting the total cross section data with a single BW curve in the first place. The level of uncertainty in the BW-fits due to the background contributions is demonstrated in Fig. 4. The total cross section from the best ELA fit is compared to the total cross section computed from this fit after switching

B. Krusche et al./Physics

Fig. 4. Contribution of background terms to the total cross section. The solid line shows the total cross section computed from the ELA fit with MR = 1544 MeV, r = 212 MeV, the dotted line the total cross section computed from the same fit after switching off all non-N*( 1535) contributions.

off all non-N* ( 1535) contributions. The contribution of background terms close to the resonance position (M 800 MeV) amounts only to a few per cent and is thus much smaller than the large differences between the data and the BW-fits using the PDG value of A;,,. The main conclusions of this work are the following: While the reaction (2)) analysed in the framework of the ELA, does not constrain MR, I? and b, simultaneously to a very narrow domain, Jixirzg any two constrains the third quite severely. Thus, taking MR as given by 1544 MeV suggested by our fits [ 451 from a broadly acceptable range of parameter values and 0.45 as the PDG central value of b,, we can constrain l? and A$2 within the relatively narrow region:

I = 212 & 20 MeV, A;,2 = ( 120 it 11 f 15) x 10M3 GeV’/*, for a reasonable, but not exhaustive, variation of the background parameters to fit the observed differential cross section. The first error is an estimate of their uncertainties characteristic of our fit in the framework of the effective Lagrangian approach (ELA) [ 51, the second reflects the uncertainty of b,. Making a simple BW-fit (Fig. 1) of the total cross section data [4,11] gives the far more constraining values (3)) which are, however, subject to an additional uncertainty due to the neglect of the background terms.

Letters B 397 (1997) 171-176

175

In summary, the current broad uncertainties of the parameters MR, l? and b,, characterizing the property of the N* ( 1535)) given above in ( 1) , reported in the 1996 edition of the Particle Properties, can be narrowed down considerably, utilizing the precisely measured differential and total eta photoproduction cross sections at Mainz [4] and Bonn [ 111 that have become recently available. In particular, fixing MR at the value suggested by the BW fits of the total cross section allows us to fix the total resonant width for the N* ( 1535) resonance within 20 MeV, a considerable improvement over the present factor of 2.5 variation reported by the PDG. The set of parameters proposed for the W(1535) by the PDG is inconsistent with the v-photoproduction data. Using the PDG values significantly underestimates the N* ( 1535) strength, even if we use the PDG upper limits. Unfortunately, it is impossible to decide if the problem is caused by the helicity coupling A:,, or the branching ratio b,. Even in the BW-fits these two parameters are so strongly correlated that they cannot be fitted at once. This question is very important. If we allow a variation of b, only within the PDG limits, AT,, must be significantly larger, which means, that the properties of the resonance are better described by older non-relativistic quark models than their latest relativistic cousins. If, on the other hand, AS2 lies within the PDG limits, b, must be considerably larger than 0.55, which, from the quark model point of view would make this resonance quite exotic. Clearly further high quality experimental data are necessary to resolve this question. Differential cross sections up to higher energies and experiments with polarization observables that are currently in progress [ 131, will help to determine the small background contributions which still cause considerable uncertainties, while the (7~, v) reaction studies [ 141 should constrain MR and b, independently. More theoretical works, particularly on the lattice, are needed to clarify the hadron structure situation at the QCD level. Our work reported here should help this process. Three of us (M.B., B.K. and N.C.M.) thank the Institute of Nuclear Theory, Seattle, for bringing us together at the stimulating CEBAF/INT N* Workshop, where this work has been planned. One of us (B.K.) is supported by Bundesministerium fur Bil-

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dung und Forschung and by Deutsche Forschungsgemeinschaft (SFB 20 1). Two of us (N.C.M. and J.F.Z.) are grateful for the US Department of Energy support. M.B. is supported by the Natural Sciences and Engineering Research Council of Canada.

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[ 101 [ 111

References [ 121 [l] [2]

[ 31 [4] [5 ]

D. Leinweber, T. Draper and R.M. Woloshyn, Phys. Rev. D 46 (1992) 3067. R. Koniuk and N. Isgur, Phys. Rev. D 21 (1980) 1868; S. Capstick, Phys. Rev. D 51 (1995) 3598; 2. Li, Phys. Rev. D 52 (1995) 4961, and priv. comm. ( 1996). R. Bijker, F. Iachello and A. Leviatan, nucl-th 9608057, and Phys. Rev. D (in press); L.Ya. Glozman and D.O. Riska, Phys. Rep. 268 (1996) 263. A.M. Sandorfi and M. Khandaker, Phys. Rev. Lett. 70 ( 1993) 3835. B. Krusche et al., Phys. Rev. L&t. 74 (1995) 3736; 75 (1995) 3023; Phys. I&t. B 358 (1995) 40. M. Benmerrouche and N.C. Mukhopadhyay, Phys. Rev. Lett. 67 (1991) 1070; M. Benmerrouche, NC. Mukhopadhyay and J.-F Zhang, Phys. Rev. D 51 (1995) 3237; N.C. Mukhopadhyay, J.-F Zhang and M. Benmerrouche, Phys. Rev. I_&. 75 ( 1995) 3022; Phys. L.&t. B 364 (1995) 1.

[ 131 [ 141

[ 151

[ 161

[ 171 [ 181

R.M. Bamett et al., Phys. Rev. D 54 (1996) 1. A. Mitra, Phys. Lett. B 51 (1974) 149. S. Capstick and W. Roberts, Phys. Rev. D 49 (1994) 4570. See, for example, R.A. Amdt, I. Strakvskii and R.L. Workman, Phys. Rev. D 52 (1995) 5381. N. Kaiser, l?B. Siegel and W. Weise, Phys. Lett. B 362 (1995) 23. M. Wilhelm, Ph.D. thesis, University of Bonn, unpublished; B. Schoch et al., Prog. Part. Nucl. Phys. 34 (1995) 43. M. Benmerrouche, Ph.D. thesis, Rensselaer Polytechnic Inst. ( 1992)) unpublished. J.-P Didilez, priv. comm. (1996); M. Rigney et al., in: Few Body (ICFBP # 14) (1994) 510. A.M. Bergdolt et al., Phys. Rev. D 48 (1993) R2969; E. Chiavassa et al., Phys. L&t. B 322 (1994) 270; B 337 (1994) 192. V. Burkert, Proceedings of, the Excited Baryons 1988 workshop, Troy New York, eds. G. Adams, N.C. Mukhopadhyay and P. Stoler (World Scientific, 1988) p. 122; M. Benmerrouche, N.C. Mukhopadhyay and J. -I? Zhang, Phys. Rev. Lett. 77 (1996) 4716. Ch. Sauermann et al., Proc. of the VI Int. Symp. on Meson-Nucleon Physics and the structure of the Nucleon, Blaubeumn, Germany (July 1995), and private communication. G. Knochlein et al., Z. Phys. A 352 (1995) 327. Z. Li, Phys. Rev. D 52 (1995) 4961, and talk at the CEBAF/INT Workshop on N* Physics (Sept. 1996).