Nucleon resonances in the fourth-resonance region

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<ul><li><p>DOI 10.1140/epja/i2011-11153-9</p><p>Regular Article Theoretical Physics</p><p>Eur. Phys. J. A (2011) 47: 153 THE EUROPEANPHYSICAL JOURNAL A</p><p>Nucleon resonances in the fourth-resonance region</p><p>A.V. Anisovich1,2, E. Klempt1,a, V.A. Nikonov1,2, A.V. Sarantsev1,2, and U. Thoma1</p><p>1 Helmholtz-Institut fur Strahlen- und Kernphysik, Universitat Bonn, Germany2 Petersburg Nuclear Physics Institute, Gatchina, Russia</p><p>Received: 17 September 2011 / Revised: 2 November 2011Published online: 14 December 2011 c Societa` Italiana di Fisica / Springer-Verlag 2011Communicated by Z.-E. Meziani</p><p>Abstract. Nucleon and resonances in the fourth-resonance region are studied in a multichannel partial-wave analysis which includes nearly all available data on pion- and photo-induced reactions o protons.In the high-mass range, above 1850MeV, several alternative solutions yield a good description of thedata. For these solutions, masses, widths, pole residues and photocouplings are given. In particular, wend evidence for nucleon resonances with spin-parities JP = 1/2+, . . . , 7/2+. For one set of solutions,there are four resonances forming naturally a spin-quartet of resonances with orbital angular momentumL = 2 and spin S = 3/2 coupling to J = 1/2, . . . , 7/2. Just below 1.9GeV we nd a spin doublet ofresonances with JP = 1/2 and 3/2. Since a spin partner with JP = 5/2 is missing at this mass,the two resonances form a spin doublet which must have a symmetric orbital-angular-momentum wavefunction with L = 1. For another set of solutions, the four positive-parity resonances are accompanied bymass-degenerate negative-parity partners as suggested by the conjecture of chiral symmetry restoration.The possibility of a JP = 1/2+, 3/2+ spin doublet at 1900MeV belonging to a 20-plet is discussed.</p><p>1 Introduction</p><p>One of the most striking successes of the quark modelwas the successful calculation of the spectrum and of themixing angles of low-lying excited baryons, using a har-monic oscillator potential and a hyperne interaction asderived from rst-order perturbative QCD [13]. In thecourse of time, the model was improved by taking intoaccount relativistic corrections [4] or by fully relativisticcalculations [5]. The eective one-gluon exchange interac-tion [14] was replaced by one-boson exchange interactionsbetween constituent quarks [6] or by instanton-induced in-teractions [5]. The improved baryon wave functions pro-vided the basis for calculations of partial decay widths [711], of helicity amplitudes [12,13], and of form factors [1417]. The spectrum of nucleon and resonances calculatedon the lattice [18] shows striking agreement with expecta-tions based on quark models: with increasing mass, thereare alternating clusters of states with positive and withnegative parity. No parity doubling is observed, and thenumber of expected states on the lattice and in quarkmodels seems to be the same. In spite of these consid-erable successes, there are still many open questions in</p><p> The N induced amplitudes, photoproduction observablesand multipoles for both solutions (BG2011-01 and 02) can bedownloaded from our web site as gures or in the numericalform (http://pwa.hiskp.uni-bonn.de).</p><p>a e-mail: klempt@hiskp.uni-bonn.de</p><p>baryon spectroscopy (for reviews, see [1921]) which needfurther investigations.</p><p>i) There are some low-mass baryon resonances whichresist a straightforward interpretation as quark model sta-tes. In eective eld theories of strong interactions, theseresonances can be generated dynamically from meson-ba-ryon interactions. Well-known examples are the Roperresonance N+1/2(1440) [22], the N1/2(1535) [23], and the1/2(1405) [24]. The relation between quark model statesand those dynamically generated is not yet explored.</p><p>ii) There is the problem of the missing resonances:quark models predict many more resonances than havebeen observed so far, especially at higher energies. Thisproblem is aggravated by the prediction of additional sta-tes, hybrid baryons, in which the gluonic string mediatingthe interaction between the quarks is itself excited [25].Their spectrum is calculated to intrude the spectrum ofbaryon resonances at 2GeV and above.</p><p>iii) Baryon excitations come very often in parity dou-blets, of pairs of resonances having opposite parity butsimilar masses. The occurrence of parity doublets is un-expected in quark models. It has led to the conjecturethat chiral symmetry could be restored when baryons areexcited [2629]. It has been suggested that the transitionfrom constituent quarks to current quarks can be followedby precise measurements of the masses of excited hadronresonances [30]. The splitting in (squared) mass betweentwo states forming a parity doublet (like (1950) F17 and</p></li><li><p>Page 2 of 19 Eur. Phys. J. A (2011) 47: 153</p><p>(2200)G17, 1.04GeV2) is slightly smaller than the meanmass square dierence per unit of angular momentum (thestring tension, 1.1GeV2). This eect can possibly be inter-preted as weak attraction between parity partners in the2GeV mass region and as onset of a regime in which chi-ral symmetry is restored [31]. This possibility depends, ofcourse, crucially on the assumption that chiral symmetryis restored in the high-mass part of the hadron excitationspectrum.</p><p>iv) A very simple phenomenological two-parametermass formula [32] describes the baryon mass spectrumwith an unexpectedly good precision. The formula canbeen derived [33] within an analytically solvable grav-itational theory simulating QCD [34] which is denedin a ve-dimensional Anti-de Sitter (AdS) space embed-ded in six dimensions. The mass formula predicts mass-degenerate spin multiplets with dened orbital angularmomentum L in which the orientation of the quark spin Srelative to L has no or little impact on the baryon mass,a prediction which needs to be conrmed or rejected byfurther experimental information.</p><p>In this paper, we report properties of nucleon reso-nances with masses of about 2GeV, a mass range which isoften called 4th-resonance region. The resonance regionsare well seen in g. 1a, starting with the (1232) tailas 1st-resonance region followed by peaks, indicating the2nd-, and 3rd- and 4th-resonance region. The propertiesof nucleon resonances are determined in a coupled-channelpartial-wave analysis of a large body of data. The gen-eral analysis method is documented in [3538], explicitformulas used to t the data are given in [39,40], ear-lier results can be found in [3944]. Recently, we haveenlarged considerably our database. In particular both,the recent high-statistics data [4553] on photoproduc-tion of hyperons but also the old low-statistics data onpion-induced hyperon production [5458] proved to bevery sensitive to properties of contributing resonances. Inthe rst paper [59], we reported evidence for N(1710)P11,N(1875)P11, N(1900)P13, (1910)P31, (1600)P33 and(1920)P33. The main aim was to investigate if reso-nances seen in the Karlsruhe-Helsinki (KH84) [60] and theCarnegie-Mellon (CM) [61] analyses of N elastic scat-tering but not observed by the Data Analysis Center atGWU [62] can be identied in inelastic reactions. The pos-itive answer encourages us to study the full spectrum ofnucleon resonances in the 2GeV region.</p><p>The data on hyperon production with the largeststatistics are those with K in the nal state. These aresensitive to nucleon resonances only. Data on K con-tribute to both, to nucleon and resonances, and thestatistical errors for data on this channel are considerablyhigher. For this reason, we concentrate here on nucleonresonances. resonances will be discussed when new high-statistics data on the p 00p and p0 productionchannels from ELSA are included in our database.</p><p>At present, existence and properties of nucleon reso-nances are mostly derived from energy-dependent ts tothe energy-independent partial-wave analyses of N elas-tic scattering data [6062]. Large discrepancies between</p><p>the results of the three groups reveal the weak points ofthese analyses: rst, the amplitudes cannot be constructedfrom the data without theoretical input. For a full ampli-tude reconstruction, the dierential cross-section d/d,target asymmetry, and spin rotation parameters need tobe known in the entire energy and angular range. With-out spin rotation parameters, only the absolute values ofthe spin-ip and spinnon-ip amplitudes |H| and |G| canbe determined but not their phases. Dispersion relationsmust be enforced but, unfortunately, their impact on thepartial-wave solutions seems not very well dened (judgedfrom the dierences in the results obtained by [6062]).Second, the inelasticity of the N amplitude is a free tparameter to be determined for every bin. It is uncon-strained by the decay modes of resonances. In practice,this freedom can be exploited to t the elastic partialwave amplitudes with equally acceptable 2 using a va-riety of models with a dierent content of resonances. Inthe approach presented here, the inelasticity of the energy-independent elastic N amplitudes are constrained by alarge number of data sets on inelastic reactions. The in-elasticity of the N amplitude is no longer a free t param-eter to be determined for every bin. Thresholds, couplingsto the dierent channels, and the opening of new channelsare properly taken into account.</p><p>We use the naming scheme adopted in [59]. For reso-nances listed in Review of Particle Properties (RPP) [63]we use the conventional names of the Particle Data Group:N(mass)L2I,2J and (mass)L2I,2J where I and J areisospin and total spin of the resonance and L the orbitalangular momentum in the decay of the resonance into nu-cleon and pion. For resonances not included in [63], we useNJP (mass) and JP (mass) which gives the spin-parity ofthe resonance directly.</p><p>2 Data, PWA method and ts</p><p>2.1 Data</p><p>The coupled-channel partial-wave analysis uses the Nelastic amplitudes, alternatively from KH84 [60] or fromSAID [62]. SAID results are given with errors; for KH84,no errors are given. We assume 5% errors for the ts.Data are included on the reactions p n, N K,N K, p 0p, p +n,p K, p K,p 00n, and p 00p, p 0p. Measure-ments of polarization variables, with polarization in theinitial or nal state or with target polarization, are in-cluded in the analysis whenever such data are available.A complete list of the reactions and references to the datais given in tables 15 of ref. [59]. The data sets we addedhere are dierential cross-section and recoil asymmetryon the +p K++ reaction in the mass region below1850MeV [6468], new CLAS data on p &gt; K+0 [69],new MAMI data on p p [70] and for the reactionp K0+ the dierential cross-section from Bonn [71].We now excluded from the analysis the p p dataon the target asymmetry since there seems to be an in-</p></li><li><p>Eur. Phys. J. A (2011) 47: 153 Page 3 of 19</p><p>0</p><p>5</p><p>10</p><p>15</p><p>20</p><p>25</p><p>30</p><p>35</p><p>40</p><p>45</p><p>1400 1600 1800 2000 2200 2400</p><p>1/2 3/2 1/2 5/2 +3/2 7/2 +</p><p>M(p), MeV</p><p> tot, b p 0p a) </p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>70</p><p>80</p><p>90</p><p>1400 1600 1800 2000 2200 2400</p><p>1/2 3/2 1/2 5/2 +3/2 7/2 +</p><p>M(p), MeV</p><p> tot, b p +n b) </p><p>0</p><p>1</p><p>2</p><p>3</p><p>4</p><p>5</p><p>6</p><p>7</p><p>8</p><p>9</p><p>1600 1800 2000 2200 2400</p><p>1/2 1/2 1/2 3/2 +1/2 5/2 </p><p>M(p), MeV</p><p> tot, b p p c) </p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>2</p><p>2.5</p><p>3</p><p>1800 2000 2200 2400M(p), MeV</p><p> tot, b p K+0 d) 1/2 1/2 1/2 3/2 3/2 7/2 +</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>0.8</p><p>1600 1800 2000 2200 2400</p><p>1/2 1/2 1/2 3/2 1/2 3/2 +</p><p>M(p), MeV</p><p> tot, b p K0+ e) </p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>2</p><p>2.5</p><p>3</p><p>1600 1800 2000 2200 2400</p><p>1/2 1/2 1/2 5/2 +1/2 7/2 +1/2 7/2 </p><p>M(p), MeV</p><p> tot, b p K+ f) </p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>2</p><p>2.5</p><p>3</p><p>1600 1800 2000 2200 2400</p><p>1/2 1/2 1/2 5/2 +1/2 7/2 +1/2 7/2 </p><p>M(p), MeV</p><p> tot, b p K+ g) </p><p>Fig. 1. The total cross-sections determined from the data (see text for the details) a) [73,74], b) [75], c) [76], d) [69], e) [71],and f,g) [53], and contributions from partial waves with resonances in the fourth-resonance region (solution BG2011-02). In (f)and (g), the contributions from two solutions labeled BG2011-01 and BG2011-02 are shown.</p><p>consistency between these data and new preliminary CB-ELSA/TAPS data [72].</p><p>The MAMI data were well tted, without need for sig-nicant changes in mass, widths or coupling constantsof the contributing resonances. In a narrow mass re-gion at about 1700MeV, statistically signicant devia-tions between data and t showed up. Dedicated ts weremade [77] to study this eect. The ts improved by in-troduction of a narrow resonance, or by introducing a Ncoupling in the S11 wave. Suggestions for experiments weremade capable to decide which alternative is realized in na-ture. For most resonances, the ELSA data set had no no-ticeable eect on their properties neither. But when thesedata were introduced in the t, an additional resonanceN3/2(1870) was needed (which was then also of substan-tial help in describing other data sets).</p><p>2.2 PWA method</p><p>The analysis method, [3540], uses relativistic invariantoperators which are constructed directly from the 4-vectors of the particles. Amplitudes are parameterized inmulti-channel K-matrices in the form</p><p>Aab(s) = Kac(I iK)1cb , (1)where is a diagonal matrix of phase volumes, I the iden-tity operator, and K the K-matrix. Its elements are pa-rameterized as</p><p>Kab =</p><p>g()a g</p><p>()b</p><p>M2 s+ fab. (2)</p><p>Here the index lists the K-matrix poles, and indicesa, b, c match the scattering channels. Background termsare partly added within the K-matrix either as constantsor in the form (a + b</p><p>s)/(s s0) with s0 simulating</p><p>left-hand cuts (s0 being negative, at a few GeV2), partlythey are added as t-channel meson-exchange or u-channelbaryon-exchange amplitude.</p><p>The photoproduction amplitude of the nal state bfrom the initial helicity state (h = 12 ,</p><p>32 ) is described in</p><p>the so-called P -vector approach which neglects rescatter-ing into the p channel:</p><p>ahb (s) = Pha (I iK)1ab . (3)</p><p>It includes, e.g., processes in which channel (a) is producedin the primary reaction and then re-scatters into the nalstate (b). The index h corresponds to the helicity ampli-tude a1/2 or a3/2. Explicit formulas for phase volumes,the parametrization of the P -vector, for K-matrix non-resonant terms and t-, u-exchange amplitudes are givenin [40]. These amplitudes are suciently exible to de-scribe the data mentioned above with good precision. Inthe pion-induced reactions the t- and u-channel exchangesare projected into the partial waves and contribution fromlowest partial waves (up to spin 3/2) are subtracted fromthe t- and u-exchange amplitudes. Thus, for the lowestpartial waves, these exchanges are taken eectively intoaccount as K-matrix non-resonant terms. The approachensures that we fully satisfy the unitarity condition forpion-induced reactions.</p></li><li><p>Page 4 of 19 Eur. Phys. J. A (2011) 47: 153</p><p>0</p><p>0.2 1745</p><p>d/d, b/sr1755 1765 1775 1785</p><p>0</p><p>0.21795 1805 1815 1825 1835</p><p>0</p><p>0.2</p><p>1845 1855 1865 1875 1885</p><p>0</p><p>0.2</p><p>1895 1905 1915 1925 1935</p><p>0</p><p>0.21945 1965 1975 1985 1995</p><p>0</p><p>0.22005 2015 2025 2035 2045</p><p>0</p><p>0.22055 2065 2075 2085 2095</p><p>0</p><p>0.22105 2115 2125 2135 2145</p><p>0</p><p>0.2 2155 2165 2175 2185 2195</p><p>0</p><p>0.2 2205</p><p>-0.5 0 0.5</p><p>2215</p><p>-0.5 0 0.5</p><p>2225...</p></li></ul>