Evidence for the N ′ (1720)3/ 2 + Nucleon Resonance from Combined Studies of CLAS π + π − p Photo- and Electroproduction Data
V.I. Mokeev, V.D. Burkert, D.S. Carman, L. Elouadrhiri, E. Golovatch, R.W. Gothe, K. Hicks, B.S. Ishkhanov, E.L. Isupov, K. Joo, N. Markov, E. Pasyuk, A. Trivedi
EEvidence for the N (cid:48) (1720)3 / + Nucleon Resonance from Combined Studies of CLAS π + π − p Photo- and Electroproduction Data
V.I. Mokeev a, ∗ , V.D. Burkert a , D.S. Carman a , L. Elouadrhiri a , E. Golovatch b , R.W. Gothe c , K. Hicks d ,B.S. Ishkhanov b , E.L. Isupov b , K. Joo e , N. Markov a,e , E. Pasyuk a , A. Trivedi c a Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA b Skobeltsyn Institute of Nuclear Physics and Physics Department, Lomonosov Moscow State University, 119234 Moscow, Russia c University of South Carolina, Columbia, South Carolina 29208, USA d Ohio University, Athens, Ohio 45701, USA e University of Connecticut, Storrs, Connecticut 06269, USA
Abstract
The analysis of the nine 1-fold differential cross sections for the γ r,v p → π + π − p photo- and electroproduction reactionsobtained with the CLAS detector at Jefferson Laboratory was carried out with the goal to establish the contributingresonances in the mass range from 1.6 GeV to 1.8 GeV. In order to describe the photo- and electroproduction data with Q -independent resonance masses and hadronic decay widths in the Q range below 1.5 GeV , it was found that an N (cid:48) (1720)3 / + state is required in addition to the already well-established nucleon resonances. This work demonstratesthat the combined studies of π + π − p photo- and electroproduction data are vital for the observation of this resonance.The contributions from the N (cid:48) (1720)3 / + state and the already established N (1720)3 / + state with a mass of 1.745 GeVare well separated by their different hadronic decays to the π ∆ and ρp final states and the different Q -evolution oftheir photo-/electroexcitation amplitudes. The N (cid:48) (1720)3 / + state is the first recently established baryon resonance forwhich the results on the Q -evolution of the photo-/electrocouplings have become available. These results are importantfor the exploration of the nature of the “missing” baryon resonances. Keywords: two pion production, resonance couplings, missing resonances
PACS:
1. Introduction
Studies of the N ∗ spectrum have been driven for along time by the search for the so-called “missing” baryonstates [1, 2, 3, 4, 5]. Different quark models predict manymore excited states than those that have been observed inexperiments [6, 7, 8]. These predictions rely on the ap-proximate SU(6) spin-flavor symmetry demonstrated bythe pattern of the observed nucleon resonances [9]. Thesemodel expectations are supported by the studies of the N ∗ spectrum from the QCD Lagrangian within Lattice-QCD(LQCD) [10], consistent with the independent results fromcontinuum QCD approaches [11, 12]. In the early few µ sexpansion phase of the universe, the transition from a de-confined mixture of almost massless bare quarks and gaugegluons to a hadron gas of confined quarks and gluons withdynamically generated masses was mediated by the fullspectrum of excited hadrons. This has been demonstratedin the studies of this phenomenon within LQCD and quarkmodels [13]. Studies of the N ∗ spectrum, therefore, ad-dress the important open questions on the symmetry of ∗ Principal corresponding author
Email address: [email protected] (V.I. Mokeev) the strong QCD dynamics underlying nucleon resonancegeneration and on the emergence of hadronic matter inthe universe.The data for exclusive meson photoproduction offer apromising avenue in the search for missing resonances[1, 2, 3, 4, 5] through their decays into final statesother than the most explored πN channel. The miss-ing resonances are expected to have substantial decaysto the ηN , K Λ, K Σ, ππN , and πηN final states ac-cessible in photoproduction, where their photocouplingsare expected to be comparable with those for the ob-served resonances [6, 7, 14]. Recently, several of the long-awaited missing resonances were discovered in a globalmulti-channel analysis of exclusive meson photoproduc-tion data [15], for which the CLAS KY photoproductiondata [16, 17, 18, 19] provided a decisive impact. Nine newnucleon resonances of three- or four-star status were in-cluded in the recent edition of the PDG [20]. This discov-ery is consistent with the expectation of SU(6) symmetryin the generation of the N ∗ spectrum. However, this sym-metry also predicts many other resonances that have notyet been observed, making a continuation of the effortson the missing resonance search an important avenue inhadron physics. Preprint submitted to Elsevier April 29, 2020 a r X i v : . [ nu c l - e x ] A p r he CLAS data on exclusive meson electroproductionhave extended the capabilities in the search for fur-ther missing resonances [21, 22, 23]. Both the πN and π + π − p electroproduction data demonstrate an increase inthe relative resonant contributions with increasing four-momentum transfer Q [24, 25], making exclusive electro-production also promising for the exploration of the N ∗ spectrum.The opportunities for observation of new nucleon reso-nances were demonstrated in early analysis of π + π − p elec-troproduction data on three independent 1-fold differentialcross sections [23]. A reasonable description of the data inthe third resonance region was achieved either by imple-menting a N (cid:48) (1720)3 / + resonance or by including onlythe known resonances but significantly increasing the de-cay width of the established N (1720)3 / + to the π ∆ finalstate.In this paper we analyze nine independent π + π − p elec-troproduction [23] and photoproduction cross sections re-cently published by the CLAS Collaboration [26]. Asuccessful description of both of these sets of data with Q -independent resonance masses, and total and partialhadronic decay widths, validates the contributions fromresonance states. We present evidence for a N (cid:48) (1720)3 / + resonance that has been observed together with the known N (1720)3 / + state from combined studies of the CLAS π + π − p photo- and electroproduction data [23, 26] for in-variant masses W from 1.6 – 1.8 GeV in the range ofphoton virtualities Q < . . The combined stud-ies of the π + π − p photo- and electroproduction data pro-vide new clarity that supports the existence of the new N (cid:48) (1720)3 / + state. Note that a global multi-channelanalysis of exclusive meson photoproduction data [27] re-ports two close resonances with J P = 3 / + spin-parityin the 1.7 – 1.8 GeV mass range, and that quark mod-els [7, 8, 28] also predict new low-lying baryon states with J P = 3 / + in this mass interval.
2. Experimental Data and Analysis Tools
In the previous studies of CLAS π + π − p electroproduc-tion data off protons [23], two invariant mass distribu-tions over M π + p and M π + π − , and the π − center-of-mass(CM) angular distributions were analyzed for W from 1.6– 1.8 GeV and Q from 0.5 – 1.5 GeV . A pronouncedresonance structure at W ≈ . Q bins covered by these data centered at 0.65 GeV ,0.95 GeV , and 1.3 GeV (see Fig. 1). A successful descrip-tion of these data was only achieved either with a muchlarger branching fraction for the N (1720)3 / + resonancedecays to the π ∆ final state in comparison with those fromexperiments with hadron probes or by implementing a new N (cid:48) (1720)3 / + baryon state with parameters determinedfrom the data fit. Both solutions offered an equally rea-sonable description of the limited previous CLAS π + π − p electroproduction data set. In the current analysis we unambiguously establishedthe resonances contributing to π + π − p photo- and electro-production in the third resonance region. We have an-alyzed the data for this channel on the nine 1-fold dif-ferential cross sections and fully integrated cross sectionsover the final state kinematic variables sorted into nine25-MeV-wide bins in W and four Q -bins at 0 GeV ,0.65 GeV , 0.95 GeV , and 1.30 GeV . The fully in-tegrated cross sections and their description achievedwithin the the JLab-Moscow (JM) meson-baryon model[29, 30, 31] are shown in Fig. 1.The production of the π + π − p final state hadrons canbe fully described by the 5-fold differential cross sectionover the invariant masses of the two pairs of the final statehadrons M ij , M jk ( i, j, k = π + , π − , p (cid:48) ) and over the threeangular variables shown in Fig. 2. After integration of the5-fold differential cross section over the different sets offour variables, nine 1-fold differential cross sections weredetermined for:a) Three invariant mass distributions: dσdM π + p (cid:48) , dσdM π + π − , dσdM π − p (cid:48) ;b) Three angular distributions over θ : dσd ( − cos θ π − ) , dσd ( − cos θ π + ) , dσd ( − cos θ p (cid:48) ) ;c) Three angular distributions over α : dσdα [ π − p ][ π + p (cid:48) ] , dσdα [ π + p ][ π − p (cid:48) ] , dσdα [ p (cid:48) p ][ π + π − ] .The chosen nine 1-fold differential cross sections are themost suitable for the exploration of the nucleon resonancesexcited in the γ r,v + p s -channel with subsequent decaysinto the π ∆ and ρp final states. The kinematic grid andthe number of data points incorporated into the analysisare listed in Table 1. Each of the nine 1-fold differentialcross sections, while computed from a common 5-fold dif-ferential cross section, offers complementary informationthat is essential to gain insight into the resonant contribu-tions.The data analysis is carried out within the JM model.This approach incorporates all essential mechanisms seenin the data that give rise to peaks in the invariant massesand the sharp dependencies in the angular distributions.Less pronounced mechanisms were established from thecorrelations between their contributions into the different1-fold differential cross sections. The full γ r,v p → π + π − p (cid:48) amplitudes are described in the JM model as a super-position of the π − ∆ ++ , π + ∆ , ρp , π + D (1520), and π + F (1685) sub-channels with subsequent decays of theunstable hadrons to the final state, and direct 2 π produc-tion mechanisms, where the reaction does not go throughthe intermediate process of forming unstable hadrons.The JM model incorporates contributions from all well-established N ∗ states with observed decays into the π ∆and ρp final states listed in Refs. [26, 31]. For the resonantamplitudes, a unitarized Breit-Wigner ansatz is employed,which makes the resonant amplitudes consistent with re-strictions imposed by a general unitarity condition [30].2 , GeV s , m b Q =0.0 GeV W, GeV s , m b Q =0.65 GeV W, GeV s , m b Q =0.95 GeV W, GeV s , m b Q =1.30 GeV Figure 1: (Color Online) Description of the fully integrated CLAS γ r,v p → π + π − p (cid:48) photo-/electroproduction cross sections achieved withinthe JM model [29, 30, 31] (shown by the black solid lines). The error bars include the combined statistical and point-to-point systematicuncertainties for the photoproduction data and only the statistical uncertainties for the electroproduction data. The full resonant contribu-tions are shown by the dashed lines and the dot-dashed lines represent the resonant parts when both the N (1720)3 / + and N (cid:48) (1720)3 / + contributions are taken out. The contributions from the N (1720)3 / + and N (cid:48) (1720)3 / + resonances are shown by the thin red and bluelines, respectively. The vertical lines locate the Breit-Wigner mass of the N (cid:48) (1720)3 / + state. The good description of the nine 1-fold differen-tial π + π − p photo- and electroproduction cross sections,achieved within the JM model for W < . Q -range up to 5.0 GeV , allows isola-tion of the resonant contributions [21, 26, 31] necessaryfor the extraction of the resonance parameters. The N ∗ photo-/electroexcitation amplitudes ( γ r,v pN ∗ photo- /electrocouplings) were determined from analyses of the π + π − p photo-/electroproduction data for the resonancesin the mass range up to 2.0 GeV from the photoproduc-tion data and up to 1.8 GeV from the electroproduc-tion data. Consistent results on the electrocouplings ofthe N (1440)1 / + and N (1520)3 / − resonances in the Q -range from 0.2 GeV to 5.0 GeV from independent anal-3 pπ − p ′ θ π − α A B θ p ′ π + θ π − θ π − θ π − θ π + Figure 2: Angular kinematic variables for the reaction γp → π + π − p (cid:48) in the CM frame. The variable set with i = π − , j = π + , and k = p (cid:48) ,includes the angular variables for θ π − (the polar angle of the π − )and α [ π − p ][ π + p (cid:48) ] , which is the angle between the planes A and B ,where plane A ([ π − p ]) is defined by the 3-momenta of the π − andthe initial state proton and plane B ([ π + p (cid:48) ]) is defined by the 3-momenta of the π + and the final state proton p (cid:48) . The polar angle θ p (cid:48) is relevant for the set with i = p (cid:48) , j = π + , and k = π − , while thepolar angle θ π + belongs to the variable set with i = π + , j = p (cid:48) , and k = π − . yses of the dominant πN and π + π − p electroproductionchannels validates the extracted N ∗ parameters from theJM model. The photocouplings of most resonances in themass range from 1.6–2.0 GeV, their hadronic decays to the π ∆ and ρp final states, as well as the electrocouplings ofseveral resonances determined within the JM model areincluded in the PDG [20].
3. Evidence for the New N (cid:48) (1720)3 / + Resonancein the π + π − p Data
The previous studies of π + π − p photo-/electroproduction with CLAS demonstrated a substantialdecrease of the relative non-resonant contributions withincreasing Q [26, 31]. In the current studies, the resonantstructure clearly seen in π + π − p electroproduction at W ≈ . Q = 0 GeV (see Fig. 1). On the other hand, the sixangular distributions are sensitive to the resonant contri-butions both in the photo- and electroproduction data.The resonance decays into the π ∆ and ρp final stateshave a substantial impact on the three invariant massdistributions shown in Fig. 3. The Q -dependence of the π + π − p photo-/electroproduction amplitudes are definedby the Q -evolution of the nucleon resonance photo-/electrocouplings and the real/virtual photon+hadronvertices in the non-resonant mechanisms. However, theresonance masses, as well as their total and partialhadronic decay widths, should remain the same in all Q -bins, as was observed in the analyses of all exclusivemeson electroproduction data from CLAS [21, 24, 30, 31]. This makes a combined analysis of the π + π − p photo-/electroproduction data of particular importance forestablishing the resonances contributing to the π + π − p channel.The analyses of the CLAS π + π − p photo- [26] and elec-troproduction [23] data were carried out within the re-cent version of the JM model in the W -range from 1.6 –1.8 GeV and for Q from 0.0 – 1.5 GeV with the goalto establish the resonances contributing in the third res-onance region. For the N (1440)1 / + , N (1520)3 / − , and∆(1620)1 / − resonances, the initial values of their π ∆ and ρp decay widths were taken from analyses of the CLAS π + π − p electroproduction data [30, 31], while for the otherresonances we used the total hadronic decay widths fromthe PDG [20] and the branching fractions for their decaysinto the π ∆ and ρp final states from Ref. [32]. The ini-tial values of the resonance photo-/electrocouplings weretaken from the parameterization in Ref. [33] of the avail-able CLAS/world data results detailed in Ref. [34]. Thestarting values of the photo-/electrocouplings and the de-cay widths into the π ∆ and ρp final states for the new N (cid:48) (1720)3 / + resonance were taken from Refs. [23, 26].In the data fit we simultaneously varied the resonancephoto-/electrocouplings, the π ∆ and ρp decay widths, andthe parameters of the non-resonant amplitudes describedin Refs. [26, 30, 31]. Q -independent hadronic decaywidths for all resonances were imposed in the fit. Theparameters of the resonant and non-resonant mechanismsof the JM model were sampled around their initial val-ues, employing unrestricted normal distributions with awidth ( σ ) of 30% of their initial values. In this way, theJM model provided a description of the observables withintheir uncertainties for most of the data points. For eachtrial set of the fit parameters, we computed the nine 1-folddifferential π + π − p cross sections and estimated the χ /dp ( dp ≡ data point) values in point-by-point comparisons.We selected the computed cross sections from the datafit within the range χ /dp < χ /dp max , where χ /dp max was determined so that the computed cross sections werewithin the data uncertainties for most data points. Themean values and RMS widths for the resonance parame-ters obtained from the fit were used as estimates of theircentral values and their corresponding uncertainties.Analyses of the π + π − p photo- and electroproductiondata were carried out independently. The resonancephoto-/electrocouplings and the total, π ∆, and ρp de-cay widths were inferred from the fits over W from 1.6– 2.0 GeV for the photoproduction data, and over W from1.6 – 1.8 GeV and Q from 0.5 – 1.5 GeV for the elec-troproduction data. In the evaluation of χ /dp for theelectroproduction data, only the statistical uncertaintieswere taken into account, while for the photoproductiondata, the combined contribution from the statistical andpoint-to-point systematic uncertainties was employed sincethe systematic uncertainties dominate the accuracy of thephotoproduction data. Parity conservation imposes therequirement of equal values of the dσdα i ( i = π + , π − , p (cid:48) )4 able 1: The kinematic grid and the number of data points for the 1-fold π + π − p differential photo-/electroproduction cross sections used inthe analysis within the JM model. Q , GeV Number of bins over Total number W , M π − π + , M π + p (cid:48) , M π − p (cid:48) of data points θ π − , θ π + , θ p (cid:48) for π + π − pα [ π − p ][ π + p (cid:48) ] , α [ π + p ][ π − p (cid:48) ] , α [ pp (cid:48) ][ π − π + ]
9, 16, 16, 16,0.0 14, 14, 14, 118814, 14, 149, 10, 10, 10,0.65 , 0.95 , 1.30 10, 10, 10, 20255, 5, 5
Table 2: N (1720)3/2 + hadronic decay widths and branching fractions into π ∆ and ρp determined from independent fits to the data oncharged double-pion photo- [26] and electroproduction [23] off protons accounting only for contributions from previously known resonances. N (1720)3/2 + N ∗ total width Branching fraction Branching fractionMeV for decays to π ∆ for decays to ρN electroproduction 126.0 ± < ± α i and 2 π − α i . This sym-metry requirement was accounted for in the computationof these cross sections within the JM model. The depar-ture of the data points from this requirement, seen onlyin the Q =1.3 GeV bin, was taken into account in theevaluation of χ /dp .A successful description of the angular θ i ( i = π + , π − , p (cid:48) ) distributions at W ≈ . J P = 3 / + spin-parity. This is consistent with the results from previ-ous studies [23]. The essential role of the J P = 3 / + spin-parity excited nucleon states in the generation of theresonant contributions in the third resonance region canbe seen in Fig. 1, where the resonant contributions inthe fully integrated π + π − p photo-/electroproduction crosssections are presented with all relevant resonances includedand when the contributions from the N (1720)3 / + and N (cid:48) (1720)3 / + resonances are taken out.We performed two different fits using: • the contributions from only well-established res-onances listed in Refs. [26, 31], including the N (1700)3 / − and N (1720)3 / + states (fit A); • the fit A assumptions also adding a new N (cid:48) (1720)3 / + resonance with mass, total, π ∆, and ρp decay widths,and photo-/electrocouplings fit to the data (fit B).Both fits result in good descriptions of the CLAS datawith a comparable quality for photo- and electroproduc-tion. Representative examples of the description of thenine 1-fold differential cross sections with fit B are shownin Fig. 3, where the cross sections from the fits within the range χ /dp < χ /dp max are shown by the family of curvesoverlaid on each plot.Note that the decay widths of the well-known N (1720)3 / + resonance into the π ∆ and ρp final statesdepend considerably on the implementation of the new N (cid:48) (1720)3 / + state. Accounting for only the well-known resonances results in contradictory values for the N (1720)3 / + decays into the ρp final state inferred eitherfrom the independent photo- or electroproduction datafits with more than a factor of four difference (see Ta-ble 2). This makes it impossible to describe both the π + π − p photo- and electroproduction cross sections with Q -independent resonance masses, as well as total and par-tial hadronic decay widths, accounting for only the well-known resonances.After implementation of the new N (cid:48) (1720)3 / + reso-nance, a successful description of all nine 1-fold differential γ r,v p → π + π − p photo-/electroproduction cross sectionshas been achieved. The total, π ∆, and ρp hadronic de-cay widths of all resonances in the third resonance regionas inferred from the fits at different Q -bins remain Q -independent (see Table 3) over the entire range of Q upto 1.5 GeV that is covered by the measurements [23, 26].This supports the existence of the new N (cid:48) (1720)3 / + res-onance. Indeed, if the implementation of this (or any) newbaryon state was unphysical, then it would not be possi-ble to reproduce the π + π − p photo-/electroproduction datain a wide Q -range with Q -independent decay widthsbecause of the evolution of the non-resonant contribu-tions with Q observed in the π + π − p electroproductiondata [31].The electrocouplings of the new N (cid:48) (1720)3 / + reso-5 p + p, GeV d s / d M , m b / G e V W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV W=1.71 GeV, Q =0.0 GeV M p + p - , GeV M p - p, GeV q p - , deg d s / ( d - c o s q ) , m b / r a d q p + , deg q p' , deg a [p - p ][p + p' ] , deg d s / d a , m b / r a d a [p + p ] [p - p' ] , deg a [ p' p ] [p - p + ] , deg0 200 050100150 1 1.5 0.25 0.5 0.75 1 1.501020 0 100 200 0 100 200 0 100 2000246 0 200 0 200M p + p, GeV d s / d M , m b / G e V W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV W=1.71 GeV, Q =0.65 GeV M p + p - , GeV M p - p, GeV q p - , deg d s / ( d - c o s q ) , m b / r a d q p + , deg q p' , deg a [p - p ][p + p' ] , deg d s / d a , m b / r a d a [p + p ] [p - p' ] , deg a [ p' p ] [p - p + ] , deg0 2000255075100 1 1.5 0.25 0.5 0.75 1 1.5051015 0 100 200 0 100 200 0 100 200024 0 200 0 200M p + p, GeV d s / d M , m b / G e V W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV W=1.71 GeV, Q =0.95 GeV M p + p - , GeV M p - p, GeV q p - , deg d s / ( d - c o s q ) , m b / r a d q p + , deg q p' , deg a [p - p ][p + p' ] , deg d s / d a , m b / r a d a [p + p ] [p - p' ] , deg a [ p' p ] [p - p + ] , deg0 200 0255075100 1 1.5 0.25 0.5 0.75 1 1.5051015 0 100 200 0 100 200 0 100 200024 0 200 0 200M p + p, GeV d s / d M , m b / G e V W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV W=1.71 GeV, Q =1.3 GeV M p + p - , GeV M p - p, GeV q p - , deg d s / ( d - c o s q ) , m b / r a d q p + , deg q p' , deg a [p - p ][p + p' ] , deg d s / d a , m b / r a d a [p + p ] [p - p' ] , deg a [ p' p ] [p - p + ] , deg0 200 Figure 3: (Color Online) Representative examples for the description of the γ r,v p → π + π − p (cid:48) nine 1-fold differential cross sections achievedwithin the JM model [26, 30, 31] for photo- and electroproduction (red curves) in comparison with the data [23, 26]. The error bars includethe combined statistical and point-to-point systematic uncertainties for the photoproduction data and only the statistical uncertainties forthe electroproduction data. The group of curves on each plot correspond to the computed cross sections selected in the data fit with χ /d.p. < χ /d.p. max (see Section 3 for details). Fits with Q -independent masses, and total and partial decay widths into the π ∆ and ρp final states, for all contributing resonances become possible only after the implementation of the new N (cid:48) (1720)3 / + state. nance were determined in independent data fits for Q inthe range from 0.5 – 1.5 GeV within the three overlapping W -intervals: 1.61 – 1.71 GeV, 1.66 – 1.76 GeV, and 1.71– 1.81 GeV (see Fig. 4). The non-resonant contributionsin the three W -intervals are different, while the extracted N (cid:48) (1720)3 / + electrocouplings agree within the uncertain-ties, which underlines the credible extraction of the electro-couplings. Furthermore, the N (cid:48) (1720)3 / + mass, as wellas the total and partial decay widths into the π ∆ and ρp final states obtained from the fits in the three W -intervals,are also consistent, which further supports the existence ofthis new state. Comparisons between the photo-/electroexcitation am-plitudes of the N (1720)3 / + state and the new N (cid:48) (1720)3 / + state determined from the CLAS π + π − p photo-/electroproduction data [23, 26] are shown in Fig. 5.The transverse A / amplitude of the N (1720)3 / + reso-nance decreases with Q more rapidly than for the new N (cid:48) (1720)3 / + state.The contributions of the N (1720)3 / + and N (cid:48) (1720)3 / + resonances to the fully integrated π + π − p photo-/electroproduction cross sections are shown inFig. 1. As Q increases the contributions from the N (cid:48) (1720)3 / + become more pronounced relative to the6 GeV S / *1000 G e V - / Figure 4: (Color Online) Photo-/electrocouplings of the new N (cid:48) (1720)3 / + state determined from independent analyses of three overlapping W -intervals: a) from 1.61 – 1.71 GeV (red triangles), b) from 1.66 – 1.76 GeV (blue squares), and c) from 1.71 – 1.81 GeV (black triangles).The blue squares at the photon point show the results of the CLAS charged double-pion photoproduction data analysis [26].Table 3: Hadronic decays into the π ∆ and ρp final states of the resonances in the third resonance region with major decays to the π + π − p finalstate determined from the fits to the data on charged double-pion photo- [26] and electroproduction [23] implementing a new N (cid:48) (1720)3 / + baryon state. Resonance N ∗ total width Branching fraction Branching fractionstates MeV for decays to π ∆ for decays to ρp ∆(1700)3 / − electroproduction 288.0 ± ± + electroproduction 116.0 ± ± (cid:48) (1720)3/2 + electroproduction 119.0 ± ± Q GeV A / *1000 G e V - / -40-20020406080100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Q GeV S / *1000 G e V - / -40-200204060 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Q GeV A / *1000 G e V - / -50-40-30-20-10010 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Figure 5: (Color Online) Comparison between the photo- and electrocouplings of the N (1720)3 / + (black triangles connected by dashedlines) and the new N (cid:48) (1720)3 / + (blue squares connected by solid lines) obtained from the CLAS π + π − p photo- and electroproduction data[23, 26]. N (1720)3 / + . Both resonances are more visible in theelectroproduction data compared to photoproduction. The sizable increase of the non-resonant contributionsseen in the π + π − p photoproduction data reduces the7 able 4: Masses and hadronic decay widths of the N (1720)3 / + and N (cid:48) (1720)3 / + resonances to the π ∆ and ρp final states determined asthe overlap between the parameter ranges from independent fits of the π + π − p photo- and electroproduction data [23, 26]. Resonance Mass, N ∗ total width, Branching fraction Branching fractionstates GeV MeV for decays to π ∆ for decays to ρpN (1720)3 / + ± N (cid:48) (1720)3 / + ± π + π − p photo-/electroproduction data are critical in order to vali-date the contributions from both the N (1720)3 / + and N (cid:48) (1720)3 / + resonances. In the analyzed data set, it isonly at the photon point that the contribution from the N (1720)3 / + is larger than that of the new N (cid:48) (1720)3 / + .The branching fraction range for the N (1720)3 / + de-cay from the photoproduction data into the ρp final state, > π + π − mass distribution. This established range makesit impossible to simultaneously describe the π + p and π + π − invariant mass distributions in the electroproduction dataassuming only the contribution from the N (1720)3 / + res-onance. This includes the pronounced ∆ ++ peaks seenin the π + p mass distributions and the absence of the ρ peak in the π + π − mass distributions (see Fig. 3). In or-der to reproduce the ∆ ++ peaks seen in the π + p massdistributions without including the N (cid:48) (1720)3 / + state,the N (1720)3 / + decay widths to the ρp final state wouldhave to be more than a factor of four smaller in electro-production compared with the values established in pho-toproduction. When a new N (cid:48) (1720)3 / + resonance is im-plemented, the ∆ ++ peaks in the electroproduction datain the π + p mass distributions can be well described bythe contributions from the new N (cid:48) (1720)3 / + state, whichhas only minor ( < ρp finalstate. A rapid decrease of the A / electrocoupling of the N (1720)3 / + with Q (see Fig. 5) allows for the descrip-tion of the π + π − invariant mass distributions both in thephoto- and electroproduction data, reproducing the high-mass part without the ρ peak in the electroproduction re-action.The masses, total decay widths, and branching frac-tions for the decays of these resonances into π ∆ and ρp final states listed in Table 4 were evaluated as the over-lap between the parameter ranges from independent fitsof the π + π − p photo- and electroproduction data. Thenew N (cid:48) (1720)3 / + decays mostly into the π ∆ final state,while the N (1720)3 / + decay widths into the π ∆ and ρp final states are comparable. The contributions fromthe N (1720)3 / + and the new N (cid:48) (1720)3 / + resonancesare well separated in the π + π − p photo-/electroproductiondata analyses despite the close masses and the same spin-parity of these states. Different patterns for the decays intothe π ∆ and ρp final states and the different Q -evolutionof the resonance electrocouplings allow us to disentangle their contributions. These differences can be seen in thecombined studies of π + π − p photo- and electroproduction,but they are elusive in the previous studies of the two-body meson-baryon channels, as well as the ππN channelslimited to photoproduction data only. Note that a globalcoupled-channel analysis of the exclusive meson photo-and hadroproduction data [27] has revealed evidence fortwo nucleon resonances of J P = 3 / + and I =1/2 for W from 1.7 – 1.8 GeV, supporting our observation of boththe N (1720)3 / + and the new N (cid:48) (1720)3 / + states.
4. Shedding Light on the Nature of New BaryonStates
The discovery of several new resonances in the globalmulti-channel analysis of exclusive meson photoproductiondata [15] is consistent with the pattern from approximateSU(6) spin-flavor symmetry in the generation of the N ∗ spectrum. Most of the states predicted in the [70 , + ] mul-tiplet have been observed. Two of them, the N (1880)1 / + and N (1900)3 / + with a 4-star status, and three otherswith a lower rating, are included in the PDG [20]. How-ever, one of the [70 , + ] multiplet states of J P = 3 / + andisospin I =1/2 [9] remains elusive. Is it possible that thenew N (cid:48) (1720)3 / + resonance established in our analysesis this expected state? In order to obtain an answer, wehave estimated the mass of this state from the SU(6) sym-metry pattern for the masses of the nucleon resonancesin the [70 , + ] and [70 , − ] multiplets. There are two res-onances in the [70 , + ] multiplet with a total quark spin S q =1/2: the still unknown state of J P = 3 / + , isospin I =1/2 and the N (1860)5 / + . Four other states of S q =3/2are the N (1880)1 / + , N (1900)3 / + , N (2000)5 / + , and N (1900)7 / + resonances. Their average mass is equalto 1.955 GeV. We assume that the difference betweenthe average mass values for the resonances of S q =1/2and S q =3/2, ∆ M ( S / − S / ), in the [70 , + ] multipletis the same as in the [70 , − ]. For the [70 , − ] multi-plet, ∆ M ( S / − S / ) = 0 .
16 GeV is obtained by av-eraging the differences between the masses of the res-onances N (1650)1 / − , N (1535)1 / − and N (1700)3 / − , N (1520)3 / − with S q =1/2 and S q =3/2. Hence, the av-erage mass for the resonances of S q =1/2, M avS =1 / , in the[70 , + ] multiplet can be estimated as: M avS =1 / = M avS =3 / − ∆ M ( S / − S / )= 1 .
955 GeV − .
16 GeV = 1 .
795 GeV . (1)8he mass of the N (1880)1 / + state is smaller by∆ M =0.075 GeV than M avS =3 / =1.955 GeV for the four res-onances of S q = 3 / , + ] multiplet. Assumingthe same ∆ M for the S q =1/2 doublet of resonances inthe [70 , + ] multiplet, the mass of the lightest resonanceof S q =1/2, M / + , can be evaluated as: M / + = M avS =1 / − ∆ M = 1 .
795 GeV − .
075 GeV = 1 .
72 GeV . (2)The estimated value of M / + is in good agreement withthe mass of the new N (cid:48) (1720)3 / + resonance from ouranalysis (see Table 4), which makes plausible the assign-ment of the state as the lightest resonance in the [70 , + ]multiplet of J P = 3 / + and isospin I =1/2.A variety of quark models predict two close resonancesof J P = 3 / + and I =1/2, consistent with those seen inour analysis. The interacting quark-diquark [28] and thehypercentral constituent quark model [7] predict two statesof J P = 3 / + and I =1/2 in the mass range from 1.7 –1.8 GeV. The conceptually different chiral quark-solitonmodel [8] with parameters fit to the baryon masses in theoctet and decuplet predicts a resonance of J P = 3 / + , I =1/2 in addition to the N (1720)3 / + as a member ofthe 27-SU(3)-baryon multiplet. The computed mass of thisstate of 1718 . ± . N (cid:48) (1720)3 / + state (see Table 4). The results onthe Q -evolution of the N (1720)3 / + and N (cid:48) (1720)3 / + resonance electrocouplings have become available from ouranalysis for the first time (see Fig. 5). Confronting ourfindings with the quark model expectations will shed lighton the missing resonance nature, elucidating the peculiarfeatures of strong QCD that have made these states elusivefor such a long time.
5. Summary
The analysis of the CLAS π + π − p photo-/electroproduction data [23, 26] has been carried out for W from 1.6 – 1.8 GeV and for Q from 0 – 1.5 GeV withthe goal to establish the nucleon resonances in the thirdresonance region contributing to this channel. Accountingfor only the well-established resonances results in morethan a factor of four difference for the decay branchingfractions of the N (1720)3 / + resonance into the ρp finalstate as inferred from independent fits of the π + π − p photo-/electroproduction data (see Table 2). This contra-diction makes it impossible to describe both the photo-and electroproduction data unless the contributions froma still unobserved resonance are added.After implementation of the N (cid:48) (1720)3 / + resonancewith photo-/electrocouplings, mass, and decay widths fitto the CLAS data [23, 26] (see Table 4 and Fig. 5), a suc-cessful description of the π + π − p photo-/electroproductiondata is achieved with Q -independent masses and totaland partial decay widths into the π ∆ and ρp final states of all contributing resonances in the third resonance re-gion. Moreover, the photo-/electrocouplings and hadronicdecay widths of all contributing resonances coincide withintheir uncertainties determined from the independent fits inthree overlapping W -intervals (see Fig. 4). The evolutionwith Q of the non-resonant contributions to π + π − p elec-troproduction observed in the previous CLAS data anal-ysis [31] makes it unlikely that the implementation of the N (cid:48) (1720)3 / + resonance can serve as an effective way todescribe the non-resonant contributions beyond the scopeof the JM model and, therefore, these results support theexistence of the new N (cid:48) (1720)3 / + state. A manifesta-tion of the new N (cid:48) (1720)3 / + baryon state was also foundin an independent global coupled-channel analysis of theexclusive meson photo- and hadroproduction data [27],which also revealed evidence for two nearby resonancesof J P = 3 / + and I =1/2 for W from 1.7 – 1.8 GeV.The first results on the Q -evolution of the photo-/electroexcitation amplitudes of the missing baryon stateshave become available for the N (cid:48) (1720)3 / + . Confrontingthese results with the quark model predictions will shedlight on the nature of the missing resonances. In the fu-ture, the observation of the new N (cid:48) (1720)3 / + state willbe also checked in the analysis of the recent high quality π + π − p electroproduction data from CLAS [25, 35, 36] inthe Q range from 0.4 – 5.0 GeV . These data will pro-vide the T T and LT interference structure functions [36]allowing for improvement in the evaluation of the reso-nance electrocouplings.Additional data on π + π − p electroproduction at Q < . are needed in order to explore the range ofphoton virtualities in Fig. 1 where the transition oc-curs from N (1720)3 / + dominance in photoproduction to N (cid:48) (1720)3 / + dominance in electroproduction. The mea-surement of beam, target, and beam-target asymmetrieswill be very helpful for the extraction of the resonanceelectrocoupling, in particular at Q < . wherethe non-resonant contributions become increasingly im-portant as Q goes to zero. The studies of ππN pho-toproduction off protons with neutral hadrons in the finalstate at ELSA and MAMI will shed light on the manifesta-tion of N (cid:48) (1720)3 / + resonance in different exclusive ππN channels needed for further confirmation of the existenceof the new state. Our results on the mass, total decaywidth, and photo-/electrocouplings of the N (cid:48) (1720)3 / + will guide the search for the manifestation of this state inother meson photo- and electroproduction channels, suchas KY , ωp , φp , πηN . The studies of exclusive ππN hadroproduction planned at JPARC [37] will allow forthe exploration of the manifestation of the N (cid:48) (1720)3 / + resonance in such reactions and to independently estab-lish from hadroproduction data the N (1720)3 / + and N (cid:48) (1720)3 / + decay widths to the π ∆ and ρp final states.9 . Acknowledgments We express our gratitude for valuable theoretical sup-port by I.G. Aznauryan, T-S.H. Lee, C.D. Roberts, E.Santopinto, and A.P. Szczepaniak. We would like to ac-knowledge the outstanding efforts of the staff of the Ac-celerator and the Physics Divisions at Jefferson Lab thatmade the experiments possible. This work was supportedin part by the U.S. Department of Energy, the NationalScience Foundation, the University of Connecticut, OhioUniversity, the Skobeltsyn Institute of Nuclear Physics,the Physics Department at Moscow State University, andthe University of South Carolina. This material is basedupon work supported by the U.S. Department of Energy,Office of Science, Office of Nuclear Physics under contractDE-AC05-06OR23177. The U.S. Government retains anon-exclusive, paid-up, irrevocable, world-wide license topublish or reproduce this manuscript for U.S. Governmentpurposes.
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