Table Of ContentThree-body nature of N∗ and ∆∗ resonances from sequential decay chains
A. Thiel1, V. Sokhoyan1, E. Gutz1,2, H. van Pee1, A.V. Anisovich1,3, J.C.S. Bacelar4, B. Bantes5, O. Bartholomy1,
D. Bayadilov1,3, R. Beck1, Yu. Beloglazov3, R. Castelijns4, V. Crede6, H. Dutz5, D. Elsner5, R. Ewald5,
F. Frommberger5, M. Fuchs1, Ch. Funke1, R. Gregor2, A. Gridnev3, W. Hillert5, Ph. Hoffmeister1, I. Horn1,
I. Jaegle7, J. Junkersfeld1, H. Kalinowsky1, S. Kammer5, V. Kleber5, Frank Klein5, Friedrich Klein5, E. Klempt1,
M. Kotulla2,7, B. Krusche7, M. Lang1, H. Lo¨hner4, I. Lopatin3, S. Lugert2, T. Mertens7, J.G. Messchendorp4,
5
1 V. Metag2, B. Metsch1, M. Nanova2, V. Nikonov1,3, D. Novinski3, R. Novotny2, M. Ostrick5,a, L. Pant2,
0 M. Pfeiffer2, D. Piontek1, A. Roy2, A.V. Sarantsev1,3, Ch. Schmidt1, H. Schmieden5, S. Shende4, A. Su¨le5,
2 V.V. Sumachev3, T. Szczepanek1, U. Thoma1, D. Trnka2, R. Varma2, D. Walther1, Ch. Wendel1, A. Wilson1,6
n (The CBELSA/TAPS Collaboration)
a
J
1Helmholtz-Institut fu¨r Strahlen- und Kernphysik, Universita¨t Bonn, Germany
9 2II. Physikalisches Institut, Universita¨t Giessen, Germany
3Petersburg Nuclear Physics Institute, Gatchina, Russia
x] 4Kernfysisch Versneller Instituut, Groningen, The Netherlands
e 5Physikalisches Institut, Universita¨t Bonn, Germany
- 6Department of Physics, Florida State University, Tallahassee, FL 32306, USA and
cl 7Physikalisches Institut, Universita¨t Basel, Switzerland
u (Dated: January 12, 2015)
n
[ TheNπ0π0 decaysofpositive-parityN∗ and∆∗ resonancesatabout2GeVarestudiedatELSAby
photoproductionoftwoneutralpionsoffprotons. Thedatarevealclearevidenceforseveralinterme-
1 diate resonances: ∆(1232), N(1520)3/2−, and N(1680)5/2+, with spin-parities JP = 3/2+, 3/2−,
v and 5/2+. The partial wave analysis (within the Bonn-Gatchinaapproach) identifies N(1440)1/2+
4 and the N(ππ)S−wave (abbreviated as Nσ here) as further isobars, and assigns the final states to
9 the formation of nucleon and ∆ resonances and to non-resonant contributions. We observe the
0 known ∆(1232)π decays of ∆(1910)1/2+, ∆(1920)3/2+, ∆(1905)5/2+, ∆(1950)7/2+, and of the
2 corresponding spin-parity series in the nucleon sector, N(1880)1/2+, N(1900)3/2+, N(2000)5/2+,
0 and N(1990)7/2+. For the nucleon resonances, these decay modes are reported here for the first
1. time. Further new decay modes proceed via N(1440)1/2+π, N(1520)3/2−π, N(1680)5/2+π, and
0 Nσ. Thelatterdecaymodesareobservedin thedecayofN∗ resonancesandat most weaklyin ∆∗
5 decays. Itisarguedthatthesedecaymodesprovideevidencefora3-quarknatureofN∗ resonances
1 ratherthan a quark-diquarkstructure.
:
v
PACSnumbers:
i
X
r
a The proposition that mesons and baryons are com- servedresonances,afactknownasthemissing-resonance
posed of constituent quarks [1, 2] paved the path to an problem. Indeed AdS/QCD [11], based on the string na-
understanding of the particle zoo. Quark models were tureofthestronginteraction,reproducestheN∗ and∆∗
developed which reproduced the masses of ground-state spectrum very successfully [12]. Quark models are also
baryons and the gross features of their excitation spec- incompatible with the existence of spin-parity doublets,
trum [3–6]. However, important details remained unex- pairs of resonances with similar masses, identical spin
plainedlikethemassesofN(1440)1/2+[7],N(1535)1/2− and opposite parities. It has been suggested that chiral
[8], andΛ(1405)1/2− [9]. These - and other - resonances symmetry might be restored when baryons are excited
can be generated dynamically from the interaction be- [13–16]. One question must find an answer: Is one of
tween their decay products, and no quark degrees of these different approaches the correct one? Or, do they
freedomarerequiredto understandtheir properties[10]. just represent different legitimate views?
High-mass baryon excitations fall onto linear Regge tra-
The distinctive feature of quark models of baryons as
jectories having the same slope as mesonic Regge trajec-
compared to other concepts is the three-body nature of
tories. This observation has led to the suggestion that
the interaction. In quark models, the internal dynamics
baryonexcitations can be interpretedas q-qq excitations
is described by two oscillators,usually denoted as~λ and
where the diquark remains in a relative S-wave. Here,
ρ~. In the simplest approximation, both oscillators are
we use the concept of diquarks in this limited sense even
harmonic;in more realistic cases,mixing of quarkmodel
though in the literature, any pair of quarks is also often
statesoccurs. Neglectingmixing,thefourpositive-parity
called a diquark. The quark-diquark picture of baryons
∆∗ resonances form a spin-quartet with intrinsic orbital
entails a much reduced number of expected resonances
and spin angular momenta L = 2 and S = 3/2. Indeed,
and may thus explain the small number of actually ob-
four isolated positive-parity ∆∗ resonances with similar
2
massesexist: ∆(1910)1/2+,∆(1920)3/2+,∆(1905)5/2+, L L L
∆(1950)7/2+,withJP =1/2+,3/2+,5/2+,7/2+. Quark excited excited + excited
models predict an additional JP =3/2+,5/2+ spin dou-
bletataboutthesamemassforwhichnoevidenceexists.
If the doublet exists, it must have weak coupling to πN
L L
and γN and can be neglected in the present discussion.
Neglecting mixing with the hypothetical JP =
3/2+,5/2+ spin doublet, the four positive-parity∆∗ res-
onances have a spin and a flavor wave function which
is symmetric with respect to the exchange of any pair
of quarks. The color wave function is completely anti-
Ground
symmetric, hence the spatialwave function φn,l must be state
symmetric. It can be cast into the form
S= √12(cid:8)hφ0s(ρ~)×φ0d(~λ)i+hφ0d(ρ~)×φ0s(~λ)i(cid:9)(L=2). (1) F(uigpupreer1ro:wC)laasnsdicLal=or1bi(tlsowofernruocwle)o.nTehxecifitarsttiotnwsowpiitchtuLre=sin2
both rows show excitations of the ρ and λ oscillators, in the
Here, the ρ and the λ oscillators are coherently excited
third picturein thefirst row both, ρ and λ are excited.
from l =l =0 (s-wave)to l =2 or l =2 (d-wave); the
ρ λ ρ λ
oscillationenergy fluctuates from ρ to λ and back to the
resonances must have a type-(3) component. Hence we
ρ oscillator. There is no radial excitation, n =n =0.
ρ λ
expect non-vanishing branching ratios for decay modes
There are as well four isolated positive-parity nucleon
resonances: N(1880)1/2+, N(1900)3/2+, N(2000)5/2+, like N(1535)1/2−π, N(1520)3/2−π.
N(1990)7/2+. These resonances have a 2∗ rating only The situation is visualized in Fig. 1 using a classical
[18], except for the 3∗ N(1900)3/2+ [19] which is ob- picture. The upper subfigures show the three configura-
served in several partial wave analyses [20]. Here, we tions: (1)wheretheρoscillatorisinthegroundstateand
assume that allfour resonancesexist andthat they form thediquarkandthethirdquarkrotatearoundthecenter
a spin-quartet [17]. Nucleon states with S =3/2 require of mass; (2) where the two quarks of the diquark carry
spatial wave functions of mixed symmetry. For L = 2 the angular momentum; and (3) where all three quarks
the wave functions have equal admixtures of rotate aroundthe center ofmass. According to the Hey-
Kelly conjecture,theconfiguration(3)doesnotde-excite
MS = √12(cid:8)hφ0s(ρ~)×φ0d(~λ)i−hφ0d(ρ~)×φ0s(~λ)i(cid:9)(L=2)(2) directly into a ground-state baryon, N or ∆(1232), plus
a pseudoscalar (or vector) meson: configuration (3) de-
MA = hφ0p(ρ~)×φ0p(~λ)i(L=2) , (3) excites into an intermediate state carrying angular mo-
and both parts need to be present to fulfill the Pauli mentum in either the λ or the ρ oscillator. These decay
principle. The partMA describesacomponentinwhich modes are depicted in the two lower subfigures.
theρandtheλoscillatorarebothexcitedsimultaneously. InthispaperwereportdecaymodesofN∗ and∆∗ res-
The quark model also predicts a spin doublet of onances produced in the reaction γp → π0π0p. The re-
positive-parityN∗ resonanceswith J =1/2and3/2and sultscoverN∗ and∆∗ resonancesinthemassrangefrom
atotalintrinsic orbitalangularmomentumL=1. Their 1500-2100MeV;analysisandresultsaredocumentedin
spatial wave functions are completely antisymmetric: detail elsewhere [22]. Here we present only results on
A = hφ0p(ρ~)×φ0p(~λ)i(L=1) . (4) preogsiiotniv.e-parity resonances in the 1900 - 2100MeV mass
InthesetwoN∗ resonances,bothoscillatorsareexcited. The data were obtained using the energy-tagged
It has been argued [21] that these resonances cannot be photon beam of the ELectron Stretcher Accelerator
formedinaπN scatteringexperiment,thatitisnotpos- (ELSA) [23] and the CBELSA/TAPS detector setup
sible to excite both oscillators in a single step. If they [24, 25]. The electrons hit a bremsstrahlung target and
are produced, they cannot decay directly into πN. We theirmomentawereanalyzedinadipolemagnetincom-
call this argument the Hey-Kelly conjecture. binationwithascintillatorhodoscope. Thephotonsthen
We assume that the type-(1) and (2) wave functions impinged on a 5cm long liquid hydrogen target [26], lo-
caneasilydisintegrateintoπN orintoπ∆(1232)orother cated in the center of the electromagnetic calorimeter
modeswithaground-statebaryonandapseudoscalar(or setup consisting of the Crystal Barrel [27] with 1290
vector) meson. The Hey-Kelly conjecture implies that CsI(Tl) crystals and the TAPS detector [28, 29] in a for-
the type-(3) component decays only by consecutive de- wardwallsetupwith528BaF modules. Thelattermod-
2
excitations of the two oscillators. Hence in a first step, ulesarecoveredwithplasticscintillatorsforchargeinfor-
an intermediate resonance with intrinsic orbital angular mation. The calorimeters cover the complete azimuthal
momentumshouldbeformed,eitherinthebaryonorthe angle and polar angles from 6◦ to 168◦. Further infor-
meson part. A spin-parity quartet of positive-parity N∗ mation on charged particles is provided by a three-layer
3
1400 1600 1800 2000 2200 W, MeV 2) 400
V E =1300-1650
s , m b e g
12 tot 1– s (g p → pp 0) G 3 350
3 tot (
300
CBELSA )
10 0
pp N(1520) 250
8 2(
M 200
6 2
150
4 100
D (1232)
2 50
1 0
0 1 2 3
500 1000 1500 2000 2500
E , MeV M2(pp 0) (GeV2)
g
Figure 2: The total cross section for γp → pπ0π0. The red Figure 3: The pπ0π0 Dalitz plot for 1300 < Eγ < 1650MeV
andbluefulldotsarefromtworunningperiodsofthisexperi- covering the fourth resonance region. There are two entries
ment. TheredopencirclesarefromCBELSA[34],greenopen per event. The largest contributions are due to cascade pro-
circles from GRAAL [35], the black open circles are derived cesseswith∆(1232)asintermediatestate. Twofurtherbands
from A2[36],forfurtherdetailssee[22]. Resultsonsingleπ0 are seen dueto cascades viaN(1520) formation. In regions I
photoproduction [37] are shown for comparison. The results and II, the fractional contributions of ∆(1232) and N(1520)
of the partial wave analysis are shown as solid lines, for the are enhanced. Thedepletion of theDalitz plot at its borders
pπ0 channel scaled down by a factor 3. is dueto thewide window in photon energy.
scintillating fiber detector [30] surrounding the target. in Table I. The table includes results on N(1535)1/2−π
After a series of kinematic cuts, the data were subjected decay modes from [25]. All resonances have sizable Nπ
to kinematic fits [31] to the γp→π0π0p hypothesis, and and/or ∆π branching ratios: for ∆∗ resonances, the
about1600000eventsinthe photonenergyrangeof900 sum of the two decay branching ratios is 61% on av-
to 2500MeV were retained with a background contami- erage, for N∗’s it is 51%. There are several allowed
nation over the full energy range of below 1%. The data branching ratios into intermediate resonances carrying
were included in the BnGa data base (see [32] and [33] one unit of intrinsic orbital angular-momentum excita-
for recent additions) covering pion and photon-induced tion (N(1520)3/2−π, N(1535)1/2−π, Nσ). Their mean
reactions. Data on three-body final states were included contributiontothefourN∗’sis23%,andtothefour∆∗’s
in the partial wave analysis in an event-by-event likeli- a factor 10 smaller. In the Nσ decay mode, we assume
hood fit. The fitted mass and angular distributions are thatfirst,aqq¯pairiscreated,theqforms-togetherwith
compared to data in [22]. the de-excited qq pair, the final state baryon, and the q¯
The total cross section for two-neutral-pionphotopro- picksupthethirdquarkoftheprimarybaryonresonance
duction (Fig. 2) shows very significant peaks in the 2nd (which still carries angular momentum) and produces a
and 3rd resonances regions and a small shoulder at an qq¯pair with JP =0+ which dresses to become a σ.
invariant mass of about W = 1.9GeV due to the 4th The N(1440)1/2+π and N(1680)5/2+π branching ra-
resonance region. For comparison we also show the to- tios are also given even though the intermediate state
tal cross section for γp → π0p from [37] with the tail of does not carry one unit of orbital angular momentum
∆(1232) and a more visible fourth resonance region. as Fig. 1 seems to imply. We assume that in the de-
Figure 3 shows the pπ0π0 Dalitz plot [22] for the excitation process, part of the excitation energy can be
range of the proton-γ invariant mass from W = 1820 to transferredto an oscillatorin a single step transition. In
2000MeV in the . Since the two neutral pions are iden- atomic physics this is known as Auger effect.
tical, there aretwo entriesper event,andthe Dalitz plot Theindividualbranchingratioshavelargeerrorsbars.
is symmetric with respect to the diagonal. The largest Hencewefittedthedatawithtwoassumptions: i)wefor-
contributions are seen at squared pπ0 invariant masses bade decays of the four ∆∗’s into N(1440)π, N(1520)π,
around 1.5GeV2 stemming from the ∆(1232) resonance N(1535)π,andN(1680)π. Thishaslittleeffectonthefit
as intermediate state. A smaller band can be seen at andtheχ2 deterioratedby692units. Weconsiderthisto
M2 ≈ 2.25GeV2 or M ≈ 1500MeV. A fit returns mass be at the border of becoming statistically significant. Of
and width compatible with the N(1520)3/2− resonance. course,these decaysarenotforbiddenbut obviously,the
Theresultsonobserveddecaymodesofpositive-parity branchingratiosforthesedecaymodesfromthefour∆∗’s
resonances in the 1850 to 2000MeV region are collected are small. ii) if decay modes into orbitally excited states
4
Table I: Branching ratios (in %) for the decays of nucleon and ∆ resonances. The errors are derived from a large number of
fits. × stands for forbidden, − for allowed decay modes which in all fits converged to zero. Further properties of these (and
other) resonances are reported in [22].
Nπ L ∆πL<J ∆πL>J N(1520)π L N(1535)πL Nσ L N(1440)πL N(1680)πL
∆(1910)1/2+ 12±3 1 × 50±16 1 - 0 5±3 2 × 6±3 1 - 3
∆(1920)3/2+ 8±4 1 18±10 1 58±14 3 <5 0 <2 2 × <4 1 - 1
∆(1905)5/2+ 13±2 3 33±10 1 - 3 - 2 <1 2 × - 3 10±5 1
∆(1950)7/2+ 46±2 3 5±4 3 - 5 - 2 - 4 × - 3 6±3 1
N(1880)1/2+ 6±3 1 × 30±12 1 - 2 8±4 0 25±15 0 - 1 - 3
N(1900)3/2+ 3±2 1 17±8 1 33±12 3 15±8 0 7±3 2 4±3 2 <2 1 - 1
N(2000)5/2+ 8±4 3 22±10 1 34±15 3 21±10 2 - 2 10±5 2 - 1 16±9 1
N(1990)7/2+ 1.5±0.5 3 48±10 3 - 5 <2 2 <2 4 - 4 <2 1 - 1
wereforbiddenforthefourN∗ resonances,theχ2 change
became 3880 units and the fit quality deteriorated visi-
bly. The four N∗ resonances decay via orbitally excited
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We thank the technical staff of ELSA and the partici- [33] A.V. Anisovich et al., Eur.Phys. J. A 49, 158 (2013).
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acknowledge support from the Deutsche Forschungsge-
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meinschaft (SFB/TR16),SchweizerischerNationalfonds, [37] O.Bartholomyetal.,Phys.Rev.Lett.94,012003(2005).
and U.S. National Science Foundation.
5
