1 the nature of the roper p 11 (1440), s 11 (1535), d 13 (1520), and beyond
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1
The nature of the Roper P11(1440),
S11(1535), D13(1520), and beyond.
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SU(6)xO(3) Classification of Baryons
D13(1520)S11(1535)
Roper P11(1440)
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The Roper Resonance – what are the issues?
Poorly understood in nrCQMs- Wrong mass ordering (~ 1700 MeV)- nrCQM gives A1/2(Q2=0) > 0, in contrast to experiment
which finds A1/2(Q2=0) < 0.
Alternative models:- Light front kinematics (many predictions)- Hybrid baryon with gluonic excitation |q3G> (prediction)- Quark core with large meson cloud |q3m> (prediction)- Nucleon-sigma molecule |Nm> (no predictions)- Dynamically generated resonance (no predictions)
Lattice QCD gives conflicting results- Roper is consistent with 3-quark excitation (F. Lee,
N*2004)- Roper is not found as state (C. Gattringer, N*2007)
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Lattice calculations of P11(1440), S11(1535)
F. Lee, N*2004
Masses of both states are well reproduced in quenched LQCD with 3 valence quarks.
C. Gattringer, N*2007
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UIM & DR Fit at low & high Q2
Observable
Data points UIM DR
0.40 0.65
3 5303 818
1.22 1.22
1.21 1.39
0.40 0.65
1.7-4.3
2 3081 716
33 000
1.69 1.48
1.97 1.75
0.40 0.65
956 805
1.14 1.07
1.25 1.30
0.40 0.65
1.7 - 4.3
918 812
3 300
1.18 1.18
1.63 1.15
0.3750.750
172 412
1.32 1.42
1.33 1.45
d
d
0d
d
/0( )
LTA
/ ( )LT
A
d
d
2Q 2
data2
data
# data points:> 50,000 , Ee = 1.515, 1.645, 5.75 GeV
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Fixed-t Dispersion Relations for invariant Ball amplitudes
Dispersion relations for 6 invariant Ball amplitudes:
Unsubtracted Dispersion Relations
Subtracted Dispersion Relation
γ*p→Nπ
(i=1,2,4,5,6)
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Causality, analyticity constrain real and imaginary amplitudes:
Born term is nucleon pole in s- and u-channels and meson-exchange in t-channel.
Integrals over resonance region saturated by known resonances (Breit-Wigner). P33(1232) amplitudes found by solving integral equations.
Integrals over high energy region are calculated through π,ρ,ω,b1,a1 Regge poles. However these contributions were found negligible for W < 1.7 GeV
For η channel, contributions of Roper P11(1440) and S11(1535) to unphysical region s<(mη+mN)2 of dispersion integral included.
Dispersion Relations
( ,0) 2 ( ,0) / 2 // /
1 1( , , ) ( , ,Re Im )i i
thr
PB s t Q B s t Q ds
s sBo n
s ur
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Fits for ep enπ+
*22 * * * *
* * 2 ( 1)( sin cos2 sin cos )L LT L TT LTpd
d k
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W = 1.53 GeV
Q2=0.4 GeV2
UIM DR
UIM vs DR Fits for ep → enπ+
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ep → enπ+
Q2=0.4GeV2
UIM Fit to Structure Functions
UIM Fit
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• Unpolarized structure function
– Amplify small resonance multipole by an interfering larger resonance multipole
Power of Interference II
• Polarized structure function
– Amplify resonance multipole by a large background amplitude
LT ~ Re(L*T)= Re(L)Re(T) + Im(L)Im(T)
LT’ ~ Im(L*T)= Re(L)Im(T) + Im(L)Re(T)
Large
Small
P33(1232)
Im(S1+) Im(M1+)
BkgP11(1440)
Resonance
Im(S1-) Re(E0+)
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UIM Fits for ep enπ+
A
e / * *sin1 n2 ( ) siL LThPolarized beam
beam helicityAe=
+--
++-
UIM Fit
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Sensitivity of σLT’ to P11(1440) strength
Shift in S1/2
Shift in A1/2
Polarized structure function are sensitive to imaginary part of P11(1440) through interference with real Born background.
ep → eπ+n
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Examples of diff. cross sections at Q2=2.05 GeV2
• W-dependence • φ-dependence at W=1.43 GeV
DR
UIM
DR w/o P11
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Legendre moments for σT+ε σL
DR UIM
Q2 = 2.05 GeV2
~cosθ ~(1 + bcos2θ)~ const.
DR w/o P11(1440)
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Multipole amplitudes for γ*p→ π+n
Q2 =0 Q2 =2.05 GeV2
ImRe_UIM Re_DR
At Q2=1.7-4.2, resonance behavior is seen in these amplitudes more clearly than at Q2 =0
DR and UIM give close results for real parts of multipole amplitudes
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Helicity amplitudes for the γp→ P11(1440) transition
DR UIM
RPP
Nπ, Nππ
Model uncertainties due to N, π, ρ(ω) → πγform factors
Nπ
CLAS
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Comparison with LF quark model predictions P11(1440)≡[56,0+]r
LF CQM predictions have common features, which agree with data: • Sign of A1/2 at Q2=0 is negative
• A1/2 changes sign at small Q2
• Sign of S1/2 is positive
1.Weber, PR C41(1990)2783 2.Capstick..PRD51(1995)35983.Simula…PL B397 (1997)13 4.Riska..PRC69(2004)0352125.Aznauryan, PRC76(2007)025212 6. Cano PL B431(1998)270
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Is the P11(1440) a hybrid baryon?
Suppression of S1/2 has its origin in the form of vertex γq→qG. It is practically independent of relativistic effectsZ.P. Li, V. Burkert, Zh. Li, PRD46 (1992) 70
Gq3
In a nonrelativistic approximation A1/2(Q2) and S1/2(Q2) behave like the γ*NΔ(1232) amplitudes.
previous data previous data
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So what have we learned about the Roper resonance?
LQCD shows a 3-quark component. Does it exclude a meson-nucleon resonance?
Roper resonance transition formfactors not described in non-relativistic CQM. If relativity (LC) is included the description is improved.
Overall best description at low Q2 in model with large meson cloud and quark core.
Gluonic excitation, i.e. a hybrid baryon, ruled out due to strong longitudinal coupling and the lack of a zero-crossing predicted for A1/2(Q2).
Other models need to predict transition form factors as a sensitive test of internal structure.
The Q2 dependence seems qualitatively consistent with the Roper as a radial excitation of a 3 quark system, may require quark form factors.
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Negative Parity States in 2nd N* Region
S11(1535) • Hard form factor (slow fall off with Q2)• Not a quark resonance, but KΣ dynamical system?
D13(1520)
-CQM:
Change of helicity structure with increasing Q2 from Λ=3/2 dominance to Λ=1/2 dominance, predicted in nrCQMs, pQCD.
Measure Q2 dependence of Transition F.F.
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The S11(1535)
• This state has traditionally studied in the S11(1535)→pη channel, which is the dominant decay:
S11(1535) → 55% (pη) ; pη selects isospin I=1/2
S11(1535) → 35% (Nπ) ; Nπ sensitive to I=1/2, 3/2
• Nearby states, especially D13(1520) have very small coupling to pη channel, making the S11(1535) a rather isolated resonance in in this channel.
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Q2=0
The S11(1535) – an isolated resonance
S11 → pη (~55%)
Resonance remains prominent up to highest Q2
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Response Functions and Legendre Polynomials
Expansion in terms of Legendre Polynomials
Sample differential cross sections for Q2=0.8 GeV2, and selected W bins. Solid line: CLAS fit, dashed line: η-MAID.
A0 → E0+ → A1/2(S11)
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S11(1535) in pη and Nπ
pη
CLAS 2007CLAS 2002previous results
CLAS
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Examples of Fits with UIM to CLAS data on Nπ
l multipoles
W, GeVW, GeV
Q2=0 Q2=3 GeV2
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S11(1535) in pη and Nπ
pη
pπ0nπ+
pπ0nπ+
pη
CLAS 2007CLAS 2002previous results
New CLAS results
A1/2 from pη and Nπ are consistent
CLAS
PDG (2006): S11→πN (35-55)% → ηN (45-60)%
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A new P11(1650) in γ*p→ηp ?CLAS
4 resonance fit gives reasonable description including S11(1535), S11(1650), P11(1710), D13(1520)
A0 → E0+ → A1/2(S11)
A1/A0 shows a sharp structure near 1.65 GeV. The observation is consistent with a rapid change in the relative phase of the E0+ and M1- multipoles because one of them is passing through resonance.
No new P11 resonance needed as long as P11(1710) mass, width, BR(pη) are not better determined
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l multipoles
The D13(1520)
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Transition amplitudes γpD13(1520)
A1/2
A3/2
Q2, GeV2 Q2, GeV2
CLAS
Previous pπ0
based data
pπ0nπ+
Nπ, pπ+π- nπ+
pπ0
preliminary
preliminary
nrCQM predictions:A1/2 dominance with
increasing Q2.
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Helicity Asymmetry for γpD13
D13(1520)A
hel
CQMs and pQCD
Ahel → +1 at Q2→∞
Ahel =A2
1/2 – A23/2
A21/2 + A2
3/2
Helicity structure of transition changes rapidly with Q2 from helicity 3/2 (Ahel= -
1) to helicity 1/2 (Ahel= +1) dominance!
CLAS
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What have we learned about the S11(15350 and D13(1520)
resonances ?
• Nπ+ and pη give consistent results for A1/2(Q2) of S11(1535)
• New nπ+ data largely consistent with analysis of previous pπ0 data for A1/2 and A3/2 of D13(1520)
• D13(1520) shows rapid change of helicity structure from A3/2 to A1/2 dominance.
• Both states appear consistent with 3-quark model orbital excitation in [70,1-]
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Test prediction of helicity conservation
Q3A1/2 Q5A3/2S11
P11
F15
D13
No scaling seen for helicity non-conserving amplitude A3/2
F15
D13
Helicity conserving amplitudeA1/2 appears to approach scaling
→ Expect approach to flat behavior at high Q2
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Single Quark Transition Model
z zA B C DJ L L L L L
1zL 1zL 1zS
1zS 2zL 1zS
EM transitions between all members of two SU(6)xO(3) multiplets expressed as 4 reduced matrix elements A,B,C,D.
Fit A,B,C to D13(1535) and S11(1520)
A3/2, A1/2 A,B,C,DSU(6)
Clebsch-Gordon
Example: 56,0 70,1 (D=0)
Predicts 16 amplitudes of same supermultiplet
orbit flip
spin flip
spin-orbit
A
B
C
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Single Quark Transition Model
Photocoupling amplitudes SQTM amplitudes
(C-G coefficients and mixing angles)
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SQTM Predictions for [56,0+]→[70,1-] Transitions
Proton
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Neutron
SQTM Predictions for [56,0+]→[70,1-] Transitions
A1/2=A3/2= 0 for D15(1675) on protons
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End of Part III
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Analysis of +-p single differential cross-sections.
Full calculationsp-++
p+0
pp
p-P++33(1600)
p+F015(1685)
direct 2production
p+D13(1520)
Combined fit of various 1-diff. cross-sections allowed to establish all significant mechanisms.
Isobar Model JM05
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Test of JM05 program on well known states.
D13(1520)
ep → ep (A1/22+S1/2
2)1/2, GeV-1/2 A3/2, GeV-1/2
Q2 GeV2Q2 GeV2
→ JM05 works well for states with significant Npp couplings.
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First consistent amplitudes for A1/2(Q2), A3/2(Q2) of D33(1700)
D33(1700)ep → ep State has dominant coupling to N