1

The nature of the Roper P11(1440),

S11(1535), D13(1520), and beyond.

2

SU(6)xO(3) Classification of Baryons

D13(1520)S11(1535)

Roper P11(1440)

3

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)

4

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

5

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

6

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)

7

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

8

Fits for ep enπ+

*22 * * * *

* * 2 ( 1)( sin cos2 sin cos )L LT L TT LTpd

d k

9

W = 1.53 GeV

Q2=0.4 GeV2

UIM DR

UIM vs DR Fits for ep → enπ+

10

ep → enπ+

Q2=0.4GeV2

UIM Fit to Structure Functions

UIM Fit

11

• 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+)

12

UIM Fits for ep enπ+

A

e / * *sin1 n2 ( ) siL LThPolarized beam

beam helicityAe=

+--

++-

UIM Fit

13

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

14

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

15

Legendre moments for σT+ε σL

DR UIM

Q2 = 2.05 GeV2

~cosθ ~(1 + bcos2θ)~ const.

DR w/o P11(1440)

16

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

17

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

18

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

19

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

20

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.

21

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.

22

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.

23

Q2=0

The S11(1535) – an isolated resonance

S11 → pη (~55%)

Resonance remains prominent up to highest Q2

24

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)

25

S11(1535) in pη and Nπ

pη

CLAS 2007CLAS 2002previous results

CLAS

26

Examples of Fits with UIM to CLAS data on Nπ

l multipoles

W, GeVW, GeV

Q2=0 Q2=3 GeV2

27

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)%

28

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

29

l multipoles

The D13(1520)

30

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.

31

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

32

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-]

33

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

34

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

35

Single Quark Transition Model

Photocoupling amplitudes SQTM amplitudes

(C-G coefficients and mixing angles)

36

SQTM Predictions for [56,0+]→[70,1-] Transitions

Proton

37

Neutron

SQTM Predictions for [56,0+]→[70,1-] Transitions

A1/2=A3/2= 0 for D15(1675) on protons

38

End of Part III

39

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

40

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.

41

First consistent amplitudes for A1/2(Q2), A3/2(Q2) of D33(1700)

D33(1700)ep → ep State has dominant coupling to N