Pion electroproduction in the Roper regionExperimental survey

S. Širca, U. of Ljubljana, Slovenia Bled | 1 July 2009

1

Motivation

� Understand (****, ***) baryon spectra: masses, widths, form-factors

� Understand structure of resonances, related to— confinement— chiral symmetry of QCD (meson cloud)

� Distinguish structure from reaction mechanisms, compare to models

� Current focus on Roper and above � 1.7 GeV

2

Key issues with P11�1440� ... and S11�1535�

� Large width of Roper

� Hard to see directly (in spectra)

� Atypical behaviour of ImT�N in P11

� Inconsistent M , � (�N XS ... 1470, 350 MeV), (jdT=dW j) ... 1375, 180 MeVfor the Roper

� Large width of S11�1535�! �N at threshold

� Level ordering (parity inversion) of P11�1440� wrt. S11�1535� on Lattice

3

SAID PWA of �N scattering in P11 channel

0

50

100

150

200ph

ase

shift

(deg

ree)

1.0 1.2 1.4 1.6 1.8Ecm (GeV)

00.20.40.60.8

1

(1−η

2 )

SM95KA84SE−SM95

1.0 1.2 1.4 1.6 1.8 2.0Ecm (MeV)

00.20.40.60.810

50

100

150

200P11 D13

4

SAID PWA of �N scattering in P11 channel contd.

ImT

ImT � jT j2

ReT

SAID FA02 MBW � �1468� 4:5�MeV, �=2 � �180� 13�MeV

Mpole � 1357� i 80 MeV (I RS)

1385� i 83 MeV (II RS)

5

Roper from �p and �N scattering

TWO structures: �I � �S � 0 in �p, little �I/�S selectivity in �N

� M � �1:39� 0:02�GeV � M � �1:48� 0:03�GeV� � �0:19� 0:03�GeV � � �0:38� 0:05�GeVseen in seen only in�N elastic, �N! N����S , and �p �N elastic, �N! ��

Morsch, Zupranski PRC 61 (1999) 024002PRC 71 (2005) 065203

6

Roper from �p scattering SPES4-� Experiment

� 2� events via Roper excitation in target� non-resonant 2� negligible

(model, Alvarez-Ruso++ 1998)� decay predominantly via � -meson

Alkhazov++ PRC 78 (2008) 025205

7

Roper in quark models

� Spherically symmetric SU(6)Radial excitation (“breathing mode”) of proton �1s�3 -! �1s�2�2s�1

Sizeable monopole strength (C0 / Sp1=2 / S1�) � dipole (M1 / Ap

1=2 / M1�)

� Hybrid modelsGluonic partner of proton �q3g�Li, Burkert, Li PRD 46 (1992) 70

Same quantum numbers as �q3�, indistinguishable by spectroscopy aloneEqual radial WF ) C0 suppressed, no “breathing”, M1 dominatesin pQCD (asymptotic electroproduction rate off �q3g� vs. �q3�)

� Constituent, semi-relativistic, relativistic QM and QM with meson DOFsExtensive studies with varying successMostly limited to masses and photo-couplings

8

Additional qq̄ components

� � 30% admixture of qqqqq̄ components in the Roper) ��theory� � ��exp�Li, Riska PRC 74 (2006) 015202

� Lowest 5q configuration in S11�1535� is qqqss̄) correct P11�1440� wrt. S11�1535� mass ordering) large S11�1535�! �N, �K couplings without OZI violationAn, Zou EPJA 39 (2009) 195

9

P11�1440� and S11�1535� on the Lattice

� close to CL, effects of CSB important

� level ordering should change with mq

Heavy q: 1st radial above 1st orbital excCL: reversed levels

Bern-Graz-Regensburg / PRD 70 (2004) 054502PRD 74 (2006) 014504 -!

“... do not attempt a chiral extrapolation of our data ... numbersseem to approach the experimental data reasonably well”

“... the Roper’s leading Fock component is a 3-quark state”0.00 0.40 0.80 1.20

(mπ)2 [GeV]

2

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

MN

[G

eV]

λ(1), a = 0.148fm

λ(2), a = 0.148fm

λ(3), a = 0.148fm

λ(1), a = 0.119fm

λ(2), a = 0.119fm

λ(3), a = 0.119fm

positive parity

N(938)

N(1440)

N(1710)

Kentucky / PLB 605 (2005) 137

“...� and � parity excited states of the nucleon tendto cross over as the quark masses are taken to the chiral limit.Both results at the physical pion mass agree with the expvalues ... seen for the first time in a lattice QCD calculation”

“...a successful description of the Roper resonance dependsnot so much on the use of the dynamical quarks, but thatmost of the essential physics is captured by using lightquarks to ensure the correct chiral behavior” 0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mas

ses

(GeV

)

mπ2(GeV2)

Nucleon

S11(1535)

Roper

1.3

1.5

1.7

0 0.1 0.2

MR/MN1.3

1.5

1.7

0 0.1 0.2

MR/MN

10

Lattice N! P11�1440� EM transition form-factors

hN�jV�jNi � uN��p0�"F�1 �q

2� � �

q�q2q=!� F�2 �q2�

���q�M�M�

#uN�p�e�iq�x;

A1=2�Q2� � kA�Q2�GM�Q2�S1=2�Q2� � kS�Q2�GS�Q2�

kA�Q2� �p

4��Q�p4M�M�2 �M2�

kS�Q2� � kA�Q2�Q�Q�Q2

M �M�2M�

Q� �q�M �M��2 �Q2

Magnetic and scalar transition form factors

GM�Q2� � F�1 �Q2�� F�2 �Q2�

GS�Q2� � F�1 �Q2�� Q2

�M �M��2 F�2 �Q

2�

11

Lattice N! P11�1440� EM transition form-factors

YP11 É VΜ É p]

Yp É VΜ É P11]Exp.

-1 0 1 2 3 4

-0.2

0

0.2

0.4

Q2HGeV2L

F1p-

P11

YP11 É VΜ É p]

Yp É VΜ É P11]

Exp.

PDG

-1 0 1 2 3 4-0.8

-0.4

0

0.4

Q2HGeV2L

F2p-

P11

YP11 É VΜ É n]

Yn É VΜ É P11]

-1 0 1 2 3 4

-0.10

-0.05

0

0.05

Q2HGeV2L

F1n-

P11

YP11 É VΜ É n]

Yn É VΜ É P11]

PDG

-1 0 1 2 3 4-0.60

-0.30

0

0.30

0.60

Q2HGeV2L

F2n-

P11

� quenched, m� � 720 MeV (!) Lin++ PRD 78 (2008) 114508

� “exploratory study”

12

“Femto-tomography” of the Roper resonance

Transition charge densities for unpolarized N ! N�:

�NN�

0 �~b� �Zd2~q?�2��2

e�i ~q?�~b1

2P�hP�; ~q?

2; � j J��0� jP�;�~q?

2; �i

�NN�

0 �~b� �Z1

0

dQ2�QJ0�bQ�FNN

�1 �Q2�

Transition charge densities for polarized N ! N�:

�NN�

T �~b� �Zd2~q?�2��2

e�i ~q?�~b1

2P�hP�; ~q?

2; s? j J��0� jP�;�

~q?2; s?i

�NN�

T �~b� � �NN�0 �b�� sin��b ��S�Z1

0

dQ2�

Q2

�M� �MN�J1�bQ�FNN

�2 �Q2�

hJ�i has the interpretation of quark charge density~b — position in the xy-plane from the transverse c.m. of baryons

Tiator, Vanderhaghen PLB 672 (2009) 344

13

“Femto-tomography” of the Roper resonance

p! N�1440� n! N�1440�

-1.5-1-0.5

00.5

11.5

bx@fmD

-1.5

-1

-0.5 0

0.5 1

1.5

by @ fmD

-1.5-1-0.5

00.5

11.5

bx@fmD

-1.5

-1

-0.5 0

0.5 1

1.5

by @ fmD

-1.5-1-0.5

00.5

11.5

bx@fmD

-1.5

-1

-0.5 0

0.5 1

1.5

by @ fmD

-1.5-1-0.5

00.5

11.5

bx@fmD

-1.5

-1

-0.5 0

0.5 1

1.5

by @ fmD

Tiator, Vanderhaghen PLB 672 (2009) 344

14

Formalism for p�~e; e0p��

Tremendous simplification when only beam is polarized:

d�d� �T � "�L �

q2"�" � 1��LT cos�� "�TT cos 2�� h

q2"�1� "��LT0 sin�

Separate strong and EM vertex:

With sufficient angular coverage: extract Legendre moments

���W; cos�� �XlDl�W�Pl�cos��

! still “easy”

! typical for CLAS (Hall B @ JLab)

15

Available data (photoproduction) example: d� , �

16

Phenomenology: extraction of resonance parameters

Ideal case:

1 At given energy E, perform complete/over-complete measurementsat all angles �, i.e. 8 observables for pseudo-scalar photo-productiond� , single-pol �, T , P , double-pol G, H, E, F

2 Extract amplitudes F�f� �i�E; ��

3 Project out partial-wave amplitudes f�LS�J�E� from F�f� �i�E; ��

4 Extract resonance poles and residues from f�LS�J�E�� speed-plot method (Höhler)� time-delay method (Wigner)� analytic continuation to complex E plane

— dispersion relations— isobar and/or K-matrix equations— dynamical scattering equations

� Electro-production: more observables, more multipoles

17

Dispersion relations

1 Build Im parts of amplitudes from s-channel resonance contributionswith Breit-Wigner parameterization; include all ****, ***, ** resonances

2 Use fixed-t dispersion relations to find Re partsThere are 18 amplitudes B��;�;0�i �s; t;Q2� for ?N! N�

ReBi�s; t;Q2� � Born� 1�

Z1thr

ImBi�s; t;Q2��

1s0 � s �

1s0 �u

�ds0

Born =

3 Constraint: Fermi-Watson theorem

� Example: P33�1232�,M2 fM3=21� ; E

3=21� ; S

3=21� g

Integral equations forM, particular + homogeneous solutionparticular sol: magnitude fixed by Born termshomogeneous sol: shapes fixed by DR, weight fitted to data

18

Advantage of dispersion relations

� Im of amplitudes determined mainly by resonance contributions

bgtotal

� SAID PWA

� Re parts of amplitudes can contain large non-resonant contributionsfixed by DR

� Example: Im parts of amplitudes in P33�1232� region can generatenon-resonant multipoles E�0�0� , E�1=2�0� , E�3=2�0� , S�0�0� , S�1=2�0� , S�3=2�0�— Re parts fixed by DR— Im parts fixed by Fermi-Watson with phenomenological ��1=2�0� , ��3=2�0�

19

Unitary Isobar Models, Dynamical Models

All used in the past for N! �, uncertainties "" beyond �

MAID — Mainz unitary isobar model MAID2003 w/o CLAS (2003) data

� effective L, adjustable parameters� resonances in BW forms� backgrounds are Born terms, �-, !-exch� total amplitudes unitarized� attempt to incorporate all EP data

into “super-global” fits) Need XS, single-, and double-pol

observables to stabilize fits

DMT — Dubna-Mainz-Taipei dynamical model

� Include �N FSI such that unitarity preserved� t � � tB � � tR � � v � g0 t�N

� t�N fitted to �N (SAID), v � fitted to N! �N

SL — Sato-Lee

20

Legendre moments of ep! en�� structure functions

Q2 � 2:05 GeV2

solid: DRdashed: UIMdotted: DR, Roper off

21

Example result: Q2-dependence of D0

UIMDR D0��T � "�L� � �tot=4�

� For Q2 large, P11�1440�, S11�1535�, D13�1520�become more dominant w.r.t. P33

� Similar: slow Q2 decrease of D0;1;2��T � "�L�( due to slow fall-off of A1=2 of the P11, S11, D13

22

More Legendre moments for (polarized) ~ep! en��

W � 1400, Q2 � 2:05

Park++ PRC 77 (2008) 015208

23

Two pions: ep! ep����

0

10

20

30

40

50

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

W (GeV)

Q2 = 0.325 GeV2

σin

tegr.

(µb)

0

10

20

30

40

50

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

W (GeV)

Q2 = 0.375 GeV2

σin

tegr.

(µb)

0

10

20

30

40

50

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

W (GeV)

Q2 = 0.425 GeV2

σin

tegr.

(µb)

π

∆

= Σ

p p

∆

'

'

p

p

∆

γ

π

Ν∗

π

π

(∆ )

p

-

,

+

∆

γ

∗

π (π )

γ

γ

π

p

π

π

-

(π )

+

π

p

∆

'

Resonant part

p

Born terms

Additionalcontact terms

γ

=

++

γ

+

+

Full

p

+

0

p

π

-

π

+

π∆

γ

∆

p

+ -

γπ Direct∆ π2π π p- + '

γ

p

π

π(

(

- π

+

)

)

πp )'

p'

'

-(

+

(π

(

'

(

p

)

+

)

π )

π

πγ

π

2

π

π

Direct

p

p

-

p '

-

-+

+

(

(

(

(γ γ

(

(

p

)

p

)

)

π

π )

p

')

p

)π

π

JM05 parametrization

'

'

-

t

-

t

+

1 2 +

=+

Fedotov++ PRC 79 (2009) 015204

24

Helicity amplitudes for �p! P11�1440�

MAID 2007+ “super-global” fits, Tiator++ PLB 672 (2009) 344

25

P11�1440� as a 3q state

Weber PRC 41 (1990) 2783

Capstick, Keister PRD 51 (1995) 3598

Cardarelli++ PLB 397 (1997) 13

Aznauryan PRC 76 (2007) 025212

� All LF RQM: sign change of A1=2, magnitude of S1=2

� Solid evidence in favour of P11�1440� as first radial excitation of 3q ground state

� All fail to describe A1=2 at low Q2

26

P11�1440� as a q3g hybrid state

Li, Burkert, Li, PRD 46 (1992) 70

� Suppression of S1=2 due to form of ?q! qg vertex

� Hybrid q3g picture ruled out

27

Much harder: p�~e; e0~p��

d�dE0e de d?p

� �0

2

�1� P � bsr � h�Ae � P0 � bsr�

�

xy

z

e

e’

q

scattering plane (lab)

reaction plane (cm)

p

0

t = n x l

ln = q x p p

d�dE0e de d?p

� �vjp?p jWK Mp

��RT � Rn

TSn�� 2"?L �RL � RnLSn�

�q"?L �1� "���RLT � Rn

LTSn� cos�� �RlLTSl � Rt

LTSt� sin���" ��RTT � Rn

TTSn� cos 2�� �RlTTSl � Rt

TTSt� sin 2��

�hq"?L �1� "���R0LT � R0nLTSn� sin�� �R0lLTSl � R0tLTSt� cos��

�hp

1� "2 �R0lTTSl � R0tTTSt ��

28

N! ��1232� at Q2 ’ 1 JLab/Hall A (E91-011)

Kelly++ PRL 95 (2005) 102001, PRC 75 (2007) 025201

29

L.C. Smith JLAB Users Group Meeting 2005

Amplification Through Interference

• Real LT Response

• Imaginary LT Response

1+

3

+

3

1Im(M ) P (1Im(S )

232)

σ= +

*Re( )Re( ) IRe( ) ( I ( )) mm

LT LTLT TL

Large

Small

σ= −

/ *

Re( )Im( ) IIm

m((

)Re( ))LT

L LLT

T T

0

11

+1- PIm(S )

(

1Re(E )440)

Resonance

Amplify small resonant multipole by interference with large resonant multipole

Amplify small resonant multipole by interference with large real background.

Resonance tails + Born terms

W

W

30

MAID07 vs. DMT01 (Roper “on”/“off”) p�~e; e0~p��0

� Different treatment of resonances in isobar models (e.g. MAID)vs. dynamical models (e.g. DMT) ... “dressed” vs. “bare” vertices

� nice distinctions in all components of ~P

31

MAID07 vs. DMT01 (full calculations) p�~e; e0~p��0

� Tremendous sensitivity to Roper

� CLAS results on P11, S11, D13 great, but lagging behind the ��1232� sophistication

� (Too) few measurements of double-polarization observables

32

Wish list: this figure at W � 1440 instead of W � 1232 MeV

0.0 0.2 0.4

-20

-15

-10

-5

0

5

0.0 0.2 0.4

Q2 (GeV2/ c2)

-60

-50

-40

-30

-20

-10

0

0.0 0.2 0.4

10

20

30

40

50

60

70

80P’x/ Pe (%) P’z/ Pe (%)Py (%)

33