1Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
N* Transition Form Factors at JLab:The Evolution of Baryonic Degrees of Freedom
Ralf W. GotheUniversity of South Carolina
Exclusive Reactions at High Momentum TransfersMay 21-24, 2007
Jefferson Lab, Newport News, VA
IntroductionN ∆, N Roper, and other N N* Transitions1π and 2π Production
2Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Physics Goals
Understand QCD in the full strong coupling regimetransition form factors to nucleon excited states
allow us to studyrelevant degrees-of-freedomwave function and interaction of the constituents
?! ?
! ?
?
!!
pπ
Models Quarks and Gluons as Quasiparticles
ChPTNucleon and
Mesons
pQCDq, g, qq
< 0.1fm 0.1 – 1.0 fm > 1.0 fm<
3Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
CLAS for Inclusive ep e’X at 4 GeVCLAS
Resonances cannot be uniquely separated in inclusive scattering
4Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
CLAS for Exclusive ep e’pX at 4 GeV
1.50. 0.5 1.0
1.0
1.5
2.0
mis
sing
stat
es
CLAS
5Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Lattice QCD indicates a small oblate deformationof the ∆(1232) and that the pion cloud makes E1+ /M1+more negative at small Q2.
Data at low Q2 needed to study effects of the pioncloud.
Need data atlow Q2
N ∆(1232) Transition Form Factors
γv Nλγp=1/2
λγp=3/2
6Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
C. Alexandrou et al., PRL, 94, 021601 (2005)
REM (%)
RSM (%)
Quenched LQCD describes REM within error bars, but shows discrepancies with RSM at low Q2 . Pion cloud effects?
Low-Q2 Mutipole Ratios for REM, RSM
Need data atlow Q2
7Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Low-Q2 Mutipole Ratios for REM, RSM
C. Alexandrou et al., PRL, 94, 021601 (2005)
preliminary
Quenched LQCD describes REM within error bars, but shows discrepancies with RSM at low Q2 . Pion cloud effects?
Significant discrepancy between CLAS and Bates/MAMI results for RSM.
C. Smith
8Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
S11 Q3A1/2
F15 Q5A3/2P11 Q3A1/2D13 Q5A3/2
F15 Q3A1/2
D13 Q3A1/2
Constituent Counting Rule
A1/2 α 1/Q3
A3/2 α 1/Q5
GM α 1/Q4*
(GeV
)
9Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
New trend towards pQCD behavior does not show up.
CLAS12 can measure REM and RSMup to Q²~12 GeV².
N → ∆ Multipole Ratios REM , RSM
0 2 4 6
-5
0
(%)
EM
R
DMT
Sato-Lee
Maid 2003
0 2 4 6
-30
-20
-10
0
(%)
SM
R
DMTSato-Lee
Maid 2003
Ji
]2/c2 [GeV2Q
REM +1
M. Ungaro
0 2 4 60.2
0.4
0.6
0.8
1
]2/c2 [GeV2Q
D /
3G* M
G
DMTSato-Lee (Bare)Sato-Lee (Dressed)BraunMaid 2003GPD
GM 1/Q4*
10Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
π electro-production (UIM, DR)
PDG estimation
π, 2π combined analysis
π electro-production (UIM, DR)
PDG estimation
π, 2π combined analysisK. Park (Data) I. Aznauryan (UIM)
preliminary
Roper Electro-Coupling Amplitudes A1/2, S1/2
nr |q3>
|q3+g>
LF |q3>
|q3+qq>
LF |q3>
nr |q3>
nr |q3>|q3+qq>
|q3+g> LF |q3>
nr |q3>
|q3+g>
LF |q3>
|q3+qq>
nr |q3>
nr |q3>|q3+qq>
|q3+g>
-80
-60
-40
-20
0
20
40
60
0 1 2 3 4
Q2 (GeV2)
A1/
2(10
-3G
eV-1
/2)
-30
-20
-10
0
10
20
30
40
50
0 1 2 3 4
Q2 (GeV2)S 1/
2(10
-3G
eV-1
/2)
-80
-60
-40
-20
0
20
40
60
0 1 2 3 4
Q2 (GeV2)
A1/
2(10
-3G
eV-1
/2)
-30
-20
-10
0
10
20
30
40
50
0 1 2 3 4
Q2 (GeV2)S 1/
2(10
-3G
eV-1
/2)
11Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
preliminary
0
20
40
60
80
100
0 1 2 3 4
Q2 (GeV2)
A1/
2(10
-3G
eV-1
/2)
-60
-50
-40
-30
-20
-10
0
10
20
30
0 1 2 3 4
Q2 (GeV2)S 1/
2(10
-3G
eV-1
/2)
S11(1535) Electro-Coupling Amplitudes A1/2, S1/2
π electro-production (UIM, DR)
PDG estimation
S11, D13 combined analysis (SQTM)K. Park (Data) I. Aznauryan (UIM)
η production (UIM, DR)
nr |q3>
LF |q3>
LF |q3>nr |q3>
nr |q3>LF |q3>
LF |q3>
nr |q3>
12Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Energy-Dependence of π+ Multipoles for P11, S11
imaginary partreal part
Q2 = 0 GeV2
The study of some baryon resonances becomes easier at higher Q2.
Q2 = 2.05 GeV2
preliminary
I. Aznauryan (UIM)
13Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Legendre Moments of Structure FunctionsQ2=2.05GeV2
M1- = 0
M1- = 0
I. Aznauryan UIM fit
The dominating final state multipole amplitude M1- of the P11(1440) resonance is at high Q2 are much more prominent than at small Q2.
K. Park
preliminary
CLAS
14Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
πΝ invariant mass / MC phase space
BES/BEPC, Phys. Rev. Lett. 97 (2006)
/J p nψ π −→ /J p nψ π +→BES Bing-Song Zou
and
Ν∗(1440): Μ = 1358 m 17 Γ = 179 m 56
Ν∗(2050): Μ = 2068 +15−40
Γ = 165 m 42
15Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Fermion Helicity Conservation
Helicity Conservationλ=λ´ for q M>>
Quark mass extrapolated to the chiral limit, where q is the momentum variable of the tree-level quark propagator using the Asquat action.
Bowman et al.(LQCD)
(GeV
)
16Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
preliminary
-100
-80
-60
-40
-20
0
20
0 1 2 3 4
A1/
2(10
-3G
eV-1
/2)
-25
0
25
50
75
100
125
150
175
200
0 1 2 3 4
A3/
2(10
-3G
eV-1
/2)
-60
-40
-20
0
20
40
0 1 2 3 4
Q2 (GeV2)
S 1/2(
10-3
GeV
-1/2
)
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
0 1 2 3 4
Q2 (GeV2)
Ahe
l
D13(1520) Helicity AsymmetryAhel = A1/2
2 – A3/22
A1/22 + A3/2
2
A1/2
A3/2
17Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Nucleon Resonances in 2π Electroproduction
p(e,e’)X
p(e,e’p)π0
p(e,e’π+)n
p(e,e’pπ+)π−
2π channel is sensitiveto N*’s heavier than1.4 GeV
Provides complementaryinformation to the 1πchannel
Many higher lying N*’sdecay preferably to ππNfinal states
Q2 < 4.0GeV2 Trigger
W in GeV
18Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
W=1.86 GeV, Q2=0.95 GeV**2
0
10
20
30
40
50
60
1 1.2 1.4 1.6 1.80
10
20
30
40
50
60
0.25 0.5 0.75 1
0
10
20
30
40
50
1 1.2 1.4 1.6 1.80
2
4
6
8
10
12
14
0 50 100 150 200
direct 2π production
Full calculationsγp→π-∆++
γp→π+∆0
γp→ρpγp→π-∆++(1600)
γp→π+F015(1685)
γp→π+D13(1520)
Combined fit of various single differential cross sections allowed to establish all significant mechanisms
Isobar Model JM05
Contributing Mechanisms to γ(∗)p → pπ+π-
JM05
19Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
CLAS photo-production
W(GeV)
Background
Resonances
Full calculation
no 3/2+
N* contributions are much smaller than non-resonant mechanisms
0
5
10
15
20
25
30
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1
electro-production
W(GeV)
M. Ripani
3/2+(1720)P?3(1720)
Full JM05 calculation with and without a new 3/2+(1720) state
Resonances in γ(∗)p → pπ+π-
20Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
W=1.7 GeV, Q2=0 GeV**2
P13(1720) branching fraction for ρpextracted by a the fit within the JM05 model (without 3/2+(1720))
Preliminary real (M. Bellis) and published (M. Ripani) virtual photon data, combined fit needs both the candidate 3/2+(1720) and the P13(1720) state
Q2 0.00 GeV2 0.65 GeV2
BF(ρp) 63%±25% 20%±10%
Discrepancy
Combined Analysis of γ(∗)p → pπ+π-
Fit without 3/2+(1720), only variation of electromagnetic and π∆ ρP hadronic couplings and masses of P13(1720), P33(1600)
Fit with 3/2+(1720)
preliminary
21Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Resonances
CLAS
Background
Full JM05
no 3/2+
3/2+(1720)P?3(1720)
Resonances and Background in γ(∗)p → pπ+π−
0102030405060708090
1.4 1.6 1.8 20
5
10
15
20
25
30
35
1.4 1.6 1.8 2
0
5
10
15
20
25
30
1.4 1.6 1.8 202468
101214161820
1.4 1.6 1.8 2
electro-productionphoto-production
JM05
22Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Combined 1π-2π Analysis of CLAS Data
PDG at Q2=0
Previous world data
2π analysis
1π-2π combined at ////Q2=0.65 GeV2
Many more examples:////P11(1440), D13(1520), S31(1650), ////S11(1650), F15(1685), D13(1700),////…
EBAC at JLab:////Full coupled channel analysis
D33(1700) D33(1700)
P13(1720) P13(1720)
Q2 GeV2
(A2 1/
2 +S2 1/
2 )(1
/2) *1
000
GeV
−1/2
Q2 GeV2A
3/2*
1000
GeV
−1/2
Q2 GeV2
(A2 1/
2 +S2 1/
2 )(1
/2) *1
000
GeV
−1/2
Q2 GeV2
A3/
2*10
00 G
eV−1/2
0255075
100125150175200225
0 0.5 1 1.5
-40
-20
0
20
40
60
80
100
120
0 0.5 1 1.5
0102030405060708090
100
0 0.5 1 1.5-120
-100
-80
-60
-40
-20
0
20
0 0.5 1 1.5
preliminary
JM05
23Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Combined 1π-2π Analysis of CLAS Data
PDG at Q2=0
2π analysis
1π-2π combined at Q2=0.65 GeV2
Previous world data
24Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
0
1
2
3
-1 -0.5 0 0.5 1
dσ(γ
* p→πo p)
/dΩ
(µb
/sr) φ=15o
0
1
2
3
4
-1 -0.5 0 0.5 1
φ=45o
0
2
4
6
-1 -0.5 0 0.5 1
φ=75o
0
2
4
6
-1 -0.5 0 0.5 1
φ=105o
0
2
4
6
-1 -0.5 0 0.5 1
φ=135o
cos θc.m.
0
2
4
6
-1 -0.5 0 0.5 1
φ=165o
cos θc.m.
0
0.5
1
1.5
2
-1 -0.5 0 0.5 1
dσ(γ
* p→πo p)
/dΩ
(µb
/sr) φ=15o
0
0.5
1
1.5
2
-1 -0.5 0 0.5 1
φ=45o
0
1
2
3
-1 -0.5 0 0.5 1
φ=75o
0
1
2
3
-1 -0.5 0 0.5 1
φ=105o
0
1
2
3
4
-1 -0.5 0 0.5 1
φ=135o
cos θc.m.
0
0.5
1
1.5
2
-1 -0.5 0 0.5 1
φ=165o
cos θc.m.
γvp → π0p
1π Data Description by N* Electro-Couplings of the Combined Analysis
W=1.52 GeV Q2=0.65 GeV2 W=1.68 GeV Q2=0.65 GeV2 JM05CLAS
25Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
W=1.54 GeV Q2=0.65 GeV2 W=1.66 GeV Q2=0.65 GeV2
The successful description of all 1π and 2π observables measured with CLAS at Q2=0.65 GeV2 demonstrates the credibility of the N* background separation.
2π Data Description by N* Electro-Couplings of the Combined Analysis
JM05CLAS
26Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
prelim
inary
Roper Electro-Coupling Amplitudes A1/2, S1/2
PDG at Q2=0
1π analysis (UIM)
1π-2π combined at////Q2=0.65 GeV2
Newest 2π analysis ////at low Q2 (JM 06)
CLAS
27Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Inclusive Structure Function in the Resonance Region
Event Generators
Genova-EG: Dipole Form Factor
SI-DIS: Deep Inelastic Scattering
3. R R
2. R R
P. Stoler, PRPLCM 226, 3 (1993) 103-171
28Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
W (GeV
)Q 2
(GeV 2)
Num
ber
of e
vent
s
1.7
1.725
1.75
1.775
1.8
1.825
1.85
1.875
1.9
5
5.5
6
6.5
7
7.5
8
0
10000
20000
30000
40000
50000
60000
Kinematical Coverage of CLAS1260 days
L= 1035 cm-2 sec-1, ∆W = 0.025 GeV, ∆Q2 = 0.5 GeV2
Genova-EG (e’,pπ+π−) detected
29Ralf W. Gothe N* Transition Form Factors Exclusive Reactions 2007
Conclusion: Do Exclusive Electron Scattering
-150-125-100
-75-50-25
0255075
0 1 2 3 4Q2 (GeV2)
A1/
2 (1
0-3G
eV-1
/2)
P11(1440) -60
-40
-20
0
20
40
60
80
0 1 2 3 4Q2 (GeV2)
S 1/2
(10-3
GeV
-1/2
)P11(1440)
Q2 = 2.05 GeV2
0 2 4 6
-5
0
(%)
EM
R
DMT
Sato-Lee
Maid 2003
0 2 4 6
-30
-20
-10
0
(%)
SM
R
DMTSato-Lee
Maid 2003
Ji
]2/c2 [GeV2Q
0 2 4 60.2
0.4
0.6
0.8
1
]2/c2 [GeV2QD
/ 3G
* MG
DMTSato-Lee (Bare)Sato-Lee (Dressed)BraunMaid 2003GPD
-100
-80
-60
-40
-20
0
20
0 1 2 3 4
A1/
2(10
-3G
eV-1
/2)
-25
0
25
50
75
100
125
150
175
200
0 1 2 3 4
A3/
2(10
-3G
eV-1
/2)
-60
-40
-20
0
20
40
0 1 2 3 4
Q2 (GeV2)
S 1/2(
10-3
GeV
-1/2
)
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
0 1 2 3 4
Q2 (GeV2)
Ahe
l
D13(1520)
D13(1520)
... to
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