1. N* Transition form factors in a light-cone relativistic quark model
I.G. Aznauryan1,2 and V.D. Burkert1
1 Jefferson Lab
2 Yerevan Physics Institute
Outline:
Motivation
The model: q3 + mesons
Description of elastic form factors
N* transition form factors at Q2 ≤ 5 GeV2
Predictions for Q2 > 5 GeV2
Conclusions/Outlook
EmNN*2012: Nucleon Resonance Structure in Exclusive Electroproduction at High Photon Virtualities

2. EmNN* University of South Carolina
Motivation
What are the relevant degrees of freedom at varying distance scales?
resolution
of probe
low
high N π
quark mass (GeV)
DSE & LQCD
Do measurements of N* transition form factors probe mq(q)?
11/24/2018
EmNN* University of South Carolina

3. Electroexcitation of Nucleon Resonances
We have now precise experimental information on the Q2 dependence of transition amplitudes for several lower mass excited states for Q2 < GeV2
L3q 1 2 e e’ γv N N’
N*,△*
A1/2, A3/2, S1/2
M, E, S multipoles
π, η, ππ
Analyses based on ~120,000 Nπ cross sections, and beam, target, and double spin asymmetries.
SU(6)×O(3)
N(1520)D13
N(1535)S11
N(1440)P11
=> talks by V. Mokeev, L. Tiator
I.G. Aznauryan et al. (CLAS), PRC80 (2009)
I.G. Aznauryan and V.D. Burkert, PPNP 67 (2012) 1
V.I. Mokeev et al. (CLAS),PRC 2012, arXiv:
Δ(1232P33
N(940)P11 1 2 N
11/24/2018
EmNN* University of South Carolina

4. LC Quark Model ingredients
I.G. Aznauryan and V.B., Phys.Rev. C85 (2012)
Nearly massless Goldstone bosons (pions) create loop contributions to electromagnetic form factors at relatively small Q2. They are essential for the description of GEn(Q2) and the magnetic dipole transition form factor G*M(Q2) of the Δ(1232).
Any quark model aiming to describe electromagnetic NN* transition form factors must include contributions from the quark core and from the pion loops (pion cloud). π π
We have significant evidence for the presence of a pion cloud from electric form factor of the neutron and the excitation of the Delta resonance.
Light-front dynamics realizes Poincare invariance and allows for the description of the vertices N,N* -> q3, Nπ through wave functions.
11/24/2018
EmNN* University of South Carolina

5. Model ingredients, cont’d
Prior work on light-front relativistic model for bound states:
Berestetski, Terentiev, Yad.Fiz. 24,1044 (1976); Yad.Fiz. 25,653 (1977)
Aznauryan et al., Phys.Lett. B112, 393( 1982); Aznauryan, Phys.Lett. B316, 391 (1993)
G. Miller computed pion-loop contributions for the nucleon e.m. form factor in LF model.
G. Miller, Phys.Rev. C66, (2002)
11/24/2018
EmNN* University of South Carolina

6. Model ingredients, cont’d
To study sensitivity to the form of the quark wave function, we employ two widely used forms for the 3-quark radial wave function,
and
(I)
(II)
I.G. Aznauryan, Phys. Lett. B316, 391 (1993)
S. Capstick and B.D. Keister, PRD51, 3598, 1995
M0 – invariant 3-quark mass
mq and qi – quark mass and transverse momentum in light-front frame
=> Φrad increases as mq decreases
Oscillator parameters α1 and α2 are chosen to give the same wave function in
non-relativistic approximation and proton and neutron magnetic moments. T
11/24/2018
EmNN* University of South Carolina

7. Running quark mass mq(Q2)
The quark mass value of mq(0)=0.22GeV is taken from the description of baryon and meson masses (S. Capstick, N. Isgur).
To describe electromagnetic form factors and N* transitions, we use functional forms (1) and (2) of mq(Q2) to test N* transition FF sensitivity to mq(Q2).
(1)
(2)
11/24/2018
EmNN* University of South Carolina

8. EmNN* University of South Carolina
Nucleon – q3 + pion cloud
form (I)
form (II)
N=q3+π; mq(Q2)
Pion cloud contributions:
Significant for Gen at Q2<2-3GeV2
Negligible for other F.F. at Q2>2GeV2
From GEp(0)=1 follows that
|N> = 0.95|q3> |Nπ>
pion
pion
pion
pion
G.E. Miller, Phys.Rev. C66, (2002)
11/24/2018
EmNN* University of South Carolina

9. Nucleon electromagnetic form factors
w.f. form (I)
w.f. form (II)
N = q3+π; mq(0)
mq(Q2)
mq(0)
N = q3+π; mq(Q2)
Combining (1) with form (I) gives results that are comparable to results when combining (2) with form (II)
The running of mq(Q2) allows for the description of GMp at Q2 < 16 GeV2 within the LC rel. quark model.
11/24/2018
EmNN* University of South Carolina

10. EmNN* University of South Carolina
Quark Form Factors
Mechanism that generates running quark mass can also generate anomalous magnetic moments of quarks and quark form factors.
L. Chang, Y.-X. Liu, C.D. Roberts, Phys. Rev. Lett. 102,
To test sensitivity of the model to quark form factors we find that a good description of
the nucleon em form factors data is obtained with the form:
with aq > 18 GeV2 for wave function Φ1, and for aq > 70 GeV2 for wave function Φ2.
For minimal values of aq the, Q2 dependencies of quark masses are:
11/24/2018
EmNN* University of South Carolina

11. Excited nucleon states
No calculations available that allow separation of |q3> and |Nπ> (|Nm>) contributions to nucleon resonances.
Coefficient c* in |N*> = c*|q3>+..., c* <1, is unknown.
Weight of cNc*<N*=q3|Jem|N=q3> in <N*|Jem|N> is not known.
Determine weight factor by fitting to the experimental amplitudes at Q2>2-5GeV2 assuming that the transitions amplitudes are dominated by the q3 core, as is the case for the nucleon e.m. form factors.
All other parameters of the model are taken from the description of the nucleon form factors.
11/24/2018
EmNN* University of South Carolina

12. EmNN* University of South Carolina
Delta resonance P33(1232)
q3 weight factors: Nπ
cN*(1) ≈ cN*(2) = 0.53±0.04
q3+Nπ
G1(Q2) ~ (GM – GE)
J.F. Jones and M.D. Scadron,
Ann.Phys.81, 1 (1973) q3 Nπ
Nπ contributions from dynamical coupled-channel approach (EBAC).
Taking into account the systematic uncertainties in the data, the Q2 -dependence of the form factors is described well at Q2 > 4 GeV2.
11/24/2018
EmNN* University of South Carolina

13. The Roper resonance P11(1440)
q3 weight factors:
JLab/CLAS
JLab/CLAS Nσ
The estimated meson cloud contribution (Nσ) for A1/2 significantly improve description of the low Q2 behavior, I.T. Obukhovsky et al., PRD84, (2011)
Need to extend data to better determine Q2 dependence of A1/2 and S1/2 at Q2 > 4.5GeV2.
11/24/2018
EmNN* University of South Carolina

14. EmNN* University of South Carolina
The D13(1520) resonance
q3 weight factors:
Meson-cloud contributions
G1(Q2) ~ (A1/2 – A3/2/√3)
G2(Q2) = f(A1/2, A3/2, S1/2)
Q2 -dependence of the form factors is described by the model at Q2>2.5 GeV2.
11/24/2018
EmNN* University of South Carolina

15. EmNN* University of South Carolina
The S11(1535) resonance
q3 weight factors:
The weights of the q3-core contribution is found
from the transverse amplitude at Q2=2GeV2. Predictions for 2 <Q2 < 7 GeV2 agree well with the data.
Quark model results for longitudinal amplitude highly sensitive to model parameters.
Large meson cloud or other contributions are needed to describe the longitudinal amplitude.
S11(1535) is the most quark-like resonance of the lower mass states.
11/24/2018
EmNN* University of South Carolina

16. EmNN* University of South Carolina
Conclusions
We obtain good description of the nucleon electromagnetic form factors at Q2 < 16GeV2 in light-front dynamics that includes q3 and π-cloud contributions.
close results are obtained for two widely used N=q3 wave functions
Running of the constituent quark mass mq(Q2) is essential to achieve good description in a wide Q2 range.
Assumption of quark form factors allows similar good description of nucleon e.m. form factors illustrating the correlation between running quark mass and quark form factors.
Qualitative agreement with QCD lattice calculations and Dyson-Schwinger equations.
11/24/2018
EmNN* University of South Carolina

17. EmNN* University of South Carolina
Conclusions cont’d
At Q2 > 2-4 GeV2 the model describes several electro-excitation amplitudes for major low mass states Δ(1232), D13(1520), S11(1535).
Predicts quark-core contributions for Q2 = 5-12 GeV2.
Situation with Roper resonance is more complex due to large meson-baryon contribution and sign change of A1/2 amplitude. There is a need for data at higher Q2 to check the Q2 evolution.
At Q2 < 2-3 GeV2, we find significant meson-cloud effects for
P33(1232) - GM*(Q2)
P11(1440) - A1/2(Q2)
S11(1535) - S1/2(Q2)
D13(1520) - G2(Q2) transition form factor
S11(1535) – A1/2(Q2) meson cloud effects are small and limited to Q2 < 1 GeV2.
Measurements of N* transition form factors do probe the running of mq(q)!
To distinguish running quark mass effects from quark form factors requires data at higher Q2.
11/24/2018
EmNN* University of South Carolina

18. EmNN* University of South Carolina
Outlook
Data for resonances at masses > 1.6 GeV, and Q2> 2 GeV2 are expected from the analysis of CLAS data in nπ+, pπ0 and pπ+π- channels.
N* transition form factors at Q2 ≤ 12 GeV2 will be measured after the JLab 12 GeV energy upgrade with the CLAS12 spectrometer (E ).
In a scheme where the quark mass is generated dynamically, quarks have their own anomalous magnetic moments, and their own form factors. There is also evidence for substructure in the nucleon of 2-3 fm extension. These should be incorporated in model predictions.
Introducing quark form factors will cause a faster Q2 fall-off of the transition amplitudes in the quark model. This will force mq(q) to drop faster with Q2 to describe the data, bringing it in closer agreement with predictions from DSE and LQCD.
11/24/2018
EmNN* University of South Carolina

19. EmNN* University of South Carolina
Additional slide
11/24/2018
EmNN* University of South Carolina

20. EmNN* University of South Carolina
The S11(1535) resonance
q3 weight factors:
Nπ data CLAS
pη CLAS/Hall C
The weight of the q3-core contribution is found from the transverse amplitude at Q2=2GeV2. Predictions for Q2 ≤ 7GeV2 agree well with the data.
Quark model results for S1/2(Q2) amplitude depend strongly on the model parameters. Large meson contribution, and possibly additional contributions are needed.
11/24/2018
EmNN* University of South Carolina