Transcript N* Transition form factors in a lightcone relativistic quark model I.G.

N* Transition form factors in a lightcone 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
Motivation
What are the relevant degrees of freedom at varying distance scales?
π
resolution
of probe
low
DSE & LQCD
quark mass (GeV)
N
high
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Electroexcitation of Nucleon Resonances
L3q
2
We have now precise experimental information on the Q2 dependence of
transition amplitudes for several lower mass excited states for Q2 < 4.5-7 GeV2
SU(6)×O(3)
Analyses based on ~120,000 Nπ
cross sections, and beam, target,
and double spin asymmetries.
e’
e
γv
N’
N
A1/2, A3/2, S1/2
M, E, S multipoles
N(1520)D13
N(1535)S11
1
π, η, ππ
N*,△*
I.G. Aznauryan et al. (CLAS), PRC80 (2009) 055203
I.G. Aznauryan and V.D. Burkert, PPNP 67 (2012) 1
V.I. Mokeev et al. (CLAS),PRC 2012, arXiv:1205.3948
=> talks by V. Mokeev, L. Tiator
0
Δ(1232P33
N(940)P11
0
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N(1440)P11
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3
LC Quark Model ingredients
I.G. Aznauryan and V.B., Phys.Rev. C85 (2012) 055202
 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
 Light-front dynamics realizes Poincare invariance and allows for the
description of the vertices N,N* -> q3, Nπ through wave functions.
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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, 032201 (2002)
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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,
(I)
and
(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
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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)
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Nucleon –
3
q
+ 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
pion
pion
From GEp(0)=1 follows that
|N> = 0.95|q3> + 0.313 |Nπ>
pion
pion
G.E. Miller, Phys.Rev. C66, 032201 (2002)
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Nucleon electromagnetic form factors
w.f. form (I)
w.f. form (II)
mq(Q2)
N = q3+π; mq(0)
N = q3+π; mq(Q2)
mq(0)
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.
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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, 1929001 92011.
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:
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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.
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Delta resonance P33(1232)
q3 weight factors:
cN*(1) ≈ cN*(2) = 0.53±0.04
Nπ
q3+Nπ
G1(Q2) ~ (GM – GE)
J.F. Jones and M.D. Scadron,
Ann.Phys.81, 1 (1973)
Nπ contributions from
dynamical coupledchannel approach (EBAC).
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Nπ
q3
Taking into account the systematic uncertainties in the
data, the Q2 -dependence of the form factors is
described well at Q2 > 4 GeV2.
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The Roper resonance P11(1440)
JLab/CLAS
q3 weight factors:
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, 014004 (2011)
Need to extend data to better determine Q2 dependence of A1/2 and S1/2 at
Q2 > 4.5GeV2.
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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.
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The S11(1535) resonance
q3 weight factors:
 The weights of the q3core 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.
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 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.
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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.
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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.
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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 (E12-09-003).
• 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.
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Additional slide
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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.
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