Electroexcitation of nucleon resonances in a light-front - - PowerPoint PPT Presentation

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Electroexcitation of nucleon resonances in a light-front - - PowerPoint PPT Presentation

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Electroexcitation of nucleon resonances in a light-front relativistic quark model Inna G. Aznauryan & Volker D. Burkert August 22, 2017 Inna

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Electroexcitation of nucleon resonances in a light-front relativistic quark model

Inna G. Aznauryan & Volker D. Burkert August 22, 2017

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Content

The approach and its parameters are specified via description of nucleon electromagnetic form factors for Q2 ≤ 20 GeV2. We therefore begin with the nucleon electromagnetic form factors.

◮ Nucleon electromagnetic form factors GEp, GMp, GEn, GMn

→ q3 + πN loops contributions in light-front dynamics → running quark mass

◮ Electroexcitation of ∆(1232) 3 2 + ◮ Electroexcitation of N+(1440) 1 2 +, N+(1520) 3 2 −, N+(1535) 1 2 −

→ q3 contribution in a LF RQM with running quark mass → inferred MB contributions (non-QM contributions)

◮ Electroexcitation of N+(1675) 5 2 − and N0(1675) 5 2 −

→ isolating MB contributions

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Nucleon electromagnetic form factors

N N N q

  • N

(a)

q N N

  • N

(c)

  • N
  • q

q

(b)

N

The contributions (a), (b), (c) can be found in Refs.: ◮ I. G. Aznauryan and V. D. Burkert, PR C85, 055202, 2012 [(a): I. G. Aznauryan, PL B316, 391, 1993; Z. f. Phys. A346, 297, 1993] ◮ G. A. Miller, PR C66, 032201, 2002 in the LF approach developed by ◮ V. B. Berestetsky and Terent’ev, Sov.J.Nucl.Phys. 25,347,1977 ◮ I. G. Aznauryan, A. S. Bagdasaryan, and N. L. Ter-Isaakyan, PL B112, 393, 1982

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Parameters

N N N q

  • N

(a)

q N N

  • N

(c)

  • N
  • q

q

(b)

N

◮ (a) Here we have two parameters: mq(Q2 = 0) and αq.

αq determines the quark momentum distribution. These parameters are fixed by GMp(0) and GMn(0). We have found mq(0) = 0.22GeV in agreement with the quark mass

  • btained from description of the baryon and meson masses in the

relativized QM by S. Godfrey and N. Isgur, PR D21, 1868, 1980; S. Capstick and N. Isgur, PR D32, 189, 1985.

◮ (b,c) Here we have also two parameters: fπNN and απN.

fπNN is known: f 2

πNN/4π = 14.5.

απN determines the π and N momentum distribution in the loop; it is fixed by GEn(Q2), because the contribution of the diagrams (b) and (c) is crucial for the description of GEn(Q2) at Q2 < 1.5 GeV2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Renormalization of the N(N∗) → 3q vertices due to the MB loops

◮ The diagrams (b) and (c) give ≈ 10% contribution to the charge of the

proton: see plot for GEp. Therefore, to keep the charge of the proton Qp = 1, we have to renormalize the vertex N → 3q. In the absence of meson-baryon loops and with the N → 3q wave function normalized as:

  • |Φ(q1, q2, q3)|2dΓ = 1, we have |N >= |3q >.

With the πN loops included, we get: |N >= 0.95|3q >+... .

◮ Similar to the nucleon, MB loops contribute to the charge of other

baryons, including resonances. Therefore, the vertices N∗ → 3q should be renormalized: |N∗ >= cN∗|3q >+... , cN∗ < 1.

◮ We find the coefficients cN∗ from experimental data on γ∗N → N∗

assuming that at Q2 > 4 GeV2 these transitions are determined only by the 3q contributions.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Coeffients of core q3 resonance excitations.:

◮ ∆(1232) 3

2 +: cN∗ = 0.88 ± 0.04

◮ N(1440) 1

2 +: cN∗ = 0.93 ± 0.05

◮ N(1520) 3

2 −: cN∗ = 0.80 ± 0.06

◮ N(1535) 1

2 −: cN∗ = 0.91 ± 0.03

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Running quark mass

0.05 0.1 0.15 0.2 0.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5

M0 2(GeV2)

mq

wave function (1) wave function (2) Q2=0 M0 2=1.35 Q2=5 M0 2=2.66 Q2=10 M0 2=3.1 Q2=20 M0 2=3.5

◮ With the fixed quark mass we have good description of all nucleon electromagnetic form factors up to Q2 = 2 GeV2. ◮ At Q2 > 2 GeV2, a constant value of the quark mass gives rise to rapidly decreasing form factors in discrepancy with experiment. ◮ Good description of the form factors up to Q2 = 20 GeV2 has been obtained with running quark mass exploring two forms of wave functions: ◮ (1) Φ1 ∼ exp(−M2

0/α2 1),

(2) Φ2 ∼ exp[−(q2

1 + q2 2 + q2 3)/α2 2];

M2

0 in the plot is mean value of

M2

0 = (q1 + q2 + q3)2.

◮ In LF RQM, the virtuality of quarks is characterized by the invariant mass of the 3-quark system M2

0 = (q1 + q2 + q3)2, which is

increasing with increasing Q2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

The proton electric form factor GEp

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9

Q2 (GeV2)

GEp /GD N+LF RQM (running quark mass) N+LF RQM (fixed quark mass) N contribution Hall A*: 2000,2002(2012),2010

◮ Hall A∗ data are obtained from the data

  • n µpGEp/GMp via multiplication by

GMp/µp using parameterization of the data on GMp/µp found in E. J. Brash et al., PR C65, 051001, 2002 ◮ Hall A, 2000: M. K. Jones et al., PRL 84, 1398, 2000 ◮ Hall A, 2002: O. Gayou et al., PRL 88, 092301, 2002 ◮ Hall A, 2012: A. J. R. Puckett et al., PR C85, 045203, 2012 ◮ Hall A, 2010: A. J. R. Puckett et al., PRL 104, 242301, 2010

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

The proton magnetic form factor GMp

  • 0.4
  • 0.2

0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 12 14 16

Q2 (GeV2)

GMp /µpGD N+LF RQM (running quark mass) N contribution N+LF RQM (fixed quark mass) Hall A Hall C DESY SLAC

◮ Hall A: I. A. Qattan et al., PRL 94, 142301, 2005 ◮ Hall C: M. E. Christy et al., PR C70, 015206, 2004 ◮ DESY: W. Bartel et al., NP B58, 429, 1973 ◮ SLAC: A. F. Sill et al., PR D48, 29, 1993

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

The neutron electric form factor GEn

  • 0.02

0.02 0.04 0.06 0.5 1 1.5 2 2.5 3 3.5 4

Q2 (GeV2)

GEn N+LF RQM (running quark mass) N+LF RQM (fixed quark mass) N contribution (*) Hall C Hall A

◮ (*): R. Schiavilla and I. Sick, PR C64, 041002, 2001 ◮ Hall C: R. Madey et al., PRL 91,122002, 2003 ◮ Hall A: S. Riordan et al., PRL 105, 262302, 2010

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

The neutron electric form factor GMn

  • 0.2

0.2 0.4 0.6 0.8 1 2 4 6 8 10

Q2 (GeV2)

GMn /µnGD N+LF RQM (running quark mass) N+LF RQM (fixed quark mass) N contribution Hall C CLAS SLAC

◮ Hall C: B. Anderson et al., PR C75, 043003, 2007 ◮ CLAS: J. Lachniet et al., PRL 102,192001, 2009 ◮ SLAC: S. Rock et al., PRL 49, 1139, 1982

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Magnetic ∆ form factor GM∆ and Quadrupole ratios REM, RSM

0.2 0.4 0.6 0.8 1 2 4 6 8 10 12

Q2 (GeV2) GM,Ash /3GD

CLAS Hall C Hall A MAMI LF RQM

→ GM described by LF RQM at Q2 > 3 − 4 GeV2

  • 8
  • 6
  • 4
  • 2

2 4 6

REM (%)

  • 50
  • 40
  • 30
  • 20
  • 10

2 4 6 8 10 12

Q2 (GeV2) RSM (%)

→ REM ≈ −2%, dominated by MB contributions → RSM described at Q2 > 3 GeV2.

◮

CLAS: from analysis I. G. Aznauryan et al., CLAS collaboration, PR C80,055203, 2009

◮

Hall C: V. V. Frolov et al., PRL 82, 45, 1999; A. N. Vilano et al., PR C80, 035203, 2009

◮

Hall A: J. J. Kelly et al., PR C75, 025201, 2007

◮

MAMI: N. F. Sparveris et al., PL B651, 102, 2007; S. Stave et al., PR C78, 025209, 2008 Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

N∆(1232) Transition amplitudes

  • 200
  • 150
  • 100
  • 50

5

Q2 (GeV2)

A1/2

  • 400
  • 300
  • 200
  • 100

5

Q2 (GeV2)

A3/2

10 20 30 40 5

Q2 (GeV2)

S1/2 → Blue curves: inferred from meson-baryon contributions. → At Q2 > 3GeV2, MB/Total < 0.15

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity amplitudes of the Roper N+(1440) 1

2 +.

  • 60
  • 40
  • 20

20 40 60 80 1 2 3 4 5

Q2 (GeV2)

N(1440)1/2+ A1/2 N p+- RPP CLAS* LF RQM DSE* MB contributions

→ LF RQM describes data at Q2 > 2.5 GeV2.

  • 40
  • 20

20 40 60 1 2 3 4 5

Q2 (GeV2)

N(1440)1/2+ S1/2 N p+- LF RQM DSE* MB contributions

→ LF RQM describes data at Q2 > 1.5 GeV2.

DSE curve renormalized to account for MB contributions.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity amplitudes of N+(1520) 3

2 −

  • 120
  • 100
  • 80
  • 60
  • 40
  • 20

20 40 1 2 3 4 5

N(1520)3/2- A1/2 MB contributions N p+- RPP CLAS* LF RQM Q2 (GeV2)

  • 100
  • 50

50 100 150 200 250 1 2 3 4 5

Q2 (GeV2) N(1520)3/2- A3/2 MB contributions LF RQM RPP CLAS* N p+-

  • 120
  • 100
  • 80
  • 60
  • 40
  • 20

20 40 60 1 2 3 4 5

Q2 (GeV2) N(1520)3/2- S1/2 MB contributions N p+- LF RQM

→ LF RQM describes data at Q2 > 2.0 GeV2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity structure of N+(1520) 3

2 −

  • 1
  • 0.75
  • 0.5
  • 0.25

0.25 0.5 0.75 1 1 2 3 4 5

N(1520)3/2- N p+- RPP CLAS* LF RQM Ahel=(A1/22-A3/22)/(A1/22+A3/22)

Q2 (GeV2)

→The helicity asymmetry Ahel shows dominant A3/2 at Q2 = 0., a zero crossing near Q2 = 0.5 GeV2, and A1/2 dominance at Q2 > 2 GeV2. →The helicity switch of this state is a longstanding quark model prediction.

→ LF RQM describes data at Q2 > 1.5 GeV2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity amplitudes of N+(1535) 1

2 −

  • 75
  • 50
  • 25

25 50 75 100 125 1 2 3 4 5 6 7 8 9

Q2 (GeV2) N(1535)1/2- A1/2 N CLAS p CLAS p Hall C CLAS* RPP MB contributions LF RQM LC SR (LO) LC SR (NLO)

  • 45
  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10
  • 5

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Q2 (GeV2) N(1535)1/2- S1/2 N CLAS LF RQM LC SR (LO) LC SR (NLO)

→ LF RQM describes A1/2 data at Q2 > 2.0 GeV2 → LC SR (NLO) describes S1/2 data at Q2 > 1.5 GeV2

for MB contributions see also:

  • D. Jido, M. Doering and E. Oset, “Transition form factors of the N*(1535) as a

dynamically generated resonance,” Phys. Rev. C 77, 065207 (2008

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity amplitudes of N+(1675) 5

2 −

→ In SQT A1/2 = 0, A3/2 = 0 on protons (Moorhouse selection rule)

  • 5

5 10 15 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Q2 (GeV2) N(1675)5/2- A1/2 (p) CLAS CLAS RPP LF RQM hCQM MB (EBAC)

  • 10
  • 5

5 10 15 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5

N(1675)5/2- A3/2 (p) CLAS RPP CLAS LF RQM hCQM MB (EBAC) Q2 (GeV2)

  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Q2 (GeV2) N(1675)5/2- S1/2 (p) CLAS LF RQM hCQM

→ q3 contribution accounts for small part of amplitudes at all Q2. → Direct measurement of MB contributions

hCQM: E. Santopinto, M.M. Giannini, Phys.Rev. C86 (2012) 065202, arXiv:1506.01207

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Helicity amplitudes of N0(1675) 5

2 −

→ Moorhouse selection rule does not apply to neutron targets.

  • 70
  • 60
  • 50
  • 40
  • 30
  • 20
  • 10

0.5 1 1.5 2 2.5 3 3.5 4 4.5

N(1675)5/2- A1/2 (n) RPP LF RQM hCQM Q2 (GeV2)

  • 100
  • 80
  • 60
  • 40
  • 20

0.5 1 1.5 2 2.5 3 3.5 4 4.5

N(1675)5/2- A3/2 (n) RPP LF RQM hCQM Q2 (GeV2)

2.5 5 7.5 10 12.5 15 17.5 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Q2 (GeV2) N(1675)5/2- S1/2 (n) LF RQM hCQM

→ q3 dominate transverse amplitudes. MB subleading at Q2 = 0

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Meson-Baryon contributions of N0(1675) 5

2 −

20

  • 20

40

N(1675)5/2-

A1/2 A3/2 MB contribu8ons

→ MB contributions at Q2 = 0 dominated by isovector amplitudes.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Do N* transition amplitudes have sensitivity to the running quark mass?

5 10 15 20 25 30 35 40 2 4 6 8 10 12 Q2 (GeV2)

N(1440)1/2+ A1/2

LF RQM CLAS12 projected running quark mass fixed quark mass

quark mass (GeV)

accessible at 6 GeV accessible at 12 GeV

LQCD

DSE

→ LF RQM shows sensitivity to running quark mass at Q2 > 4 GeV2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Conclusions

◮ The LF RQM with parameterized running quark mass describes

both the elastic electromagnetic form factors of proton and neutron, as well as the nucleon resonance electrocoupling amplitudes (transition form factors) in the range of photon virtuality 2 − 3 < Q2 < 12GeV2.

◮ The results show sensitivity to the running quark mass

parametrization, especially at Q2 > 4 − 5GeV2.

◮ Meson-baryon contributions are significant at Q2 < 1.5 − 2.5GeV2

as inferred from the different of LF RQM predictions and data. They show a consistent behavior for all studied resonances.

◮ A direct extraction of MB contributions for N(1675) 5

2 − is consistent

with a rapid drop of the helicity amplitudes with Q2.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

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Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary

Comment on gauge invariance

N N N q

  • N

(a)

q N N

  • N

(c)

  • N
  • q

q

(b)

N

◮ Sum of the diagrams (b) and (c) for the nucleon is gauge invariant. ◮ For γN → N∗, MB loop contributions like (b) and (c) are not gauge

invariant; for these transitions gauge invariance requires additional contributions with the photon coupled to the NBM and BMN∗ vertices.

Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model