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

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

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 Q 2 ≤ 20 GeV 2 . We therefore begin with the nucleon electromagnetic form factors. ◮ Nucleon electromagnetic form factors G Ep , G Mp , G En , G Mn → q 3 + π N loops contributions in light-front dynamics → running quark mass + ◮ Electroexcitation of ∆(1232) 3 2 + , N + (1520) 3 ◮ Electroexcitation of N + (1440) 1 − , N + (1535) 1 − 2 2 2 → q 3 contribution in a LF RQM with running quark mass → inferred MB contributions (non-QM contributions) − and N 0 (1675) 5 ◮ Electroexcitation of N + (1675) 5 − 2 2 → isolating MB contributions Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Nucleon electromagnetic form factors � � � � q q � � q N N N N N N N N q N (a) (c) (b) 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

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Parameters � � � � q q � � q N N N N N N N N q N (a) (c) (b) ◮ (a) Here we have two parameters: m q ( Q 2 = 0) and α q . α q determines the quark momentum distribution. These parameters are fixed by G Mp (0) and G Mn (0). We have found m q (0) = 0 . 22GeV in agreement with the quark mass obtained 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: f π NN and α π N . f π NN is known: f 2 π NN / 4 π = 14 . 5. α π N determines the π and N momentum distribution in the loop; it is fixed by G En ( Q 2 ), because the contribution of the diagrams (b) and (c) is crucial for the description of G En ( Q 2 ) at Q 2 < 1 . 5 GeV 2 . Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Renormalization of the N ( N ∗ ) → 3 q vertices due to the MB loops ◮ The diagrams (b) and (c) give ≈ 10% contribution to the charge of the proton: see plot for G Ep . Therefore, to keep the charge of the proton Q p = 1, we have to renormalize the vertex N → 3 q . In the absence of meson-baryon loops and with the N → 3 q wave function normalized as: | Φ( q 1 , q 2 , q 3 ) | 2 d Γ = 1, we have | N > = | 3 q > . � With the π N loops included, we get: | N > = 0 . 95 | 3 q > +... . ◮ Similar to the nucleon, MB loops contribute to the charge of other baryons, including resonances. Therefore, the vertices N ∗ → 3 q should be renormalized: | N ∗ > = c N ∗ | 3 q > +... , c N ∗ < 1. ◮ We find the coefficients c N ∗ from experimental data on γ ∗ N → N ∗ assuming that at Q 2 > 4 GeV 2 these transitions are determined only by the 3 q contributions. Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Coeffients of core q 3 resonance excitations. : + : c N ∗ = 0 . 88 ± 0 . 04 ◮ ∆(1232) 3 2 + : c N ∗ = 0 . 93 ± 0 . 05 ◮ N (1440) 1 2 ◮ N (1520) 3 − : c N ∗ = 0 . 80 ± 0 . 06 2 ◮ N (1535) 1 − : c N ∗ = 0 . 91 ± 0 . 03 2 Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Running quark mass ◮ With the fixed quark mass we have good description of all nucleon electromagnetic form 0.25 factors up to Q 2 = 2 GeV 2 . m q ◮ At Q 2 > 2 GeV 2 , a constant value of the quark mass gives rise to rapidly decreasing form factors 0.2 in discrepancy with experiment. ◮ Good description of the form factors up to 0.15 Q 2 =0 M 0 2 =1.35 Q 2 = 20 GeV 2 has been obtained with running Q 2 =5 M 0 2 =2.66 quark mass exploring two forms of wave functions: Q 2 =10 M 0 2 =3.1 Q 2 =20 M 0 2 =3.5 ◮ (1) Φ 1 ∼ exp ( − M 2 0 /α 2 0.1 1 ), Φ 2 ∼ exp [ − ( q 2 1 + q 2 2 + q 2 3 ) /α 2 (2) 2 ]; wave function (1) M 2 0 in the plot is mean value of 0.05 M 2 0 = ( q 1 + q 2 + q 3 ) 2 . wave function (2) ◮ In LF RQM, the virtuality of quarks is characterized by the invariant mass of the 0 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3-quark system M 2 0 = ( q 1 + q 2 + q 3 ) 2 , which is M 0 2 (GeV 2 ) increasing with increasing Q 2 . Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary The proton electric form factor G Ep ◮ Hall A ∗ data are obtained from the data on µ p G Ep / G Mp via multiplication by G Ep /G D 1 G Mp /µ p using parameterization of the data on G Mp /µ p found in E. J. Brash et 0.8 al., PR C65, 051001, 2002 0.6 ◮ Hall A, 2000: M. K. Jones et al., PRL 84, 1398, 2000 0.4 ◮ Hall A, 2002: O. Gayou et al., PRL 88, 0.2 092301, 2002 0 ◮ Hall A, 2012: A. J. R. Puckett et al., PR � N+LF RQM (running quark mass) C85, 045203, 2012 -0.2 � N+LF RQM (fixed quark mass) � N contribution ◮ Hall A, 2010: A. J. R. Puckett et al., -0.4 PRL 104, 242301, 2010 Hall A * : 2000,2002(2012),2010 -0.6 0 1 2 3 4 5 6 7 8 9 Q 2 (GeV 2 ) Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary The proton magnetic form factor G Mp 1.2 G Mp / µ p G D ◮ Hall A: I. A. Qattan et al., PRL 94, 1 142301, 2005 0.8 ◮ Hall C: M. E. Christy et al., PR C70, 0.6 015206, 2004 ◮ DESY: W. Bartel et al., NP B58, 429, 0.4 � N contribution 1973 � N+LF RQM (running quark mass) 0.2 � N+LF RQM (fixed quark mass) ◮ SLAC: A. F. Sill et al., PR D48, 29, 1993 0 Hall A Hall C -0.2 DESY SLAC -0.4 0 2 4 6 8 10 12 14 16 Q 2 (GeV 2 ) Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary The neutron electric form factor G En G En ◮ (*): R. Schiavilla and I. Sick, PR C64, 0.06 041002, 2001 (*) Hall C ◮ Hall C: R. Madey et al., PRL 91,122002, 0.04 Hall A 2003 ◮ Hall A: S. Riordan et al., PRL 105, 0.02 262302, 2010 0 � N+LF RQM (running quark mass) � N+LF RQM (fixed quark mass) � N contribution -0.02 0 0.5 1 1.5 2 2.5 3 3.5 4 Q 2 (GeV 2 ) Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary The neutron electric form factor G Mn G Mn / µ n G D 1 ◮ Hall C: B. Anderson et al., PR C75, 0.8 043003, 2007 0.6 ◮ CLAS: J. Lachniet et al., PRL 102,192001, 2009 0.4 � N+LF RQM (running quark mass) ◮ SLAC: S. Rock et al., PRL 49, 1139, 1982 � N+LF RQM (fixed quark mass) 0.2 � N contribution 0 Hall C CLAS -0.2 SLAC 0 2 4 6 8 10 Q 2 (GeV 2 ) Inna G. Aznauryan & Volker D. Burkert Electroexcitation of nucleon resonances in a light-front relativistic quark model

Content The Model EM FF Delta(1232) N* on protons N* on neutrons Running quark mass Summary Magnetic ∆ form factor G M ∆ and Quadrupole ratios R EM , R SM 6 1 R EM (%) G M,Ash /3G D 4 2 0 0.8 -2 -4 -6 -8 0.6 CLAS 0 Hall C R SM (%) Hall A -10 0.4 MAMI -20 -30 0.2 -40 LF RQM -50 0 2 4 6 8 10 12 0 0 2 4 6 8 10 12 Q 2 (GeV 2 ) Q 2 (GeV 2 ) → R EM ≈ − 2%, dominated by MB contributions → G M described by LF RQM at Q 2 > 3 − 4 GeV 2 → R SM described at Q 2 > 3 GeV 2 . ◮ 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