Baryon Excitation through Meson Hadro and Photoproduction in
Baryon Excitation through Meson Hadro- and Photoproduction in a Coupled-Channels Framework Agung B. Waluyo Cornelius Bennhold Department of Physics The George Washington University Agung B. Waluyo, George Washington University Nstar 2005, page
Outline • Introduction • Chiral Symmetry Inspired Model • Examples of findings – P 11(1440), D 13(1700), and P 31 states. – “Missing” resonances. – Reactions: N N, N , and N • Summary and Conclusion Agung B. Waluyo, George Washington University Nstar 2005, page
Quantum Chromodynamics (QCD) --- the fundamental theory of the strong interaction (in terms of quarks and gluons) • At high energy, perturbative (asymptotic freedom) • At low energy, non-perturbative (confinement) Agung B. Waluyo, George Washington University Nstar 2005, page 3
Nucleon resonance spectral “lines” don’t quite look like this: 70 …but more like this: ( b) 60 50 40 30 Nucleon resonances are broad and overlapping! 20 10 0 Agung B. Waluyo, George Washington University 200 400 600 800 1000 1200 1400 E (Me. V) Nstar 2005, page
Chiral Symmetry Inspired Model is within a coupled-channels framework • Each resonance can be reached through each asymptotic channel • All channels couple through all other channels through intermediate state • Hadronic T matrices are directly related to photon multipoles (El±, and Ml±) Agung B. Waluyo, George Washington University Nstar 2005, page
The Bethe-Salpeter equation: M = V + V G 0 T Solved in the K-matrix approximation. Hadronic rescattering amplitude: The physics is in the driving terms Agung B. Waluyo, George Washington University K K = + , , K, 2 K Nstar 2005, page
Background contributions Baryon poles N, , and Meson resonance poles , , , a 0, and K* Constructed from chiral lagrangians Gauge Invariant Contact Term Higher order chiral contact terms ( PT) Agung B. Waluyo, George Washington University Coupling Constant are treated as free parameters! Nstar 2005, page
Hadronic Contact Terms Weinberg-Tomozawa Symmetric: Higher Order Contact Terms k and k’: four-momenta of incoming and outgoing meson P = (p+p’), p and p’: four-momenta of incoming and outgoing baryons Anti Symmetric: Agung B. Waluyo, George Washington University ’s are free parameters Nstar 2005, page
Higher Order Electromagnetic Contact Terms q and k: four-momenta meson and photon, P = (p+p’), p and p’: four-momenta of incoming and outgoing baryons. Agung B. Waluyo, George Washington University : photon polarization vector ’s: free parameters Each term is gauge invariant by construction. Nstar 2005, page
Resonance contributions N*, * A 1/2, A 3/2 helicity amplitudes masses N* Free parameters adjusted to data N N branching ratios K How do we describe high-spin N* states? (3/2 , 5/2 ) Breit-Wigner Rarita-Schwinger Pascalutsa Lorentz covariance × Proper spin degrees × Field theory Gauge couplings × × Technical ease × × Agung B. Waluyo, George Washington University Nstar 2005, page
What data do we fit for W 2 Ge. V? PW/Multipole Solutions 1. N N GW-DAC current solution 2. N N GW-DAC current solution Observables 1. N, N N 2. N, N K 3. N 2 N total partial wave (Manley 1981) We only show the results that do not include the N, K , and K hadroproduction data. The more complete global fits are still ongoing. Agung B. Waluyo, George Washington University Nstar 2005, page 11
Resonance Regions According to PDG! Agung B. Waluyo, George Washington University Nstar 2005, page
Examples of findings New Topic Agung B. Waluyo, George Washington University Nstar 2005, page 13
P 11(1440) N N partial wave Mass (Ge. V) total (Me. V) N N multipole N (%) 2 N(%) Waluyo 1500 630 58 42 Penner 1518(5) 668(41) 57(1) 43(1) Vrana 1479(80) 490(120) 72(5) - PDG 1430 -1470 250 -450 60 -70 30 -40 Agung B. Waluyo, George Washington University Similar! Nstar 2005, page
D 13(1700) N N multipole N N partial wave Different! Mass (Me. V) total(Me. V) N (%) 2 N (%) Waluyo 1728 181 0. 4 41 13 22 22 Penner Not found - - - Vrana 1736(33) 175(133) 4(2) 96(58) 0(1) - - PDG 1650 -1750 50 -150 5 -15 85 -95 0. 0 -0. 1 <3 - Agung B. Waluyo, George Washington University Nstar 2005, page
Where is the ground state of P 31(? ) N N partial wave N N multipole Is it at. . 1750 or 1910 ? (*) (****) Agung B. Waluyo, George Washington University Nstar 2005, page
What are coupled-channels models results for the ground state of P 31? Model Giessen GW Rarita-Schwinger Pascalutsa Mainly from P 33 to P 31 No offshell! Results P 31(1750) P 31(1910) When Pascalutsa couplings are applied P 31(1910) N* couplings Off-shell problem Message: for the P 31 wave, background contributions are important to obtain the final result! Agung B. Waluyo, George Washington University Nstar 2005, page
“Missing” Resonances? Agung B. Waluyo, George Washington University Nstar 2005, page 18
Compare experimental N* and quark model states experimentally uncertain N* Quark model predictions experimentally known N* Quark models predict many more states than are seen experimentally! Capstick and Roberts quark model 1/2+ 3/2+ Agung B. Waluyo, George Washington University 5/2+ 7/2+ 1/2 - 3/2 - 5/2 - 7/2 - Nstar 2005, page
Search in N N partial wave in 1800<W<2000 Me. V Therefore we need information from other channels! 3 rd S 11? 3 rd D 13? 3 rd P 11? PDG P 13(1900) PDG F 15(2000) No flux available! Agung B. Waluyo, George Washington University Nstar 2005, page
Do we find missing resonances in the range of 1800<W<2000 Me. V? (100 < N* < 600 -700 Me. V) N* Width (Me. V) 2 improved? Y/N? 3 rd S 11 < 20 N 3 rd P 11 < 30 N 3 rd D 13 409 Y Agung B. Waluyo, George Washington University Nstar 2005, page 21
Threshold Region: S 11(1535), D 13(1520), S 11(1650) Differential cross section for p p N* S 11(1535) D 13(1520) S 11(1650) N large small Data: M. Dugger et. al. CLAS coll. PRL 89, 2002 Agung B. Waluyo, George Washington University Nstar 2005, page
d /d for p p at higher energies N* Contribution D 15(1675) Very small D 13(1700) Very small P 11(1710) Large P 13(1720) Large D 13(1900) Small P 13(1900) Large F 15(2000) Very small Agung B. Waluyo, George Washington University Data: M. Dugger et. al. CLAS coll. PRL 89, 2002 Nstar 2005, page
Polarization observable for p p N* Contribution S 11(1535) Dominant D 13(1520) Small D 13(1700) Small D 13(1900) Small F 15(1680) Small F 15(2000) Small Agung B. Waluyo, George Washington University Data: J. Ajaka - Graal colloboration PRL 81, 1998. Nstar 2005, page
d /d for p K+ at lower energies Subthreshold Contributions From lower N* N* Contribution P 13(1720) Backward rise D 13(1700) Forward rise Data: Mc Nabb et. al. , CLAS 2003 No contributions from D 15(1675) and F 15(1680) ( K =0)! Agung B. Waluyo, George Washington University Nstar 2005, page
d /d for p K+ at higher energies N* Contribution P 13(1900) Backward rise D 13(1900) Forward rise Data: Mc Nabb et. al. , CLAS 2003 No contribution from F 15(2000) ( K =0)! Agung B. Waluyo, George Washington University Nstar 2005, page
-polarization observable for p K+ N* Contribution D 13(1700) at lower W D 13(1900) at higher W Data: Mc Nabb et. al. , CLAS 2003 Cos Agung B. Waluyo, George Washington University Nstar 2005, page
d /d for p K+ 0 at lower energies Subthreshold contributions from lower N* N* Contribution D 13(1700) Forward peaking P 13(1720) Backward rise Data: Mc Nabb et. al. , CLAS 2003 K* provides strength in the entire energy region. Agung B. Waluyo, George Washington University Nstar 2005, page
d /d for p K+ 0 at higher energies N* Contribution S 31(1900) Very Small P 31(1910) Small P 33(1920) Small D 35(1930) Large Data: Mc Nabb et. al. , CLAS 2003 Agung B. Waluyo, George Washington University Nstar 2005, page
Summary and Conclusion • We have investigated 21 N* and states for W < 2. 0 Ge. V through Meson hadroand photoproduction in a coupled-channels framework: o o • Bethe-Salpeter equation K-matrix approximation 2 system a scalar-isovector -meson New chiral contact terms Consistent Pascalutsa couplings for spin-3/2 and 5/2 resonances We extract N* properties and find : o Similarities for the N* in the 1 st N* region o Differences for the N* in the 3 rd and higher N* regions o 3 rd S 11, P 11, and P 13 “missing” resonances do not appear at 1900 Me. V, but 3 rd D 13 appears at 1946 Me. V • We are able to describe observables well: N N, p K+ , N + 0, and p K 0 + • Improve model: o Fit to -photoproduction observables o 2 N , N, … o Beyond K-matrix Agung B. Waluyo, George Washington University Nstar 2005, page
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