HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 1

Seminar Subatomic PhysicsChapter 3: New developments in hadronic particle production

• Nucleon resonances• Baryon models• Partial-wave analysis• Coupled channels• Bethe-Salpeter equation• K-matrix approximation

CLAS at Jlab

TAPS+CrystalBarrel at ELSA

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 2

pion nucleonscattering

Isospin coupling,invariant mass (4-mom. sum)and phase-shift analysisyield energy (mass), I, L, J

resonance assignment:L2I,2J (mass)and width (lifetime)

(1232) P33

(1950)

N(1680)

N(1520)

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 3

nucleon g.s. and excitationspartly explained in the quark model

chromomagnetic(hyperfine) interaction

radially excited spatial states

Roper res.

(1710)

(1440)

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 4

nucleon resonances in quark potential model:qualitative understanding

mas

s (M

eV)

confining potential

fmGeVb

llbV ii iconf

/1 tension string

and string with

gluonic excitations

wellpoorlyknown

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 5

pion nucleon scattering

- p X reaction channels:influence of channel opening

unitary reaction model needsto include all important channels

real part of S11 partial wave ampl.

influence of neglecting channels

w/o N final state

N width 2 N

cros

s se

ctio

n (

mb

)

1020

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 6

partial-wave analysisquantum scattering in 3 dimensions (halfplane =0)

ikzin e

)( fr

eikrscatt

0)(cot

2/

2/11

2

1)(

)()(cos)12(1

)(

)2/(

.

2

0

.

.

lreson

resonl

EEl

reson

EEill

lll

E

iEEie

iET

ETPlk

f

scattering amplitude

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 7

baryon resonanceselastic: unitary circle inelastic

cross section reaches unitary limit

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 8

actual D13 resonance analysis

requires high quality cross sections,polarization observables

coupled-channel K-matrixapproach

w/o D13(1900) state

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 9

calculations at tree-level

neglect: hadronic final-state interaction violation of unitarityrequires: coupled-channels method

including rescattering e.g. N K

using: hadronic form-factors

violates: gauge invariancerepaired by contact term

K

Y

K

K

K

Y

Y

Y

N

N N*

Y

K

example: K photoproduction

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 10

ladder approximationsolution to scattering problem: iterate interaction potential V

Bethe-Salpeter equation: 4-dim. integral equation, (all allowed intermediate 2-particle states)

Bethe-Salpeter propagator sqGsqGsqG MBbs ,,,

K-matrix approximation: modify Re(Gbs) without violating unitarity

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 11

Summary:motivation:

low-energy QCD in confinement regime

not accessible by perturbation theory

•QCD lattice theory: numerical solutions

•effective quark models

program to study

hadronic and electromagnetic excitation of nucleon

analysed by dynamical model description satisfying

unitarity, analyticity, Lorentz- and gauge-invariance

masses, decay widths of resonance states

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 12

Literature:

1. Scattering Theory:

Sakurai, Modern Quantum Mechanics, Addison-Wesley 1994 p.379-399

 

2. Compton scattering on the proton and light nuclei in the Delta resonance region (K Matrix approach)

O. Scholten, Acta Physica Polonica 33 (2002) 847-871

 

3. Vector meson production with photons and nucleon resonance analysis

in a coupled channel approach

G. Penner, U. Mosel, nucl-th/0207069

4. Pseudoscalar and vector meson production in NN collisions

K. Nakayama, nucl-th/0108032

HL-ch.3 Sept. 2002 Student Seminar Subatomic Physics 13

Seminar contributions

semester week

calendar week

date topic name

1 36 4 sept. 1.1 oscillations

3 38 18 sept. 1.2 solar neutrinos

4 39 25 sept. 1.3 mass limits

5 40 2 oct. 1.4 -less double decay

6 41 9 oct. 2.1 quantum Monte Carlo

7 42 16 oct. 2.2 ab initio shell model

8 43 23 oct. 2.3 supernova detection

9 44 30 oct. 3.1 scattering theory

10 45 6 nov. study week Münster

11 46 13 nov. 3.2 Compt. scatt. & K-matrix

12 47 20 nov. 3.3 coupl. ch. reson. analysis

13 48 27 nov. 3.4 meson prod. in NN coll.