Seminar Subatomic Physics
Chapter 3: New developments in hadronic particle production
• Nucleon resonances
TAPS+CrystalBarrel at ELSA
• Baryon models
• Partial-wave analysis
• Coupled channels
• Bethe-Salpeter equation
• K-matrix approximation
CLAS at Jlab
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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(1232) P33
pion nucleon
scattering
(1950)
Isospin coupling,
invariant mass (4-mom. sum)
and
phase-shift analysis
yield energy (mass), I, L, J
resonance assignment:
L2I,2J (mass)
and width (lifetime)
N(1680)
N(1520)
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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nucleon g.s. and excitations
partly explained in the quark model
radially excited
spatial states
(1710)
Roper res.
(1440)
chromomagnetic
(hyperfine) interaction
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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nucleon resonances
Vconf  bi li with string li and
string tension b  1GeV / fm
mass (MeV)
confining potential
in quark potential model:
qualitative understanding
well
poorly
known
gluonic excitations
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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pion nucleon scattering
- p  X reaction channels:
influence of channel opening
cross section (mb)
20
10
unitary reaction model needs
to include all important channels
real part of S11 partial wave ampl.
N width 2 N
influence of neglecting channels
w/o N final state
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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partial-wave analysis
quantum scattering in 3 dimensions (halfplane =0)
 scatt
 in  e ikz
eikr

f ( )
r
scattering amplitude
1 
f ( )   (2l  1)Pl (cos  )Tl ( E )
k l 0
1
1
/2
2 i l
E  Ereson.
Tl ( E )  l e  1  


2i
  i Ereson.  E   i / 2


E
(  / 2 )
  cot  l ( E )  E

 0
reson.
HL-ch.3 Sept. 2002
l
Student Seminar Subatomic Physics
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baryon resonances
elastic: unitary circle
inelastic
cross section reaches unitary limit
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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actual D13 resonance analysis
w/o D13(1900) state
requires high quality cross sections,
polarization observables
HL-ch.3 Sept. 2002
coupled-channel K-matrix
approach
Student Seminar Subatomic Physics
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calculations at tree-level
K
N N*

N
Y
K
Y

Y
neglect: hadronic final-state interaction
 violation of unitarity
requires: coupled-channels method
including rescattering
e.g. N  K
using: hadronic form-factors
K
Y
violates: gauge invariance
repaired by contact term
K
example: K photoproduction
K
Y
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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ladder approximation
solution to scattering problem: iterate interaction potential V
Bethe-Salpeter equation: 4-dim. integral equation,
 (all allowed intermediate 2-particle states)



 
Bethe-Salpeter propagator Gbs q, s  GB q, s GM q, s

K-matrix approximation: modify Re(Gbs) without violating unitarity
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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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
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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
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Student Seminar Subatomic Physics
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Seminar contributions
semester calendar date
week
week
topic
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.
HL-ch.3 Sept. 2002
Student Seminar Subatomic Physics
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13