Multipole expansion in single pion production

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Multipole expansion in single pion production

D.Rein

Z.Phys. C – Particles and Fields 35,43-64 (1987)

Monireh Kabirnezhad

November 24^th 2014

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Wroclaw Neutrino Group

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Warsaw Neutrino Group(NCBJ)

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Single-Pion Production Single-Pion Production

Single-pion

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Resonant interactions are described by Rein-Sehgal Model

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For non-resonant interactions 3 Born graphs are suggested

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Outgoing leptons are massless

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2 more possible diagrams will be added to the model.

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non-zero lepton mass correction will be implemented.

In This model:

Corrections:

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Rein-Sehgal Model

is based on helicity amplitudes derived in a relativistic quark model by Feynman, Kislingerand Ravndal (FKR).

The helicity amplitudes depend on the spin projection of the initial and final states, and on the transition currents F+ (F−, F0) corresponds to the

gauge boson with positive (negative, zero) helicity:

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need to have a model to treat non-resonant

contribution as resonant interaction in the same frame of description .

Plan for Non-resonant interactions

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Non-Resonant background

A model for non-resonant background is provided by generalized

Born graphs for single pion production

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General Framework

Combination of amplitudes Corresponding to the

outgoing hadrons Isospin

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Isospin: Amplitude Decomposition

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Vector Current Conservation (CVC) :

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1.

Lorentz Covariance

Allows the vector and axial vector matrix elements to be decomposed:

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In the hadronic centre of frame the following choince of basis elements is made:

2. Isobaric Expansion

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Helicity Amplitudes

Gauge boson's polarization vectors Nucleon spinors

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● Lorentz Covariance

● Isobaric Expansion

Two expansions can be equated by using:

3. equating two expansions

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Multipole Expansion

The expansion coefficients refer to final pion_nucleon states of

definite total angular momentum, but not definite parity. To have parity eigenstates we sum or subtract amplitudes with opposite helicity

quantum number. Like:

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Cross-Section

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Resonance Contributions

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Lepton mass Implementation

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Lepton mass has effect on phase space.

This effect appear after integration.

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Lepton mass has effect on kinematics

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Lepton mass has effect on dynamics

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Kinematics

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Comparison between

Jakub's result and mine

For Born diagrams

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Contact-Term ... the 4

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diagram

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Comparison between

massive and massless lepton

for 4_diagrams

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Pion_Pole diagram

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Pion_Pole diagram

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Comparison between Jakub's result and mine for 5-diagrams

after mass correction

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