Single-pion Productionin

Neutrino Interactions

Monireh Kabirnezhad

15th of October 2013

Narodowe Centrum Badań Jądrowych (NCBJ)Wrocław Uniwersytet

2

Motivation

Past

Present

Neutrinos Only interact through “weak force”

Neutrinos are good probe for checking the validity of the theory of weak interactions and electroweak unification

We need an accurate knowledge of the neutrino-nucleus cross sections for neutrino oscillation experiments to be able to measure oscillation parameters accurately.

3

Weak interactions

Prediction of neutrino by Pauli

Current-current interaction by Fermi (1934)

How weak?

The cross-section of these few MeV neutrinos is such that the mean free path in steel would be 10 light-years

4

Weak Interactions revisited

Parity is violated in Weak interaction by Madam Wu in the late 1950sWeak interaction maximally violates parity

Neutrinos only interact weakly with a (V-A) interaction

Modern Version:

5

Neutrino Interactions

Point-like scattering

Neutrino- Nucleon Scattering

Neutrino- Nucleus Scattering

● Quasi- Elastic● Resonance ● Deep Inelastic

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Neutrino-Electron Scattering ee ee

W

e

ee

e

0Z

e e

ee

eggeeeG

H AVeeeeF

eff )()1()1()1(2

5555

Tree level Feynman diagrams:

7

Neutrino-Nucleon interactions

N

7

8

Neutrino nucleon cross sectionNeutrino nucleon cross section

QE Single-pion

P. L

ipar

i, N

ucl

. Ph

ys. P

roc.

Su

pp

l. 1

12

, 27

4 (

20

02

)

NN'

N

X

DIS

NR

8

9

Quasielastic scatteringQuasielastic scattering

And are axial form factors. Their Q- dependence is neither fully constrained by theory nor by experiment.

and are independent vector form factors by applying Charge current conservation (CVC) arametrization

J¹QE =

µ° ¹ ¡ q=q¹

q2

¶F V1 + i

2MN¾¹ ®q®F V2

+ ° ¹ °5FA + q¹ °5MNFP

Axial-vector part can be fitted just by neutrino production data which has poor statistics, but Electroproduction as well as neutrino production data used for the vector form factors measurement with better statistics.

10

Form Factors

Due to the poor statistics of neutrino-production data, we can not measure Axial-vector form factor, but the simplest parametrization is the dipole form:

Measurement of vector form factors from electron and neutrino scattering data

With unknown axial mass that can be fitted from data

11

Contributions of the various form factors to the total cross section for

The FP contribution is very small and almost not visible; the solid linerepresents the total cross section.

Total cross section for

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Single-Pion ProductionSingle-Pion Production

Single-pion

N'N N

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Excitation of baryon resonances

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Resonance-excitation cross-section

Integrated cross section for CC induced resonance production on the proton (left panels) and on the neutron (right panels). The different lines indicate the different resonances. In the case of scattering on protons only the excitation of isospin 3/2 resonances is possible.

15The three charged-current channels are plotted together with pion-production data from ANL and BNL on H2 and D2 .

CC pion production throughCC pion production through resonance Exitation resonance Exitation

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Rein-Sehgal Model

A successful model to describe the excitation of resonances for EM interactions up to W = 2GeV, and has been widely used in the neutrino experiment generators

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

The helicity amplitudes depend 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 like:

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CC pion-production cross sections predictions are made for the pure resonance model (dashed line) and for resonances plus the fitted non-resonant (full line)

This model describes the final state entirely in terms of resonances, leaving no room for a possible non-resonant interaction.

For non-resonant contribution, we can simply add resonant amplitudes of I=1/2 (which is needed), with adjustable parameter!

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Single pion production in neutrino interaction has resonant and nonresonant contributions.

Resonance interaction can be predicted by Rein-Sehgal Model, while non-resonant contribution is considered to arise from Born-terms,

So we 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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Rein Model

A dynamical model for non-resonant background is provided bygeneralized Born graphs for single pion production

Knowing the amplitudes of these diagram from Feynman rules, we can find the helicity amplitudes for different helicity of incoming and outgoing nucleons and gauge bosons.

For every isospin 3*4=12 helicity amplitudes for each, vector and axial vector current interactions

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Multipole Expansion

The expansion coefficients refer to final pion_nucleon states of defenite 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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The procedure of my work

First step is to take just first Born diagram and just considering the axial part of the helicity amplitudeDecompose it to the eigenstates with definite angular momentum:

and parity:

And substitute to the cross-section formula.

23difreferential cross section calculation for l = 0; 1; 2; 3; 4 and theresult is the same as performing integration for the amplitude instead of expansion

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Next Steps

Implement all Born-graphs (vector and axial parts) in my code and compare cross-section from multipole expansion with cross-section by performing integration from amplitudes

Add the resonance parts from Rein-Sehgal model to the cross-section “coherently”

Compare my final result with existence data (If it will be ok, we can implement it to the neutrino generator :-)

performing some correction, like add non-zero lepton mass, or adding more diagrams to the Born-graphs