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Chiral symmetry and form factors of neutrino-nucleon interactions.
Kanshin Kirill Vereshkov Grigory Southern Federal University, Russia

QFTHEP '11, Sochi 24th Sept.­ 1st Oct.


Outline
1. Previous studies of elastic eN scattering 2. The united theory of leptonnucleon interactions

· Neutrino Charged Currents · Neutrino Neutral Currents

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Part I Elastic eN scattering (Previous studies)


Vector meson dominance for eN scattering
The idea was originally suggested by Sakurai(1969). Photon hadronize to the set of (k) or 0(k) meson via quark loop. Amplitudes for the hadronization should be introduced in the proper way: 1) either purely phenomenologically 2) or using some regular method
Kanshin K., Vereshkov G. Southern Federal University, Russia Chiral symmetry and form factors of neutrino-nucleon interactions.

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The further development of the model of V.D. was conducted by
E.L. Lomon "Extended Gari-Krumpelmann model fits to nucleon electromagnetic form factors" Phys. Rev. C 64, 035204 (2001) "Structure of the nucleon from electromagnetic form factors." Eur.Phys.J.A19(2004)

F. Iachello

G. Vereshkov O. Lalakulich

"Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form factors" Eur. Phys. J. A34 (2007) and others

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


The cross section of the elastic eN scattering is parameterized by two functions GE(Q2) and GM(Q2) ­ electric and magnetic form factors correspondingly. Results obtained by Vereshkov and Lalaculich using V.D. model:

proton FFs
Kanshin K., Vereshkov G. Southern Federal University, Russia

neutron FFs
Chiral symmetry and form factors of neutrino-nucleon interactions.

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Part II The united theory of lepton-nucleon interactions


Physical principles
· Vector and pseudovector dominance model
· Hadronization of intermediate bosons to the set of mesons. · Multi-gauge theory

· Chiral symmetry of strong interactions
· Parameters are the same for electron and neutrino processes
Additional form factors are taken into account because of axial couplings.
Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Parameters.
is coupling constant
We inroduce Dirac terms as

, where

weight of each particular generation

For the gauge invariance:

corresponding meson field

Not only Dirac () but Pauli () terms should be introduced to the model with their own parameters k as well. There are two sets of parameters wk and k for 1) scalar (,f) mesons 2) vector(,a) mesons. To describe four meson fields four gauge groups are necessary.
Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Objects of the theory and gauge groups.

1.

Higgs sector

2.

3.
4. 5.

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Charged currents


Mixing.
Higgs field and one from SM generate quadratic form via spontaneous symmetry breaking with non-zero vacuum expectation value. It 's diagonalization leads to small mixing between fields:

In this way we receive effective lepton ­ meson vertex.
Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


-decay
Standard expression originates from effective Fermi theory:

where = 1.25 is defined from experiments

Connection with the gauge theory:
is formed by

mixing parameter group constants meson propagators

occurs due to u-d quark twist Expression for via theoretical parameters: (witch is used for refit of eN data)
Kanshin K., Vereshkov G. Southern Federal University, Russia

- sum rule

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Quasi elastic N scattering
In this case the cross section is parameterized by four form factors:

1. 2. 3. 4.

Vector Dirac F1(Q2) Vector Pauli F2(Q2) Axial Dirac GA(Q2) Pseudoscalar GPS(Q2)

First and second are not independent , they strongly related with GE(Q2) and GM(Q2) from eN scattering . Contribution of GPS(Q2) is proportional to lepton masses and negligible.

Thus, only GA(Q2) should be determined from experimental data.

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Quasi elastic N scattering

In high Q2 region QCD gains its power, that 's why we should take into account QCD asymptotes, which were calculated in following papers:
S.J. Brodsky, G.R. Farrar, Phys.Rev. D11,1309 (1975) G.P. Lepage, S.J. Brodsky, Phys. Rev. D22,2157 (1980) A.V. Belitsky, X.d. Ji, F. Yuan, Phys Rev Lett. 91, 092003 (2003) S.J. Brodsky, J.R. Hiller, D.S. Hwang, V.A. Karmanov, Phys. Rev., D69, 0760001 (2004)

In case of three meson generations, if all sum rules and eN results are mentioned there are no free parameters for GA(Q2).
Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


The theory describes scattering on free nucleons. That is why only deuterium chamber experiments could be used. Results are following:


Neutral currents


Mixing
An additional mechanism is required to introduce effective e- vertex. It is U(1) mixing.

Cross term in kinematic sector is not forbidden by symmetry principles:

Diagonalization of both kinematic and Higgs quadratic forms leads to mixing of five fields

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Elastic N scattering
The main goal is to reproduce data on elastic N scattering. Only one deuterium chamber experiment is available ­ BNL E-734. Current status: ­ Mixing has been done successfully ­The full lagrangian of neutral current sector has been written. It does not contain undetermined parameters. ­ Comparison with experimental data is not finished yet.
Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.


Conclusions.
· Gauge theory of lepton ­ nucleon interactions has been investigated. · It is based on meson dominance and chiral symmetry of strong interactions. · Asymptotic conditions, fit of eN data and -decay data allow to parameters.
The theory also gives an opportunity of studying some other processes caused by strong interactions.

fix

all the

Kanshin K., Vereshkov G. Southern Federal University, Russia

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Chiral symmetry and form factors of neutrino-nucleon interactions.