PoS(QFTHEP2011)075 http://pos.sissa.it/ considered as multipole expansion multiplied on pQCD ) 2 Q ( A G ∗ [email protected] [email protected] Speaker. asymptotes is in a good agreement with experimental data. Phenomenological multigauge model of -nucleonof interaction based strong on interactions chiral and symmetry shown vector/pseudovector that within dominance the framework model ofmeson is the masses suggested. model and the parameters constant It ofelastic of the was (anti)neutrino- hadronization scattering beta of processes decay fundamental is have vectorweak been formed . nucleon by investigated form and Then, factor it quasi (FF) was found that ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c The XXth International Workshop High EnergySeptember Physics 24-October and 1, Quantum 2011 Field Theory Sochi Russia Institute of Physics, Southern Federal University,E-mail: Rostov-on-Don 344090, Russia G.M. Vereshkov Institute of Physics, Southern Federal University,E-mail: Rostov-on-Don 344090, Russia K.A. Kanshin Chiral symmetry and form factors of neutrino-nucleon interactions. PoS(QFTHEP2011)075 . ] 1 is a (1.1) (2.1) N - and two τ . In case 2 F - are actual , K.A. Kanshin i 1 F w . ) 2 -decay and charged Q ( β bosons hadronize to 1 , G ± multigauge approach µν i , µ i W A A : two vector Ψ meson dominance 2 Ψ . q µν µ 2 − , γ σ 1 ¯ ¯ elastic scattering presented in [ Ψ Ψ = i i = 2 N w κ is generation (family) index, a 1 Q 1 − N N = i = ∑ i ∑ i e g , g are multigauge fields and ) 2 µ i Q A . ( 1 en a = F i 2 − w multipli f ying multipli f ying ) 1 −−−−−−−→ −−−−−−−→ 2 N = ∑ i µ Q µν A ( A Ψ ep a µ Ψ F γ µν ¯ is any fermionic field, scattering. In particular, we introduce multipole expansions of Ψ σ ) = g N 2 Ψ ¯ Ψ Q g − ( a ν ]: F 2 interaction it claims that intermediate vector N Dirac: − Pauli: ν form factors. However vector FFs are not independent, they can be expressed in terms 3 G is a coupling constant, , 1 g to the cross section is proportional to lepton mass, so in case of light (non G CCQE processes are parameterized by four functions of give the unique opportunity to probe axial structure of , that is why clear In this work we suggest phenomenological -meson gauge theory of The main assumption of the model is the vector and axial vector In order to account the sets of with different masses we use 3 G So far as this work is just a generalization of the theory of current quasi elastic (CCQE) to the neutrino processes weof consider vector weak FFs asprocesses) well it determined. is usually Besides, neglected. contribution Thus, in this paper we will focus on only CCQE form factors and compare the resultsnucleon with processes, available nuclear experimental effects data. were We not studied taken only into free account. theoretical interpretation of experimental data onover, precise axial knowledge nucleon of FFs weak is nucleon ofspheric FFs great neutrino is importance. experiments. vital More- for present and future accelerator and atmo- Chiral symmetry and form factors of neutrino-nucleon interactions. 1. Introduction axial of ones from elasticcurrent -nucleon hypotheses scattering. (CVC) [ This relation originates from conserved vector 2. Basics and features of charged current Use of multigauge groups allows toeters, introduce for a example set in of Dirac gauge terms fields of with lagrangian their it own means: coupling param- where the sets of vector and axialexchange. mesons, so interaction between neutrino and nucleon occurs via meson total number of generations (willparameters be of discussed the later), theory. Following relation is required to save gauge invariance: This is the first sum ruledipole moment (SR) of imposed nucleon on Pauli parameters. terms Moreover, are to necessary: account anomalous magnetic PoS(QFTHEP2011)075 ) 2 ( i R (2.2) gauge SU ) 1 × ( i R ) 2 K.A. Kanshin U ( i L × 2 ρ ) 2 ω SU 1 m m ( i 2 ρ 2 ρ 2 L W − − m m U m 1 f 2 2 a ∼ ∼ ∼ m m isotopic chiral groups. In ) ∼ ∼ Vacuum shift 2 ( i ) ) R 2 2 ( ( SU i i ) R R ) 2 corresponding to 2 × ( , ( i 1 SU SU ) i L i ) ) R  a 1 i interactions involves at least four sets 2 2 ( × × ± 1 ( ( i SU R ) ) ) SU a N 1 1 1 U and × ( ( ( EW EW × L L i which are formed by + i i i ) − R R R × ) i i ρ 1 ) 1 U U U ν ± ( SU SU ω ( 2 i L ρ i ( R × × × × × i L U ) ) ) i U ) ) Group 1 2 2 3 ε × 1 1 ( ( ( SU × ( ( i i i ) L L L ) + motivated by gauge symmetries. Thus we have two 2 × U 1 ( i ± EW EW ) ( SU SU 1 κ . U U ( i W EW × × scattering. scattering. L i EW L ∑ κ ) ) = U N 1 1 U SU ( ( ± i i L L − e U U W  of strong interactions requires coupling constants of left and right and µ and Pauli µ ν i N  w  − p n or ν   Field = e e ν 1. This way lepton-meson vertex is introduced. N coupling. Consequently, parameters of vector and axial form factors will be the  Higgs sector  N = 2 l i ρ 2 W − chiral symmetry 1 m m a ∼ i ε and Finally, By adding nucleon-meson terms to the lepton doublets we receive fermionic The remaining degrees of freedom have to be mixed with the Standard Model Higgs After lagrangian had been constructed one could study real physical processes. Assuming chiral symmetry of the vacuum we put vacuum shifts of left and right (1st and 2nd Full theory of both neutral and charged current N − fields act only in elastic fields to be equal andρ this way reduces number of parameters. Moreover, it leads to equality of same. sector of lagrangian. InHiggs order fields to as construct a effectivemeson lepton-meson representation masses vertexes additional of Higgs one both fields hasin are mesonic to the required. and table: introduce Summary electro-weak of gauge the objects groups. of the theory To is generate given and then identified withenormous additional (245 meson GeV) sets. valuesmall of However and vacuum it lepton-Higgs has shift, vertex been so neglected. is contribution suppressed of by these mesons is expected to be where in the table) Higgs fields equal. Spontaneousfields. symmetry Its breaking diagonalization generates quadratic leads form to of the boson small mixing (only charged bosons considered): have to be taking into consideration, while isoscalar Chiral symmetry and form factors of neutrino-nucleon interactions. however there is no similar relation for of mesons which could be classified by case of charged currents, only sets of isovector mesons types of parameters: Dirac PoS(QFTHEP2011)075 C θ (3.2) (4.1) (4.2) (3.1) (4.3) is the C θ , the so- 0; cos , A ) = M 2 K.A. Kanshin ( is formed by 2 Q 2 F i EW L 1 Q G 2 a SU m + i i 2 ρ w m 1 0 0 0 N ∑ = i = = = i i i 2 ρ 2 ρ 4 ρ are the same for both electron ) = i 2 m m m w i i i Q ( twist, and finally we have got the κ κ w . 1 1 1 1 ¯ ) d e N N N ∑ ∑ ∑ = = = G 2 α i i i u 3  2 A 2 + Q M 1 i α i 1 ( 2 ρ + 2 a 2 C i is the coupling constant of m 1 m Q 2 ρ θ → → i  m W + w g i i cos 4 1 and the phenomenological parameter 2 ρ κ N = 2 F ) = ∑ i m 2 α G 6 4 1 = Q 1 1 N ∑ = ( Q Q i 16 α -decay amplitude which originates from Fermi theory of ∼ ∼ = ) = ) ) 2 β ] is a dimensionless phenomenological parameter, precisely dipole 1 | 2 2 2 3 G Q Q Q ( ( ( M | 2 1 2 e F F G 2689 [ , . ) -decay constant 1 2 β : Q = ( 2 α i 1 α Q 2 ρ F m + is the Fermi constant, where i i region the conventional dipole form of axial form factor reveals satisfactory fit 2 ρ w 2 2 W m Q m 1 2 W 2 N ∑ = g i √ 4 scattering and the axial FF ) = 2 = N . At low Q F ) ( 2 G − 1 -decay Within the framework of presented model we have obtained the following multipole expres- Taking into account this relation and the fact that parameters As we have already mentioned the main purpose of studying CCQE scatterng was fitting of Squared amplitude has been calculated within the framework of the theory as well and param- To reproduce the correct asymptotic behavior of the form factors at infinity the additional sum Standard expression for squared e F Q ν β ( 1 sions of form factors: following expression for called axial-vector dipole mass. mixing parameters, coupling constants ofmust gauge be groups inserted and meson due propagators to at hadronization via non-perturbative It is parameterized by the of the experimental data: G Cabibbo mixing angle, and CC neutrino parts of theand theory no one any had significant to changes refit occurred, data parameters on have electron not scattering. changed This a has lot. 4. been done eters of the theory has been identified with ones from the Fermi theory. Thus, determined by experiments. rules are required: Chiral symmetry and form factors of neutrino-nucleon interactions. 3. weak interactions is following: Here PoS(QFTHEP2011)075 ], 6 ) on (4.7) (4.5) (4.6) ], [ 5 4.2 ) ], [ 2 4 reconstruction Q K.A. Kanshin ( 1 e G ) 2 , Q 2 2 FFs in [ ( / 1 a are magnetic moments 3 mesons is suppressed p = q n − a µ > i ) with available deuterium  ) = 2 2 Λ and 4.7 Q / ( p 2 1 µ Q G . We have obtained six sum rules are determined from six sum rules. + from ( 1 and Pauli N ) 1 70 (4.4) ) . 3 ) ) ) 2 = 3 , 2 2 ) , where ]) Q a , 2 n ln ' ( 1 1 1 a µ Q 1 1260 1640 1930 g ( ( ( ( G in final FFs. So, we present just a = 2 1 1 1 − e F i a a a ) = n ) ( ) + 0 . 2 µ 2 i ( 5 region one has to multiply form factors ( 1 n Q Λ κ 2 − 2 ( / F ) ) p 2 ) 2 Q , q µ Q 1 and 770 = i + − 1450 1700 ( ) = i ( ( w p 1 2 data but not fit. As we have already mentioned nuclear ef- ρ κ ( ρ ρ µ Q 1 ln N ( calculated for Dirac N = ∑ i 2 a are the same with ones used in electron part of theory. So, they 2 F − ) = h a Q 0 e ( p + p 2 of 1 a F g ) 2 ) a 2 Q h ) = ( Q there is no free fit parameters 2 a ( ] is presented in the Fig. ) and ) which have to be imposed on parameters. To satisfy them at least three 1 q Q e F ( 10 ) 1.1 a 4.4 2 q ],[ 9 Q ), ( ( 1 ],[ q 8 4.3 3 both sets of parameters = ), ( . These mesons are following: ) = form factors based on 2 N N 3.2 N Q ( 1 − Thus we obtain final expressions of FFs: We emphasize that We are planning to apply this multigauge scheme based on chiral symmetry and meson dom- To account pQCD asymptotes in high Besides, from ( Now let us discuss the number of meson generations ), ( F 1. Elastic electron-nucleon scattering (presented in [ 2. Charged current quasi elastic neutrino-nucleon scattering (shortly3. described here) Neutral current elastic neutrino-nucleon scattering (under investigation at the moment) ν ]. The general expression is following: 7 2.1 have been already determined from electron data. Thus, we consider onlynumber three generations, however in the theory there is no any restrictions on where all the parameters of fects was out of consideration. The comparison of inance to the neutral currentnucleon as interactions well which and consists of thus three to parts: complete the full theory of (quasi)elastic lepton- 5. Perspectives and conclusion logarithmic functions [ experiments [ generations must be taken into account.precise The data first on reason to heavy use axial only mesons. three Another families one is is that that there contribution is of no Chiral symmetry and form factors of neutrino-nucleon interactions. ( by increasing mass. And finally, threecase generations of fit of electron data was accurate enough. In the of and neutron correspondingly we get: PoS(QFTHEP2011)075 groups ) 3,5 1 ( U K.A. Kanshin -lepton vertex ω 3,0 2,5 , T.Kitagaki , al. et 2 . Diagonalization of both kine- , K.L. Miller et al. Milleret K.L. , , N.J. Baker N.J. al. et , µ 2 2 B , 223 (2007) ν ∂ 34 − 2,0 ν B , µ Reconstructionfrom eNdata ∂ BNLD81, D83,FNAL 2 µν ANLD82,

ω = Q __ 6 µν 1,5 µν B

Eur. Phys. J. A B , 1 4 − group, ]. Reconstruction of axial formfactor 1,0 ) 1 Logarithmic corrections and soft phenomenology in the ( EW U Figure 1: 0,5 -boson and photon). Moreover, in order to introduce effective Z 0,0

1,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 A

- mesons,

(Q G

) field corresponds to 2 ω µ , arXiv:0705.1476 [hep-ph] B 0 1 [ multipole model of the nucleon form-factors Another perspective application of the approach is a studying of some other processes caused The third part is more complicated then previous ones because of mixing of five boson fields a , 0 [1] G. Vereshkov and O. Lalakulich, ρ by strong interactions, such as resonance and single production orReferences many-pion production. matic and Higgs sectors leadsmined to parameters. the required mixing. The theory of NC will not contain undeter- Here is gauge invariant, so cross term in the kinematic sector of the lagrangian is not forbidden: ( an additional mixing mechanism is required. It is based on the fact that stress tensor of Chiral symmetry and form factors of neutrino-nucleon interactions. PoS(QFTHEP2011)075 et , , 37 28 K.A. Kanshin Phys. Rev. D (1982) 537. , J. Phys. G 26 , Phys. Rev. D , (2004) 076001 69 Phys. Rev. D , ∗ ]. pp − , Institut National de Physique The Covariant structure of light front µ Phys. Rev. D → , Review of physics p Scattering in Deuterium − µ → 7 hep-ph/0212351 Weak interactions (1981) 2499. A Perturbative QCD analysis of the nucleon’s Pauli form-factor 23 Exclusive Processes in Perturbative Quantum Chromodynamics Scaling Laws for Large Momentum Transfer Processes (2003) 092003 [ 91 ]. Phys. Rev. D , [Particle Data Group Collaboration], Quasielastic Neutrino Scattering: A Measurement of the Weak Nucleon Axial , Study Of The Reaction -neutrino D (1980) 2157. , et al. et al. 22 et al. Phys. Rev. Lett. , ) 2 High-Energy Quasielastic Muon-neutrino n Q (1975) 1309. , ( 2 hep-ph/0311218 al. Vector Form-Factor (1983) 436. Nucle’aire et de Physique des Particules, Paris 1977. 075021 (2010). 11 Phys. Rev. D F wave functions and the behavior of hadronic form-factors L. Hyman [ N. P. Samios [2] J.-M. Gaillard, M. K. Gaillard, M. Nikolic’, [3] K. Nakamura [5] G. P. Lepage and S. J. Brodsky, [4] S. J. Brodsky and G. R. Farrar, [6] A. V. Belitsky, X. -d. Ji and F. Yuan, [7] S. J. Brodsky, J. R. Hiller, D. S. Hwang and V. A. Karmanov, [8] K. L. Miller, S. J. Barish, A. Engler, R. W. Kraemer, B. J. Stacey, M. Derrick, E. Fernandez and [9] N. J. Baker, A. M. Cnops, P. L. Connolly, S. A. Kahn, H. G. Kirk, M. J. Murtagh, R. B. Palmer and Chiral symmetry and form factors of neutrino-nucleon interactions. [10] T. Kitagaki, S. Tanaka, H. Yuta, K. Abe, K. Hasegawa, A. Yamaguchi, K. Tamai and T. Hayashino