Neutrino Cross Section Calculations (Status Report) Emmanuel A. Paschos University of Dortmund March 21st, 2007

Main Properties  Neutrinos are important because they have only weak and gravitational interactions  They provided the first evidence for physics beyond the standard model  There are expectations that they have important consequences, but we do not know yet what the exact implications are

A LOOK AT HISTORY L. Michel 1966 TABLE 1 Problems of the Weak Interactions G=0.72x10 -5 M p -2 =0.83x10 -5 GeV -2 today´s value :( )x10 -5 GeV -2 structure at small distances : W`s or what ? discovered Cabibbo angle sinθ =0.21 now CKM Matrix Δ I =1/2 partly understood no neutral leptonic currents ? discovered why two kinds of leptons separately conserved ? μ-e symmetry, but μ-e mass difference ? μ-e-τ symmetry CP- violation ε, ε´, B-mesons V-A nature, P and C violation and two component neutrinos seem well understood

The mixing of neutrinos implies mass differences. The small masses suggest a high mass scale; a popular realization is the see-saw mechanism. Since the elements in the mass matrix are not equal  there is a symmetry that is broken; 1) if Global : Goldstone bosons 2) if Local : additional Higgs particles. To answer many of the questions we need precise determination of the cross sections.

Neutrinos have Masses A mass like M=M R N R C(bar) N R is called Majorana Mass and creates a Majorana mass state Ψ =1/√2 (N R C +N R ) Two kinds of mass terms: ♣ Dirac : ν L(bar) N R ♣ Majorana : N R C(bar) N R We wish to know the masses, mixings and phases of neutrinos, as well as other particles that are associated with them (Goldstone or pseudo-Goldstone mesons).

Cross sections at medium and higher energies have been studied for a long time. At the time of the discovery of neutral currents several reactions could have been more accurately determined.....there are new efforts to measure them accurately, because we need them for oscillation experiments.

Contents Overview of the cross sections Δ and higher resonances (work with J-Y. Yu, O. Lalakulich, M. Sakuda,EAP) Quasi elastic ( A. Bodek et al.) Coherent pion production(A. Kartavtsev, G.Gounaris, EAP) Importance of the results Summary

Anatomy of cross sections σ, qe = 0.50x cm 2 σ (Δ) = 0.60 x cm 2 σ(coh,π) =(1.0 to 3.0)x cm 2 σ, dis = 0.65x E, ν (Gev) cm 2 for E, ν = 10 GeV : 6.5x cm 2

Aims Determine the Δ-peak in various channels (accuracy of 10%) Observe dσ/dQ 2, σ(E v ) Observe several channels, perhaps one of the next resonanances Nuclear effects for various Nuclei With accurate vector couplings we can check the axial couplings C A 6 (Q 2 )

More recent Work Leitner, Alvarez-Ruso and Mosel Nucl-th/ Hernandez,Nieves and Velverde hep-th/ Sato, Lee and Sakuda,

Part II: J μ (k´,k)=C o ε μ (long) + Σ C λ ε μ (λ) ε μ(long) = 1/√Q 2 (q o,0,0,q 3 ) i ε μ (λ) = 1/√Q 2 (q 3,0,0,q o ), for λ = 0 1/√2(0,1,+i,0), λ=+1 1/√2(0,1, -i,0) λ= ε μ (λ) q μ =0 or for neutral current J µ q µ =0

Aims: estimate to better than 5% accuracy measure Q 2 dependence – Adler Test measure σ(E v ) use results to estimate background for ν e N  e - X oscillation studies

Relevance for other topics ♣ Precise values of cross sections are needed in LBL in order to determine Δm 2 and mixings angles : θ 13 especially In MINOS, Icarus and OPERA the signal is excess of events in v µ  v e CC reactions; good knowledge of reactions is necessary. Exper. in accelerators complementary to double CHOOZ (Huber, Kopp, Lindner, Rolinec, Rodejohann and Winter...) ♣ The mixing and oscillations are important for CP violation. ♣ Relevant for Leptogenesis which is a good candidate for Baryon Asymmetry in Universe..... ♣ If there are additional scalar particles, do they have observable consequences?

Summary There is considerable improvement in the estimates of cross sections aiming for an accuracy of 5% to 15%, depending on the reaction. We are interested on the dynamics of the reactions as well as their importance for properties of the neutrinos (Oscillations).