1. NOW 2008 (5th Neutrino Oscillation Workshop)
Conca Specchiulla 6-13 September 2008
V. Antonelli, G. Battistoni, P. Ferrario1, S. Forte
(Università degli Studi di Milano e I.N.F.N. Sezione di Milano e 1Università di Valencia)
(Nucl. Phys. B Proc. Suppl. 168 (2007) ; IFAE 2007, pagg )
Neutrino physics and the Standard Model: Precision measurements with future neutrino beams

2. Standard Model and neutrino physics
Neutrino (n) interacts only weakly: ideal candidate to test e.w. interactions
S.M. and n physics up to now.Parallel history since ’60s:
- Standard Model: strong confirmations; precision tests (LEP, high energies)
- n physics. Relevant role in the past: Gargamelle, discovery of neutral currents; possible measurement of Weinberg angle; proof of neutrino masses and mixing need to modify Standard Model; theories beyond the S.M.
Future ?
Search of physics beyond the S.M., 2 ways:
1) Higher energy
2) High intensity (Low energy tests of S.M.: search for rare processes; measurements of S.M. parameters with low E and very high intensity n beams) Fu

3. Open Problems in Neutrino Physics
Despite the relevant recent results,
Still many open problems
- Nature of neutrino (Dirac o Majorana)
Absolute value and hierarchy of masses (direct,
inverse or quasi-degenere)
Exact determination of mixing parameters:
13=0 or 13 ≠ 0
- Search for CP violation

4. ROLE OF ACCELERATOR n EXPERIMENTS
Up to now main results from solar and atmospheric n. Recent contributions from K2K and MINOS (accelerator) and KamLAND (reactor).
All results from disappearance exp. ; only claim from appearance was LSND disproved by MiniBOONE.
Why ?
- Solar n scale: below kinematical threshold for muon production
- Atmospheric scale: nm nt leading oscillation . t identification needed, difficult task (CNGS)
nm ne oscillation (suppressed by q13 ; high intensity source needed) . Future
CNGS (1st run August 2006): search for nt appearance , very few events. Possible improvement of q13 limit (from 11° to 7°)
The q13 puzzle:
- if q13 ~ 10° no need for new accelerators
- if q13 > than ~ 3° need for new detectors (Mton water Cerenkov) and superbeams
- if q13 ~ 1° new generation of experiments needed : b beams and n factories
- if q13 < 1° CP phase not accessible with terrestrial experiments

5. Future of neutrino physics (from accelerators)
1st stage: Conventional n beams from a secondary meson beam (K2K, MINOS, CERN/G.Sasso, T2K 1st phase) and Double Chooz (reactor) partial improvement of 13 ; Not enough to study the leptonic CP violation
2nd stage: Superbeams (T2K 2nd phase, NoA, CERN)
beam luminosity increase: 13 precise measurement and/or (eventual) CP violation
search
- T2K (Japan, 2009) 2nd phase:  beam from JParc to SuperK (L=295 Km)
- NoA (USA): use the beam of NuMI at FNAL, detector at about 800 Km
-CERN: possible superbeam exploiting the CERN SPL
3rd stage (end of next decade): n from primary beam decays
Neutrino factories:  from decay of muons (tens of GeV) in accumulation rings
( )
Beta beams:  beams from  decays(few GeV or lower E)
Example:
6He for anti-v beam; and 18Ne for  beams

6.  weak and e.m. forces mixed
WEINBERG ANGLE
Electroweak unification: SU(2) x U(1) simmetry invariance
 weak and e.m. forces mixed
couplings
SU(2)  g
U(1)  g’
n-e- elastic scattering: competitive for Weinberg angle measurement at ‘‘high energy’’ n factories;
at lower energies the lower cross sections compensated by high intensities.
For E ~MN (quasi) elastic contributions to n-nucleon interactions are sizable (see figure).
Elas
ela n-

7. Neutral current scattering amplitudes
FORM FACTORS introduction

8. Weinberg angle determination
6 cross sections: neutrino (antineutrino) neutral currents on proton (neutron) and neutrino (antineutrino) charged currents
Fixing the values of the electric form factors there are 6 parameters left :Weinberg angle and 5 form factors
(GpM, GnM , GSM , GA , GSA)
Analytical study: System of 6 equations coupled 2 by 2; The equation for Weinberg angle can be solved analytically in terms of measurable quantities (cross sections combination and kinematical variables)
Simultaneous fit of Weinberg angle and hadronic form factors is feasible.

9. Detector choice : Liquid Argon TPC
Numerical study
From data analysis simultaneous fit of the values of Weinberg angle and hadronic form factors.
Experimental requirements and caveat
Select the QE (Quasi elastic) scattering. Elastic and quasi elastic cross sections: optimal region around 1 GeV (ex. T2K)
Neutral currents must be identified: only recoiling proton can be measured, no NC on neutron from 6 to 4 cross sections, loss of information.
Different Q2 bins should be investigated: good kinematic reconstruction neeeded.
Detector choice : Liquid Argon TPC
- Pro: in principle p down to 50 MeV can be identified.
- Con: Difficult to assemble a large mass; nuclear reinteractions in Ar are more important than in water.
For p > 300 MeV Q2 > 0.1 GeV2 , about 75% of the events surviving. Measurements at near detector already competive with detector below kton (around 500 ton)
Interesting possibility, mainly for superbeams

10. Numerical analysis and results
1st possible approach:
Assume the form factors expressions known and perform a simultaneous fit of Weinberg angle and hadronic form factors
-Possible to reach a good level of accuracy
-Confirmation that the dipole approximation is not enough for the magnetic and electric form factors of nucleons
2° kind of analysis (‘‘blind analysis’’)
- We make no assumptions on the functional form of form factors and riproduce them by means of a neural network.
Studied different possible combinations of form factors to fit simultaneously with the Weinberg angle
The network works quite well and the results of the fit are satisfactory

11. A simple example (1st KIND OF ANALYSIS)
Simultaneous determination of sin2qW and GMS(Q2)
GSA known with bad accuracy (about 30%), but cross sections weekly dependent on GSA. We assume dipole form and take 1s variation for forward value GSA(0)= -0,13 ± 0.09
Using for neutrino energy: En = 1 GeV
Detector : 10 ktons Liquid Ar
Assuming in data generation sin2qw =
From simultaneous fit of sin2qw and GMS, varying GAS, we get:
sin2qw = ± (stat) ± (syst)

12. Analysis with Neural Network
Simultaneous fit of sin2qW and magnetic form factor GMS (one of the less known)
The form factor is very well reproduced by the neural network
Accuracy of the angle fit is satisfactory, even if it is very sensitive to the value of the magnetic form factor.
‘‘Experimental’’ value : sin2qW = ; Result of the fit: sin2qW = ±
Simultaneous fit of sin2qW and magnetic form factor for proton or neutron (GMP or GMN )
GMP reproduced quite well (despite some problems in low Q2 bins).
Weinberg angle fit is satisfactory.
Simultaneous fit of sin2qW and different combinations of form factors: attention to possible correlations and possible existence of ‘‘fake solutions’’ .

13. CONCLUSIONS
Standard Model: working very well up to the electroweak scale
Useful to improve parameters knowledge at medium-low energies.
Role of n physics and future experiments with high intensity beams
n(anti-v)-nucleon interaction:dependent from Weinberg angle and hadronic form fac.
Analytical study and estimate of accuracy in sin2W determination
Numerical analysis of the problem
Examples: b beams and superbeams potentiality
Measurements realistic with present Icarus technology
Examples of numerical analysis:
assuming a known functional form for hadronic form factors
with no assumptions on hadronic form factors
Measurement at energies low with respect to LEP is interesting to
verify theory consistency and/or eventual signals of physics beyond S.M.

14. Beta-Beams PRO Only 1 flavor in the beam
Well known and determined energy (kinematics well known
and nucleon recoil negligible)
Beams well collimated and with value of (/ECM) higher than
 factories
Proposals:
- Cern- Frejus (L about 130 Km; ‘‘low’’ beam E)
- Higher E beams and longer baselines (Cern-G.Sasso/Canarie)
proposed for neutrino physics, but useful also to study Standard
Model ?
Analysis already available for neutrino factories
Interesting to extend it to beta-beams

15. T2K
Neutrino beam from protosinchrotron of 50 GeV, MW at JParc
Off-axis beam to SuperKamiokande (L = 295 Km) Begins spring 2009
Main goals:
- sin2 13 measurement with sensitivity 20 times better than Chooz
Measurement of m232 and sin2 23 (atmospheric parameters) at 1-2%
( disappearance)
- searchfor sterile  (weak currents disappearance)
Tests of Standard Model parameters: low energy measurements, different from LEP; eventual possibility of signals of new physics

16. Beta-Beams PRO Only 1 flavor in the beam
Well known and determined energy (kinematics well known
and nucleon recoil negligible)
Beams well collimated and with value of (/ECM) higher than
 factories
Proposals:
- Cern- Frejus (L about 130 Km; ‘‘low’’ beam E)
- Higher E beams and longer baselines (Cern-G.Sasso/Canarie)
proposed for neutrino physics, but useful also to study Standard
Model ?
Analysis already available for neutrino factories
Interesting to extend it to beta-beams

17. Detector alternatives
Water Cherenkov:
Pro: there is the possibility of assembling a very large mass (some MTon)
Con: the Cherenkov threshold prevents the detection of recoiling protons with p<1 GeV.
2) Liquid Argon TPC
Pro: in principle p down to 50 MeV can be identified.
Con: Difficult to assemble a large mass; nuclear reinteractions in Ar are more important than in water
For p > 300 MeV Q2 > 0.1 GeV2 , about 75% of the events surviving. Measurements at near detector already competive with detector below kton (around 500 ton)
Interesting possibility mainly for superbeams