Introduction to Neutrino Interaction Physics NUFACT08 Summer School June 2008 Benasque, Spain Paul Soler

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1 Introduction to NUCT08 Summer School -3 June 008 Benasque, Spain Paul Soler

2 4. uasi-elastic, resonant, coherent and diffractive scattering 4. Motivation 4. Charged current quasi-elastic scattering 4.3 Neutral current elastic scattering 4.4 Resonant pion production 4.5 Coherent pion production 4.6 Experiments NUCT08 Summer School

3 4. Motivation Many neutrino oscillation experiments need to achieve E/L ~ 0-3 GeV/km, so for distances ~000 km, we need interactions around GeV. or example, TK, MINOS, atmospheric experiments require knowledge of cross-section between 0.4 and GeV/c to perform accurate m 3 and θ 3 analysis TK NUCT08 Summer School 3

4 4. Motivation round GeV there is a complicated region where deep inelastic scattering (DIS, quasi-elastic (EL scattering and resonance production (for example, π production co-exist NUCT08 Summer School 4

5 4. Charged current quasi-elastic scattering uasi-elastic neutrino-nucleon scattering reactions (small q : affects nucleon as a whole ν n p ν p n ν ν W W n p p n M p Heff ν, n V, G cosθc γ ( γ ν pγ ( q vector form factor ( q axial vector form factor [ ][ ( q q n] ( ( γ 5 V NUCT08 Summer School cos θ C (Cabbibo 5 angle 5

6 NUCT08 Summer School 6 4. Charged current quasi 4. Charged current quasi-elastic scattering elastic scattering In reality, it is more complicated and we need Llewelyn-Smith formalism to calculate E differential cross-sections:, B, C are complicated functions of two vector form factors V (, V (, the axial form factor ( and the pseudoscalar form factor P (. ( m g 4 ( ν m ME u s ( M B ( 4 ( ( 4 4 ( ( ( P P M M m M m τ τ τ τ τ ( τ C 4 ( ( ( V n p V m τ τ 4M τ C M u s B M u s E M G d d 4, ( ( 8 m ν ν ν π σ See Zeller, hep-ex/0306, for details ( ( m M P π ( ( ( V n p V m τ τ orm factors: assume dipole approximation N n N p and ( ± g

7 4. Charged current quasi-elastic scattering orm factors introduced since proton, neutron not elementary. Depends on vector and axial weak charges of the proton and neutron. Conservation of Vector Current (CVC relates form factors to electron scattering Main physics to be extracted from E scattering data are empirical form factor parameters (fits to m, m V, deviations from dipole approximation V ( q ( q V m V GeV (0 ( q / m (0 V ( q / m σ( ν n σ( ν p e e E GeV Neutrino Interaction 38 Physics NUCT08 0 Summer School m. 03 GeV 7

8 4.3 Neutral current elastic scattering Neutral current elastic neutrino-nucleon scattering reactions are related to the CC quasielastic (small q : about 5% of CC EL ( ( ν ν p p ( ( ν ν n n ( ν ( ν ( ν ( ν Z 0 Z 0 p p n n lso need to calculate form factors NUCT08 Summer School 8

9 4.4 Resonant pion production Between the elastic and inelastic region is an area associated with pion production through the excitation of baryon resonances ν N l N * and N* π N' l Invariant mass squared: W If x then quasi-elastic scattering but if x< then you can excite different pion states: W 0 ( W M Neutrino Interaction Physics NUCT08 π ( WSummer MSchool Γ M M ν( T ( MT m, ( MT T π m π Rein and Sehgal s model describes low energy pion production by a coherent superposition of all possible resonances Cross-section: dσ T( νn ln* Γ( W M d dw 3ME spins with: Γ Γ 9 / 4 x,...

10 4.4 Resonant pion production or example, possible resonances are or N ν π ν N n π ll possible channels: 3 in CC and 4 in NC p Very little data, has large statistical errors, mainly from old bubble chamber experiments NUCT08 Summer School 0

11 4.4 Resonant pion production or example, possible resonances are or N ν π ν N n π ll possible channels: 3 in CC and 4 in NC p NC data is even worse! NUCT08 Summer School

12 4.4 Resonant pion production Duality: use electron scattering data to improve precision of model Can observe individual resonances with good agreement data and model Bodek and Yang NUCT08 Summer School

13 4.5 Coherent pion production Neutrinos can also produce pions coherently (low and high ν The neutrino coherently scatters off the whole nucleus with negligible energy transfer to the whole nucleus of mass This results in a forward scattered single pion (background in oscillation searches because forward peaked Neutral and charged current processes are possible: 0 ν ν π π ν Rein and Sehgal s model also describes coherent pion production: Cross-section: dσ G M m f E y π ν ( d dydt π 6π m f πn (0 pion- nucleon scattering amplitude r fπ 0. 93mπ pion decay constant t x / λ abs e pion absorption b ( / 3 R / 3 impact parameter ( πn b t σ tot ( r e abs NUCT08 Summer Exponential School in t distribution Re[ fπ N(0 ] Im[ fπ N(0 ] ( ( E p ( ( p ( q pπ i i i i 3 i

14 4.5 Coherent pion production Charged current single pion coherent cross-section: NC cross-section is half of CC: coh coh σ NC σcc NUCT08 Summer School 4

15 4.6 Experiments Recent experiments carrying out measurements in the ~GeV region: KK near detectors (ie. SciBar: completed MINOS near detector: running MiniBoone: running SciBoone: moved SciBar to ermilab, operating at the Booster beamline Minerva (under construction TK (under construction NUCT08 Summer School 5

16 4.6 Experiments KK SciBar and SciBoone ν NUCT08 Summer School Observed CC E interaction n p 6

17 4.6 Experiments MiniBoone: measurement of CCE scattering itted form factor, effective axial mass: π 0 event NC π 0 measurement: 8,000 events Ratio coherent/non-coherent: NUCT08 Summer School 7

18 4.6 Experiments Minerνa: a detector for precision interaction physics at ermilab Scintillator bar wavelength shifting fibre NUCT08 Summer School Resonance event CCE event ν 8 n p

19 5. Nuclear Effects 5. ermi smearing and Pauli blocking 5. Nuclear re-interactions NUCT08 Summer School 9

20 5. ermi smearing and Pauli blocking Nuclear effects in neutrino scattering: In a nucleus, the target nucleon has a momentum which modifies scattering Modelled as ermi gas that fills up all available states until some initial state ermi momentum, k The Pauli exclusion principle ensures that states cannot occupy states that are already filled (Pauli blocking Particles that escape nuclear medium may be re-scattered and deflected by the ermi momentum, especially at low energies. We need better understanding of the ermi motion or example, MiniBoone have already published a paper suggesting a modification to the ermi gas model based on matching E scattering in all values of with their data. NUCT08 Summer School 0

21 5. ermi smearing and Pauli blocking Effects on Structure unctions: In charged lepton scattering, have observed shadowing and modifications to PDs due to nucleons. t small x, coherent interaction of a hadronic component of the virtual photon with target nucleus - shadowing It is not clear if this is also present in neutrino structure functions since at low x, dominated by axial current nti-shadowing These effects need to be studied in detail with high statistics neutrino scattering Shadowing ermi motion NUCT08 Summer School EMC effect

22 5. Re-interactions Nuclear effects in resonance region: Production of resonance may be affected by nuclear medium (see plot of photoabsorption data Resonant structure gets washed out Pions may either rescatter or be absorbed. This needs to be measured NUCT08 Summer School

23 Conclusions Neutrino interactions have provided valuable insight into the theory of weak interactions Maximal parity violation, V- theory and finally the Glashow-Weinberg- Salam electroweak theory were developed in part from information on neutrino interactions Neutrino interaction data is used to probe the electroweak theory, such as in the measurements of sin θ W. Neutrino interactions have also provided information on the structure of nucleons Structure function measurements and scaling violations have been observed ( 3 is only accessible through neutrino interactions Neutrino oscillations allow us to probe the grand unification energy scale, but it is crucial that we understand further the ~ GeV energy region to be able to exploit oscillation experiments to the maximum new generation of experiments is commencing to lead the way towards a new precision era in neutrino interaction physics NUCT08 Summer School 3