# Presentation: 304410

## Neutrino-nucleon interactions: what can we learn from electromagnetic interactions and quark-hadron duality?

- Hallsie Reno
- Trento, May 2005

## Advertisement for neutrino physics in context of this workshop

- (Ultra)-high energy neutrinos:

- Neutrino induced air showers
- Neutrino interactions in ice
- Radio Cherenkov signals, detected in situ or with balloon borne detector

- Rule of thumb:

- Unitarity
- Onset of saturation
- Log(1/x) corrections

## (Advertisement)

- Medium energy neutrinos:

- 100’s GeV – 100’s TeV

- Neutrino scattering:
- 	NuTeV’s measurement of the weak mixing angle 	differs from the world average
- 	challenge to assumptions about

- Neutrino production:

- “Prompt” neutrino flux

## (Advertisement)

- “Low” energy neutrinos:

- Atmospheric neutrinos from

- Neutrino beams like NuMI and CNGS.

## Talk about “low” energy neutrinos

- I’m interested in a practical solution to calculate neutrino cross sections that at the same time includes the “best” that we can do.
- Talk:

- Specifically what low energies, why are we interested? (Neutrino oscillations)
- Components of the cross section.
- Help from local hadron duality?
- Help from phenomenological approach to PDFs at low Q?
- Put it together – and look for some independence in parameters?

## Neutrino Cross Section – Required Figure

- Lipari, Lusignoli and Sartogo, PRL 74 (1994)

- Deep inelastic scattering
- Quasi-elastic scattering
- Pion production

- 0.1 GeV

- 100 GeV

- Neutrino data at these energies is not extensive. Antineutrino data even less.
- C.f. G.P. Zeller, hep-ex/0323062

## Neutrino Oscillations

- Atmospheric neutrinos: L=Earth diameter=12000 km
- Average E around a few GeV

- http://neutrino.kek.jp/index-e.html

- Atmospheric neutrinos, coming from all angles, give a wide range of L/E

- Muon neutrino deficit, as a function of L/E, shows evidence of neutrino oscillation.

- muon neutrino disappearance

## Neutrinos from Fermilab

- http://www-numi.fnal.gov

- Multiply evt. totals by 3.4 to get nu_mu events per year (without oscillations).

- 735 km

## Neutrino Cross Section-Required Figure

- Lipari, Lusignoli and Sartogo, PRL 74 (1994)

- Deep inelastic scattering
- Quasi-elastic scattering
- Single pion production

- NuMI

- Low energy beam is best for MINOS distance.

## CERN to Gran Sasso – Tau neutrino appearance

- _[http://www.mi.infn.it/~psala/Icarus/cngs.html](http://www.mi.infn.it/~psala/Icarus/cngs.html)__        L=1000 km_

## Tau neutrino appearance

- Threshold energy for tau production: 3.5 GeV

- Part of our initial motivation to look at the cross section: tau mass, proton mass, charm mass effects along with NLO QCD.
- Cf. S. Kretzer & MHR, PRD 66,69

## Calculation – how is it done?

- Quasi-elastic
- Resonance
-               dominated by Delta
- Deep Inelastic Scattering
- 		 avoid double counting –     	 use a cut on W

- Concern about missing nonresonant contributions at lower W....

## Issues in Quasi-elastic Scattering

- From J. Monroe/MiniBoone for NuInt04, hep-ex/0408019

- Preliminary MiniBoone data appear to disagree with Monte Carlo models at low Q.
- Nuclear models?

- Llewellyn Smith formalism with dipole form factors.

## Resonances

- Monte Carlos, e.g., NUANCE by D. Casper, implements the Rein and Sehgal, Ann. Phys. 133 (1981) 79 updated to current masses, widths. Uses harmonic oscillator quark wavefunctions in model.
- Resonance production up to some W value (say 2 GeV for NUANCE, or 1.4 GeV as in “Required figure”).
- Fermi Gas model of Smith and Moniz.
- Includes some final state interactions.
- There have been recent studies, including by E. Paschos and collaborators & Hagiwara, Mawatari and Yokoya & Sobczyk, Nowak and Graczyk and others on resonance contributions.

## DIS

- Standard DIS formula, 5 structure functions:

- (Generalized Callan-Gross relation)
- Target mass corrected
- See Kretzer & MHR

## Neutrino-Nucleon Scattering with TMC

- Georgi-Politzer, DeRujula OPE approach.

- Nachtmann variable

## TMC in parton picture

- Ellis, Furmanski and Petronzio showed that the TMC result can be obtained with:

- Parton momentum on shell but not collinear with the proton in parton level cross section.
- Generalized kT dependent PDF of a general form, but NOT of the form:

- TMC come from mismatch of P(proton) and p (quark) (one massive and one massless) .
- They also come from kT limited to less than M.

## Electromagnetic Scattering : Related Processes

- Extensive study of ep scattering, in the resonance region and beyond, by Jefferson Lab groups, SLAC exps.
- Local quark-hadron duality shown for a range of W. Local duality means restricted range of x integration of the structure function and data give same result

- Unpolarized case: at fixed Q, for a range of W (restricted x range) including resonances, above the Delta resonance,  integral of F2 agrees well between data and NLOTMC, even better if large x resummation is done.
- Shown by Fantoni, Bianchi and Liuti.

- “Quark hadron duality in electron scattering, Melnitchouk, Ent & Keppel, hep-ph/0501217 (Phys. Rept.)

## Use local duality for neutrino scattering

- Local duality not explicitly demonstrated in neutrino scattering – one motivation for the MINERvA experiment.
- Nevertheless use it in neutrino scattering in the region where local duality holds for ep scattering.
- (Add large x resummation as per Fantoni et al.)
- Should be in the regime where W is larger than 1.4 GeV  to use this.

## A phenomenological approach: Bodek Park & Yang 

- Fit ep scattering data
- Use GRV98 PDFs
- Redefine scaling variable

## Bodek-Park-Yang hep-ph/0411202

- Rescale valence and sea distributions
- Overall normalization

-   Structure function:

## Bodek-Park-Yang meets JLAB

- E. Christy provided me with parameterization of ep data, “Christy param.”

## Comparisons in the ep case

- dot-dash: LO and LO-TMC
- dotted: NLO and NLO-TMC

- Can see the need for large x resummation here...

## More comparisons in ep case 

- Range of Q^2 with steps of 0.2 GeV^2.

## Prescription of BPY-completely phenomenological

- Use the modified PDFs fit to DIS electromagnetic scattering for neutrino scattering for W greater than 1.35 GeV.
- Use explicit calculations for resonance region and quasi-elastic. Note: there are not simple Clebsch-Gordon factors in converting to neutrino scattering.
- (Work on fits to axial vector modifications at low energy.)

## BTW: PDF uncertainties: using 40 CTEQ6 PDFs

- more uncertainty in u, d distributions

## How do NLOTMC corrected neutrino structure functions compare with electromagnetic structure functions of BYP?

## ep and neutrino-nucleon scattering

## Comparison in neutrino nucleon structure function

- assume axial vector contribution is same as vector contribution, and take new combinations to get neutrino structure functions:

## How do NLOTMC corrected neutrino structure functions compare with electromagnetic structure functions of BYP?

- Not so well at low Q

## Neutrino cross section

- Half the cross section is from Q less than 1 GeV for this energy....
- The same figure for LO or NLOTMC with a minimum Q2=0.8 GeV2.

- NLOTMC structure functions don’t match BPY parameterization well at Q=1 GeV.

## Neutrino DIS cross section

- Circumstance of large M/Q and strong coupling.
- The “K factor” for DIS for this energy is only 1.08-1.11 for Qmin less than 1.3 GeV and W greater than 1.4 GeV.
- Need phenomenological assistance for low Q, especially low x...

## Neutrino cross section – dependence on matching scale?

- Delta cross section for W up to 1.4 GeV. Need Delta contribution up to other values of W.

- One hopes not!

## An option

- Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering.
- Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV.
- Use a resonance model below W=1.4-2.0 GeV.
- Include quasi-elastic scattering.
- Vary (x,Q,W) boundaries to see that the total cross section remains unchanged.

## An option

- Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering.
- Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV.
- Use a resonance model below W=1.4-2.0 GeV.
- Include quasi-elastic scattering.
- Vary (x,Q,W) boundaries to see that the total cross section remains unchanged.

- Tau neutrino scattering cross section is under better control theoretically.
- Ultimately, the muon neutrino cross section will be measured by MINERvA.

- Is this step necessary?
- NNLO – could this solve the x=0.1 discrepancy?