Mary Hall Reno

Neutrino-nucleon interactions: what can we learn from

electromagnetic interactions and quark-hadron duality?

Hallsie Reno

Trento, May 2005

Mary Hall Reno

Advertisement for neutrino physics in context of this workshop

910E GeV (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

2

2 2

410

WUHE Q M

Qx

ME E

Mary Hall Reno

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( ) ( )

( ) ( )p nV V

s x s x

u x d x

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:

CosmicRay p Air ccX

c s

“Prompt” neutrino flux

Mary Hall Reno

(Advertisement)

100E GeV “Low” energy neutrinos:

Atmospheric neutrinos from

,p Air K X

Neutrino beams like NuMI and CNGS.

Mary Hall Reno

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?

Mary Hall Reno

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

Mary Hall Reno

Neutrino Oscillations

2 2 2

2 2

sin 2 sin (1.27 / )

/ , / , /

m L E

m eV L km E GeV

P

•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

Mary Hall Reno

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

Mary Hall Reno

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.

Mary Hall Reno

CERN to Gran Sasso – Tau neutrino appearance

http://www.mi.infn.it/~psala/Icarus/cngs.html L=1000 km

Mary Hall Reno

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

Mary Hall Reno

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….

Mary Hall Reno

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.

Mary Hall Reno

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.

Mary Hall Reno

DIS

Standard DIS formula, 5 structure functions:

1 2 5

4

2 2

0

0,N

xF F xF

F

M LO

(Generalized Callan-Gross relation)

Target mass corrected

See Kretzer & MHR

Mary Hall Reno

Neutrino-Nucleon Scattering with TMC

Georgi-Politzer, DeRujula OPE approach.

Nachtmann variable

Mary Hall Reno

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:

2 2( , ) ( ) exp( )T Tx k f x N bk

•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.

Mary Hall Reno

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.)

Mary Hall Reno

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.

Mary Hall Reno

A phenomenological approach: Bodek Park & Yang

• Fit ep scattering data

• Use GRV98 PDFs

• Redefine scaling variable

2

2

2 2 2 2

2

2

2 ( )

(1 ) 2

1 4 /

0.538

0.305

w

x Q B

Q Ax

M x Q

A GeV

B GeV

:

: w

solid line

dashed line

Mary Hall Reno

Bodek-Park-Yang hep-ph/0411202

• Rescale valence and sea distributions

• Overall normalization

2 202

21

2 2 2

2 21 2

(1 )( )

1/(1 /(0.71 ) )

0.291 ; 0.189

D vv v

v

D

v v

G Q Cu u

Q C

G Q GeV

C GeV C GeV

• Structure function:

2 2 22 ( , ) ( , )q w wF x Q e q Q

Mary Hall Reno

Bodek-Park-Yang meets JLAB

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

Mary Hall Reno

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...

Mary Hall Reno

More comparisons in ep case

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

Mary Hall Reno

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.)

Mary Hall Reno

BTW: PDF uncertainties: using 40 CTEQ6 PDFs

more uncertainty in u, d distributions

Mary Hall Reno

How do NLOTMC corrected neutrino structure functions compare with

electromagnetic structure functions of BYP?

Mary Hall Reno

ep and neutrino-nucleon scattering

Mary Hall Reno

Comparison in neutrino nucleon structure function

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

Mary Hall Reno

How do NLOTMC corrected neutrino structure functions compare with

electromagnetic structure functions of BYP?

Not so well at low Q

Mary Hall Reno

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.

Mary Hall Reno

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…

Mary Hall Reno

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!

Mary Hall Reno

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.

Mary Hall Reno

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?