Un-ki Yang, Manchester 1

Modeling Neutrino Structure Functions at low Q2

Arie BodekUniversity of Rochester

Un-ki YangUniversity of Manchester

NuInt 2009, Barcelona, Spain, May 18 – 22, 2009

Un-ki Yang, Manchester 2

A Model for all Q2 region?

The high Q2 region of lepton-nucleon scattering is well understood in terms of quark-parton model by a series of e/m/n DIS experiments.

But the low Q2 region is relatively poorly understood in neu-trino scattering: very important for neutrino oscillation ex-periments. Many interesting issues… PDFs at high x? Non-perturbative QCD? target mass, higher twist effects? Duality works for resonance region? Axial vector contribution? Different nuclear effects (e/ m vs )n ?

Build up a model for all Q2 region

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Challenges at Low Q2

GRV

F2

A model to describe all Q2 region for e/m/n scatterings [ DIS, resonance, even photo-production(Q2=0) ]

• Resonance region is overlapped with a DIS region• Hard to extrapolate DIS contribution to low Q2 region

from high Q2 data, because of non-pQCD effects Describe DIS+resonance together using quark-parton

model

Resonance scattering in terms of quark-parton model?

Duality works, many studies by JLab

Higher twist effects, PDFs at high x? SLAC, JLab data

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Effective LO Approach

Quark-Parton model:• NLO pQCD +TM+HT,

and NNLO pQCD+TM: good for DIS and res-onance

• A HT extracted from the NLO analysis: ~ NNLO pQCD term: in-dep. of e/ /m n

Effective LO approach: Use a LO PDFs with a new

scaling variable to absorb TM, HT, higher orders• A reference for (,d):

study nuclear effect

ξW =Q2 + B

{Mν [1+ (1+Q2 / ν 2 )] + A}

Q2

Q2 +CF2 (ξw ,Q2 )[LO]

mf=M*(final state)

P=M

q

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Use GRV98 LO x w= [Q2+B ] / [ Mn (1+(1+Q2/n2)1/2 ) +A]

Different K factors for valence and sea

Ksea = Q2/[Q2+Csea] Kval = [1- GD

2 (Q2) ] *[Q2+C2V] / [Q2+C1V], GD

2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4

Freeze the evolution at Q2 = 0.8

Very good fits are obtained using SLAC/NMC/BCDMS p, d

with low x HERA/NMC F2

A=0.418, B=0.222, Csea = 0.381

C1V = 0.604, C2V= 0.485 2/DOF= 1268 / 1200

Fit with xw DIS F2(d)

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DIS F2 at low x

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F2(p) resonance

Photo-production (p)

(s g-proton) = 4 /pa Q2 * F2(w, Q2)

where F2(w, Q2)

= Q2 /(Q2 +C) * F2(w )

Resonance and photo-production data

Not included in the fit

2xF1 data

All DIS e/ F2 data are well described

Photo-production data (Q2=0) also work: thus included in the lat-est fit

2xF1 data (Jlab/SLAC) also work:

using F2(w)+R1998

Jlab 2xF1

Comparison with neutrino data

• Assume vector = axial • Apply nuclear corrections

using e/ scattering data Underestimated at low x=0.015 Total anti-neutrino cross section

lower by 5%?

: red, : blue,(w) ---- (x)

CCFR diff cross at En= 55 GeV

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NLO Correction to xF3?

Scaling variable, w absorbs higher order effect on F2 , but not xF3; F2 data used in the fitting

Check double ratio

=> not 1 but indep. of Q2

xF3(NLO)

xF3(LO)/F2 (NLO)

F2 (LO)

NLO ratio: using VFS

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Effect of xF3 NLO correction

Parameterized xF3 correction as a function of x

Neutrino cross section down by 1%

Anti-neutrino cross section up by 3%

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Axial-vector contribution

In our neutrino cross section model

assumed Kaxial = Kvector

Toward axial-vector contribution• Kaxial = 1• Extract Kaxial using existent neutrino data (underway)

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Axial-vector contribution

CCFR diff. cross at En= 55 GeV

Kaxial = Q2/(Q2+C) Kaxial = 1

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Axial-vector contribution

CCFR diff. cross at En= 35 GeV

Kaxial = Q2/(Q2+C) Kaxial = 1

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Summary and Discussions

Effective LO model with w describes all DIS and resonance data as well as photo-production data:

• Provide a good reference for neutrino cross section, (,d)

• Possible studies for axial vector contribution at Q2<1 and diff. nuclear effect

• High energy neutrino data at low Q2 is in favor of addi-tional axial vector contribution

Things to do

• Need to tune axial vector contribution using existent neutrino data and possibly with coming MINERnA

• Different nuclear effects (e vs n, F2 vs xF3):

Jlab and MINERnA data are very crucial

Comparison with CDHSW data

En= 23 GeV

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F2, R comparison with NNLO pQCD+TM

F2 R

Eur. Phys. C13, 241 (2000) Bodek & Yang