Axial and Vector SFs for Lepton-Nucleon Scattering

Arie BodekUniversity of Rochester

Un-ki YangUniversity of Manchester

NuFact11, August 1-6, Geneva

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Neutrino Cross Section Quasi-Elastic / elastic (W=M): nm + n m- + p

• by form factors Resonance (low Q2, W< 2): nm + p m- + p + p

• by Rein and Seghal model (overlap with DIS) Deep Inelastic Scattering: nm + p m- + X

• by quark-parton model (non-pQCD effect, high x PDFs) Describe DIS, resonance within quark-parton model:

with PDFS, it is easy to convert (e) into (n) Challenges

• High x PDFs at very low Q2

• Resonance scattering within quark-parton model• What happens at Q2=0? • Axial vector contribution

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Modeling neutrino cross sections NNLO pQCD +TM approach:

describes the DIS and reso-nancedata very well:

Bodek-Yang LO approach: (pseudo NNLO) Use effective LO PDFs with a

newscaling variable, xw to ab-sorb target mass, higher twist, missing QCD higher orders

mf=M*(final state)

P=M

q

xW =Q2 + B

{Mν [1+ (1+Q2 / ν 2 )] + A}

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Bodek-Yang Effective LO PDFs Model1. Start with GRV98 LO (Q2min=0.80)2. Replace xbj with a new scaling, xw

3. Multiply all PDFs by K factors for photo prod. limit and higher twist [ (g)= 4pa/Q2 * F2(x, Q2) ]

Ksea = Q2/[Q2+Csea]Kval = [1- GD 2 (Q2) ] * [Q2+C2V] / [Q2+C1V] motivated by Adler Sum rule where GD

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

4. Freeze the evolution at Q2 = Q2min

- F2(x, Q2 < 0.8) = K(Q2) * F2(xw, Q2=0.8)

5. Fit all DIS F2(p/D) with low x HERA data, photo-production data

A=0.621

B=0.380

C2v(u)=0.264

C2v(d)=0.323

C1v(u)=0.417

C1v(d)=0.341

Csea(u)

=0.369

Csea(d,s)

=0.561

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Fit Results on DIS F2(p/D) data

Excellent Fitting:• red solid line: effective LO using xw• black dashed line: xbj

F2(p)

F2(D)

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Low x HERA and NMC data

Fit works at low x

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Photo-production data Additional KLW factor for

valence quarks:

Kval = KLW*[1- GD 2 (Q2) ] * [Q2+C2V] / [Q2+C1V]

KLW = (n2+Cn)/n2

This makes a duality work all the way down to Q2=0(for charged leptons)

Photo-production data with n>1 GeV are included in the fitting

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F2 Resonance and FL

Predictions are in good agreement with resonance data (not included in the fitting); duality works for electrons and

muons for our effective LO PDFs

F2(p)

FL(p)

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Neutrino cross sections Effective LO model with xw describe all DIS and resonance

F2 data as well as photo-production data (Q2=0 limit): vector contribution works well

Neutrino Scattering:• Effective LO model works for xF3?• Nuclear correction using e/m scattering data • Axial vector contribution at low Q2?• Use R=R1998 to get 2xF1

• Implement charm mass effect through xw slow rescaling algorithm for F2, 2xF1, and xF3

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Effective LO model for xF3? Scaling variable, xw absorbs

higher order effect for F2, but the higher order effects for F2 and xF3 are not the same

Use NLO QCD to get double ratio

not 1 but indep. of Q2

Enhance anti-neutrino cross section by 3%

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Nuclear Effects: use e/m data

Fe/D D/(n+P)

Lead/Fe

UpdatedFe/D

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Axial Vector Structure Functions Type I: Axial Vector = Vector (A=V) Type II:

• 0.6 was chosen to satisfy the prediction from PCAC by Kulagin, agrees with CCFR/CHROUS data for F2 extrapolation to (Q2=0)

• But, the non-zero PCAC component of F2axial at low Q2: purely longitudinal

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Comparison with CCFR (Fe), CHORUS (Pb) data

Blue point: CHORUS/theory (type II) Blue line: theory (type I)/(type II)• Red point: CCFR/theory (type II)

nu nubar

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Comparison with CCFR(Fe) , CHORUS (Pb) data

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Test of the Adler Sum Rule This sum rule should be valid at all values of Q2

Vector

Axial

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Total cross sections BY(DIS, W>1.4) + Q.E. + Resonance

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Summary of changes from 2004 2004: BY Model (currently implemented in Neutrino Monte

Carlo) has V=A and H(x)=1 (same scaling violation in F2 and xF3). It has been used for W>1.8 Gave

2011: Addition of H(x) correction to xF3 plus axial K factor by PCAC (A=PCAC) to F2

• Change anti-neutrino cross sections by ~6%; better agreement with experimental data

• Better agreement in d/dxdy at low Q2

• Better agreement with the total cross sections• Addition of low W K factor (KLW) extend the validity of model down to

W=1.4 GeV, thus providing overlap with resonance models

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Summary & Discussions BY Effective LO model with xw describe all e/m DIS and

resonance data as well as photo-production data (down to Q2=0): provide a good reference for vector SF for neutrino cross section

d/dxdy data favor updated BY(DIS) type II model K factors for axial vectors in BY(DIS) type II model are based

on PCAC and could be further tuned with new neutrino data (Q2<0.3, e.g. MINERnA)

BY(DIS) type II model (axial=PCAC) provide a good reference for both neutrino and anti-neutrino cross sections (W>1.8). Low energy neutrino experiments can normalize their data to our model to extract their flux

Model also works well down to W=1.4 GeV, thus providing overlap with resonance models