Neutrino Nucleon Cross Sections: GeV to ZeV

Hallsie Reno

University of Iowa

January 2009

The best cross section measurements

Particle data group http://pdg.lbl.gov

50 350 GeV

Plan

• Review generic neutrino nucleon cross section calculation (with structure functions)

• Comment on issues at lower energies (say, E=10 GeV)

• Discuss extrapolations at high energies

Cross section

Dimensional analysis, low Q:

Structure function approach

Neglecting lepton mass corrections. See Kretzer&Reno, 2002

Parton model approach

Charged current structure functions, in terms of parton distribution functions (PDFs), to leading order:

Extensive program of extraction of PDFs, eg.

Watt, Martin, Stirling, Thorne, arXiv 0806.4890 [hep-ph]

Gluck, Jimenez-Delgado, Reya, Eur. Phys. J C53 (2008)

Nadolsky et al (CTEQ), Phys. Rev. D78 (2008)

Low energy cross section issues

• Target mass corrections are potentially important• Low Q structure functions important, where perturbative

QCD is not valid

• Need more experimental measurements

Theory:

Experiment:

Take a look at this first.

“Low energy” cross section

Lipari, Lusignoli and Sartogo, PRL 74 (1995)

DIS=“deep” inelastic scattering (with W cutoff to avoid double counting), qel=quasi-elastic, one pion exclusive contribution

Aside, no double counting

Count up exclusive contributions (say 1 pion) up to some total invariant mass W0, then do the inelastic contributions for W larger than this cutoff.

for DIS

More cross section compilations, circa 2003

G. Zeller, hep-ex 0312061

Recent low energy cross section measurements, e.g. MiniBooNE

Here, coherent pi0 production, compared with Rein-Seghal based MC.

MiniBooNE, Phys. Lett. B664 (2008)

Quasi-elastic MiniBooNE measurements:

Refinement of nuclear model parameters.

MiniBooNE, PRL 100 (2008)

Target mass corrections

• Classic papers:

• Three corrections: Nachtmann variable, parton vs hadron structure function, pT

•Georgi & Politzer, PRD 14 (1976) & with deRujula, Ann. Phys. 103 (1977)

•Barbieri et al, Nucl. Phys. B 117 (1976), Phys. Lett. B 64 (1976)•Ellis, Furmanski and Petronzio, Nucl. Phys. B 212 (1983)

Nachtmann variable

Target mass corrections: kinematic higher twist

Hadron-parton “mismatch”

Leads to corrections

See Aivazis, Olness and Tung, PRD 50 (1994)

Another correction: pT

• Parton model picture

•Parton is on-shell but has some intrinsic transverse momentum.

•Transverse momentum up to a scale of M is approximately “collinear” and integrated separately from the hard scattering part.

•Ellis, Furmanski and Petronzio showed this can give the same results as what I will show next, the (see Georgi, Georgi et al)

OPERATOR PRODUCT EXPANSION (OPE)

Complicated formulas:

electromagnetic case

leading plus convolution terms

More complicated formulas

Target mass corrections-F2 electromagnetic

Schienbein … MHR… et al, J Phys G 35 (2008)

Most important for large x, low Q. I am interested here in the neutrino-nucleon cross section.

Target mass corrections

Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005)No extrapolation to low Q- take F2 constant below 1.14 GeV=Q

Antineutrino scattering has smaller y, so smaller Q.

Target mass corrections, importance of low Q

Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005)

Big contribution from low Q: these cross sections must have some large uncertainties…

Challenge: to find a suitable low Q form for the structure functions.

An extrapolation to low Q that works:

Capella, Kaidalov, Merino and Tranh Van CKMT, Phys. Lett. B 337, 358 (1994), Moriond 1994, 7 parameters in

for electromagnetic scattering.

See, Reno, Phys. Rev. D 74 (2006)

sea, small x

valence, large x

Valence component

Sea component

Now convert to neutrino scattering

See also CKMT Moriond proceedings.

•The sea distribution changes only in overall normalization to match F2 reasonably well with the NLO+TMC evaluation:

fixed at

•Note that for the sea part,

This is what you would estimate using the charged current and electromagnetic structure functions:

CKMT for neutrinos

• Expect that the underlying non-perturbative process is governed by the same power law and form factor for the sea part:

• For the valence part, recalculate B and f :

• Valence x and Q dependence shouldn’t change between electromagnetic and charged current scattering.

• For F1, use a parameterization of R from Whitlow et al, Phys. Lett. 1990

CKMT for neutrinos

• For F3, use

• The denominator of 1.1 adjusts the integral of the valence quark part to give a Gross-Llewellyn-Smith sum rule results of 3x0.9 (QCD corrected.)

Strange quark

Calculate cross section

• Use NLO+TMC above a minimum value of Q, attach a parameterization for lower values of Q. Should be insensitive to where the patch is made.

• Results shown below are for transition between parton model and CKMT parameterization at Q=2 GeV.

Neutrino charged current cross sectionLO+TMC

Low Q extrapolations, from NLO+TMC, with CKMT (and Bodek et al) extrapolation.

NLO + TMC, no special low Q extrapolation.MHR, Phys. Rev. D74 (2006)

Anti-neutrino charged current cross section

Low Q extrapolations, from NLO+TMC, with BYP and CKMT

MHR, Phys. Rev. D74 (2006)

Ultra-high energy neutrino nucleon scattering

22 222

2 2

2( , ) ( , )(1 )F W

W

G ME Mdxq x Q xq x Q y

dxdy Q M

Medium energy,

High energy:

W boson propagator Quark (parton) distribution functions

Given

Refs, eg.: Gandhi et al., PRD 58 (1998), Astropart. Phys. 5 (1996)

Mocioiu, Int. J. Mod. Phys. A20 (2005)

Gluck, Kretzer, Reya, Astropart. Phys. 11 (1999)

Structure functions (to get PDF extractions)

From B. Foster’s 2002 Frascati Talk

LHC! Takes us up to

Theory Issues: how to extrapolate?

ln Q

ln 1/x

non-

pert

urba

tive

BF

KL

DGLAP

transition region

DGLAP=Dokshitzer, Gribov, Lipatov, Altarelli & Parisi

BFKL=Balitsky, Fadin, Kuraev & Lipatov

Deep Inelastic Scattering Devenish & Cooper-Sarkar, Oxford (2004)

saturation

“Evolution” of PDFs

•LO analysis improved to NLO analysis, heavy flavor

•quark and gluon distributions rise at small x for Q>a few GeV.

EHLQ: Eichten, Hincliffe, Lane and Quigg, 1984.

Double Logarithmic Approx (DLA) or

at low x.

Some extrapolations: 1984 to 2007

Quigg, Reno, Walker (1986), Gandhi et al. (1996,1998), also McKay et al (1986), Gluck et al (1999)

DGLAP evolution: log Q. Shown here are power law and double logarithmic extrapolations at small x. As time goes on, a better treatment of heavy flavor.

BFKL/DGLAP vs DGLAPBFKL evolution matched to DGLAP accounting for some subleading ln(1/x), running coupling constant,matched to GRV parton distribution functions

Kwiecinski, Martin & Stasto, PRD59 (1999)093002

CC Cross Sections

KMS: Kwiecinski, Martin & Stasto, PRD56(1997)3991;

KK: Kutak & Kwiecinski, EPJ,C29(2003)521

more realistic screening, incl. QCD evolution

Golec-Biernat & Wusthoff model (1999), color dipole interactions for screening.

Other results

Fiore et al. PRD68 (2003), with a soft non-perturbative model and approx QCD evolution.

See also, Machado Phys Rev. D71 (2005)

factor ~2

1( )N AL N

More recent results

KK

Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys. Rev. D 74 (2006) 043008

Henley & Jalilian-Marian 2006

Includes QCD corrections, see also Basu, Choudhury and Majhi, JHEP 0210 (2002)

More recent results

Cooper-Sarkar & Sarkar, JHEP 0801 (2008), new analysis of HERA data incl. heavy flavor, lower cross section at UHE (closer to CTEQ6 results, which also have a better extraction of heavy flavor.

Other recent results

Fig. from Armesto, Merino, Parente & Zas, Phys. Rev. D 77 (2008)

Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys. Rev. D 74 (2006)

HERA: extrapolations with lambda=0.5,0.4,0.38

KOPA: DLA, Kotikov & Parente

ASW: saturation effects, Armesto, Salgado & Wiedeman

General Conclusions

• The theory of “low energy” neutrino-nucleon cross section still needs work. More experimental measurements will certainly help this.

• UHE neutrino cross section relies on extrapolations well beyond experimental measurements, however, many extrapolations end in the same “neighborhood” for the cross section.

• The cross section affects overall event rates, but also attenuation.

Fin