Post on 25-Dec-2015
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
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
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)
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)
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
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.