Transcript Neutrino Nucleon Cross Sections

Neutrino Nucleon Cross
Sections: GeV to ZeV
Hallsie Reno
University of Iowa
January 2009
The best cross section
measurements
50
Particle data group http://pdg.lbl.gov
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
Theory:
• Target mass corrections are potentially important
• Low Q structure functions important, where perturbative
QCD is not valid
Experiment:
• Need more experimental measurements
Take a look at this first.
“Low energy” cross section
DIS=“deep” inelastic scattering (with W cutoff to avoid double counting),
qel=quasi-elastic, one pion exclusive contribution
Lipari, Lusignoli and Sartogo, PRL 74 (1995)
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
Quasi-elastic MiniBooNE
measurements:
Refinement of nuclear
model parameters.
Here, coherent pi0 production,
compared with Rein-Seghal based
MC.
MiniBooNE, Phys. Lett. B664 (2008)
MiniBooNE, PRL 100 (2008)
Target mass corrections
• Classic papers:
•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)
• Three corrections: Nachtmann variable,
parton vs hadron structure function, pT
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:
leading plus
convolution terms
electromagnetic
case
More complicated formulas
Target mass corrections-F2
electromagnetic
Most important for large x, low Q. I
am interested here in the neutrinonucleon cross section.
Schienbein … MHR… et al, J Phys G 35 (2008)
Target mass corrections
Antineutrino scattering has
smaller y, so smaller Q.
Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005)
No extrapolation to low
Q- take F2 constant
below 1.14 GeV=Q
Target mass corrections,
importance of low Q
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.
Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005)
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
sea, small x
valence, large x
for electromagnetic scattering.
See, Reno, Phys. Rev. D 74 (2006)
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
Strange quark
•
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.)
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 section
LO+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
Medium energy,
High energy:
2G ME
d

dx dy

2
2
F
Given
2
 M

2


xq
(
x
,
Q
)

xq
(
x
,
Q
)(1

y
)
 2
2  
 Q  MW 
2
W
W boson propagator
Quark (parton) distribution functions
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)
LHC! Takes us up to
From B. Foster’s 2002 Frascati Talk
Theory Issues: how to extrapolate?
BFKL=Balitsky, Fadin,
Kuraev & Lipatov
transition region
BFKL
ln 1/x
non-perturbative
saturation
Deep Inelastic Scattering Devenish &
Cooper-Sarkar, Oxford (2004)
DGLAP
ln Q
DGLAP=Dokshitzer,
Gribov, Lipatov, Altarelli
& Parisi
“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
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.
Quigg, Reno, Walker (1986), Gandhi et al. (1996,1998), also McKay et al (1986),
Gluck et al (1999)
BFKL/DGLAP vs DGLAP
BFKL evolution matched to
DGLAP accounting for some
subleading ln(1/x), running
coupling constant,matched to
GRV parton distribution functions
Kwiecinski, Martin & Stasto, PRD
59 (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
L  (  N N A )
1
Fiore et al. PRD68 (2003),
with a soft non-perturbative
model and approx QCD
evolution.
See also, Machado Phys Rev.
D71 (2005)
factor ~2
More recent results
KK
Includes QCD corrections,
see also Basu, Choudhury
and Majhi, JHEP 0210
(2002)
Henley & Jalilian-Marian 2006
Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys.
Rev. D 74 (2006) 043008
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
HERA: extrapolations
with lambda=0.5,0.4,0.38
KOPA: DLA, Kotikov &
Parente
ASW: saturation effects,
Armesto, Salgado &
Wiedeman
Fig. from Armesto, Merino, Parente & Zas, Phys. Rev. D 77 (2008)
Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys. Rev. D 74
(2006)
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