Mary Hall Reno
Neutrino-nucleon interactions: what can we learn from
electromagnetic interactions and quark-hadron duality?
Hallsie Reno
Trento, May 2005
Mary Hall Reno
Advertisement for neutrino physics in context of this workshop
910E GeV (Ultra)-high energy neutrinos:
•Neutrino induced air showers
•Neutrino interactions in ice
Radio Cherenkov signals, detected in situ or with balloon borne detector
Rule of thumb:•Unitarity
•Onset of saturation
•Log(1/x) corrections
2
2 2
410
WUHE Q M
Qx
ME E
Mary Hall Reno
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( ) ( )
( ) ( )p nV V
s x s x
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Medium energy neutrinos: 100’s GeV – 100’s TeV
Neutrino scattering:
NuTeV’s measurement of the weak mixing angle differs from the world average
challenge to assumptions about
Neutrino production:
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“Prompt” neutrino flux
Mary Hall Reno
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100E GeV “Low” energy neutrinos:
Atmospheric neutrinos from
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Neutrino beams like NuMI and CNGS.
Mary Hall Reno
Talk about “low” energy neutrinos
• I’m interested in a practical solution to calculate neutrino cross sections that at the same time includes the “best” that we can do.
• Talk:
•Specifically what low energies, why are we interested? (Neutrino oscillations)
•Components of the cross section.
•Help from local hadron duality?
•Help from phenomenological approach to PDFs at low Q?
•Put it together – and look for some independence in parameters?
Mary Hall Reno
Neutrino Cross Section – Required Figure
Lipari, Lusignoli and Sartogo, PRL 74 (1994)
•Deep inelastic scattering
•Quasi-elastic scattering
•Pion production
0.1 GeV 100 GeV
Neutrino data at these energies is not extensive. Antineutrino data even less.C.f. G.P. Zeller, hep-ex/0323062
Mary Hall Reno
Neutrino Oscillations
2 2 2
2 2
sin 2 sin (1.27 / )
/ , / , /
m L E
m eV L km E GeV
P
•Atmospheric neutrinos: L=Earth diameter=12000 km
•Average E around a few GeV
http://neutrino.kek.jp/index-e.html
Atmospheric neutrinos, coming from all angles, give a wide range of L/E
Muon neutrino deficit, as a function of L/E, shows evidence of neutrino oscillation.
muon neutrino disappearance
Mary Hall Reno
Neutrinos from Fermilab
http://www-numi.fnal.gov
Multiply evt. totals by 3.4 to get nu_mu events per year (without oscillations).
735 km
Mary Hall Reno
Neutrino Cross Section-Required Figure
Lipari, Lusignoli and Sartogo, PRL 74 (1994)
•Deep inelastic scattering
•Quasi-elastic scattering
•Single pion production
NuMI
Low energy beam is best for MINOS distance.
Mary Hall Reno
CERN to Gran Sasso – Tau neutrino appearance
http://www.mi.infn.it/~psala/Icarus/cngs.html L=1000 km
Mary Hall Reno
Tau neutrino appearance
Threshold energy for tau production: 3.5 GeV
Part of our initial motivation to look at the cross section: tau mass, proton mass, charm mass effects along with NLO QCD.
Cf. S. Kretzer & MHR, PRD 66,69
Mary Hall Reno
Calculation – how is it done?
• Quasi-elastic• Resonance dominated by Delta• Deep Inelastic Scattering
avoid double counting – use a cut on W
Concern about missing nonresonant contributions at lower W….
Mary Hall Reno
Issues in Quasi-elastic Scattering
From J. Monroe/MiniBoone for NuInt04, hep-ex/0408019
Preliminary MiniBoone data appear to disagree with Monte Carlo models at low Q.
Nuclear models?
Llewellyn Smith formalism with dipole form factors.
Mary Hall Reno
Resonances
• Monte Carlos, e.g., NUANCE by D. Casper, implements the Rein and Sehgal, Ann. Phys. 133 (1981) 79 updated to current masses, widths. Uses harmonic oscillator quark wavefunctions in model.
• Resonance production up to some W value (say 2 GeV for NUANCE, or 1.4 GeV as in “Required figure”).
• Fermi Gas model of Smith and Moniz.
• Includes some final state interactions.
• There have been recent studies, including by E. Paschos and collaborators & Hagiwara, Mawatari and Yokoya & Sobczyk, Nowak and Graczyk and others on resonance contributions.
Mary Hall Reno
DIS
Standard DIS formula, 5 structure functions:
1 2 5
4
2 2
0
0,N
xF F xF
F
M LO
(Generalized Callan-Gross relation)
Target mass corrected
See Kretzer & MHR
Mary Hall Reno
Neutrino-Nucleon Scattering with TMC
Georgi-Politzer, DeRujula OPE approach.
Nachtmann variable
Mary Hall Reno
TMC in parton picture
Ellis, Furmanski and Petronzio showed that the TMC result can be obtained with:
•Parton momentum on shell but not collinear with the proton in parton level cross section.
•Generalized kT dependent PDF of a general form, but NOT of the form:
2 2( , ) ( ) exp( )T Tx k f x N bk
•TMC come from mismatch of P(proton) and p (quark) (one massive and one massless) .
•They also come from kT limited to less than M.
Mary Hall Reno
Electromagnetic Scattering : Related Processes
• Extensive study of ep scattering, in the resonance region and beyond, by Jefferson Lab groups, SLAC exps.
• Local quark-hadron duality shown for a range of W. Local duality means restricted range of x integration of the structure function and data give same result
Unpolarized case: at fixed Q, for a range of W (restricted x range) including resonances, above the Delta resonance, integral of F2 agrees well between data and NLOTMC, even better if large x resummation is done.
Shown by Fantoni, Bianchi and Liuti.
“Quark hadron duality in electron scattering, Melnitchouk, Ent & Keppel, hep-ph/0501217 (Phys. Rept.)
Mary Hall Reno
Use local duality for neutrino scattering
•Local duality not explicitly demonstrated in neutrino scattering – one motivation for the MINERvA experiment.
•Nevertheless use it in neutrino scattering in the region where local duality holds for ep scattering.
•(Add large x resummation as per Fantoni et al.)
•Should be in the regime where W is larger than 1.4 GeV to use this.
Mary Hall Reno
A phenomenological approach: Bodek Park & Yang
• Fit ep scattering data
• Use GRV98 PDFs
• Redefine scaling variable
2
2
2 2 2 2
2
2
2 ( )
(1 ) 2
1 4 /
0.538
0.305
w
x Q B
Q Ax
M x Q
A GeV
B GeV
:
: w
solid line
dashed line
Mary Hall Reno
Bodek-Park-Yang hep-ph/0411202
• Rescale valence and sea distributions
• Overall normalization
2 202
21
2 2 2
2 21 2
(1 )( )
1/(1 /(0.71 ) )
0.291 ; 0.189
D vv v
v
D
v v
G Q Cu u
Q C
G Q GeV
C GeV C GeV
• Structure function:
2 2 22 ( , ) ( , )q w wF x Q e q Q
Mary Hall Reno
Bodek-Park-Yang meets JLAB
E. Christy provided me with parameterization of ep data, “Christy param.”
Mary Hall Reno
Comparisons in the ep case
dot-dash: LO and LO-TMC
dotted: NLO and NLO-TMC
Can see the need for large x resummation here...
Mary Hall Reno
More comparisons in ep case
Range of Q^2 with steps of 0.2 GeV^2.
Mary Hall Reno
Prescription of BPY-completely phenomenological
• Use the modified PDFs fit to DIS electromagnetic scattering for neutrino scattering for W greater than 1.35 GeV.
• Use explicit calculations for resonance region and quasi-elastic. Note: there are not simple Clebsch-Gordon factors in converting to neutrino scattering.
• (Work on fits to axial vector modifications at low energy.)
Mary Hall Reno
BTW: PDF uncertainties: using 40 CTEQ6 PDFs
more uncertainty in u, d distributions
Mary Hall Reno
How do NLOTMC corrected neutrino structure functions compare with
electromagnetic structure functions of BYP?
Mary Hall Reno
ep and neutrino-nucleon scattering
Mary Hall Reno
Comparison in neutrino nucleon structure function
assume axial vector contribution is same as vector contribution, and take new combinations to get neutrino structure functions:
Mary Hall Reno
How do NLOTMC corrected neutrino structure functions compare with
electromagnetic structure functions of BYP?
Not so well at low Q
Mary Hall Reno
Neutrino cross section
•Half the cross section is from Q less than 1 GeV for this energy….•The same figure for LO or NLOTMC with a minimum Q2=0.8 GeV2.
•NLOTMC structure functions don’t match BPY parameterization well at Q=1 GeV.
Mary Hall Reno
Neutrino DIS cross section
•Circumstance of large M/Q and strong coupling.
•The “K factor” for DIS for this energy is only 1.08-1.11 for Qmin less than 1.3 GeV and W greater than 1.4 GeV.
•Need phenomenological assistance for low Q, especially low x…
Mary Hall Reno
Neutrino cross section – dependence on matching scale?
Delta cross section for W up to 1.4 GeV. Need Delta contribution up to other values of W.
One hopes not!
Mary Hall Reno
An option
• Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering.
• Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV.
• Use a resonance model below W=1.4-2.0 GeV.• Include quasi-elastic scattering.• Vary (x,Q,W) boundaries to see that the total cross section remains
unchanged.
Mary Hall Reno
An option
• Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering.
• Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV.
• Use a resonance model below W=1.4-2.0 GeV.• Include quasi-elastic scattering.• Vary (x,Q,W) boundaries to see that the total cross section remains
unchanged.
Tau neutrino scattering cross section is under better control theoretically.
Ultimately, the muon neutrino cross section will be measured by MINERvA.
Is this step necessary?
NNLO – could this solve the x=0.1 discrepancy?