Docstoc

Reno

Document Sample
Reno Powered By Docstoc
					 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

(Ultra)-high energy neutrinos:

            •Neutrino induced air showers
            •Neutrino interactions in ice
            Radio Cherenkov signals, detected in
            situ or with balloon borne detector



                                                   •Unitarity
  Rule of thumb:
                                                   •Onset of saturation
                                                   •Log(1/x) corrections


                           Mary Hall Reno
                    (Advertisement)

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:

                                             “Prompt” neutrino flux


                           Mary Hall Reno
                    (Advertisement)

“Low” energy neutrinos:


           Atmospheric neutrinos from




            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
  0.1 GeV                          100 GeV



                                                    •Deep inelastic scattering
                                                    •Quasi-elastic scattering
                                                     •Pion production
                                                 Neutrino data at these energies is
                                                 not extensive. Antineutrino data
                                                 even less.
                                                 C.f. G.P. Zeller, hep-ex/0323062
Lipari, Lusignoli and Sartogo, PRL 74 (1994)




                                Mary Hall Reno
                      Neutrino Oscillations


                                                      muon neutrino disappearance


Atmospheric neutrinos, coming
from all angles, give a wide range
of L/E
•Atmospheric neutrinos:
L=Earth diameter=12000 km
•Average E around a few
GeV
Muon neutrino deficit, as a
function of L/E, shows evidence
of neutrino oscillation.                        http://neutrino.kek.jp/index-e.html

                                     Mary Hall Reno
             735 km

                   Neutrinos from Fermilab


                                             Multiply evt. totals
                                             by 3.4 to get
                                             nu_mu events per
                                             year (without
                                             oscillations).




http://www-numi.fnal.gov
                           Mary Hall Reno
    Neutrino Cross Section-Required Figure

                                                   •Deep inelastic scattering
                                                   •Quasi-elastic scattering
                                                   •Single pion production




                                      Low energy beam
                                      is best for MINOS
                                      distance.

                         NuMI
Lipari, Lusignoli and Sartogo, PRL 74 (1994)
                                  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

                                         Llewellyn Smith formalism with
                                         dipole form factors.



                                        Preliminary MiniBoone data
                                        appear to disagree with Monte
                                        Carlo models at low Q.
                                        Nuclear models?



From J. Monroe/MiniBoone for NuInt04,
hep-ex/0408019



                                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:




             (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:




      •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




                                 Mary Hall Reno
         Bodek-Park-Yang hep-ph/0411202

•   Rescale valence and sea
    distributions
•   Overall normalization




• Structure function:




                              Mary Hall Reno
Bodek-Park-Yang meets JLAB




                           E. Christy provided me with
          Mary Hall Reno   parameterization of ep data,
                           “Christy param.”
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

                        •NLOTMC structure
                        functions don’t match BPY
                        parameterization well at
                        Q=1 GeV.

                        •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.




       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?
                                One hopes not!




                                Delta cross section for W up
                                to 1.4 GeV. Need Delta
                                contribution up to other
                                values of W.




               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
Is this step necessary?
NNLO – could this solve the
                                  An option
x=0.1 discrepancy?

  • 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.

                                     Mary Hall Reno

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:12/3/2011
language:English
pages:35