Neutrinos and Local Duality

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Neutrinos and Local Duality

• F. M. Steffens
• Mackenzie Uni.
• São Paulo Brazil

Based on FMS,KT, PRD 70 094040 (2004)
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Our particular interest The isoscalar
F2nN neutrino Structure Function
At large x, we should have
Similarly for the the isoscalar F2mN muon
Structure Function
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Test this using local duality
A failure of this equality may imply
Unexpected strangeness at large x, perhaps
intrinsic strange quarks Possible
Charge symmetry breaking in the quark
distributions Violation of local duality
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QCD justification for local duality de Rùjula,
Georgi, Politzer,
PRD 4, 2901 (1977)
Show that using the Nachtmann variable, the lower
moments of F(x,Q2) are, actually, independent of
Q2 The lower moments are the most important to
reconstruct the x (or x) dependence of the
structure functions
Fres(x, Q2) F(x)
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In reality, Fres(x, Q2) oscillates around the
scaling function as the resonance poles are
approached The oscillations come from higher
twist contributions
But they cancel on the average
The scaling function is calculated at very high
Q2 the resonance peaks

have moved to the

large x region
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The elastic part of the hadronic tensor for
neutrino scattering
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Local Duality at the Nucleon Pole
Nachtmann variable at the pion threshold
Scaling
Elastic
Or
and taking the dervivative we get...
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xth Q2/(Q2 mp (2M mp ))
Similarly
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All put together
Calculated using a world data parametrization
F2mN (F2mp F2mn)/2
KT, H. Kim, K. Saito, nu-th/0307013 M.J.Mussolf,
T.W.Donelly, NPA 546 (92) 509 T.Kitagaki, PRD 38
(83) 436
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Q2 2.5 GeV2 W2 1.25 GeV2
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Some limitations For x lt 0.78, Q2 lt 1
GeV2 Calculation should not be
trusted Experimental uncertainty on the
Elastic Form Factors around 10 at Q2 2
GeV2 (hep-ex/0308005) Local duality
in general
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On the other hand, going the inverse way
WM, NPA 680, 52c (2000)
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How can we undestand our result? One
possible contribution to our result could come
from possible charge symmetry violation of
quark distributions at large x. Using
the charged ratio (CB,JTL,AWT,PRL81,4075 (1998))
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From V. Barone, C. Pascaud, F. Zoner, EPJC 12,
243 (2000)
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In the large x region any contribution from
antiquarks should be negligible. Hence,
To match the calculation
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Nuclear Corrections
KT, KS, FMS, PLB 612, 5 (2005)
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Summary
Local duality used to study the relation between
the isoscalar structure functions as probed by
neutrinos and muons Possible violation of
charge symmetry in the valence distributions
at very large x ? Violations of local
duality for the elastic peak?