Neutrino-Nucleon Deep Inelastic Scattering

44 Pages·2006·1.42 MB·English

ν
NNeeuuttrriinnoo--NNuucclleeoonn
DDeeeepp IInneellaassttiicc SSccaatttteerriinngg
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NNeeuuttrriinnoo--NNuucclleeoonn
ν
‘‘nn aa NNuuttsshheellll
• Charged - Current: W± exchange • Neutral - Current: Z0 exchange
(cid:131) Quasi-elastic Scattering: (cid:131) Elastic Scattering:
(Target changes but no break up) (Target unchanged)
ν + n → μ− + p ν + N → ν + N
μ μ μ
(cid:131) Nuclear Resonance Production: (cid:131) Nuclear Resonance Production:
(Target goes to excited state) (Target goes to excited state)
ν + n → μ− + p + π0 (N* or Δ) ν + N → ν + N + π (N* or Δ)
μ μ μ
n + π+
(cid:131) Deep-Inelastic Scattering: (cid:131) Deep-Inelastic Scattering
(Nucleon broken up) (Nucleon broken up)
ν + quark → μ− + quark’ ν + quark → ν + quark
μ μ μ
Linear rise with energy
Resonance Production
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ν
SSccaatttteerriinngg VVaarriiaabblleess
Scattering variables given in
terms of invariants
•More general than just deep
inelastic (neutrino-quark)
scattering, although
interpretation may change.
( )2 ( )
' '
4-momentum Transfer2: Q2 = −q2 = − p − p ≈ 4EE sin2(θ/2)
Lab
( )
'
Energy Transfer: ν= (q⋅P)/M = E − E = (E − M )
T h T Lab
Lab
( )
'
Inelasticity: y = (q⋅P)/( p⋅P) = (E − M )/ E + E
h T h
Lab
Fractional Momentum of Struck Quark: x = −q2 /2( p⋅q) = Q2 /2M ν
T
Recoil Mass2 : W2 = (q + P)2 = M 2 +2M ν−Q2
T T
2
Q
CM Energy2 : s = (p + P)2 = M 2 +
T xy
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ν
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ν
PPaarrttoonn IInntteerrpprreettaattiioonn ooff DDIISS
2 2 2 2 2
m = x P = x M
Mass of target quark
q T
μ ν
Mass of final state quark
2 2
m = (xP + q)
,
q
q = pν − pμ
In “infinite momentum
frame”, x is momentum of
partons inside the nucleon
2 2
Q Q
x = =
Neutrino scatters off a 2P ⋅ q 2M ν
T
parton inside the nucleon
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SSoo wwhhyy iiss ccrroossss--sseeccttiioonn ssoo
ν
llaarrggee??
• (at least compared to νe- scattering!)
• Recall that for neutrino beam and target at rest
2
Q ≡s
2 2
G max G s
σ ≈ F ∫ dQ2 = F
TOT
π π
0
2
s = m + 2m E
e e ν
• But we just learned for DIS that effective mass of each
m = xm
target quark is
q nucleon
• So much larger target mass means larger σ
TOT
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CChhiirraalliittyy,, CChhaarrggee iinn CCCC νν--qq
ν
SSccaatttteerriinngg
• Total spin determines
*
inelasticity distribution
Flat in y
(cid:131) Familiar from neutrino-
electron scattering
♠
1/4(1+cosθ∗)2 = (1-y)2
♠
dσνp G2s * ∫(1-y)2dy=1/3
( )
= F xd(x)+ xu(x)(1− y)2
• Neutrino/Anti-neutrino CC
dxdy π
each produce particular Δq
dσνp G2s * ♠
( )
= F xd(x)+ xu(x)(1− y)2 in scattering
dxdy π
−
νd → μ u
+
νu → μ d
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ν
FFaaccttoorriizzaattiioonn aanndd PPaarrttoonnss
• Factorization Theorem of QCD allows amplitudes for hadronic
processes to be written as:
∑
A(l + h → l + X ) = ∫ dxA(l + q(x) → l + X )q (x)
h
q
(cid:131) Parton distribution functions (PDFs) are universal
(cid:131) Processes well described by single parton interactions
(cid:131) Parton distribution functions not (yet) calculable from first principles in
QCD
• “Scaling”: parton distributions are largely independent of Q2
scale, and depend on fractional momentum, x.
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ν
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MMoommeennttuumm ooff QQuuaarrkkss && ν
AAnnttiiqquuaarrkkss
• Momentum carried by quarks
much greater than anti-quarks
in nucleon
q(x)
q (x)
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