Introduction to Neutrino Interaction Physics NUFACT08...
Transcript of Introduction to Neutrino Interaction Physics NUFACT08...
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Introduction to Neutrino Interaction PhysicsNUFACT08 Summer School
Introduction to Neutrino Interaction PhysicsIntroduction to Neutrino Interaction Physics
NUFACT08 Summer SchoolNUFACT08 Summer School
11-13 June 2008Benasque, Spain
Paul Soler
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Neutrino Interaction Physics
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4. Quasi-elastic, resonant, coherent and diffractive scattering
4.1 Motivation
4.2 Charged current quasi-elastic scattering
4.3 Neutral current elastic scattering
4.4 Resonant pion production
4.5 Coherent pion production
4.6 Experiments
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4.1 Motivation4.1 Motivation� Many neutrino oscillation experiments need to achieve
E/L ~ 10-3 GeV/km, so for distances ~1000 km, we need interactions around 1 GeV.
� For example, T2K, MINOS, atmospheric experiments require knowledge of cross-section between 0.4 and 2 GeV/c to perform accurate ∆m2
23 and θ23 analysis
T2K
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4.1 Motivation4.1 Motivation� Around 1 GeV there is a complicated region where deep inelastic
scattering (DIS), quasi-elastic (QEL) scattering and resonance production (for example, 1π production) co-exist
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4.2 Charged current quasi4.2 Charged current quasi--elastic scatteringelastic scattering
� Quasi-elastic neutrino-nucleon scattering reactions (small q2): affects nucleon as a whole
−W
µν
pn
−µ
pn +→+ −µν µ
== −nHpM eff ,, µνµ
np +→+ +µν µ
+W
µν
p n
+µ
factorformvector)( 2 =qFV
factorformvectoraxial)( 2 −=qFA
angle)(Cabbibo975.0cos =Cθ
[ ] ( )[ ]nqFqFpG
AVcF
5
22
5 )()()1(2
cosγγνγγµ
θµµ
µ +−
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4.2 Charged current quasi4.2 Charged current quasi--elastic scatteringelastic scattering
� In reality, it is more complicated and we need Llewelyn-Smith formalism to calculate QE differential cross-sections:
� A, B, C are complicated functions of two vector form factors F1
V(Q2), F2V(Q2), the axial form factor FA(Q2) and the pseudoscalar
form factor FP(Q2).
2
2
2
2
1
)(
+
=
A
AA
m
Q
gQF
224)( µν mQMEus −−=−
)( 212
2
FFFM
QB A +=
( )
+−+++−+−+−−+
+= 2
2
222
212
2
212
22
12
2
22
4)2()(4
4)1()1(1)(
PPAA FM
QFFFF
M
mFFFFF
M
QmA
µµ τττττ
( )2
2
2
1
2 FFFA τ++=4
1C
2
2
2
2
1
1)1(
)1(1)(
++
−++=
V
npV
m
QQF
τ
µµτ
2
2
4M
Q=τ
−+
−= C
M
usB
M
usA
E
MG
dQ
d F
4
2
22
22
2
, )()(
8m
ν
νν
π
σ
See Zeller, hep-ex/0312061, for details
)(2
)( 2
22
22 QF
Qm
MQF AP
+=
π
2
2
2
22
1)1(
)1(1)(
++
−++=
V
npV
m
QQF
τ
µµτ
Form factors: assume
dipole approximation NnNp and µµµµ 913.1793.1 −==
028.02573.1)0( ±−== AA gF
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Neutrino Interaction Physics
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� Form factors introduced since proton, neutron not elementary.
� Depends on vector and axial weak charges of the proton and neutron.
� Conservation of Vector Current (CVC) relates form factors to electron scattering
� Main physics to be extracted from QE scattering data are empirical form factor parameters (fits to mA, mV, deviations from dipole approximation)
4.2 Charged current quasi4.2 Charged current quasi--elastic scatteringelastic scattering
≈= )()( pn ee νσνσ
GeVmA 032.1=
GeVmV 84.0=
( )222
2
/1
)0()(
V
VV
mq
FqF
−=
( )222
2
/1
)0()(
A
AA
mq
FqF
−=
2
38
110975.0
× −
GeV
E
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4.3 Neutral current elastic scattering4.3 Neutral current elastic scattering
� Neutral current elastic neutrino-nucleon scattering reactions are related to the CC quasielastic (small q2): about 15% of CC QEL
pp +→+−−
µµ νν)()(
0Z
µν)(−
p p
µν)(−
0Z
µν)(−
n n
µν)(−
nn +→+−−
µµ νν)()(
Also need to
calculate form
factors
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� Between the elastic and inelastic region is an area associated with pion production through the excitation of baryon resonances
� Invariant mass squared:
� If x=1 then quasi-elastic scattering but if x<1 then you can excite different pion states:
4.4 Resonant 4.4 Resonant pionpion productionproduction
)1(222 xMMW TT −+= ν
'** NNandNlNl +→+→+ πν
,...)2(,)( 222
ππ mMmMW TT ++=
∑ −Γ→=spins
MWlNNTMEdWdQ
d)(*)(
2
1
32
1 2
22ν
σ
4/)(2
1)(
22
0
Γ+−
Γ=−Γ
MWMW
π
� Rein and Sehgal’s model describes low energy pion production by a coherent superposition of all possible resonances
� Cross-section:
with:
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� All possible channels: 3 in CC and 4 in NC
4.4 Resonant 4.4 Resonant pionpion productionproduction
+−++− ++→∆+→+ πµµν µ pN+−+− ++→∆+→+ πµµν µ nN
� For example, possible resonances are ∆++ or ∆+
Very little data, has large statistical
errors, mainly from old bubble
chamber experiments
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� All possible channels: 3 in CC and 4 in NC
4.4 Resonant 4.4 Resonant pionpion productionproduction
+−++− ++→∆+→+ πµµν µ pN+−+− ++→∆+→+ πµµν µ nN
� For example, possible resonances are ∆++ or ∆+
NC data is even worse!
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4.4 Resonant 4.4 Resonant pionpion productionproduction
� Duality: use electron scattering data to improve precision of model
� Can observe individual resonances with good agreement data and model
Bodek and Yang
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4.5 Coherent 4.5 Coherent pionpion productionproduction
� Neutrinos can also produce pions coherently (low Q2 and high ν)
� The neutrino coherently scatters off the whole nucleus with negligible energy transfer to the whole nucleus of mass A
� This results in a forward scattered single pion (background in oscillation searches because forward peaked)
� Neutral and charged current processes are possible:
( ) ( )22||2 )()()( ∑∑ ⊥−−≈−−=i ii ii ppEpqt π
0πνν µµ ++→+ AA+− ++→+ πµν µ AA
( ) abs
tb
A
ANtot Fe
Qm
mryEAf
MG
dydtdQ
d −
++−=
2
22
22222
2
2
2)1(
16
1)1(
2
πνπ σ
ππ
σ
� Rein and Sehgal’s model also describes coherent pion production:
� Cross-section:
amplitude scattering nucleon-pion=)0(Nfπ
parameterimpact == 3/2)3/1( Rb
constantdecay pion== ππ mf 93.0
absorption pion==− λ/x
abs eF
[ ][ ])0(Im
)0(Re
N
N
f
fr
π
π≡
Exponential in |t| distribution
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4.5 Coherent 4.5 Coherent pionpion productionproduction
� Charged current single pion coherent cross-section:
� NC cross-section is half of CC:cohCC
cohNC σσ
2
1=
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4.6 Experiments4.6 Experiments
� Recent experiments carrying out measurements in the ~1GeV region:– K2K near detectors (ie. SciBar): completed
– MINOS near detector: running
– MiniBoone: running
– SciBoone: moved SciBar to Fermilab, operating at the Booster beamline
– Minerva (under construction)
– T2K (under construction)
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4.6 Experiments4.6 Experiments
� K2K SciBar and SciBoone
Observed CC QE interaction
pn +→+ −µν µ
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4.6 Experiments4.6 Experiments
� MiniBoone: measurement of CCQE scattering– Fitted form factor, effective axial mass:
ππππ0000 event
– NC π0 measurement: 28,000 events
Ratio coherent/non-coherent:
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4.6 Experiments4.6 Experiments
� Minerνa: a detector for precision interaction physics at Fermilab
Scintillator bar
+ wavelength shifting fibre
CCQE event pn +→+ −µν µResonance event
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5. Nuclear Effects5.1 Fermi smearing and Pauli blocking
5.2 Nuclear re-interactions
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5.1 Fermi smearing and Pauli blocking5.1 Fermi smearing and Pauli blocking
� Nuclear effects in neutrino scattering:– In a nucleus, the target nucleon has a momentum
which modifies scattering
– Modelled as “Fermi gas” that fills up all available states until some initial state Fermi momentum, kF
– The Pauli exclusion principle ensures that states cannot occupy states that are already filled (Pauli blocking)
– Particles that escape nuclear medium may be re-scattered and deflected by the Fermi momentum, especially at low energies.
– We need better understanding of the Fermi motion
– For example, MiniBoone have already published a paper suggesting a modification to the Fermi gas model based on matching QE scattering in all values of Q2 with their data.
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5.1 Fermi smearing and Pauli blocking5.1 Fermi smearing and Pauli blocking
� Effects on Structure Functions:– In charged lepton scattering, have observed shadowing and
modifications to PDFs due to nucleons.
– At small x, coherent interaction of a hadronic component of the virtual photon with target nucleus - shadowing
– It is not clear if this is also present in neutrino structure functions since at low x, dominated by axial current
Shadowing
Anti-shadowing
EMC effect
Fermi motion
These effects need to be
studied in detail with high
statistics neutrino scattering
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5.2 Re5.2 Re--interactionsinteractions
� Nuclear effects in resonance region:– Production of resonance may be
affected by nuclear medium (see plot of photoabsorption data)
– Resonant structure gets washed out
– Pions may either rescatter or be absorbed. This needs to be measured
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ConclusionsConclusions
� Neutrino interactions have provided valuable insight into the theory of weak interactions– Maximal parity violation, V-A theory and finally the Glashow-Weinberg-
Salam electroweak theory were developed in part from information on neutrino interactions
– Neutrino interaction data is used to probe the electroweak theory, such as in the measurements of sin2θW.
� Neutrino interactions have also provided information on the structure of nucleons – Structure function measurements and scaling violations have been
observed (F3 is only accessible through neutrino interactions)
� Neutrino oscillations allow us to probe the grand unification energy scale, but it is crucial that we understand further the
~1 GeV energy region to be able to exploit oscillation experiments to the maximum
� A new generation of experiments is commencing to lead the way towards a new precision era in neutrino interaction physics