introduction to neutrino interaction physics nufact08...
TRANSCRIPT
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
Neutrino Interaction Physics
NUFACT08 Summer School2
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
Neutrino Interaction Physics
NUFACT08 Summer School3
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
Neutrino Interaction Physics
NUFACT08 Summer School4
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
Neutrino Interaction Physics
NUFACT08 Summer School5
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 +−
Neutrino Interaction Physics
NUFACT08 Summer School6
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
Neutrino Interaction Physics
NUFACT08 Summer School7
� 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
Neutrino Interaction Physics
NUFACT08 Summer School8
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
Neutrino Interaction Physics
NUFACT08 Summer School9
� 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:
Neutrino Interaction Physics
NUFACT08 Summer School10
� 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
Neutrino Interaction Physics
NUFACT08 Summer School11
� 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!
Neutrino Interaction Physics
NUFACT08 Summer School12
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
Neutrino Interaction Physics
NUFACT08 Summer School13
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
Neutrino Interaction Physics
NUFACT08 Summer School14
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=
Neutrino Interaction Physics
NUFACT08 Summer School15
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)
Neutrino Interaction Physics
NUFACT08 Summer School16
4.6 Experiments4.6 Experiments
� K2K SciBar and SciBoone
Observed CC QE interaction
pn +→+ −µν µ
Neutrino Interaction Physics
NUFACT08 Summer School17
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:
Neutrino Interaction Physics
NUFACT08 Summer School18
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
Neutrino Interaction Physics
NUFACT08 Summer School19
5. Nuclear Effects5.1 Fermi smearing and Pauli blocking
5.2 Nuclear re-interactions
Neutrino Interaction Physics
NUFACT08 Summer School20
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.
Neutrino Interaction Physics
NUFACT08 Summer School21
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
Neutrino Interaction Physics
NUFACT08 Summer School22
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
Neutrino Interaction Physics
NUFACT08 Summer School23
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