Neutrino

diffraction

k.ishikawa,m.sentoku, and y.tobita
hokkaido university• Is neutrino interference (diffraction) observable?
Neutrino is a quantum mechanical wave and interacts
with matter extremely weakly.

Neutrino should show a phenomenon of interference or diffraction, in a
double slit-like experiment.
However, it is very hard to control the neutrino ,since it interacts with any
material so weakly.
Hence a new method must be considered.
Our answer and proposal ” Neutrino diffraction is observable . Use a pion(and other particle) decay process !”1

Electron interference (bi-blism;Tonomura)

Number of events
N_a<N_b<N_c<N_dinterference pattern
becomes clear and visiblein d2

Unknown facts on neutrinos• Absolute neutrino mass•
Tritium decay electron spectrum•¥nu-less double Beta decay•
Cosmology gives bound.
Unclear now !
• How many ? 3?
• Mixing matrix
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Scattering ,interference, and diffraction ofneutrino ( our works)
１．Neutrino is a wave , so it varies in space and time,and follows “Superposition principle”
２．Neutrino is identified from physical reactions thatare caused by the neutrino.
３. １ and ２ are combined. This method is different
from an ordinary oscillation analysis and supply a
new physical quantity.
４．Diffraction was found theoretically and is observed
easily with a large number of events.
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An example

of a wave phenomenon

On mass shell neutrino is in the intermediate state.
External particles are plain waves.

Large correlation andamplification
Yabuki and Ishikawa, PTP(2002)
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Real pion decays
experiment

which?

Particle decay(traditional ?)Distance L=cT

Decay of wave ,wavepacket（ishikawa-shimomura)

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Transition in a finite time-interval• S[T]

Finite-size correction

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What is the finite-size effect ？
１．Quantum mechanical transition in a finite timeinterval Ｔ.

２．Violates the energy conservation
３．States at ultra-violet energy region, J , gives auniversal correction.
４．Relativistic invariance >> large momentumstates8Neutrino diffraction(ishikawa and tobita)
decay amplitude

Neutrino’s momentum and position

Probability is expressed

Correlation function(Only If energy-momentum
is conserved)
1.Correlation function has a light-cone singularity which is generated by a superposition ofrelativistic waves.
2.The energy non-conserving term gives the finite-size correction, which does not suppress
the electron mode．
93 Asymptotic boundary conditions are satisfied with a wave packet（ＬＳＺ）.

Correlation function• Integration variable is change to•Integral region is separated in two parts

Finite size correction(energy non-conserving)

Normal termExtract the light-cone singularity
AboutTo extract light-conesingularity expanding inconvergence condition:

Green’s functionLight-cone singularity

Integration in space-time coordinates

Long-range termThree flavor neutrino

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Diffraction effect (muon ¥nu)

Large finite-size correction

PLength(M)14¥nu-nucleon total cross section

Exp.:
NOMAD & MINOS

theory：normal+diffraction
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Helicity suppression• The finite-size correction comes from the energy
non-conserving term.
• The pi > e+neutrino_e mode is suppressed by the
angular momentum conservation and the energymomentum conservation.
• Since the finite-size correction does not conserve
the energy, it violates the helicity suppression .
• When the neutrino is detected, the electronmode is enhanced.
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Diffraction Events(enhances electron neutrino）
Diffraction

neutrino
oscillationExp.
（lSND,TWN)

Normalcalculation(helicitysuppression)

Distance[M]17Diffraction prediction of the electron neutrino diffraction(T2K、on axis)18

L_{decay-detector} = 170[m], axis = 2.5 degree, Detector 3[m]x3[m]～10% excess (maximum)

19Comparisons with previous experiments• Diffraction effect has been observed but that has notbeen recognized. So, unusual events have been regarded
as anomalous events . They are explained with theneutrino diffraction.
• High energy neutrino nucleon scattering cross section
decreases with the energy slowly. This is understood by
the diffraction effect of the neutrino process.

• High precision experiment may provide the neutrino
absolute mass.
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Anomalous properties of the diffraction
１ neutrino diffraction is easily observed once thestatistics becomes large. quantum interference
２ energy conservation is violated : finite-size effect
３ lepton number appears to be non-conserved.
P(L) decreases with L , so unitarity appears to beviolated. But they are not.： finite-size effect andretarded effect.
４ pion life time varies due to the measurement,
quantum Zeno effect . However the majority of thepion are unchanged because the neutrino
interacts with matter so weakly.
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The neutrino diffraction is a finite-sizecorrection• Why does the neutrino diffraction emerge?
1.Transition in a finite time interval Ｔ,, violates the energy conservation .
2.States at ultra-violet energy region
give a universal correction.
3. Relativistic invariance >> large momentumstates
22Other channels• 1. muon decay• 2. neutron decay• 3.nucleus decays• 4.neutrino scattering(In progress)
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New phenomena caused by finite-size
effects
１．Emission of light particles .
Energy non-conserving transition lead backgroundnoises that has universal properties.
“theory of universal noises “
２．Interference and diffraction.
interference of a new scale that is very different
from wave length “physics of a new scale ”
３．Absorption ：“Coherent absorption phenomena”
24conclusion• With enough number of neutrino events,
the neutrino diffraction is easy to observe andmay provide the absolute neutrino mass.

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