Site hosted by Build your free website today!

Neutrino Mass Evidence - Student Project
Phys4410 Intro. to Nuclear and Particle Physics

[Neutrinos]   [History about Neutrinos]   [Experimental vs Theoretical]   [Reference]

 ¤ Neutrino Mass Evidence:
Theoretical vs Experimental

  • Neutrino Properties - Experimental

→ A Review of Neutrino Oscillation Search at Accelerators by S. R. Mishra
→ Searches for Non-SM Physics with the KARMEN Experiment by K. Eitel
→ Results of the Palo Verde Long Baseline Reactor Neutrino Experiment by J. Wolf
→ The Observatory for Multiflavor Neutrinos from Supernovae by R. N. Boyd
→ Lead Perchlorate as a Neutrino Detection Medium by S. R. Elliott, P. J. Doe, R. G. H. Robertson and C. Paul
→ Direct Neutrino Mass Measurement with a Superconductive Detector by M. R. Gomes, P. Valko and T. A. Girard
→ Nuclear Spin Isospin Response and Spectroscopy of ββ-Rays from 100Mo for Neutrino Studies in Nuclei by H. Ejiri

  • Neutrino Properties - Theoretical

Neutrino and the Standard by B. R. Holstein


The poem by John Updike,

Neutrinos they are very small
They have no charge and have no mass
And do not interact at all.....

(Contemporary Issues)

1) Use of neutrino scattering in order to study the Q² evolution of deep inelastic structure functions as a test of perturbative QCD.
2) Use of such deep inelastic structure functions in order to check the valadity of various sum rules.

Two of the issues are well known. So the author discussed 3 of the following applications of neutrino studies.

1) Goldberger-Treiman Discrepancy
2) Axial Charge Radius
3) Nucleon Strangeness Content
1) Goldberger-Treiman Discrepancy: In QCD, (borken) Chiral symmetry implies the existence of the Goldberger-Treiman (GT) relation, which connects the strong pion-nucleon coupling gπNN and the axial coupling gA(0) measured in neutron beta decay, where

MNgA(0) = FπgπNN(0)

where Fπ = 92.3 MeV is the pion decay constant.

2) Axial Charge Radius: Neutrino scattering result associated with confirmation of a prediction of Chiral perturbation theory and therefore of QCD.
Recent calculation by Bernard, Kaiser, and Meissner in heavy Baryon chiral perturbation theory implies that the old low energy theorem is incorrect.
Using triangle diagram,

A(elec.) = r²A(neu.) - (3/64)(1/F²π)(12/π² - 1)

Result: Prediction of 0.046fm² difference from chiral symmetry agrees well in size and sign with that seen experimentally.

3) Nucleon Strangeness Content: the paper of Donoghue and Nappi is wrong. IDEA: In the limit of vanishing quark masses the nucleon mass should approach some nonzero value M0.

Mass Matrix for Atmospheric, Solar, and LSND Neutrinos by S. P. Rosen

"Today we have sets of evidence for neutrino oscillations, and therefore neutrino mass, coming from atmospheric, solar, and LSND neutrino observations. It is very curious that the first two sets suggest large mixing angles but relatively small mass differences whereas the third suggests small mixing with a relatively large Δm². It is generally accepted, in the event that all three sets of evidence are confirmed, that it will be necessary to introduce a fourth, sterile neutrino to describe the mass and mixing spectrum."

Atmospheric Neutrinos:
1) Most likely large mixing of νμ and ντ
2) Δm²: order of 10-3 eV²
Solar Neutrinos:
1) Large mixing between νe and νsterile
2) Δm²: order of 10-7 to 10-4 eV²
LSND (Liquid Scintillator Neutrino Detector):
1) Small mixing of νe and νμ
2) Large Δm²: order of 1 eV²

The νatmospheric and νsolar as doublets, and taking one of the two doublets as a pseudo-Dirac neutrino, the mass difference is consistent with the theoretical Majorana mass limit obtained from analyzing all of the current data, namely

‹ mββ › < 6 * 10-3 eV

What is Coherent in Neutrino Oscillations - the Analog with a Two-slit Experiment by H. J. Lipkin

Amplitudes with the same energy and different energiesare detected coherently and produce oscillation.

Amplitudes with different energies are incoherent.

Quantum mechanics alone shows the existence of a neutrino mass difference to be required to explain the observed Superkamiokande.

"Simple quantum mechanics alone, without the full apparatus of the standard , shows that the Superkamiokande results require the existence of two different mass eigenstates for neutrinos. The energy spectrum of atmospheric neutrinos cannot change between their source at the top of the atmosphere and their detection in a detector on earth if neutrinos are not absorbed, do not decay and interactions conserve energy. If there is only one neutrino mass value, the energy and momentum spectra will be identical for the upward and downward going neutrinos incident on the detector and no difference can be observed. The observation of the up-down difference therefore indicates that there are at least two different mass eigenstates, and that the difference can arise from interference between the waves of states having different masses and therefore different momenta if they have the same energy."

  • Neutrino Properties - Experimental

A Review of Neutrino Oscillation Search at Accelerators

Definition of Anomaly: measurement that cannot be readily explained using physics processes allowed by the standard .
Superkamiokande: A ring-imaging water Cherenkov detector containing 50 kilotons of ultra-pure water in a cylindrical stainless steel tank.

Contained events: Neutrino interactions occuring inside this fudicial volume.
Fully Contained (FC) events are those which have no exiting signature in the outer veto detector, and comprise the bulk of the contained event sample.
FC sample further divides into sub-GeV (Evis < 1330 MeV) and multi-Gev (Evis > 1330 MeV), mainly for historical reason.
characterization of events:
Showering (e-like), non-showering (μ-like) based on the obeserved Cherenkov light pattern.
LSND - Liquid Scintillator Neutrino Detector
MINOS - Main Injector Neutrino Oscillation Search

If neutrinos are massive, they should exhibit flavor oscillation. Its origin is from the anticipated deep symmetry between quarks and leptons.

It is probable that leptons share two basic properties with quarks:

1) members of different families have different masses
2) mass eigenstates do not coincide with the weak eigenstate.
This implies that it requires neutrino flavors oscillation into one another with probability,
Px → νy) = sin²2θ12sin²(1.27Δm²L/E)
P: probability for flavor 'x' to oscillate into flavor 'y.'
θ12: weak mixing angle between the mass eigenstates 1 and 2.
L: the neutrino flight path measured in km.
E: the neutrino energy measured in GeV.
Δm² = | m1 - m2 | measured in GeV (Usually mc² is expressed in m and letting c = 1).

Three neutrino anomalies exist (could be interpreted as evidence for neutrino oscillations).

Atmospheric Neutrino (most compelling) - MINOS
Solar Neutrino Deficit
The Excess of Electron-like events - LSND

If any of the oscillation clues are correct, they are smaller by at least seven orders of magnitude (→ Grand Unification).

Brief Review of Present Evidence for Neutrino Oscillations

1.1 Atmospheric Neutrinos
In 1998, Superkamiokande experiment reported neutrino oscillation 'discovery' result which observations were due to νμ → ντ oscillation. Also possibly, a sub-dominant νμ → νe oscillation (U13).
Cosmic rays hitting the earth's atmosphere creates πμ + νμe + νe + νμ + νμ
(by exclusion of earlier experiments, the RATIO of νμ/ νe ~ 2 as predicted, by simulation, to be substantially below unity.)
The evidence of oscillations comes from the zenith angle distribution.
For proper combination of Δm² and E, events from the farside of earth (range of 10,000 km distance) should be considered for neutrino oscillations (because it has a higher porbability that an osciallation will occur.).
From data measured for multi-GeV Superkamiokande, e-like data agree with the absence of oscillation whereas μ-like data strongly depends on oscillation hypothesis.
The hypothesis of νμ → ντ oscillation with sin²2θ = 0.99 and Δm² = 3.1 * 10-3 (eV)² agrees with Superkamiokande's data → Possibility of νμ → νsterile oscillation at the 99.9% confidence level. Also, Superkamiokande can suggest the possibility that entire oscillation comes from νμ → νe, but it is still an open question which requires more experimental data from MINOS experiment.

1.2 Solar Oscillations
"Five experiments have measured the flux of solar neutrinos. All have reported results that are a fraction of the rates calculated from types of the sun."
If the neutrino oscillation causes the solar deficit, we can make two possible interpretations:
1) Vacuum oscillations: To get a value 0.33 of the Homestake experiment, a small multiple of the oscillation length is needed to match exactly with the distance between the earth and the sun. This leads to mass difference squared (Δm²) of about 10-10 (eV)² and maximum mixing angles.
2) Matter oscillations taking place in the sun: Matter oscillations have the ability to convert completely νe → νμ in a triangular region of the sin²2θ versus Δm² plot approximately 50% conversion will occur near the edges of the triangular region.

1.3 The LSND Experiment
LSND (Los Alamos) - Neutrinos from pions stopped in a water target.
Decay Mode: π+ → μ+ + νμ → e+ + νe + ν*μ + νμ
The Experiment Targets on: ν*μ → ν*e oscillations ( ν*e is detected by observing ν*e + p → e+ + n, followed by a γ from n + p → d + γ.
Updated results: Observation of 22 events (calculated background of 4.6 +/-0.6 events, consistent and more accurate results from earlier results.

[Neutrinos]   [History about Neutrinos]   [Experimental vs Theoretical]   [Reference]

End Theoretical vs Experimental Page - Neutrino 
[Back to Top]