Testing Relativity Theory With Neutrinos

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Testing Relativity TheoryWith Neutrinos

• Brett Altschul
• University of South Carolina
• May 15, 2008

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Overview
Lorentz invariance is extremely well tested.
Yet many candidate theories of quantum gravity
predict Lorentz violation in certain regimes,
especially at very high speeds. Neutrino physics
offers interesting ways to test whether
relativity still holds very close to the speed of
light.
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Outline

• Introduction
• The Standard Model Extension (SME)
• Tests of Relativity with Neutrinos
• Conclusion

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Introduction
In the last fifteen years, there has been growing
interest in the possibility that Lorentz symmetry
may not be exact. There are two broad reasons for
this interest Reason One Many theories that
have been put forward as candidates to explain
quantum gravity involve LV in some regime. (For
example, string theory, non-commutative geometry,
loop quantum gravity)
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Reason Two Lorentz symmetry is a basic building
block of both quantum field theory and the
General Theory of Relativity, which together
describe all observed phenomena. Anything this
fundamental should be tested. Much of the story
of modern theoretical physics is how important
symmetries do not hold exactly. There is no
excellent beauty that hath not somestrangeness
in the proportion. Francis Bacon
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Standard Model Extension (SME)

• Idea Look for all operators that can contribute
  to Lorentz violation.
• Then one usually adds restrictions
• locality
• superficial renormalizability
• gauge
  invariance
• etc...

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With those restrictions, the Lagrange density for
a free fermion looks like
A separate set of coefficients will exist for
every elementary particle in the theory.
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One important effect of these Lorentz-violating
terms is to modify the velocity. For example,
with c present
From this expression, we can see when the
effective field theory breaks down. The velocity
may become superluminal when .
If , this is
. More generally, momentum eigenstates may not be
eigenstates of velocity.
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Most Lorentz-violating effects at high
relativistic energies depend on a particles
maximum achievable velocity (MAV).
The corresponding energy-momentum relation is
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The photon sector contains more superficially
renormalizable couplings.
Most of these couplings are easy to constrain
with astrophysical polarimetry. However, some
will require more complicated measurements (e.g.
with Doppler shifts or electromagnetostatics).
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The coefficients need not be diagonal in flavor
space either. Like neutrino masses, they may mix
different species. In fact, three-parameter
Lorentz-violating models can explain all observed
neutrino oscillations (including LSND). However,
many possible parameters have not been
probed. The full neutrino sector has 102
Lorentz-violating parameters.
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Neutrino Tests of Relativity

• Since neutrinos are always relativistic, they are
  an interesting laboratory for looking for changes
  to special relativity.
• Constraints on can be set in two ways
• time of flight measurements, and
• energy-momentum measurements.

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Its well known that SN1987A neutrinos traveled
to Earth with a speed that differed from
by a fraction . However, this
boundapplies only to electronneutrinos moving
in onedirection.
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We can get better bounds by looking at energetic
constraints.We now feel con-fident that
ultra-high-energy cosmicrays are
primarilyprotons, with en-ergies up toGeV.
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The protons have to live long enough to travel
tens of Mpc to reach Earth. Normally, that would
be no problem, but relativity violations might
cause fast-moving protons to decay, even if
theyre stable at rest.
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If the protons has speeds greater than 1, they
would emit vacuum Cerenkov radiation.
The primary cosmic rays must also be immune to
-decay, . This is
where the neutrinos come in.
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This decay is disallowed only if
This is only a one-sided bound if the neutrino
MAV is isotropic. However, an anistropic MAV is
bounded on both sides at the level.
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The bounds are the same for the . Just swap
the positron for a . The constraints on the
MAV for are worse by a factor of 3, since in
a decay, themass makes a significant
contribution. Most other particles that a
proton could decay into are also subject to
similar or better bounds.
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Conclusion
Lorentz violation is an interesting possibility
to be part of the Theory of Everything.Lorentz
tests for ultrarelativistic particles like
neutrinos are parameterized by the MAV.The fact
that primary cosmic ray protons dont decay into
neutrons sets stronger limits on the neutrino MAV
than time-of-flight measurements.
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Thanks to V. A. Kostelecký and E. Altschul.
Thats all, folks!