##

Transverse Muon Polarization and Time Reversal Invariance Violation

The transverse muon polarization (*P*_{T}) in the
*K*^{+} → π^{0}μ^{+}ν decay
(*K*^{+}_{μ3}) is the pollarization compornet
The transverse muon polarization normal to decay plane (*P*_{T})
in the *K*^{+} → π^{0}μ^{+}ν decay
is a T-odd correlation of
*
P*_{T} = σ_{μ}•
(**p**_{π0} ×
**p**_{μ+})
/
|**p**_{π0}
× **p**_{μ+}|
.
A non-vanishing *P*_{T} would be a clear sign for T violation
because the spurious effect from final state interactions is known to be
negligibly small (order of magnitude of 10^{-6}.
The imaginary part of the ratio of two decay form factors
*ξ = f*_{-}(q^{2}) / f_{+}(q^{2})
is responsible for T violation and *P*_{T} can be written as

with *Imξ* and a kinematical factor.
E246 is aiming for a sensitivity of about *σ(Imξ) = 0.01*.
Under the assumption of CPT invariance, T violation provides a test of
CP violation models.
The most distinct feature here is the fact that the standard model has
no experimentally detectable contribution up to a vertex correction
contribution of ≈10^{-7}.
Thus, *P*_{T} is a sensitiveˇˇprobe of new physics beyond
the standard model.
The very small final state interaction is in sharp contrast to
*K*_{L}→π^{-}μ^{+}ν
(K^{0}μ3)
in which there is a spurious *P*_{T} as large as 10^{-3}.
This gives a unique advantage to *K*^{+}_{μ3}
in the *P*_{T} study.
The history of *P*_{T} experiments is long but there has
been only one *K*^{+}_{μ3} experiment performed
before using an in-flight decay technique.