Transverse Muon Polarization and Time Reversal Invariance Violation

The transverse muon polarization (PT) in the K+ → π0μ+ν decay (K+μ3) is the pollarization compornet The transverse muon polarization normal to decay plane (PT) in the K+ → π0μ+ν decay is a T-odd correlation of PT = σμ• (pπ0 × pμ+) / |pπ0 × pμ+| . A non-vanishing PT 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-(q2) / f+(q2) is responsible for T violation and PT can be written as

  P_T \cong {\rm Im}\xi \cdot \frac{m_{\mu}}{m_{K}} \cdot \frac{\vert
  \vec{p}_{\mu}\vert}{E_{\mu}+\vert\vec{p}_{\mu}\vert \vec{n}_{\mu}\cdot
  \vec{n}_{\nu} - m^2_{\mu}/m_K}

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, PT is a sensitiveˇˇprobe of new physics beyond the standard model. The very small final state interaction is in sharp contrast to KL→π-μ+ν (K0μ3) in which there is a spurious PT as large as 10-3. This gives a unique advantage to K+μ3 in the PT study. The history of PT experiments is long but there has been only one K+μ3 experiment performed before using an in-flight decay technique.
Kmu3 decay plane
Matrix equation

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KEK-PS-E246 collaboration