Probing new physics and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> violation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display=

We study the processes <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>ν</a:mi> <a:mi>τ</a:mi> </a:msub> <a:mi>n</a:mi> <a:mo stretchy="false">→</a:mo> <a:msub> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>c</a:mi> </a:msub> <a:msup> <a:mi>τ</a:mi> <a:mo>−</a:mo> </a:msup> <a:mo stretchy="false">(</a:mo> <a:msup> <a:mi>π</a:mi> <a:mo>−</a:mo> </a:msup> <a:msub> <a:mi>ν</a:mi> <a:mi>τ</a:mi> </a:msub> <a:mo stretchy="false">)</a:mo> </a:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mover accent="true"> <g:mi>ν</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mi>τ</g:mi> </g:msub> <g:mi>p</g:mi> <g:mo stretchy="false">→</g:mo> <g:mi mathvariant="normal">Λ</g:mi> <g:msup> <g:mi>τ</g:mi> <g:mo>+</g:mo> </g:msup> <g:mo stretchy="false">(</g:mo> <g:msup> <g:mi>π</g:mi> <g:mo>+</g:mo> </g:msup> <g:msub> <g:mover accent="true"> <g:mi>ν</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mi>τ</g:mi> </g:msub> <g:mo stretchy="false">)</g:mo> </g:math> , with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>τ</q:mi> </q:math> polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mi>C</s:mi> <s:mi>P</s:mi> </s:mrow> </s:math> -violating contributions. We propose an observable that provides a genuine <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:mi>C</u:mi> <u:mi>P</u:mi> </u:mrow> </u:math> -odd signal due to its sensitivity to particular transverse components of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>τ</w:mi> </w:math> polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msup> <y:mi>τ</y:mi> <y:mo>±</y:mo> </y:msup> <y:mo stretchy="false">→</y:mo> <y:msup> <y:mi>π</y:mi> <y:mo>±</y:mo> </y:msup> <y:msub> <y:mi>ν</y:mi> <y:mi>τ</y:mi> </y:msub> </y:math> constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.