Probing new physics with polarization components of the tau lepton in quasielastic e−p→Λcτ− scattering process

Kinematics restricts the ability of rare charm decays to explore the charged lepton-flavor-violation processes mediated by the quark-level <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi><a:mo stretchy="false">→</a:mo><a:mi>u</a:mi><a:mo>ℓ</a:mo><a:mi>τ</a:mi></a:math> transition. To fill the gap, we propose exploring new physics (NP) through the quasielastic scattering process <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mi>e</d:mi><d:mo>−</d:mo></d:msup><d:mi>p</d:mi><d:mo stretchy="false">→</d:mo><d:msup><d:mi>τ</d:mi><d:mo>−</d:mo></d:msup><d:msub><d:mi mathvariant="normal">Λ</d:mi><d:mi>c</d:mi></d:msub></d:math> and the polarization of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>τ</h:mi></h:math> lepton. As analyzing modes for the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>τ</j:mi></j:math> polarization, we consider the decays <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi>τ</l:mi><l:mo>−</l:mo></l:msup><l:mo stretchy="false">→</l:mo><l:msup><l:mi>π</l:mi><l:mo>−</l:mo></l:msup><l:msub><l:mi>ν</l:mi><l:mi>τ</l:mi></l:msub></l:math>, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>τ</o:mi><o:mo>−</o:mo></o:msup><o:mo stretchy="false">→</o:mo><o:msup><o:mi>ρ</o:mi><o:mo>−</o:mo></o:msup><o:msub><o:mi>ν</o:mi><o:mi>τ</o:mi></o:msub></o:math>, and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mi>τ</r:mi><r:mo>−</r:mo></r:msup><r:mo stretchy="false">→</r:mo><r:msup><r:mo>ℓ</r:mo><r:mo>−</r:mo></r:msup><r:msub><r:mover accent="true"><r:mi>ν</r:mi><r:mo stretchy="false">¯</r:mo></r:mover><r:mo>ℓ</r:mo></r:msub><r:msub><r:mi>ν</r:mi><r:mi>τ</r:mi></r:msub></r:math>, and show that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>τ</w:mi></w:math> polarization components can be extracted from analyzing the kinematics of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>τ</y:mi></y:math> visible decay products. In the framework of a general low-energy effective Lagrangian, we then perform a detailed analysis of the polarization components in various aspects and scrutinize possible NP signals. With one upcoming experimental setup, we finally demonstrate promising event rate can be expected for the cascade process and, even in the worst-case scenario—no signals are observed at all—it can still provide a competitive potential for constraining the NP, compared with those from the high-<ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>p</ab:mi><ab:mi>T</ab:mi></ab:msub></ab:math> dilepton invariant mass tails at high-energy colliders.