Probing the CP structure of the top quark Yukawa at the future muon collider

Abstract

A bstract We study the top-Higgs coupling with a CP violating phase ξ at a future multi-TeV muon collider. We focus on processes that are directly sensitive to the top quark Yukawa coupling: $$ t\overline{t}h $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>h</mml:mi> </mml:math> , tbhμν , and $$ t\overline{t} h\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>hν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> with $$ h\to b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> <mml:mo>→</mml:mo> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and semileptonic top decays. At different energies, different processes dominate the cross section, providing complementary information. At and above an energy of $$ \mathcal{O}(10) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mn>10</mml:mn> </mml:mfenced> </mml:math> TeV, vector boson fusion processes dominate. As we show, in the Standard Model there is destructive interference in the vector boson fusion processes $$ t\overline{t} h\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>hν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and tbhμν between the top quark Yukawa and Higgs-gauge boson couplings. A CP-violating phase changes this interference, and the cross section measurement is very sensitive to the size of the CP-violating angle. Although we find that the cross sections are measured to $$ \mathcal{O}\left(50\%\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>50</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:mfenced> </mml:math> statistical uncertainty at 1 σ , a 10 and 30 TeV muon collider can bound the CP-violating angle | ξ | ≲ 9.0 ° and | ξ | ≲ 5.4 ° , respectively. However, cross section measurements are insensitive to the sign of the CP-violating angle. To determine that the coupling is truly CP violating, observables sensitive to CP-violation must be measured. We find in the $$ t\overline{t}h $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>h</mml:mi> </mml:math> process the azimuthal angle between the $$ t+\overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> plane and the initial state muon+Higgs plane shows good discrimination for ξ = ±0.1 π . For the tbhμν and $$ t\overline{t} h\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>hν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> processes, the operator proportional to $$ \left({\overrightarrow{p}}_{\mu}\times {\overrightarrow{p}}_h\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>×</mml:mo> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>h</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> · $$ {\overrightarrow{p}}_t $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>t</mml:mi> </mml:msub> </mml:math> is sensitive to the sign of CP phase ξ . From these observables, we construct asymmetry parameters that show good distinction between different values and signs of the CP violating angle.

Topics & Concepts