Lepton flavor-violating Higgs decays mediated by ultralight gauge boson

Abstract We present an analysis of the lepton-flavor violating decay of the Higgs boson mediated by an ultralight gauge boson, $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> . Our analysis matches a model generating the lepton flavor-violating interaction $$\bar{\ell }_i\ell _j\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mi>χ</mml:mi> </mml:mrow> </mml:math> at tree level with an effective field theory, safeguarding a physical massless $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> -boson limit of the observables. By utilizing the upper bounds on $$H\rightarrow \ell _i {\bar{\ell }}_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> </mml:math> decays from CMS and ATLAS Collaborations, we establish an indirect upper limit on the nonstandard decay $$H\rightarrow \ell _i {\bar{\ell }}_j\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>j</mml:mi> </mml:msub> <mml:mi>χ</mml:mi> </mml:mrow> </mml:math> . The analysis encompasses various observables such as the lepton energy spectrum, Dalitz plot distribution, and Lepton Charge and Forward-Backward Asymmetries.