Light lepton-flavor-violating flavon: The messenger of neutrino mixing and lepton <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:math>

In neutrino physics, a class of models with local or global family symmetries may be invoked, and then a flavon field is needed to realize full neutrino mixing. This flavon may leave hints in lepton <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>g</a:mi> <a:mo>−</a:mo> <a:mn>2</a:mn> </a:math> and address their possible anomalies. In this work, we explore this idea in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo stretchy="false">(</c:mo> <c:mrow> <c:mi>B</c:mi> <c:mo>−</c:mo> <c:mi>L</c:mi> </c:mrow> <c:msub> <c:mo stretchy="false">)</c:mo> <c:mrow> <c:mi>i</c:mi> <c:mi>j</c:mi> </c:mrow> </c:msub> </c:math> gauge extension to the standard model (SM), in which realistic neutrino mixing requires both a SM singlet flavon <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>s</g:mi> </g:math> and a vectorlike lepton (VLL) doublet. The dominant coupling between the flavon and leptons is in the manner of lepton-flavor-violation (LFV). Through an analytical analysis of the SM lepton-VLL mixing matrix, we find that the parameter space of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>s</i:mi> <i:mover accent="true"> <i:mi>μ</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mi>e</i:mi> </i:math> -type flavon to explain <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mo stretchy="false">(</m:mo> <m:mi>g</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> <m:msub> <m:mo stretchy="false">)</m:mo> <m:mi>μ</m:mi> </m:msub> </m:math> has been completely excluded by the specific LFV process, muonium-antimuonium oscillation. But the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>s</q:mi> <q:mover accent="true"> <q:mi>μ</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> <q:mi>τ</q:mi> </q:math> -type flavon still has the opportunity to account for the excess in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo stretchy="false">(</u:mo> <u:mi>g</u:mi> <u:mo>−</u:mo> <u:mn>2</u:mn> <u:msub> <u:mo stretchy="false">)</u:mo> <u:mi>μ</u:mi> </u:msub> </u:math> or the deficit in <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mo stretchy="false">(</y:mo> <y:mi>g</y:mi> <y:mo>−</y:mo> <y:mn>2</y:mn> <y:msub> <y:mo stretchy="false">)</y:mo> <y:mi>e</y:mi> </y:msub> </y:math> ; however, it faces the strong constraint from <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>τ</cb:mi> <cb:mo stretchy="false">→</cb:mo> <cb:mi>μ</cb:mi> </cb:math> conservation and, in particular, the lepton flavor universality (LFU) test of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>Z</fb:mi> </fb:math> boson decay, which arises due to our way to realize the LFV flavon. The surviving flavon is highly predictable, with mass in the narrow window <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>m</hb:mi> <hb:mi>τ</hb:mi> </hb:msub> <hb:mo>≲</hb:mo> <hb:msub> <hb:mi>m</hb:mi> <hb:mi>s</hb:mi> </hb:msub> <hb:mo>≲</hb:mo> <hb:mn>2</hb:mn> <hb:msub> <hb:mi>m</hb:mi> <hb:mi>τ</hb:mi> </hb:msub> </hb:math> and LFV coupling strength <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mo>∼</jb:mo> <jb:msup> <jb:mn>10</jb:mn> <jb:mrow> <jb:mo>−</jb:mo> <jb:mn>2</jb:mn> </jb:mrow> </jb:msup> </jb:math> . Besides, it leaves a TeV scale VLL with a multilepton signature at the LHC.