The recent confirmation of the muon $$g-2$$ anomaly by the Fermilab $$g-2$$ experiment may harbinger a new era in $$\mu $$ and $$\tau $$ physics. In the context of general two Higgs doublet model, the discrepancy can be explained via one-loop exchange of sub-TeV exotic scalar and pseudoscalars, namely H and A, that have flavor changing neutral couplings $$\rho _{\tau \mu }$$ and $$\rho _{\mu \tau }$$ at $$\sim 20$$ times the usual tau Yukawa coupling, $$\lambda _\tau $$ . Taking $$\rho _{\ell \ell ^\prime }\sim \lambda _{ \mathrm min(\ell , \ell ^\prime )}$$ , we show that the above solution to muon $$g-2$$ then predicts enhanced rates of various charged lepton flavor violating processes, which should be accessible at upcoming experiments. We cover muon related processes such as $$\mu \rightarrow e \gamma $$ , $$\mu \rightarrow eee$$ and $$\mu N \rightarrow e N$$ , and $$\tau $$ decays $$\tau \rightarrow \mu \gamma $$ and $$\tau \rightarrow \mu \mu \mu $$ . A similar one-loop diagram with $$\rho _{e\tau }= \rho _{\tau e} = \mathcal{O}(\lambda _e)$$ induces $$\mu \rightarrow e\gamma $$ , bringing the rate right into the sensitivity of the MEG II experiment. The $$\mu e\gamma $$ dipole can be probed further by $$\mu \rightarrow 3e$$ and $$\mu N \rightarrow eN$$ . With its promised sensitivity range and ability to use different nuclei, the $$\mu N \rightarrow eN$$ conversion experiments can not only make discovery, but access the extra diagonal quark Yukawa couplings $$\rho _{qq}$$ . For the $$\tau $$ lepton, we find that $$\tau \rightarrow \mu \gamma $$ would probe $$\rho _{\tau \tau }$$ down to $$\lambda _\tau $$ or lower, while $$\tau \rightarrow 3\mu $$ would probe $$\rho _{\mu \mu }$$ to $$\mathcal{O}(\lambda _{\mu })$$ .
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"title": "Charged lepton flavor violation in light of muon $$g-2$$ <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>"
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"value": "The recent confirmation of the muon $$g-2$$ <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math> anomaly by the Fermilab $$g-2$$ <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math> experiment may harbinger a new era in $$\\mu $$ <math> <mi>\u03bc</mi> </math> and $$\\tau $$ <math> <mi>\u03c4</mi> </math> physics. In the context of general two Higgs doublet model, the discrepancy can be explained via one-loop exchange of sub-TeV exotic scalar and pseudoscalars, namely H and A, that have flavor changing neutral couplings $$\\rho _{\\tau \\mu }$$ <math> <msub> <mi>\u03c1</mi> <mrow> <mi>\u03c4</mi> <mi>\u03bc</mi> </mrow> </msub> </math> and $$\\rho _{\\mu \\tau }$$ <math> <msub> <mi>\u03c1</mi> <mrow> <mi>\u03bc</mi> <mi>\u03c4</mi> </mrow> </msub> </math> at $$\\sim 20$$ <math> <mrow> <mo>\u223c</mo> <mn>20</mn> </mrow> </math> times the usual tau Yukawa coupling, $$\\lambda _\\tau $$ <math> <msub> <mi>\u03bb</mi> <mi>\u03c4</mi> </msub> </math> . Taking $$\\rho _{\\ell \\ell ^\\prime }\\sim \\lambda _{ \\mathrm min(\\ell , \\ell ^\\prime )}$$ <math> <mrow> <msub> <mi>\u03c1</mi> <mrow> <mi>\u2113</mi> <msup> <mi>\u2113</mi> <mo>\u2032</mo> </msup> </mrow> </msub> <mo>\u223c</mo> <msub> <mi>\u03bb</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mi>\u2113</mi> <mo>,</mo> <msup> <mi>\u2113</mi> <mo>\u2032</mo> </msup> <mo>)</mo> </mrow> </msub> </mrow> </math> , we show that the above solution to muon $$g-2$$ <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math> then predicts enhanced rates of various charged lepton flavor violating processes, which should be accessible at upcoming experiments. We cover muon related processes such as $$\\mu \\rightarrow e \\gamma $$ <math> <mrow> <mi>\u03bc</mi> <mo>\u2192</mo> <mi>e</mi> <mi>\u03b3</mi> </mrow> </math> , $$\\mu \\rightarrow eee$$ <math> <mrow> <mi>\u03bc</mi> <mo>\u2192</mo> <mi>e</mi> <mi>e</mi> <mi>e</mi> </mrow> </math> and $$\\mu N \\rightarrow e N$$ <math> <mrow> <mi>\u03bc</mi> <mi>N</mi> <mo>\u2192</mo> <mi>e</mi> <mi>N</mi> </mrow> </math> , and $$\\tau $$ <math> <mi>\u03c4</mi> </math> decays $$\\tau \\rightarrow \\mu \\gamma $$ <math> <mrow> <mi>\u03c4</mi> <mo>\u2192</mo> <mi>\u03bc</mi> <mi>\u03b3</mi> </mrow> </math> and $$\\tau \\rightarrow \\mu \\mu \\mu $$ <math> <mrow> <mi>\u03c4</mi> <mo>\u2192</mo> <mi>\u03bc</mi> <mi>\u03bc</mi> <mi>\u03bc</mi> </mrow> </math> . A similar one-loop diagram with $$\\rho _{e\\tau }= \\rho _{\\tau e} = \\mathcal{O}(\\lambda _e)$$ <math> <mrow> <msub> <mi>\u03c1</mi> <mrow> <mi>e</mi> <mi>\u03c4</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>\u03c1</mi> <mrow> <mi>\u03c4</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mi>O</mi> <mrow> <mo>(</mo> <msub> <mi>\u03bb</mi> <mi>e</mi> </msub> <mo>)</mo> </mrow> </mrow> </math> induces $$\\mu \\rightarrow e\\gamma $$ <math> <mrow> <mi>\u03bc</mi> <mo>\u2192</mo> <mi>e</mi> <mi>\u03b3</mi> </mrow> </math> , bringing the rate right into the sensitivity of the MEG II experiment. The $$\\mu e\\gamma $$ <math> <mrow> <mi>\u03bc</mi> <mi>e</mi> <mi>\u03b3</mi> </mrow> </math> dipole can be probed further by $$\\mu \\rightarrow 3e$$ <math> <mrow> <mi>\u03bc</mi> <mo>\u2192</mo> <mn>3</mn> <mi>e</mi> </mrow> </math> and $$\\mu N \\rightarrow eN$$ <math> <mrow> <mi>\u03bc</mi> <mi>N</mi> <mo>\u2192</mo> <mi>e</mi> <mi>N</mi> </mrow> </math> . With its promised sensitivity range and ability to use different nuclei, the $$\\mu N \\rightarrow eN$$ <math> <mrow> <mi>\u03bc</mi> <mi>N</mi> <mo>\u2192</mo> <mi>e</mi> <mi>N</mi> </mrow> </math> conversion experiments can not only make discovery, but access the extra diagonal quark Yukawa couplings $$\\rho _{qq}$$ <math> <msub> <mi>\u03c1</mi> <mrow> <mi>qq</mi> </mrow> </msub> </math> . For the $$\\tau $$ <math> <mi>\u03c4</mi> </math> lepton, we find that $$\\tau \\rightarrow \\mu \\gamma $$ <math> <mrow> <mi>\u03c4</mi> <mo>\u2192</mo> <mi>\u03bc</mi> <mi>\u03b3</mi> </mrow> </math> would probe $$\\rho _{\\tau \\tau }$$ <math> <msub> <mi>\u03c1</mi> <mrow> <mi>\u03c4</mi> <mi>\u03c4</mi> </mrow> </msub> </math> down to $$\\lambda _\\tau $$ <math> <msub> <mi>\u03bb</mi> <mi>\u03c4</mi> </msub> </math> or lower, while $$\\tau \\rightarrow 3\\mu $$ <math> <mrow> <mi>\u03c4</mi> <mo>\u2192</mo> <mn>3</mn> <mi>\u03bc</mi> </mrow> </math> would probe $$\\rho _{\\mu \\mu }$$ <math> <msub> <mi>\u03c1</mi> <mrow> <mi>\u03bc</mi> <mi>\u03bc</mi> </mrow> </msub> </math> to $$\\mathcal{O}(\\lambda _{\\mu })$$ <math> <mrow> <mi>O</mi> <mo>(</mo> <msub> <mi>\u03bb</mi> <mi>\u03bc</mi> </msub> <mo>)</mo> </mrow> </math> ."
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