Abstract
Recent progress on muon $g-2$ measurement prompts one to take it even more seriously. In the general two Higgs doublet model that allows extra Yukawa couplings, we take a simplified approach of single enhanced coupling. We fix the charged lepton flavor violating coupling, $\rho_{\tau\mu} = \rho_{\mu\tau}$, via the one-loop mechanism, for illustrative masses of the heavy scalar $H$ and pseudoscalar $A$, where we assume $m_A = m_{H^+}$. Since extra top Yukawa couplings are plausibly the largest, we turn on $\rho_{tt}$ and find that LHC search for $gg \to H,\,A \to \tau\mu$ gives more stringent bound than from $\tau\to \mu\gamma$ with two-loop mechanism. Turning on a second extra top Yukawa coupling, $\rho_{tc}$, can loosen the bound on $\rho_{tt}$, but LHC constraints can again be more stringent than from $B \to D\mu\nu$ vs $De\nu$ universality. This means that evidence for $H,\,A \to \tau\mu$ may yet emerge with full LHC Run 2 data, while direct search for $\tau^\pm\mu^\mp bW^+$ or $t\bar cbW^+$ (plus conjugate) may also bear fruit.
Highlights
After extended meticulous efforts, the Fermilab Muon g − 2 experiment announced recently their first measurement [1], aμðFNALÞ 1⁄4 116592040ð54Þ × 10−11 ð0.46 ppmÞ
Taking ρττ ≲ OðλτÞ to keep the one-loop effect small, the large ρτμ needed for muon g − 2 can induce τ → μγ with finite ρtt [8] through the two-loop diagram of Fig. 1, which places a bound on ρttρτμ, where the Belle experiment has recently updated [24] with full data
Referring to the 4.2σ “white space of disagreement” between theory and experiment, the question “What monsters may be lurking there?” from the April 7 announcement presentation by the Muon g − 2 experiment became the quote of the day
Summary
The Fermilab Muon g − 2 experiment announced recently their first measurement [1], aμðFNALÞ 1⁄4 116592040ð54Þ × 10−11 ð0.46 ppmÞ. The alignment that cγ or h–H mixing is small, can account for Eq (3) without requiring ρτμ to be small, which is analogous [22] to another FCNC process, t → ch (with coupling ρtccγ) This is the starting point for a one-loop mechanism [see Fig. 1 (left)] to account for the muon g − 2 anomaly [9,10], originally stimulated by the CMS hint [19] for h → τμ. Taking ρττ ≲ OðλτÞ to keep the one-loop effect small, the large ρτμ needed for muon g − 2 can induce τ → μγ with finite ρtt [8] through the two-loop diagram of Fig. 1 (right), which places a bound on ρttρτμ, where the Belle experiment has recently updated [24] with full data. We find the bound to be weaker than the bounds from τ decays discussed here
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