Search for a Light Higgs Boson in Single-Photon Decays of $\mathrm{\Upsilon }(1S)$ Using $\mathrm{\Upsilon }(2S)\to {\pi }^{+}{\pi }^{-}\mathrm{\Upsilon }(1S)$ Tagging Method

We search for a light Higgs boson ($A^0$) decaying into a ${\tau }^{+}{\tau }^{-}$ or ${\mu }^{+}{\mu }^{-}$ pair in the radiative decays of $\mathrm{\Upsilon }(1S)$. The production of $\mathrm{\Upsilon }(1S)$ mesons is tagged by $\mathrm{\Upsilon }(2S)\to {\pi }^{+}{\pi }^{-}\mathrm{\Upsilon }(1S)$ transitions, using $158\times {10}^6$ $\mathrm{\Upsilon }(2S)$ events accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant $A^0$ signals in the mass range from the ${\tau }^{+}{\tau }^{-}$ or ${\mu }^{+}{\mu }^{-}$ threshold to $9.2\mathrm{GeV}/c^2$ are observed. We set the upper limits at 90% credibility level (C.L.) on the product branching fractions for $\mathrm{\Upsilon }(1S)\to \gamma A^0$ and $A^0\to {\tau }^{+}{\tau }^{-}$ varying from $3.8\times {10}^{-6}$ to $1.5\times {10}^{-4}$. Our results represent an approximately twofold improvement on the current world best upper limits for the $\mathrm{\Upsilon }(1S)\to \gamma A^0(\to {\tau }^{+}{\tau }^{-})$ production. For $A^0\to {\mu }^{+}{\mu }^{-}$, the upper limits on the product branching fractions for $\mathrm{\Upsilon }(1S)\to \gamma A^0$ and $A^0\to {\mu }^{+}{\mu }^{-}$ are at the same level as the world average limits, and vary from $3.1\times {10}^{-7}$ to $1.6\times {10}^{-5}$. The upper limits at 90% credibility level on the Yukawa coupling $f_{\mathrm{\Upsilon }(1S)}$ and mixing angle $\sin {\theta }_{A^0}$ are also given.

Figure 1

The (a) $E^{*}(\gamma )$ and (b) $M({\mu }^{+}{\mu }^{-})$ distributions from the $\mathrm{\Upsilon }(2S)$ data sample.

Figure 2

The fitted result corresponding to the maximum local significance of $3.5\sigma$ with $A^0$ mass fixed at $9.2\mathrm{GeV}/c^2$ for $A^0\to {\tau }^{+}{\tau }^{-}$. The blue solid curves show the best fitted result, and the red dashed curves show the fitted total backgrounds. The green curves show the signal component.

Figure 3

The fitted result corresponding to the maximum local significance of $3.0\sigma$ with $A^0$ mass fixed at $8.51\mathrm{GeV}/c^2$ for $A^0\to {\mu }^{+}{\mu }^{-}$. The blue solid curves show the best fitted result, and the red dashed curves show the fitted total backgrounds. The green curves show the signal component.

Figure 4

The (a),(b) statistical significances, (c),(d) upper limits at 90% C.L. on $\mathcal{B}[\mathrm{\Upsilon }(1S)\to \gamma A^0]\mathcal{B}(A^0\to {\tau }^{+}{\tau }^{-})$ ($B_1{B}_2$) and $\mathcal{B}[\mathrm{\Upsilon }(1S)\to \gamma A^0]\mathcal{B}(A^0\to {\mu }^{+}{\mu }^{-})$ ($B_1{B}_3$), and (e),(f) upper limits at 90% C.L. on $f_{\mathrm{\Upsilon }(1S)}^2\mathcal{B}(A^0\to {\tau }^{+}{\tau }^{-})$ ($f_{\mathrm{\Upsilon }(1S)}^2{B}_2$) and $f_{\mathrm{\Upsilon }(1S)}^2\mathcal{B}(A^0\to {\mu }^{+}{\mu }^{-})$ ($f_{\mathrm{\Upsilon }(1S)}^2{B}_3$) as a function of $m_{A^0}$. The blue curves show the Belle results, and the red curves show the BaBar results [29, 30].

Figure 5

The surviving parameter space on the plane of $\sin {\theta }_{A^0}$ and $m_{A^0}$. The constraints from LEP [50] (direct production of Higgs), BESIII [51] ($J/\psi$ decay), Belle ($\mathrm{\Upsilon }(1S)$ decay), LHCb [52, 53] ($B^{+/0}$ decay), NA62 [54, 55, 56] ($K^{+}$ decay), KTeV [13, 57, 58] ($K_L$ decay), CHARM [13, 59, 60, 61, 62] (beam dump), PS191 [63] (beam dump), SN1987A [64], BBN [65], and the prospect of future SHiP [13, 62] (beam dump) are shown.