Hidden sector explanation of $B$-decay and cosmic-ray anomalies

There are presently several discrepancies in $b\to s{\ell }^{+}{\ell }^{-}$ decays of $B$ mesons suggesting new physics coupling to $b$ quarks and leptons. We show that a $Z^{\prime }$, with couplings to quarks and muons that can explain the $B$-decay anomalies, can also couple to dark matter in a way that is consistent with its relic abundance, direct detection limits, and hints of indirect detection. The latter include possible excess events in antiproton spectra recently observed by the AMS-02 experiment. We present two models, having a heavy (light) $Z^{\prime }$ with $m_{Z^{\prime }}\sim 600(12)\mathrm{GeV}$ and fermionic dark matter with mass $m_{\chi }\sim 50(2000)\mathrm{GeV}$, producing excess antiprotons with energies of $\sim 10(300)\mathrm{GeV}$. The first model is also compatible with fits for the Galactic center GeV gamma-ray excess.

Figure 1

Solid (red): predicted branching ratio for $Z\to 4\mu$ via $Z\to Z^{\prime }{\mu }^{+}{\mu }^{-}$ for light $Z^{\prime }$, $m_{Z^{\prime }}=12\mathrm{GeV}$, versus $g_l$. Horizontal lines denote the $1\sigma$ experimentally allowed region. Vertical line is upper limit from $\nu$ trident production.

Figure 2

Allowed regions from flavor constraints, for several values of $n_q\equiv g_q/g_l$; dark (blue) band gives observed $R_K$. The preferred couplings from dark matter constraints (for the heavy $Z^{\prime }$ model) are shown by the vertical red dashed line (from the $n_q=2$, $n_{\chi }=5$ model, where $n_q=g_q/g_l$ and $n_{\chi }=g_{\chi }/g_q$).

Figure 3

The UV scale $\mathrm{\Lambda }$ where ${\alpha }_{\chi }=g_{\chi }^2/4\pi =1$, versus $m_{Z^{\prime }}$, using the relic density value of $g_{\chi }$ from (33) at the scale $m_{\chi }=70\mathrm{GeV}$ as the IR boundary condition for renormalization group (RG) running.

Figure 4

Left: ATLAS limit on $pp\to Z^{\prime }\to \mu \overline{\mu }$ production and decay, and predictions of two models that are close to the constraint; right: same for $pp\to Z^{\prime }\to b\overline{b}$ or $t\overline{t}$ as limited by searches for dijet or $t\overline{t}$ final states. The dijet limit is adjusted upward from the published value of $\sigma B_{qq}A$ by assuming the event acceptance is $A=0.6$ [64].

Figure 5

Antiproton spectra from $\chi \chi \to Z^{\prime }{Z}^{\prime }\to b\overline{b}b\overline{b}$ for $m_{Z^{\prime }}=12\mathrm{GeV}$ and several dark matter masses, compared to the best fit $\chi \chi \to Z^{\prime }{Z}^{\prime }\to q\overline{q}q\overline{q}$ spectra found in Ref. [27].

Figure 6

Values of $g_{\chi }$ and $f$ that give the correct relic density for $m_{\chi }=1950\mathrm{GeV}$ (MED and MAX propagation models) and $m_{\chi }=1800\mathrm{GeV}$ (MIN model).

Figure 7

Values of $m_{\phi }$ versus $f$ that give the observed antiproton excess at high energies, for the respective cosmic ray propagation models as labeled. The orange region is excluded by CMB constraints for DM with $m_{\chi }=1800\mathrm{GeV}$. For all curves $g_{\chi }$ is taken to be the value that gives the correct relic density [Eq. (46)]. Where two values of $g_{\chi }$ give the correct relic density (see Fig. 6 where $g_{\chi }$ can be double-valued), the larger one is used, since this requires a smaller Sommerfeld enhancement for the Galactic $\overline{p}$ signal.