Electroweak-charged bound states as LHC probes of hidden forces

We explore the LHC reach on beyond-the-standard model (BSM) particles $X$ associated with a new strong force in a hidden sector. We focus on the motivated scenario where the SM and hidden sectors are connected by fermionic mediators ${\psi }^{+,0}$ that carry SM electroweak charges. The most promising signal is the Drell-Yan production of a ${\psi }^{\pm }{\overline{\psi }}^0$ pair, which forms an electrically charged vector bound state ${\mathrm{\Upsilon }}^{\pm }$ due to the hidden force and later undergoes resonant annihilation into $W^{\pm }X$. We analyze this final state in detail in the cases where $X$ is a real scalar $\varphi$ that decays to $b\overline{b}$, or a dark photon ${\gamma }_d$ that decays to dileptons. For prompt $X$ decays, we show that the corresponding signatures can be efficiently probed by extending the existing ATLAS and CMS diboson searches to include heavy resonance decays into BSM particles. For long-lived $X$, we propose new searches where the requirement of a prompt hard lepton originating from the $W$ boson ensures triggering and essentially removes any SM backgrounds. To illustrate the potential of our results, we interpret them within two explicit models that contain strong hidden forces and electroweak-charged mediators, namely $\lambda$-supersymmetry (SUSY) and non-SUSY ultraviolet extensions of the twin Higgs model. The resonant nature of the signals allows for the reconstruction of the mass of both ${\mathrm{\Upsilon }}^{\pm }$ and $X$, thus providing a wealth of information about the hidden sector.

Figure 1

The collider processes studied in this paper. Here ${\psi }^{+,0}$ are the mediators, new particles that carry SM electroweak (but not color) charge, which we take to be vectorlike fermions. Their Drell-Yan pair production leads to the formation of electroweak-charged bound states due to a hidden force. The annihilation of the electrically charged bound state ${\mathrm{\Upsilon }}^{\pm }$ produces a $W^{\pm }X$ pair, where $X$ is the hidden force carrier. We take $X$ to be either a real scalar $\varphi$, which decays back to the SM via mass mixing with the SM-like Higgs boson, or a dark photon ${\gamma }_d$ that decays via kinetic mixing with the SM photon. The $\varphi \to b\overline{b}$ and ${\gamma }_d\to \ell \ell$ decays are selected, which can be either prompt or displaced on collider time scales.

Figure 2

Reconstructed $M_{Wbb}$ for signal and backgrounds in the analysis of ${\mathrm{\Upsilon }}^{\pm }\to W\varphi$ with prompt $\varphi \to b\overline{b}$, assuming $m_{\varphi }=100\mathrm{GeV}$. The signal distributions are shown for two representative parameter points with $M_{\mathrm{\Upsilon }}=800$, 1000 GeV, taking the hidden force coupling $\lambda =2.5$ and $C=1$. The orange curve shows the fitted total background that was used to calculate the signal significance.

Figure 3

Left: Projected 95% C.L. bounds on $\sigma (\mathrm{\Upsilon })\mathrm{BR}(\mathrm{\Upsilon }\to W\varphi )\mathrm{BR}(\varphi \to b\overline{b})$ from the LHC search for prompt $\varphi \to b\overline{b}$ and $W\to \ell \nu$. See Sec. 2a for details. Right: Projected 95% C.L. bounds on $\sigma (\mathrm{\Upsilon })\mathrm{BR}(\mathrm{\Upsilon }\to W{\gamma }_d)\mathrm{BR}({\gamma }_d\to ee+\mu \mu )$ from the LHC search for prompt ${\gamma }_d\to \ell \ell$ and $W\to {\ell }^{\prime }\nu$. See Sec. 2b for details. In both analyses, the invariant mass cuts were varied according to the hypothetical masses of the BSM particles. However, the cross section limits were computed using local, and not global, significance.

Figure 4

Left: 95% C.L. upper bound on $\sigma (\mathrm{\Upsilon })\mathrm{BR}(\mathrm{\Upsilon }\to W\varphi )\mathrm{BR}(\varphi \to b\overline{b})$ from the LHC search for prompt $W\to \ell \nu$ and displaced $\varphi \to b\overline{b}$. The quantity $c{\tau }_{\varphi }{M}_{\mathrm{\Upsilon }}/(2m_{\varphi })$ approximates the decay length of $\varphi$ in the lab frame. The result is insensitive to $m_{\varphi }$, as can be seen from the small deviation between the solid (s) and dashed (d) curves. The local minimum on the left corresponds to decays inside the ID, while the minimum on the right corresponds to the $\mathrm{HCAL}+\mathrm{MS}$. Right: 95% C.L. upper bound on $\sigma (\mathrm{\Upsilon })\mathrm{BR}(\mathrm{\Upsilon }\to W{\gamma }_d)\mathrm{BR}({\gamma }_d\to \mu \mu )$ from the LHC search for prompt $W\to \ell \nu$ and displaced ${\gamma }_d\to \mu \mu$. Both analyses are described in Sec. 2c. We assume the searches to be background free; hence the cross section bounds for $3000{\mathrm{fb}}^{-1}$ are simply obtained by dividing those in the plots by a factor 10.

Figure 5

Contours of the ratio in Eq. (8) that gives at the LHC with $300{\mathrm{fb}}^{-1}$ the same bound on $\sigma (\mathrm{\Upsilon })$ from the $\mathrm{\Upsilon }\to WX$ and $\mathrm{\Upsilon }\to \ell \nu$ final states. Here we consider prompt $\varphi \to b\overline{b}$ and ${\gamma }_d\to \ell \ell$ decays.

Figure 6

Left: 95% C.L. upper bound on ${\alpha }_{\lambda }$ in $\lambda$-SUSY from the search for prompt $(W\to \ell \nu )(s\to b\overline{b})$ at the LHC with $300{\mathrm{fb}}^{-1}$. In the orange-shaded region the LHC can fully rule out the existence of Higgsino bound states, by setting a limit on ${\alpha }_{\lambda }$ that is below the smallest value required for bound state formation, $4m_s/M_{{\mathrm{\Upsilon }}_{\tilde{h}}}$. Right: 95% C.L. upper bound on ${\alpha }_{\lambda }$ in $\lambda$-SUSY from the search for prompt $W\to \ell \nu$ and displaced $s\to b\overline{b}$ at the LHC with $300{\mathrm{fb}}^{-1}$. The relation ${\alpha }_{\lambda }>4m_s/M_{{\mathrm{\Upsilon }}_{\tilde{h}}}$ that makes bound state formation possible is implicitly assumed to hold. In the region to the left (right) of the vertical dashed line, $s$ decays in the ID ($\mathrm{HCAL}+\mathrm{MS}$). In the region hatched in black the $s$ decays in the ID with boost factor $\gtrsim 10$, making the identification of the DV challenging (see text for details).

Figure 7

Estimate of the scale $\mathrm{\Lambda }$ where perturbativity is lost in the $\lambda$-SUSY model, as a function of the low-energy value of ${\alpha }_{\lambda }$, for representative values of $\kappa$. $\mathrm{\Lambda }$ is defined as the scale where the two-loop contributions to the running of $\lambda$ and $\kappa$ become of the same size as the one-loop terms.

Figure 8

The signal of the exotic fermion bound state in the UV-extended fraternal twin Higgs. The outgoing twin gluons (curly lines) hadronize into twin glueballs. The lightest glueball ${\widehat{G}}_{0^{++}}$ decays to $b\overline{b}$ through the Higgs portal, either promptly or at a macroscopic distance.

Figure 9

95% C.L. exclusions on the UV-extended fraternal twin Higgs from the LHC searches for signals of the exotic fermion bound state ${\mathrm{\Upsilon }}_{\mathcal{K}}^{\pm }$. We set $f=1\mathrm{TeV}$. In black, we show the exclusion from the search for prompt $W\to \ell \nu$ and displaced $\widehat{G}\to b\overline{b}$ with $300{\mathrm{fb}}^{-1}$. The maximum of reach on the left (right) corresponds to $c{\tau }_{\widehat{G}}(M_{{\mathrm{\Upsilon }}_{\mathcal{K}}}/2m_{\widehat{G}})\sim 400(10)\mathrm{cm}$, which optimizes the sensitivity in the $\mathrm{HCAL}+\mathrm{MS}$ (ID). In the region hatched in black the $\widehat{G}$ decays in the ID with boost factor $\gtrsim 10$, making the identification of the DV challenging (see text for details). In orange, we show the current and projected exclusions from the search for ${\mathrm{\Upsilon }}_{\mathcal{K}}^{\pm }\to \ell \nu$. In the area shaded in grey, the exotic quarks decay before the bound state annihilation takes place.