Prospects for discovering strongly decaying doubly heavy $T_{bc}$ tetraquark states at LHCb

TL;DR

The paper addresses the search for a strongly decaying doubly heavy tetraquark $T_{bc}$ with $J^P=0^+$ in $pp$ collisions at $\sqrt{s}=13$ TeV at LHCb, focusing on the $T_{bc} \to B^- D^+$ channel. It develops a phenomenological background model including single- and double-parton scattering, and models the signal with a Breit–Wigner distribution convolved with a detector resolution to evaluate discovery prospects. By scanning over $m(T_{bc})$, $\Gamma(T_{bc})$, $\sigma(T_{bc})$, and $\sigma_{eff}$ and computing the significance $Z$, the study provides quantitative requirements on integrated luminosity and production-rate times branching-ratio needed for a $5\sigma$ observation. The results indicate that Run 2–4 data should allow a discovery for moderate cross sections ($\sim 20$–$60$ nb), while Run 5 would extend sensitivity to smaller $\sigma(T_{bc})\times\mathcal{B}$ values; these findings offer concrete guidance for LHCb searches of exotic heavy hadrons and help constrain the $T_{bc}$ parameter space.

Abstract

We investigate the discovery potential of the $T_{bc}$ states with $J^P = 0^+$ in proton-proton ($pp$) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~\mathrm{TeV}$. The study focuses on the decay channel $T_{bc} \to B^- D^+$. A phenomenological approach is employed to construct the background model based on the associated production of $B$ and $D$ mesons, incorporating previously published LHCb results. Background processes are simulated using $\texttt{MadGraph5\_aMC@NLO}$ and $\texttt{Pythia8.3}$. We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton-scattering cross section ($σ_{\mathrm{eff}}$) relevant for the $B D$ meson background. The integrated luminosity required for a $5σ$ discovery at LHCb is evaluated under various assumptions. We find that a $5σ$ observation is achievable for a production cross section of $103~\mathrm{nb}$, which is expected to be within reach during Run~4. In addition, we estimate the minimum observable $σ(T_{bc}) \times \mathrm{BR}(T_{bc} \to B^- D^+)$ for a $5σ$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

Figures (5)

• Figure 1: Comparison of the rapidity difference $\Delta y$ between the $B^\mp$ and $D^\pm$ mesons for the DPS background. The black dashed line represents published LHCb Run 2 data, while the red solid and blue dotted lines correspond to the reweighted and unweighted DPS simulations, respectively. Results are shown for $\sigma_{\rm eff} = 15~\mathrm{mb}$.
• Figure 2: Differential cross sections for associated $B^\mp D^\pm$ production via SPS and DPS mechanisms. Left: $\Delta\phi$ distribution; middle: $\Delta y$ distribution; right: invariant mass $M(B^\mp D^\pm)$ distribution, shown for $\sigma_{\mathrm{eff}} = 15$ mb. The upper (lower) panels correspond to the SPS prediction obtained at NLO in the 3FNS (LO in the 4FNS). The SPS contribution is shown as a red shaded band, with uncertainties dominated by renormalization and factorization scale variations, while the DPS contribution is shown as a blue hatched band. In the upper panels, the black solid line denotes the combined SPS+DPS central prediction, defining the baseline background scenario. In the lower panels, the red dashed line indicates the maximal SPS contribution obtained from the upper bound of the LO 4FNS prediction, while the black solid line shows the corresponding SPS (max)+DPS prediction, defining the conservative maximal background scenario.
• Figure 3: Combined distribution of the $T_{bc}$ signal and background in the $BD$ invariant-mass spectrum for an effective DPS cross section $\sigma_{\mathrm{eff}} = 15 ~\mathrm{mb}$, $m(T_{bc})=7229~\mathrm{MeV}$, and $\Gamma(T_{bc}) = 10~\mathrm{MeV}$. The black curve represents the associated $B^\mp D^\pm$ background, the red curve the $T_{bc}$ signal, and the blue curve their sum.
• Figure 4: Statistical significance $Z$ of the $T_{bc}$ signal in the $BD$ invariant-mass spectrum as a function of the integrated luminosity $\mathcal{L}_{\mathrm{int}}$, for different $T_{bc}$ mass and width assumptions and values of the effective DPS cross sections $\sigma_{\mathrm{eff}}$. A baseline background scenario (DPS + NLO SPS in the 3FNS), a production cross section $\sigma(T_{bc})=103$ nb, and a branching fraction $\mathcal{B}(T_{bc}\to B^-D^+)=0.5$ are assumed. The left, middle, and right panels correspond to $\sigma_{\mathrm{eff}}=5~\mathrm{mb}$, $15~\mathrm{mb}$, and $30~\mathrm{mb}$, respectively. Different colors denote different $T_{bc}$ mass and width assumptions: $M=7167~\mathrm{MeV}$ with $\Gamma=0.5,~5~\mathrm{MeV}$, and $M=7229~\mathrm{MeV}$ with $\Gamma=10,~40~\mathrm{MeV}$, where $M \equiv m(T_{bc})$ and $\Gamma \equiv \Gamma(T_{bc})$. The dashed line indicates the $5\sigma$ discovery threshold.
• Figure 5: Discovery significance of $T_{bc}$ as a function of integrated luminosity for different $T_{bc}$ mass and width parameters, assuming the baseline background scenario, $\sigma(T_{bc}) = 103~\mathrm{nb}$, and $\mathcal{B}(T_{bc}\to B^-D^+)=0.5$.