LHC constraints on a $\mathbf{(}B-L{\mathbf{)}}_3$ gauge boson

In this paper, we explore the constraints that the LHC can place on a massive gauge boson $X$ that predominantly couples to the third generation of fermions. Such a gauge boson arises in scenarios where the $B-L$ of the third generation is gauged. We focus on the mass range $10\le m_X\lesssim 2m_W$, where current constraints are lacking, and develop a dedicated search strategy. For this mass range, we show that (semi)-leptonic $b^{+}{b}^{-}{\tau }^{+}{\tau }^{-}$ is the optimal channel to look for the $X$ at the LHC. The QCD production of $b$ quarks, combined with the cleanliness of the leptons coming from the decay of the $\tau$, allows us to detect the $X$ gauge boson with couplings of $g_X\sim (0.005–0.01)$, for $m_X<50\mathrm{GeV}$, and a coupling of $O(0.1)$ for a heavier $X$ gauge boson with $100{\mathrm{fb}}^{-1}$ of integrated luminosity. This is about a factor of 2–10 improvement over previous constraints coming from the decay of $\mathrm{\Upsilon }\to {\tau }^{+}{\tau }^{-}$. Extrapolating to the full HL-LHC luminosity of $3000{\mathrm{fb}}^{-1}$, the bounds on $g_X$ can be enhanced by another factor of $\sqrt{2}$ for $m_X<50\mathrm{GeV}$.

Figure 1

The branching ratio of $X$ to various final states for $\tan \beta =1$ (left) and $\tan \beta =5$ (right), with the assumption that the new scalars and the sterile neutrino are heavier than $m_X/2$. The branching ratio differs significantly depending on the value of $\tan \beta$. The highest branching ratio in the heavy mass region is to ${\tau }^{+}{\tau }^{-}$, due to a combination of large $q_X$ and large electromagnetic charge.

Figure 2

The signal Feynman diagrams corresponding to the production of $b\overline{b}{\ell }^{+}{\ell }^{-}{\cancel{E}}_T$ final state.

Figure 3

The SM backgrounds to $b\overline{b}{\ell }^{+}{\ell }^{-}+{\cancel{E}}_T$ production at the LHC. In these diagrams, $\ell =\mu$, $e$, and ${\tau }_{\ell }$ refers to a $\tau$ that decays leptonically. The first line in the Feynman diagrams corresponds to the first mentioned background in Eq. (6). The second and third backgrounds in Eq. (6) are shown in the second line of these Feynman diagrams, where the gauge bosons decay to ${\tau }_{\ell }$ and $\ell$, respectively.

Figure 4

Left: The area-normalized distribution of invariant mass of the two leptons ($m_{\ell \ell }$) for one of the signal benchmarks $m_X=30\mathrm{GeV}$, compared with the dominant backgrounds. These distributions are after the basic cuts, and $Z^{(\star )}\to \ell \ell$ and ${\gamma }^{*}\to \ell \ell$ have been listed as separate contributions since the interference between them is small. To make the distribution less cluttered, we did not include the reducible backgrounds [Eq. (12)]; however, the distributions of $c\overline{c}{\ell }^{+}{\ell }^{-}$ and $j_l{j}_l{\ell }^{+}{\ell }^{-}$ behave like $b\overline{b}{\ell }^{+}{\ell }^{-}$, and $c\overline{c}{\tau }_{\ell }^{+}{\tau }_{\ell }^{-}$ looks similar to $b\overline{b}{\tau }_{\ell }^{+}{\tau }_{\ell }^{-}$. Right: The area-normalized $m_{\ell \ell }$ distribution for various $X$ masses are shown. The distribution of $m_{\ell \ell }$ becomes less faithful to $m_X$ as we increase the mass of $X$.

Figure 5

The $m_{\ell \ell }$ distribution of the backgrounds scaled according to their cross section. The signal benchmark chosen for this plot is $(m_X,g_X)=(30\mathrm{GeV},0.02)$. However, since the cross section of the signal is very small compared to the backgrounds, we multiplied the signal distribution by a factor of 10 to make it more visible in the plot. This distribution is only after the basic cuts. By imposing $m_{\ell \ell }<25$, we can keep most of the signal, while throwing away a large portion of the background.

Figure 6

The comparison between area-normalized $\mathrm{\Delta }R(ll,{\cancel{E}}_T)$ (left) and $\mathrm{\Delta }\varphi (ll,{\cancel{E}}_T)$ (right) distributions. Only basic cuts have been imposed on these distributions. Even though these two plots are highly correlated, $\mathrm{\Delta }\varphi (ll,{\cancel{E}}_T)$ exhibits a better signal-background separation. That is because the pseudorapidity information of the ${\cancel{E}}_T$ vector is not available at the LHC. Due to the similar behavior of the reducible backgrounds with their corresponding irreducible background, their contribution is ignored in these plots.

Figure 7

The area-normalized distribution of the transverse missing energy after the basic cuts is shown. Similar to previous distribution plots, we have ignored the reducible background’s contribution.

Figure 8

By imposing an optimized cut on the mentioned variables, the LHC can probe the indicated parameter space up to $3\sigma$ significance, with $100{\mathrm{fb}}^{-1}$ integrated luminosity. The solid red line represents the significance with the systematic uncertainties mentioned in the section. The dashed red line is the significance when the systematic uncertainties are half. The green lines show the projected sensitivity at HL-LHC with $3{\mathrm{ab}}^{-1}$ integrated luminosity. The bound from $\mathrm{\Upsilon }\to {\tau }^{+}{\tau }^{-}$ at BABAR [40] in shown in blue. Due to the low efficiency of the trigger cut, our sensitivity to very light $m_X$ is weak; for $20\mathrm{GeV}<m_X<40\mathrm{GeV}$, we have our maximum sensitivity, and then the sensitivity drops again as $m_X$ increases due to a combination of a lower signal cross section and a decline in the discriminatory power of the cuts. In Sec. 3a1, we will motivate and study some variables that enhance the sensitivity to heavier $m_X$ ($>50\mathrm{GeV}$). The presented bounds are for $\tan \beta =5$. However, for any $\tan \beta >1$, the sensitivity is almost the same.

Figure 9

The area-normalized distribution of various benchmarks (left) and the signal-backgrounds comparison (right) with respect to $M_{T2}$ are shown. The signal prefers a small value of $M_{T2}$, whereas the $b\overline{b}{V}_{\ell +{\tau }_{\ell }}{V}_{\ell +{\tau }_{\ell }}$ backgrounds have a broad featureless distribution.

Figure 10

The invariant mass of $b$ and lepton that minimizes $(m_{{\ell }_i{b}_k}-m_t{)}^2+(m_{{\ell }_j{b}_n}-m_t{)}^2$ is shown here. The distribution of both reconstructed tops is very similar, and so we are showing only one combination. The signal distribution, shown in solid blue, is for the benchmark $m_X=80\mathrm{GeV}$. The most important background is $t\overline{t}$, shown in dashed red.

Figure 11

The contribution of $M_{T2}$ and $m_{bl}$ to improving the sensitivity for $m_X=80\mathrm{GeV}$. The dashed line indicates the $3\sigma$ significance with only the basic cuts and $25<m_{\ell \ell }<60\mathrm{GeV}$ with $100{\mathrm{fb}}^{-1}$ integrated luminosity. The solid line is the $3\sigma$ significance with the same amount of luminosity with the basic cuts $+25<m_{\ell \ell }<60\mathrm{GeV}+m_{T2}<16\mathrm{GeV}+m_{b\ell }<100\mathrm{GeV}$. The extra cuts improve the sensitivity by roughly factor of 1.7.

Figure 12

The reach up to $3\sigma$ significance after $100{\mathrm{fb}}^{-1}$ integrated luminosity is shown. The current bound coming from $\mathrm{\Upsilon }\to {\tau }^{+}{\tau }^{-}$ at BABAR [40] excludes the blue region.