Large mass splittings for fourth generation fermions allowed by LHC Higgs boson exclusion

In the context of the standard model with a fourth generation, we explore the allowed mass spectra in the fourth-generation quark and lepton sectors as functions of the Higgs mass. Using the constraints from unitarity and oblique parameters, we show that a heavy Higgs allows large mass splittings in these sectors, opening up new decay channels involving $W$ emission. Assuming that the hints for a light Higgs do not yet constitute an evidence, we work in a scenario where a heavy Higgs is viable. A Higgs heavier than $\sim 800\mathrm{GeV}$ would in fact necessitate either a heavy quark decay channel $t^{\prime }\to b^{\prime }W/b^{\prime }\to t^{\prime }W$ or a heavy lepton decay channel ${\tau }^{\prime }\to {\nu }^{\prime }W$ as long as the mixing between the third and fourth generations is small. This mixing tends to suppress the mass splittings and hence the $W$-emission channels. The possibility of the $W$-emission channel could substantially change the search strategies of fourth-generation fermions at the LHC and impact the currently reported mass limits.

Figure 1

The perturbative unitarity bounds on $(m_{t^{\prime }},m_{b^{\prime }})$ are shown above as dashed-lines for $\sin {\theta }_{34}=0.0$ (green/light) and 0.3 (blue/dark). The solid lines are obtained from the analytical expression for the unitarity bound given in 74 by substituting the respective values of $\sin {\theta }_{34}$. The corresponding bounds on the fourth-generation lepton masses are $m_{{\tau }^{\prime },{\nu }^{\prime }}<1.2\mathrm{TeV}$ [74].

Figure 2

The 95% C.L. allowed regions in the $m_h–{\Delta }_q$ plane. In the top two panels, ${\Delta }_{\ell }$ is varied over $|{\Delta }_{\ell }|\le 200\mathrm{GeV}$, while in the bottom two panels ${\Delta }_{\ell }$ is restricted to be less than $M_W$. In the left two panels, ${\theta }_{34}$ is varied over $\sin {\theta }_{34}\le 0.3$, while in the right two panels, ${\theta }_{34}$ has been fixed to zero (no mixing). The parameters $m_q$ and $m_l$ are varied over their complete allowed range. The grey shaded region is excluded at 95% by the LHC data. The dashed blue lines correspond to $|{\Delta }_q|=m_W$.

Figure 3

The 95% C.L. allowed regions in the $m_h–{\Delta }_{\ell }$ plane. In the top two panels, ${\Delta }_q$ is varied over $|{\Delta }_q|\le 200\mathrm{GeV}$, while in the bottom two panels ${\Delta }_q$ is restricted to be less than $M_W$. In the left two panels, ${\theta }_{34}$ is varied over $\sin {\theta }_{34}\le 0.3$, while in the right two panels, ${\theta }_{34}$ has been fixed to zero (no mixing). The parameters $m_q$ and $m_l$ are varied over their complete allowed range. The grey shaded region is excluded at 95% by the LHC data. The dashed blue lines correspond to $|{\Delta }_{\ell }|=m_W$.

Figure 4

The 95% C.L contours in the ${\Delta }_q–{\Delta }_{\ell }$ plane, for $m_h=400\mathrm{GeV}$ (black dotted lines), $m_h=600\mathrm{GeV}$ (red dashed lines) and $m_h=800\mathrm{GeV}$ (blue/solid), respectively. The left (right) panel shows the results when $\sin {\theta }_{34}=0.0(0.3)$. All the other parameters are varied over their $2\sigma$ allowed ranges. The vertical blue dashed lines correspond to $|{\Delta }_q|=M_W$, while the horizontal green (dotted) lines correspond to $|{\Delta }_{\ell }|=M_W$.

Figure 5

Shaded region in the left (right) panel indicates the values of the branching ratios of $t^{\prime }\to b^{\prime }W$ ($b^{\prime }\to t^{\prime }W$) allowed at 95% C.L. by all the constraints considered in this paper.

Figure 6

Allowed values of $m_{t^{\prime }}-m_{b^{\prime }}$ (shaded region) for $m_h=600\mathrm{GeV}$ as a function of $\sin {\theta }_{34}$ after marginalizing over the other NP parameters.