Loop induced $H^{\pm }\to W^{\pm }Z$ decays in the aligned two-Higgs-doublet model

We present a complete one-loop computation of the $H^{\pm }\to W^{\pm }Z$ decay in the aligned two-Higgs-doublet model. The constraints from the electroweak precision observables, perturbative unitarity, vacuum stability, and flavor physics are all taken into account along with the latest Large Hadron Collider searches for the charged Higgs. It is observed that a large enhancement of the branching ratio can be obtained in the limit where there is a large splitting between the charged and pseudoscalar Higgs masses as well as for the largest allowed values of the alignment parameter ${\varsigma }_u$. We find that the maximum possible branching ratio in the case of a large mass splitting between $m_{H^{\pm }}$ and $m_A$ is $\approx {10}^{-3}$ for $m_{H^{\pm }}\in (200,700)\mathrm{GeV}$.

Figure 1

The region of scalar mass splitting in the $|m_{H^{\pm }}-m_H|$ vs the $|m_{H^{\pm }}-m_A|$ plane, allowed by the Higgs signal strength in the diphoton channel, perturbativity bounds on the quartic scalar couplings $|{\lambda }_{2,3,7}|<4\pi$, stability of scalar potential, unitarity of $S$-wave scattering amplitudes, and electroweak precision data.

Figure 2

The regions in the ${\varsigma }_u-{\varsigma }_d$ plane that are allowed by flavor physics data (blue points) and constraints from the $tb$ decay channel of the charged Higgs where $H^{\pm }$ is produced in association with a top quark at the 13 TeV LHC (green points). The regions are shown for two choices of the charged Higgs mass $m_{H^{\pm }}=200$ and 500 GeV.

Figure 3

The regions in the ${\varsigma }_u-{\varsigma }_{\ell }$ plane that are allowed by flavor physics data (blue points) and constraints from the $\tau {\nu }_{\tau }$ decay channel of the charged Higgs where $H^{\pm }$ is produced in association with a top quark at the 13 TeV LHC (green points). The regions are shown for two choices of the charged Higgs mass $m_{H^{\pm }}=200$ and 500 GeV.

Figure 4

The boson-loop triangle diagrams for $H^{+}\to W^{+}Z$ in the ’t Hooft-Feynman gauge.

Figure 5

The boson-loop and tadpole diagrams for $H^{+}\to W^{+}Z$ in the ’t Hooft-Feynman gauge.

Figure 6

The fermion-loop diagrams for $H^{+}\to W^{+}Z$ in the ’t Hooft-Feynman gauge. Note that $i$ in $u_i$, $d_i$, ${\ell }_i$, and ${\nu }_i$ stands for the fermion generation.

Figure 7

The decay width $\mathrm{\Gamma }(H^{+}\to W^{+}Z)$ as a function of $m_H^{+}$ for various values of ${\varsigma }_u$ and ${\varsigma }_d$ with $\cos \tilde{\alpha }=0.95$, $|m_{H^{\pm }}-m_A|>200\mathrm{GeV}$ and $m_H=m_{H^{\pm }}\pm 15\mathrm{GeV}$. The couplings ${\lambda }_{3,7,8}$ take the values allowed by the theoretical constraints, whereas the alignment parameter ${\varsigma }_{\ell }=50$.

Figure 8

Decay width $\mathrm{\Gamma }(H^{+}\to W^{+}Z)$ as a function of ${\varsigma }_u$ for different mass splittings between charged and $CP$-odd scalars with $\cos \tilde{\alpha }=0.95$. The parameter ${\varsigma }_d$ is varied in the allowed range, whereas the other parameters are fixed as discussed in the text. The figures are shown for two choices of charged Higgs mass $m_{H^{+}}=200$ and 500 GeV.

Figure 9

The decay width $\mathrm{\Gamma }(H^{+}\to W^{+}Z)$ as a function of $m_A$ for different values of the Yukawa alignment parameter ${\varsigma }_u$ with ${\varsigma }_d=0.1$, ${\varsigma }_{\ell }=50$, $\cos \tilde{\alpha }=0.95$, $m_H=m_{H^{+}}+10\mathrm{GeV}$, and ${\lambda }_{2,3}=0$. The figures are shown for two values of charged Higgs mass $m_{H^{+}}=200$, 500 GeV.

Figure 10

The branching ratio $\mathrm{\Gamma }(H^{+}\to W^{+}Z)$ as a function of $m_A$ for ${\lambda }_{2,3}=0$, ${\varsigma }_d=0.1$, ${\varsigma }_{\ell }=50$, $m_H=m_{H^{+}}+10\mathrm{GeV}$, and $\cos \tilde{\alpha }=0.95$. The other dominant branching ratios of $H^{+}$ are also shown. In the left plot, the solid lines are for ${\varsigma }_u=0.01$, and the dashed lines are for ${\varsigma }_u=1.15$.

Figure 11

The branching ratio $\mathrm{BR}(H^{+}\to W^{+}Z)$ as a function of $m_H^{+}$ for values of ${\varsigma }_u$, ${\varsigma }_d$, and ${\varsigma }_{\ell }$ and the ${\lambda }_{3,7}$ parameters allowed by the theoretical and the experimental constraints discussed in the text.

Figure 12

The cross section of $H^{+}$ production in association with a top quark followed by its decay to $W^{+}Z$ as a function of $m_{H^{+}}$.

Figure 13

The cross-section of $H^{+}$ production through $WZ$ fusion at the 13 TeV LHC, with the form factor $\mathcal{F}$ set to unity and $\mathcal{G}=\mathcal{H}=0$.

Figure 14

$\sigma$ for $H^{\pm }$ production through $WZ$ fusion with subsequent decay of $H^{\pm }$ to $W^{\pm }Z$. The line in green is the current bound from LHC.