Establishing the Primary HEFT as a Precision Benchmark for UV-HEFT Matching

Abstract

We match the real Higgs triplet model (RHTM) onto HEFT under different parameter choices and power-counting schemes, thereby obtaining several representative HEFT formulations and clarifying their relations. We establish the primary HEFT (pHEFT) as a benchmark framework, demonstrating that alternative HEFT constructions can be systematically derived from it. A key advantage of the pHEFT construction is its parameter choice, which maintains linear relations between the UV Lagrangian parameters and squared heavy masses. By strictly employing the inverse squared heavy masses as the expansion parameters without imposing additional constraints, pHEFT preserves maximal ultraviolet (UV) information and ensures higher perturbative accuracy by avoiding the additional truncations inherent in more complex, non-linear formulations or extra constraints. Through the analysis of the $Z_2$-symmetric real singlet model and the 2HDM, we illustrate the criteria for identifying viable primary HEFT constructions in UV models with scalar extensions. Furthermore, for the first time, we derive the HEFT operators of the RHTM involving fermions.

Figures (6)

• Figure 1: Comparison between the UV model and the pHEFT and dHEFT in the differential cross-section of $hh\rightarrow hh$, for a center-of-mass energy $\sqrt{s}=300\,\mathrm{GeV}$ and a scattering angle $\theta_0=\pi/4$. We set $\xi=0.01$, $m_{\phi^\pm}=450\,\mathrm{GeV}$, and $m_K=520\,\mathrm{GeV}$. The Higgs mass and electroweak vacuum expectation value are fixed to their experimentally measured values: $m_h=125\,\mathrm{GeV}$ and $v_\text{EW}=246\,\mathrm{GeV}$. The top panel presents the cross section over $s_\gamma\in[-0.1, 0.1]$, while the three lower panels provide detailed views of three selected subintervals.
• Figure 2: Similar to Fig. \ref{['fig:xs_hh_pHEFT_mK520']}, now shown for $\sqrt{s}=600\,\mathrm{GeV}$, $\theta_0=\pi/8$, $\xi=0.005$, $m_{\phi^\pm}=700\,\mathrm{GeV}$, and $m_K=820\,\mathrm{GeV}$. When $s_\gamma>0.084$, the model becomes unstable because the boundedness-from-below conditions ($Z_1, Z_2\geq 0$ and $|Z_3|\leq 2\sqrt{Z_1 Z_2}$Song:2025kjp) are violated.
• Figure 3: Similar to Fig. \ref{['fig:xs_hh_pHEFT_mK520']}, now shown for $\sqrt{s}=900\,\mathrm{GeV}$, $\theta_0=\pi/2$, $\xi=0.1$, $m_{\phi^\pm}=1000\,\mathrm{GeV}$, and $m_K=1200\,\mathrm{GeV}$. The value $\xi = 0.1$ is chosen for illustration only and is not intended to be phenomenologically viable, having been excluded by existing measurements. When $s_\gamma>-0.064$, the model becomes unstable because of the boundedness-from-below conditions ($Z_1, Z_2\geq 0$ and $|Z_3|\leq 2\sqrt{Z_1 Z_2}$) are violated.
• Figure 4: Comparison between the UV model and the pHEFT and $Z_2$-HEFT in the differential cross-section of $hh\rightarrow hh$, for a center-of-mass energy $\sqrt{s}=300\,\mathrm{GeV}$ and a scattering angle $\theta_0=\pi/4$. We set $\xi=0.01$, $m_{\phi^\pm}=499\,\mathrm{GeV}$, and $m_K=500\,\mathrm{GeV}$. The Higgs mass and electroweak vacuum expectation value are fixed to their experimentally measured values: $m_h=125\,\mathrm{GeV}$ and $v_\text{EW}=246\,\mathrm{GeV}$. The top panel presents the cross section over $s_\gamma\in[-0.1, 0.1]$, while the three lower panels provide detailed views of three selected subintervals.
• Figure 5: Similar to Fig. \ref{['fig:xs_hh_Z2HEFT_mC499']}, now shown for $\sqrt{s}=300\,\mathrm{GeV}$, $\theta_0=\pi/4$, $\xi=0.01$, $m_{\phi^\pm}=498\,\mathrm{GeV}$, and $m_K=500\,\mathrm{GeV}$.