Focusing on the bosonic sector, we make a first matching of the real Higgs triplet extension (RHTE) of the standard model to the Higgs effective field theory (HEFT), which is also known as electroweak chiral Lagrangian (EWChL), including effects of the NLO HEFT operators at tree level. In the RHTE, the ratio $\textit{ξ}$ of two VEVs separately from triplet and doublet is a tiny quantity, due to the constrained custodial symmetry violation. Based on the nonlinear representation [1] of RHTE and functional method, we get the HEFT in the power counting of $\textit{ξ}$. By comparing its phenomenological results of $\textit{hh}$ → $\textit{hh}$, $\textit{WW}$ → $\textit{hh}$, $\textit{ZZ}$ → $\textit{hh}$ to SMEFT’s, we show its convergence property is as good as SMEFT’s. Besides we explicitly show that the HEFT is available in the phase transition region where SMEFT fails.

South Korea

Huayang Song

China

Xia Wan

Matching the real Higgs triplet extension of Standard Model to HEFT

We introduce a non-linear representation of ultraviolet (UV) complete model, $\textit{U representation}$, under which matching HEFT to general scalar extensions of the standard model is straightforward. The main idea is to express a scalar multiplet in its symmetric tensor representation rotated by $\textit{U}$ matrices, where $\textit{U}$ matrix is exponential form of Goldstones based on Pauli matrices and meanwhile is a special SU(2) rotation. All together the doublet is expressed in $\textit{U}$ matrix multiplying a doublet column (or a bidoublet matrix), which is composed of physical Higgs. Under these forms, in the UV Lagrangian there leave no mass mixing or kinetic mixing among $\textit{U}$ matrix and physical states, thus the Goldstones could be kept in $\textit{U}$ matrix throughout HEFT matching, and the matching process under functional method is much simplified. As an example, using $\textit{U representation}$ we show a complete matching between HEFT and the real triplet extension of Standard Model in a decoupling scenario.

A non-linear representation of general scalar extensions of the Standard Model for HEFT matching

The new measurement of the W boson mass from the CDF collaboration shows a significant tension with the standard model prediction, which evidences violation of custodial symmetry in the scalar sector. We study the scalar extensions of the standard model, which can be categorized into two classes, the scalar sector with custodial symmetry (Georgi-Machacek model and its generalizations) and the scalar sector without custodial symmetry, and explore how these extensions fit to electroweak precision data and the new CDF   $m_W$  . The favored oblique parameters originate from either the large mass splitting in the multiplet via the loop contribution or the large vacuum expectation value, which breaks custodial symmetry at the tree level. In particular, we find that   $m_W$   GeV new particles are allowed in the scalar extension scenarios.

Jiang-Hao Yu

Custodial symmetry violation in scalar extensions of the standard model  

$ CP $   violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders. We study the   $ CP $   properties of   $ CP $   vertexes between Higgs and gauge boson pairs by defining a   $ CP $   violation phase angle ξ, which indicates the mixture of   $ CP $  -even and   $ CP $  -odd Higgs states in   $ CP $   in new physics. A series of   $ CP $   amplitudes,   $ CP $  , and   $ CP $  , with a   $ CP $   phase angle are studied systematically to explicitly explain why   $ CP $   violation can only be probed independently in the   $ CP $   process. We obtain a novel amplitude decomposition relation that illustrates that if two preconditions (multilinear momentum dependent vertexes, and the current   $ CP $   of   $ CP $   is formally proportional to a photon's polarization vector) are satisfied, a higher-point amplitude can be decomposed into a summation of a series of lower-point amplitudes. As a practical example, the amplitude of the   $ CP $   and   $ CP $   processes can be decomposed into a summation of many   $ CP $   amplitudes. We calculate these amplitudes in the framework of the on-shell scattering amplitude method, considering both massless and massive vector gauge bosons with the   $ CP $   violation phase angle. The above two approaches provide consistent results and clearly reveal the   $ CP $   violation ξ dependence in the amplitudes.

Ke-Yao Feng

You-Kai Wang

Chao Wu

Exploring Amplitudes With Violation Using Decomposition and the On-shell Scattering Amplitude Method  

We calculate the spinor helicity amplitudes of anomalous 
					 decay. After embedding these analytic formulas into the MCFM package, we study the interference effects between the anomalous 
					 process and the SM processes, which are indispensable in the Higgs off-shell region. Subsequently, the constraints on the anomalous couplings are estimated using LHC experimental data.
				

Hua-Rong He

Anomalous 
					 decay and its interference effects on gluon–gluon contribution at the LHC Supported by the National Natural Science Foundation of China (11847168), the Fundamental Research Funds for the Central Universities of China (GK201803019, GK202003018, 1301031995) and the Natural Science Foundation of Shannxi Province, China (2019JM-431, 2019JQ-739)

The diphoton invariant mass distribution from the interference between 
					 and 
					 is almost antisymmetric around the Higgs mass 
					. We propose a new observable 
					, the ratio of the sign-reversed integral around 
					 (e.g. 
					) and the cross-section of the Higgs signal, to quantify this effect. We study 
					 both in the Standard Model (SM) and new physics with various CP violating 
					 couplings. 
					 in SM could reach a value of 10%, while for CP violating 
					 coupling 
					 could range from 10% to −10%, which could probably be detected in the HL-LHC experiments. 
					 with both CP violating 
					 and 
					 couplings is also studied, and its range of values is found to be slightly larger.
				

Probing the CP violating Hγγ coupling using interferometry Supported by the National Natural Science Foundation of China (11405102, 11847168), the Fundamental Research Funds for the Central Universities of China (GK201603027, GK201803019, 1301030621), and the Natural Science Foundation of Shannxi Province, China (2019JM-431)

A top quark mass measurement scheme near the production threshold in future colliders, e.g. the Circular Electron Positron Collider (CEPC), is simulated. A fitting method is adopted to determine the number of energy points to be taken and their locations. Our results show that the optimal energy point is located near the largest slope of the cross section v. beam energy plot, and the most efficient scheme is to concentrate all luminosity on this single energy point in the case of one-parameter top mass fitting. This suggests that the so-called data-driven method could be the best choice for future real experimental measurements. Conveniently, the top mass statistical uncertainty can also be calculated directly by the error matrix even without any sampling and fitting. The agreement of the above two optimization methods has been checked. Our conclusion is that by taking 50 fb−1 total effective integrated luminosity data, the statistical uncertainty of the top potential subtracted mass can be suppressed to about 7 MeV and the total uncertainty is about 30 MeV. This precision will help to identify the stability of the electroweak vacuum at the Planck scale.

Wei-Guo Chen

An optimal scheme for top quark mass measurement near the threshold at future collidersSupported by National Science Foundation of China (11405102) and the Fundamental Research Funds for the Central Universities of China (GK201603027, GK201803019)