We investigate the implications of spontaneous <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the general two Higgs doublet model, which leads to a nondecoupling structure of the Higgs sector. All the masses of the Higgs bosons are purely determined by the vacuum expectation value of the Higgs fields, and are thus constrained to be smaller than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> by the perturbative unitarity bound. Such a nondecoupling nature predicts sizable deviations from the Standard Model expectations in the observables of the discovered Higgs boson (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math>). We find that the magnitude of deviations in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>h</mi><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></mrow></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>h</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>γ</mi></mrow></msub></math>) are larger than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>10</mn><mo>%</mo><mo stretchy="false">(</mo><mn>4</mn><mo>%</mo><mo stretchy="false">)</mo></math> in the Higgs alignment limit. Moreover, we show that a robust correlation emerges between the deviations in the one-loop corrected <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>h</mi><mi>h</mi></math> coupling and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>h</mi><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></mrow></msub></math> to be, e.g., 200% (50%) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>10.3</mn><mo>%</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>10.8</mn><mo>%</mo></math>), respectively, under the constraints from theoretical bounds and current experimental data. Using a few benchmark points, we highlight that flavor-violating decays of the additional Higgs bosons can be sizable due to the constrained structure of the Yukawa interactions.

India

Tanmoy Mondal

Japan

Kei Yagyu

Probing spontaneous <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation through precision Higgs observables

We discuss triple <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> boson signatures via the decay chain of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><mi>ϕ</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math>, with a new light scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>, at future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> factories such as the Circular Electron-Positron Collider and Future Circular Collider. These new bosons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> naturally appear in models with a new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge symmetry which is spontaneously broken and introduced in various new physics scenarios. The branching ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><mi>ϕ</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math> can be larger than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>12</mn></mrow></msup></math>, which gives <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> events at Tera-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> experiments, when a product of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>X</mi></msub></math> (new gauge coupling) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo>−</mo><msup><mi>Z</mi><mo>′</mo></msup></math> mixing) is larger than around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>. We find that the search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math> can significantly improve the current bound on a kinetic mixing parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> in the dark photon case, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>ε</mi><mo>≳</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo stretchy="false">)</mo></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>X</mi></msub><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> can be explored at Tera-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> experiments. We also show that a sufficiently large number of events with multilepton plus hadronic jets can be obtained in benchmark points, which cannot be realized by the usual decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> in the standard model.

China

Takaaki Nomura

Triple <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> signatures at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> factories

We investigate multi-lepton jet events from the decay of the 125 GeV Higgs boson ($\textit{h}$) into quadruple new gauge bosons ($\textit{Z}$′) at the LHC. Such an exotic decay is realized via the process of $\textit{h → ϕϕ → Z}$′$\textit{Z}$′$\textit{Z}$′$\textit{Z}$′ with new scalar boson $\textit{ϕ}$ in models with an additional U(1) gauge symmetry. Charged leptons coming from the $\textit{Z}$′ decay tend to be observed as lepton-jets rather than isolated leptons when the masses of $\textit{Z}$′ and $\textit{ϕ}$ are smaller than $$ \mathcal{O} $$ (10) GeV, because of the highly-boosted effects. Performing the signal and background analyses, we find that the branching ratio of $\textit{h}$ → 4$\textit{Z}$′ is maximally constrained to be smaller than of order 10 (10 ) by using the muonic-lepton jets assuming the integrated luminosity of 140 fb (3000 fb ) at LHC. For lighter $\textit{Z}$′ ($\textit{<}$ 2$\textit{m}$ ), we can use the electronic-lepton jets instead of the muon-jets, by which the upper limit on the branching ratio is obtained to be of order 10 –10 . These bounds can be converted into the constraint on model parameters such as a mixing angle between $\textit{h}$ and $\textit{ϕ}$. It is shown that stronger bounds on the mixing angle are obtained in the dark photon case as compared with the previous constraints given by flavor experiments and the Higgs decay $\textit{h → Z}$′$\textit{Z}$′ in the mass range of $$ {m}_{Z^{\prime }} $$ ≲ 10 GeV.

Jinmian Li

Multi-lepton jets from quadruple $\textit{Z}$′ via the Higgs decay at LHC

We discuss multi-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> signatures coming from decays of Higgs bosons in models with a spontaneously broken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math> symmetry, which can be observed as “lepton jets” or multilepton final states depending on the mass range of new bosons. We consider anomaly-free <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math> models without introducing new fermions except for right-handed neutrinos, in which the Higgs sector is composed of an isospin doublet and a singlet fields with zero and nonzero <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math> charges, respectively. The multi-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> signatures can then be obtained via the decays of the discovered (extra) Higgs boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>), i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo stretchy="false">→</mo><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math>, and/or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>ϕ</mi><mi>ϕ</mi><mo stretchy="false">→</mo><mn>4</mn><msup><mi>Z</mi><mo>′</mo></msup></math> as far as kinematically allowed. We give the upper limit on the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi></math> into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup><msup><mi>Z</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><msup><mi>Z</mi><mo>′</mo></msup></math> from the current experimental data in each model. We also show the deviation in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>h</mi><mi>h</mi></math> coupling from the standard model prediction at one-loop level, and find that its amount is typically smaller than 1%.

Multi-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> signatures of spontaneously broken local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mo>′</mo></msup></math> symmetry

In models with non-minimal Higgs sectors, enforcing (near) Higgs alignment, necessary to prevent significant deviations in the Higgs boson coupling from the standard model prediction, causes a serious fine-tuning problem. We demonstrate that the Higgs alignment is naturally deduced from the multicritical point principle (MPP) in the general two Higgs doublet model while keeping non-zero CP-violating phases. Furthermore, we discuss the possibility of realizing the Yukawa alignment from the MPP, which is necessary to prevent flavor-changing neutral currents mediated by Higgs bosons at tree level, and find that it seems difficult to realize it by the MPP due to the non-diagonal structure of the CKM matrix.

Taiwan

Hikaru Kawai

South Korea

Kiyoharu Kawana

Kin-ya Oda

Higgs alignment from multicritical-point principle in two Higgs doublet models

We propose a new renormalization scheme in the two Higgs doublet models with a softly-broken <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> symmetry and CP-conservation in the Higgs sector. In this scheme, counterterms for mixing angles of the Higgs bosons are determined by using the decay rates of the discovered Higgs boson h, i.e., <math><mi>h</mi><mo>→</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> and <math><mi>h</mi><mo>→</mo><mi>Z</mi><msup><mrow><mi>Z</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>→</mo><mi>Z</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> at next leading order (NLO) instead of using the renormalized two-point functions which are adopted in the previous scheme. We require that the decay rates at NLO are determined to be the corresponding predictions at NLO in the Standard Model (SM) times square of the scaling factor which describes the deviation of h couplings at tree level from the SM value. The mixing angles then maintain the meaning of the “alignmentness”, i.e., how the properties of h are close to the SM predictions, while they lose such meaning in the previous scheme. We compare the predictions of the decay rates at NLO given in the new scheme and those in the previous scheme.

Shinya Kanemura

Mariko Kikuchi

New renormalization scheme in the two Higgs doublet models

We discuss the Higgs phenomenology in models with a new <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> gauge symmetry including the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> scenario, where three right-handed neutrinos are inevitably introduced due to the gauge anomaly cancellations. We find that the decay branching ratio of the discovered Higgs boson into a pair of new massive gauge bosons (<math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math>) can significantly be enhanced in the Dirac neutrino case as compared with the Majorana case for a fixed value of the new gauge coupling and the mass of <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> under constraints from current experimental data. Because of such an enhancement, the Dirac case can indirectly be discriminated from the Majorana case via the Higgs decay.

K.A. ShivaSankar

Arindam Das

Enhancement of the Higgs decay into a ′ Pair in Models With (1) Gauge Symmetry

In ordinary thermodynamics, around first-order phase transitions, the intensive parameters such as temperature and pressure are automatically fixed to the phase transition point when one controls the extensive parameters such as total volume and total energy. From the microscopic point of view, the extensive parameters are more fundamental than the intensive parameters. Analogously, in conventional quantum field theory (QFT), coupling constants (including masses) in the path integral correspond to intensive parameters in the partition function of the canonical formulation. Therefore, it is natural to expect that, in a more fundamental formulation of QFT, coupling constants are dynamically fixed a posteriori, just as the intensive parameter in the microcanonical formulation. Here, we demonstrate that the automatic tuning of the coupling constants is realized at a quantum phase transition point at zero temperature, even when the transition is of higher order, due to the Lorentzian nature of the path integral. This naturally provides a basic foundation for the multicritical point principle. As a concrete toy model for solving the Higgs hierarchy problem, we study how the mass parameter is fixed in the <math><msup><mi>ϕ</mi><mn>4</mn></msup></math> theory at the one-loop level in the microcanonical or further generalized formulation of QFT. We find that there are two critical points for the renormalized mass: zero and of the order of ultraviolet cutoff. In the former, the Higgs mass is automatically tuned to be zero and thus its fine-tuning problem is solved. We also show that the quadratic divergence is absent in a more realistic two-scalar model that realizes the dimensional transmutation. Additionally, we explore the possibility of fixing quartic coupling in <math><msup><mi>ϕ</mi><mn>4</mn></msup></math> theory and find that it can be fixed to a finite value.

Quantum phase transition and absence of quadratic divergence in generalized quantum field theories

We propose a novel signature with four-photon final states to probe <math><mi>C</mi><mi>P</mi></math>-violating (CPV) extended Higgs sectors via <math><mrow><mi>f</mi><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>→</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>→</mo><mn>4</mn><mi>γ</mi></mrow></math> processes with <math><msub><mi>H</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math> being additional neutral Higgs bosons. We focus on the nearly Higgs alignment scenario, in which the discovered Higgs boson almost corresponds to a neutral scalar state belonging to the isospin doublet field with the vacuum expectation value <math><mrow><mi>v</mi><mo>≃</mo><mn>246</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. We show that the branching ratios of <math><msub><mi>H</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>→</mo><mi>γ</mi><mi>γ</mi></math> can simultaneously be sizable when CPV phases in the Higgs potential are of order one due to the enhancement of charged-Higgs boson loops. Such branching ratios can be especially significant when the fermiophobic scenario is taken into account. As a simple example, we consider the general two Higgs doublet model, and demonstrate that the cross section for the four-photon process can be 0.1 fb at LHC with the masses of <math><msub><mi>H</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math> to be a few 100 GeV in the Higgs alignment limit under the constraints from electric dipole moments (EDMs) and LHC Run-II data. We also illustrate that the searches for EDMs and diphoton resonances at high-luminosity LHC play complementary roles to explore CPV extended Higgs sectors.

Kento Katayama

Multiphoton signatures as a probe of <math><mi>C</mi><mi>P</mi></math> violation in extended Higgs sectors

A correction to this paper has been published: https://doi.org/10.1007/JHEP06(2023)069