We study flavor-changing bottom quark radiative decay $ b {\rightarrow} s \gamma $ induced at the one-loop level within the minimal gauged two-Higgs-doublet model (G2HDM). Among the three new contributions to this rare process in G2HDM, we find that only the charged Higgs $ {\cal{H}}^\pm $ contribution can be constrained by the current global fit data in $\textit{B}$-physics. The other two contributions from complex vectorial dark matter $ {\cal{W}} $ and dark Higgs $ {\cal{D}} $ are not sensitive to the current data. Incorporating theoretical constraints imposed on the scalar potential and electroweak precision data for the oblique parameters, we exclude mass regions $ m_{\cal{H}}^\pm \lesssim 250 $ GeV and $ m_{\cal{D}} \lesssim 100 $ GeV at the 95% confidence level.

China

Che-Hao Liu

Vietnam

Van Que Tran

Qiaoyi Wen

Fanrong Xu

Tzu-Chiang Yuan

New contributions to $\textit{b}$ → $\textit{sγ}$ in the minimal G2HDM * Supported in part by the National Natural Science Foundation of China (19Z103010239, 12350410369 (VQT), U1932104 (FRX)) and the NSTC (111-2112-M-001-035 (TCY))

<p>We investigate the global structure of the gauged two-higgs-doublet model (G2HDM), a framework that extends the Standard Model by introducing a dark sector governed by the gauge symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>X</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>H</mi></msub></math>. The full gauge symmetry of the theory, including the visible sector, is given by the universal covering group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>G</mi><mo stretchy="false">˜</mo></mover><mo>=</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>Y</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>C</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>X</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>H</mi></msub></math>. However, the true gauge group may instead be a quotient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo>=</mo><mover accent="true"><mi>G</mi><mo stretchy="false">˜</mo></mover><mo>/</mo><mi mathvariant="normal">Γ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi></math> is the center of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>G</mi><mo stretchy="false">˜</mo></mover></math> or a subgroup thereof, leading to different global structures that cannot be distinguished by local experiments. We explore the physical implications of these global structures, analyzing their effects on Wilson, ’t Hooft, and dyonic line operators, as well as the periodicity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> angles associated with each group factor. Furthermore, we determine the minimal electric and magnetic charges that arise after electroweak symmetry breaking, highlighting their dependence on the choice of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi></math>. These findings provide a systematic characterization of the G2HDM’s global properties and their potential phenomenological consequences.</p>

Rui Yang

Jiaming Guo

Linghai Li

Xun Xue

Taiwan

Line operators in the gauged two-Higgs-doublet model

Recent reports from the Large Hadron Collider indicate two excesses: one in the lighter Higgs mass region around 95 GeV, and another in the rare <italic>Z&#947;</italic> final state of the Standard Model (SM) 125 GeV Higgs decay. These anomalies are analyzed within the minimal gauged two-Higgs-doublet model (G2HDM). A viable parameter space in G2HDM is identified that can account for both excesses. Within the viable parameter space, we find a strong correlation between the signal strengths of the SM 125 GeV Higgs decays into <italic>&#947;&#947;</italic> and <italic>Z&#947;</italic> modes. However, this correlation does not extend to the lighter 95 GeV Higgs.

Morocco

Abdesslam Arhrib

Khiem Hong Phan

When the Standard Model Higgs meets its lighter 95 GeV twin

We investigate the possibility of a strong first-order electroweak phase transition (FOEWPT) during the early universe within the framework of the gauged two-Higgs doublet model (G2HDM) and explore its detectability through stochastic gravitational wave signals. The G2HDM introduces a dark replica of the Standard Model electroweak gauge group, inducing an accidental symmetry which not only leads to a simple scalar potential at tree-level but also offers a compelling vectorial dark matter candidate. Using the high temperature expansion in the effective potential that manifests gauge invariance, we find a possible two-step phase transition pattern in the model with a strong first-order transition occurring in the second step at the EW scale temperature. Collider data from the LHC plays a crucial role in constraining the parameter space conducive to this two-step transition. Furthermore, satisfying the nucleation condition necessitates the masses of scalar bosons in the hidden sector to align with the electroweak scale, potentially probed by future collider detectors. The stochastic gravitational wave energy spectrum associated with the phase transition is computed. The results indicate that forthcoming detectors such as BBO, LISA, DECIGO, TianQin and Taiji could potentially detect the gravitational wave signals generated by the FOEWPT. Additionally, we find that the parameter space probed by gravitational waves can also be searched for in future dark matter direct detection experiments, in particular those designed for dark matter masses in the sub-GeV range using the superfluid Helium target detectors.

United States

Michael Ramsey-Musolf

Van Tran

Gravitational waves and dark matter in the gauged two-Higgs doublet model

We explore a novel scenario involving Abelian–non-Abelian kinetic mixing within the framework of the Standard Model effective field theory (SMEFT) and its extension with a real triplet scalar field. In SMEFT, this mixing arises exclusively from a dimension-6 operator involving the Standard Model Higgs doublet, while the real triplet scalar field introduces an additional dimension-5 operator. We derive the modifications to electroweak gauge boson properties and impose constraints using electroweak precision data. In SMEFT, we find that <math><mi>Z</mi></math>-pole data at the Large Electron–Positron Collider imposes a stringent constraint on the kinetic mixing parameter, requiring it to be less than <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>), which corresponds to a new physics scale of about 10 TeV. In the <math><mrow><mi>SMEFT</mi><mo>+</mo><mi>triplet</mi></mrow></math> scenario, the constraint can be significantly relaxed with a sizeable triplet vacuum expectation value while preserving custodial symmetry in a finely tuned parameter space. Future measurements from the Circular Electron Positron Collider could probe the kinetic mixing parameter down to an order of magnitude smaller. Constraints from the Higgs signal strength data, <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, and muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) are also discussed.

Exploring Abelian–non-Abelian kinetic mixing in SMEFT and beyond

We survey the scalar electroweak multiplets that can originate from a grand unified theory (GUT) like <math altimg='si1.svg'><mi>S</mi><mi>U</mi><mo stretchy='false'>(</mo><mn>5</mn><mo stretchy='false'>)</mo></math>, <math altimg='si2.svg'><mi>S</mi><mi>O</mi><mo stretchy='false'>(</mo><mn>10</mn><mo stretchy='false'>)</mo></math> or <math altimg='si3.svg'><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub></math>. We compute the oblique parameters <italic>S</italic>, <italic>T</italic> and <italic>U</italic> for a general scalar electroweak multiplet and then apply the results to the leptoquark, as well as the color sextet and octet cases, allowed by the GUT survey. Constraints from precision measurement data of the Standard Model <italic>W</italic> boson mass and <italic>&#961;</italic> parameter to the mass splittings within each of these multiplets are presented. Extension to general vector electroweak multiplets is briefly discussed.

Liang Chen

Ta-Wei Chan

Thomas W. Kephart

Wai Yee Keung

GUT origins of general electroweak multiplets and their oblique parameters

In view of the recent high precision measurement of the Standard Model W boson mass at the CDF II detector, we compute the contributions to the oblique parameters S, T and U coming from the two additional Higgs doublets (one inert and one hidden) as well as the hidden neutral dark gauge bosons and extra heavy fermions in the gauged two-Higgs-doublet model (G2HDM). While the effects from the hidden Higgs doublet and new heavy fermions are found to be minuscule, the hidden gauge sector  $$SU(2)_H \times U(1)_X$$  <math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mi>H</mi> </msub> <mo>×</mo> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   with gauge coupling strength  $$\gtrsim 10^{-2}$$  <math> <mrow> <mo>≳</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math>   and gauge boson mass  $$\gtrsim 100$$  <math> <mrow> <mo>≳</mo> <mn>100</mn> </mrow> </math>   GeV can readily explain the W boson mass anomaly but is nevertheless excluded by the dilepton high-mass resonance searches at the Large Hadron Collider. On the other hand, the new global fits to the oblique parameters due to the new W boson mass measurement can give discernible impacts on the mass splitting and mixing angle for the inert Higgs doublet in G2HDM. We also study the impact on the signal strength of diphoton mode of the 125 GeV Higgs boson  $$h \rightarrow \gamma \gamma $$  <math> <mrow> <mi>h</mi> <mo>→</mo> <mi>γ</mi> <mi>γ</mi> </mrow> </math>   and the detectability of the yet to be observed process  $$h \rightarrow Z \gamma $$  <math> <mrow> <mi>h</mi> <mo>→</mo> <mi>Z</mi> <mi>γ</mi> </mrow> </math>   at the High Luminosity Large Hadron Collider. Current constraints for the dark matter candidate  $$W^\prime $$  <math> <msup> <mi>W</mi> <mo>′</mo> </msup> </math>   including the dark matter relic density, dark matter direct detections and invisible Higgs decays are also taken into account in this study.

Thong Nguyen

Scrutinizing a hidden SM-like gauge model with corrections to oblique parameters

We compute the electromagnetic form factors of the l  i  l  j  γ vertex at one-loop level in the minimal G2HDM which has a sub-GeV vector dark matter candidate. The results are applied to the radiative decay rates for the charged lepton flavor violating processes l  i  → l  j  γ, and the anomalous magnetic dipole moment and the electric dipole moment of the charged lepton. To numerically compute the branching ratio for μ → eγ and compare with the latest experimental limit from MEG, we adapt our previous parameter space scan that is consistent with the relic density and constraints from direct searches of dark matter, W and Z mass measurements, as well as the LHC Higgs signal strengths and invisible width. While the extra contributions are at least an order of magnitude smaller than required to explain the ~4.2σ discrepancy in the muon anomaly, the existing MEG limit imposes stringent constraint on the parameter space. The remaining viable parameter space can be further probed by the MEG II sensitivity for μ → eγ as well as from the direct searches of sub-GeV dark matter in foreseeable future. Higher loop contributions may be significant to resolve the discrepancy in the muon anomaly and generate a non-vanishing electric dipole moments for the standard model quarks and leptons in G2HDM.

Charged lepton flavor violating radiative decays l  i  → l  j  γ in G2HDM

We present a detailed study of the non-abelian vector dark matter candidate W  t  with a MeV–GeV low mass range, accompanied by a dark photon A′ and a dark Z′ of similar masses, in the context of a gauged two-Higgs-doublet model with the hidden gauge group that has the same structure as the Standard Model electroweak gauge group. The stability of dark matter is protected by an accidental discrete Z 2 symmetry (h-parity) which was usually imposed ad hoc by hand. We examine the model by taking into account various experimental constraints including dark photon searches at NA48, NA64, E141, ν-CAL, BaBar and LHCb experiments, electroweak precision data from LEP, relic density from Planck satellite, direct (indirect) detection of dark matter from CRESST-III, DarkSide-50, XENON1T (Fermi-LAT), and collider physics from the LHC. The theoretical requirements of bounded from below of the scalar potential and tree level perturbative unitarity of the scalar sector are also imposed. The viable parameter space of the model consistent with all the constraints is exhibited. While a dark Z′ can be the dominant contribution in the relic density due to resonant annihilation of dark matter, a dark photon is crucial to dark matter direct detection. We also demonstrate that the parameter space can be further probed by various sub-GeV direct dark matter experimental searches at CDEX, NEWS-G and SuperCDMS in the near future.

Raymundo Ramos

A Sub-GeV Low Mass Hidden Dark Sector of SU(2) H  × U(1) X

We investigate a non-Abelian vector dark matter candidate <math><msup><mi>W</mi><mo>′</mo></msup></math> with a MeV–GeV low mass range, accompanied by a dark photon <math><msup><mi>A</mi><mo>′</mo></msup></math> and a dark <math><msup><mi>Z</mi><mo>′</mo></msup></math> in the context of a gauged two-Higgs-doublet model. The model is scrutinized by considering various experimental constraints including dark photon searches, electroweak precision data, the relic density of dark matter together with its direct and indirect searches, monojet and Higgs data from the LHC. The viable parameter space indicates that while a dark <math><msup><mi>Z</mi><mo>′</mo></msup></math> can be the dominant contribution in the relic density due to resonant annihilation of the dark matter, a dark photon is crucial to dark matter direct detection. The model can be further probed in the near future by sub-GeV dark matter and dark photon experiments.