Two Higgs Doublet ModelEdit
The Two Higgs Doublet Model (2HDM) is a well-studied extension of the Standard Model that broadens the scalar sector by introducing a second complex SU(2) doublet. This simple augmentation preserves gauge invariance and renormalizability, while yielding a richer spectrum and a wider range of phenomenology. After electroweak symmetry breaking, the model predicts two CP-even neutral Higgs bosons (often denoted h and H), one CP-odd neutral Higgs boson (A), and a pair of charged Higgs bosons (H±). The state discovered at about 125 GeV in 2012, and subsequently studied, is commonly identified with the lighter CP-even state h in many realizations of the model, though the precise assignment depends on the parameter choices.
The 2HDM is framed in terms of a scalar potential for two Higgs doublets, typically labeled Φ1 and Φ2, and a Yukawa sector that can be arranged to suppress flavor-changing neutral currents (FCNCs) at tree level. A central feature is the ratio tanβ of the vacuum expectation values (VEVs) of the two doublets, along with a mixing angle α that diagonalizes the CP-even mass matrix. A soft Z2 symmetry, often imposed to prevent FCNCs, leads to several common realizations of the Yukawa sector, notably Type I, Type II, Type X (lepton-specific), and Type Y (flipped). Each realization makes distinct predictions for how the Higgs fields couple to fermions, especially the down-type and up-type quarks and charged leptons.
Theoretical framework
Scalar sector and spectrum: The model starts with two complex SU(2) doublets and a scalar potential that, after spontaneous symmetry breaking, yields five physical scalars: h, H, A, and H±. The masses and mixings are governed by parameters in the potential (including a soft-breaking term m12^2) and the angle α. The couplings of the Higgs states to gauge bosons and fermions depend on α and tanβ, differentiating the 2HDM from the single-Higgs Standard Model.
Yukawa sector and FCNC suppression: If both doublets couple to fermions with no additional structure, FCNCs would appear at tree level, which data constrain strongly. Imposing a discrete Z2 symmetry and assigning fermions to couple to only one of the doublets mitigates this problem. This leads to the four canonical Yukawa textures (Type I, Type II, Type X, Type Y), each with a characteristic pattern of couplings to up-type quarks, down-type quarks, and leptons. In the language of phenomenology, the couplings scale with combinations of α and tanβ, yielding distinctive collider signatures.
CP properties and CP violation: The Higgs sector can conserve CP or, in more general realizations, admit CP violation within the scalar sector if complex parameters are present in the potential. CP-violating 2HDMs mix CP-even and CP-odd components, affecting production and decay patterns and providing potential sources for observable CP-violating effects in Higgs processes or electric dipole moments.
Alignment and decoupling: Two important limiting behaviors shape the phenomenology. The alignment limit occurs when sin(β−α) ≈ 1, in which case the lighter CP-even state h has couplings to gauge bosons and fermions nearly identical to the SM Higgs. In the decoupling limit, the extra scalars become heavy and effectively decouple from low-energy observables, producing an appearance very close to the SM with only small residual deviations.
Classification and phenomenology
Type I: All fermions couple predominantly to one of the doublets. The Yukawa couplings to fermions are suppressed by a factor related to cotβ, with distinctive production and decay patterns at colliders.
Type II: Up-type quarks couple to one doublet while down-type quarks and charged leptons couple to the other. This is the texture adopted in many supersymmetric realizations and has strong implications for tanβ-enhanced couplings to down-type fermions, influencing decays like A→ττ or H±→τν in certain regions of parameter space.
Type X (lepton-specific): Quarks couple to one doublet and leptons couple to the other, producing enhanced leptonic decays in certain tanβ regimes.
Type Y (flipped): A hybrid pattern with up-type quarks and leptons coupling to different doublets compared to down-type quarks, yielding a mix of collider signatures.
Collider signatures and constraints: The extended scalar spectrum opens a range of search channels at hadron colliders. Production mechanisms include gluon fusion and associated production with heavy quarks, while decays can proceed through standard gauge-boson channels (e.g., H→WW, ZZ) or through Higgs-to-Higgs channels (e.g., H→hh, A→Zh) depending on mass hierarchies and tanβ. At high tanβ, down-type fermion decays (notably to ττ and bb) can dominate, while at lower tanβ, bosonic decay channels may be more important. The charged Higgs H± has characteristic production and decay routes, such as tb and τν, with the exact pattern depending on its mass.
Experimental status and constraints: The observed Higgs boson at 125 GeV has properties close to SM expectations, which translates into tight constraints on deviations in the couplings governed by α and tanβ. Direct searches at the LHC for additional Higgs states, along with precision flavor data (for example, rare B-meson decays and CP-violating observables) and electroweak precision measurements, carve out viable regions in the 2HDM parameter space. In particular, flavor observables like B→X_sγ impose lower bounds on charged-Higgs masses in many Type II scenarios, while the alignment limit can mimic SM-like behavior even with relatively light extra scalars. The MSSM represents a well-known supersymmetric realization of a 2HDM-type Higgs sector, where radiative corrections are essential to achieve the observed 125 GeV state.
Theoretical issues and debates
Naturalness and model-building prospects: The 2HDM is a minimal, renormalizable extension that adds rich structure without fully resolving the hierarchy problem. Debates in the field focus on whether and where new scalar states should appear, how they might stabilize the electroweak scale, and how to balance naturalness with experimental constraints.
Alignment without decoupling: A notable topic concerns whether SM-like Higgs behavior can be achieved with relatively light extra scalars (alignment without decoupling) or only when the additional states are heavy (decoupling). Different regions of parameter space realize these possibilities, with implications for search strategies at current and future colliders.
CP violation and EDM constraints: If the model introduces CP violation in the Higgs sector, it must contend with stringent limits from electric dipole moment measurements. This drives considerations of parameter choices and potential correlations with collider observables.
Flavor constraints and model variants: The various Yukawa realizations respond differently to flavor data. These tensions influence which versions of the 2HDM remain viable under current experimental scrutiny and guide the design of future searches.
Experimental probes and future prospects
Current landscape: The LHC experiments ATLAS and CMS continue to test the 2HDM parameter space through precision measurements of the 125 GeV Higgs and direct searches for additional scalars. Global fits combine collider data with flavor and electroweak observables to delineate allowed regions.
Future facilities and prospects: Upgrades to the LHC and potential next-generation colliders promise improved sensitivity to extended Higgs sectors. Precision measurements of Higgs couplings, Higgs pair production, and direct detection of additional Higgs states would refine the viable landscape of 2HDMs and test specific Yukawa textures.
Theoretical developments: Methodologies such as effective field theory approaches, global fits, and collider-flavor synergy are employed to translate data into constraints on the underlying scalar potential and Yukawa structure. These tools help map the interplay between h, H, A, and H± across different realizations.