Mediciones radiológicas

Following the discussion in the previous section, it is worth considering a non-minimal Higgs sector. A minimal extension to the SM Higgs sector is that of a 2HDM. In general, the additional complexity in the Higgs sector allows for flavour-changing neutral currents (FCNCs) at tree-level, which are experimentally disfavoured. The phenomenology of several 2HDMs which allow sufficiently suppressed tree-level FCNCs are discussed in Ref. [40]. A simplified approach to studying 2HDMs is by using the result by Glashow and Weinburg [45], which found that Higgs boson mediated FCNCs are absent, at tree-level, if all fermions of a particular charge couple to only one Higgs doublet. Hence FCNCs can be explicitly eliminated from the models by choosing appropriate Higgs-fermion couplings. Additionally, in the simplified models, the Higgs sector is considered to conserve CP. Assuming two Higgs doublets (Φ1and Φ2), and the most general scalar potential9V(Φ1, Φ2) satisfying the simplifications above, the VEVs of each doublet (denoted as v1and v2, respectively) can each be assumed to be real and positive, with v=qv2₁+ v2

2≈ 246 GeV. After EWSB the complex doublets can be written about their minimum,

Φa=  φ_a+ (va+ ρa+ iχa)/ √ 2  , for a = (1, 2), (2.2)

where φ_a+are complex fields, and ρaand χaare real fields. There are eight DOFs in this Higgs sector, three of which are absorbed by the longitudinal polarisation of the three massive gauge bosons (after choosing the correct gauge). The remaining five DOFs are physical scalar Higgs fields with respective scalar bosons: two charged Higgs (H±), one neutral CP-odd Higgs (A0), and two neutral CP-even Higgs (h0and H0, where by convention m_h0 < m_H0). There

are six free parameters in the 2HDM Higgs sector, four Higgs masses (since m_H+= m_H−),

the ratio of the VEVs (tan β _≡v2_v1), and the mixing angle of the neutral CP-even Higgs bosons (α). The physical mass eigenstates of the Higgs fields can be written as linear combinations of the above fields,

h0= ρ1sin α− ρ2cos α, (2.3)

H0=_−ρ2sin α− ρ1cos α, (2.4)

A0= χ1sin β− χ2cos β, (2.5)

H±= φ₁±sin β_{− φ2}±cos β. (2.6)

(2.7) 9_{The full form of the potential is given in Ref. [40].}

2.2 Two-Higgs-Doublet-Models

As with the SM the fermion and vector boson masses are defined by their relation to the VEV, e.g., m_W2 = g2₂v2 = g2(v21+v22)

2 . Similarly, the coupling strengths are given by the respective interaction terms of particle fields with the Higgs fields. In the vector boson sector, neutral couplings of the form h0VV, H0VV, ZA0h0, and ZA0H0, are allowed. Notably missing from the Lagrangian are A0VV terms. As a consequence, the strength of the Higgs di-boson vertex can be expressed relative to the SM coupling strength gSM_HVV irrespective of the Higgs boson mass, ξH 0 VV ≡ g_H0_VV gSM_HVV = cos(β− α), (2.8) ξh 0 VV ≡ g_h0_VV gSM_HVV = sin(β− α), (2.9)

where ξ has been defined as a scale factor to the Higgs-gauge coupling strength relative to the SM. If h0 is assumed to be the discovered 125 GeV SM-like Higgs, H0 becomes gauge-phobic at cos(β_{− α) ≈ 0 (Eq. (2.8)), giving the SM limit where the h}0_{VV vertex has} the SM coupling strength. The zero superscript is dropped from h0, H0and A0, i.e., h denotes the SM-like Higgs, H the heavy CP-even Higgs, and A the CP-odd, unless otherwise stated. As discussed above, one way of guaranteeing no tree-level FCNCs from the Higgs sector can be imposed by carefully coupling fermions with the same quantum numbers to the same Higgs doublets. This allows for four such choices, which by themselves fix the Higgs- fermionic couplings. The first choice is referred to as Type-I 2HDM, where all fermions couple to one scalar doublet, Φ2by convention, while vector bosons couple to the other, Φ1. In Type-II 2HDM, all down-type fermions couple to Φ1, while up-type quarks couple to Φ2. In both cases, all down-type fermions couple to the same Higgs doublet. The additional two choices invert this requirement. In the Lepton-specific model, the up- and down-type quarks couple to Φ2, while down-type leptons couple to Φ1. The last type is where down-type leptons and up-type quarks couple to Φ2, while down-type quarks couple to Φ2, referred to as the Flipped 2HDM. The models are summarised in Table 2.1.

Table 2.1 Coupling of 2HMD Higgs doublets to SM fermions in the four models without FCNCs [40].

Model Type-I Type-II Flipped Lepton-specific

vector bosons Φ1 Φ1 Φ1 Φ1

up-type quarks Φ2 Φ2 Φ2 Φ2

down-type quarks Φ2 Φ1 Φ1 Φ2

With the above four models defined, the 2HDM Yukawa couplings can be expressed in terms of the SM Yukawa couplings Yf of Eq. (1.22). In the neutral Higgs sector10 the Yukawa coupling terms are [7, 40],

L2HDM (neutral) Yukawa =− Y_f √ 2(ξ f h f f h¯ + ξ f Hf f H¯ − ξ f Af γ¯ 5_{f A),} (2.10)

where f are summed over fermion spinors, and ξ_φf are scale factors for φ = h, H, A: they are defined in Table 2.2, where ξupφ, ξ_downφ , and ξ_ℓφ are for up-type quarks, down-type quarks, and leptons, respectively.

The ξ factors scale the corresponding coupling strengths of the 2HDM Higgs bosons to SM particles with respect to the SM Higgs boson couplings. The terms will translate into ∝ ξ2scaling of the Higgs boson cross-sections and partial widths. However, determining precisely the 2HDM Higgs boson cross-sections and branching fractions is dependant on the Higgs boson mass spectrum, and the kinematically allowed processes. In general there are no tight restrictions on the relative masses of the 2HDM Higgs bosons and the calculation has to be performed for several reference values, as was done in Ref. [40]. However, if we intend to explain the observed 125 GeV Higgs boson with such a model, we should assign this boson to one of the CP-even neutral Higgs bosons. As stated above, it is usually assumed that the lighter h is the discovered 125 GeV Higgs boson11. Since the h Higgs couplings to SM particles are well defined in 2HDM, measurements of the 125 GeV Higgs boson cross-section and branching fractions can be used to constrain the parameter space. This is done in the coupling modifier framework in Sections 2.5 and 8.3, where the scale factors in Table 2.2 directly scale the Higgs boson cross-section and branching fraction. Although this is a simplified picture, since one should also consider modifications to the total cross-section from processes like a heavy Higgs decaying to a pair of 125GeV Higgs bosons, H_{→ hh, and} higher order loop corrections, it is found be adequate at the SM limit, i.e., cos(β_{− α) ≈ 0.} The validation of this approximation is performed in Section 8.3.1.1.

10_{The charged Higgs boson introduces flavour-changing charged currents (FCCCs) to the Higgs Yukawa}

terms, with their strengths dependant on ξA

up, ξdownA , and ξℓA. The quark terms include CKM matrix-elements. The full expression can be found in Ref. [40] and is not repeated here.

11_{For one, no lighter scalar boson has as of yet been discovered. Secondly, it avoids the additional complica-}

tion of having H as the 125 GeV boson: effects from decays like H_{→ hh and H → ZA, which are highly mass}

2.3 The Minimal Supersymmetric Standard Model