Extended scalar sectors, effective operators and observed data

The available data on the 125 GeV scalar $h$ is analysed to explore the room for new physics in the electroweak symmetry breaking sector. The first part of the study is model-independent, with $h$ couplings to standard model particles scaled by quantities that are taken to be free parameters. At the same time, the additional loop contributions to $h \rightarrow \gamma\gamma$ and $h \rightarrow Z\gamma$, mediated by charged scalar contributions in the extended scalar sector, are treated in terms of gauge-invariant effective operators. Having justified this approach for cases where the concerned scalar masses are a little above the $Z$-boson mass, we fit the existing data to obtain marginalized 1$\sigma$ and 2$\sigma$ regions in the space of the coefficients of such effective operators, where the limit on the $h \rightarrow Z\gamma$ branching ratio is used as a constraint. The correlation between, say, the gluon fusion and vector-boson fusion channels, as reflected in a non-diagonal covariance matrix, is taken into account. After thus obtaining model-independent fits, the allowed values of the coefficients are translated into permissible regions of the parameter spaces of several specific models. In this spirit we constrain four different types of two Higgs doublet models, and also models with one or two $Y = 2$ scalar triplets, taking into account the correlatedness of the scale factors in $h$-interactions and the various couplings of charged Higgs states in each extended scenario.

Parametrization of new physics to observe h → γγ and h → Z γ decays via new physics effects • There can be an extended Higgs sector comprising of additional neutral and charged scalars with their mixing may cause the coupling of the 125 GeV scalar to SM particles to be modified in some ways: • There can be heavy states running in the loop modifying Higgs couplings, can be parametrized to express it in terms of SM gauge-invariant higher dimensional effective operators: • These constitute the most general set of dimension-6 effective operators which give rise to the hγγ and hZ γ vertices and as there are no tree level diagrams exist in this two cases, the effective vertices can make some useful contributions, structured as, After parametrizing new physics effects, we investigate the region of parameter space favored by the 8 and 13 TeV results at the LHC. Our eight-dimensional parameter space, spanned by the four scale factors κ V , κ t , κ b , κ τ and After parametrizing new physics effects, we investigate the region of parameter space favored by the 8 and 13 TeV results at the LHC. Our eight-dimensional parameter space, spanned by the four scale factors κ V , κ t , κ b , κ τ and f BB , f WW , f B , f W , the Wilson coefficients in the dimension-6 hVV operators.
• In order to constrain new physics from more than one independent measurements, For corelated experimental searches, these correlations affect the Log-likelihood function as, Where C −1 is the inverse of the covariance matrix C ij = cov(μ i ,μ j ) Atri Dey Extended scalar sectors, effective operators and observed data December 14, 2018 5 / 22 After parametrizing new physics effects, we investigate the region of parameter space favored by the 8 and 13 TeV results at the LHC. Our eight-dimensional parameter space, spanned by the four scale factors κ V , κ t , κ b , κ τ and f BB , f WW , f B , f W , the Wilson coefficients in the dimension-6 hVV operators.
• In order to constrain new physics from more than one independent measurements, For corelated experimental searches, these correlations affect the Log-likelihood function as, Where C −1 is the inverse of the covariance matrix C ij = cov(μ i ,μ j ) • We consider all the correlations between gluon fusion and vector-boson fusion production for each of the major Higgs decay channels.

Atri Dey
Extended scalar sectors, effective operators and observed data December 14, 2018 • This χ 2 is then minimized to get the region allowed by the experimental data at the 1-and 2σ levels in each two-parameter subspaces, where all remaining parameters have been marginalized. Figure 2: Allowed regions at 1σ(red) and 2σ(blue) levels in the some of the parameter space of scale factors and dimension-6 couplings.
• Various new physics models predict extended electroweak symmetry breaking sectors. It is naturally of interest to link the model-independent analysis presented above to specific theoretical scenarios.
• With this in view, we now translate the results of the global fit to those pertaining to extended Higgs models which give some contribution to new physics (like 2HDM, Higgs triplet models), taking into account the additional constraints that connect model parameters in each case.

Atri Dey
Extended scalar sectors, effective operators and observed data December 14, 2018 7 / 22 • Various new physics models predict extended electroweak symmetry breaking sectors. It is naturally of interest to link the model-independent analysis presented above to specific theoretical scenarios.
• With this in view, we now translate the results of the global fit to those pertaining to extended Higgs models which give some contribution to new physics (like 2HDM, Higgs triplet models), taking into account the additional constraints that connect model parameters in each case.
• To make some bridge between model dependent and model independent approach to study new BSM physics we need some consistency between this two approachs.
two-Triplet-model with g eff Parametrization of new physics Global fit Interest to make connections Validation to make connection Allowed parameter spaces Covariance matrix • d i = content of data bin i; • t i = model prediction for bin i; • s ij = systematic uncertainty from source j on the contents of bin i; • σ i = statistical uncertainty on the contents of bin i; • α j = fit parameters. When this χ 2 is minimised w.r.t α i 's then • Type-I 2HDM: Here all fermions are assumed to couple to the same doublet, so that This can be achieved by imposing the discrete symmetry on the L Yukawa , Φ 1 → −Φ 1 .
• Type-II 2HDM: Here up-type quarks to couple to one doublet, and down-type quarks and leptons to couple to another. Under this assumption L Yukawa = y 1 ijQiL Φ 1 d jR + y 2 ijQiLΦ 2 u jR + y 5 ijLiL Φ 1 e jR This can be enforced by demanding that the L Yukawa remains invariant under Φ 1 → −Φ 1 and d R → −d R and e R → −e R .

Atri Dey
Extended scalar sectors, effective operators and observed data December 14, 2018