Physics Models for SM Higgs Boson Couplings

This page lists the physics models that can be used to perform measurements of the Higgs Boson couplings in the Standard Model (SM). These models follow the recommendations of the LHC Higgs Cross Section Working Group LHCHXSWG YR3 and have been used in the combination of the ATLAS and CMS measurements of the Higgs boson properties.

LHC HCG Models

The following models are used in the LHC Higgs Combination Group (LHC HCG) to perform measurements of the Higgs boson couplings. They are well defined only for a SM Higgs boson mass of a few GeV around the measured value $m_H\approx 125$ GeV. The models are implemented in the python file LHCHCGModels.py.

You can produce the model by including the following option in the text2workspace.py command:

-P HiggsAnalysis.CombinedLimit.LHCHCGModels:model

	model	--PO	POIs	Description
Couplings with resolved loops	K1	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_W,kappa_Z,kappa_b, kappa_t, kappa_tau,kappa_mu	Higgs boson couplings to fermions and bosons in loops such as the $gg\to H$ and $H\to \gamma \gamma$ loops are scaled using the appropriate SM Higgs couplings. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, $H\to Z\gamma$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Couplings with effective loops	K2	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z, kappa_b, kappa_t, kappa_tau,kappa_mu,kappa_Zg	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K2Width	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z,c7_Gscal_tot, kappa_t, kappa_tau,kappa_mu,kappa_Zg	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$. In this model, the total Higgs width is allowed to float by effectively replacing the coupling ${\kappa }_b$ as a parameter of interest. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K2Inv	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z,kappa_b, kappa_t, kappa_tau,kappa_mu,kappa_Zg,BRinv	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$ and the branching ratio to invisible particles (any process with decay string hinv is scaled by this). The total width is modified accordingly. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K2InvC	--PO dohmm, --PO dohzg, --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z, kappa_b, kappa_t, kappa_tau,kappa_mu,kappa_Zg,BRinv,kappa_c	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$ and the branching ratio to invisible particles (any process with decay string hinv is scaled by this), and the coupling to charm quarks is included as a parameter of interest. The total width is modified accordingly. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K2Undet	--PO dohmm, --PO dohzg, --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z, kappa_b, kappa_t, kappa_tau,kappa_mu,kappa_Zg,BRinv,BRundet	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$ and the branching ratio to invisible particles (any process with decay string hinv is scaled by this), and the undetected decay modes are scaled by BRundet. The total width is modified accordingly. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K2UndetWidth	--PO dohmm, --PO dohzg, --PO BRU --PO higgsMassRange=x,y	kappa_g,kapppa_gam,kappa_Zgam,kappa_W,kappa_Z, c7_Gscal_tot, kappa_t, kappa_tau,kappa_mu,kappa_Zg,BRinv,BRundet	Higgs boson couplings to fermions and bosons in which the $gg\to H$, $H\to \gamma \gamma$ and $H\to Z\gamma$ loops are scaled by their own effective couplings ${\kappa }_g^2$, ${\kappa }_{\gamma }^2$ and ${\kappa }_{Z\gamma }^2$ and the branching ratio to invisible particles (any process with decay string hinv is scaled by this), and the undetected decay modes are scaled by BRundet. The total width Higgs width is allowed to float by effectively replacing the coupling ${\kappa }_b$ as a parameter of interest. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Couplings to vector bosons and fermions	K3	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_V,kappa_F	Higgs boson couplings to bosons and fermions. By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, $H\to Z\gamma$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
	K3Inv	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	kappa_V,kappa_F, BRinv	Higgs boson couplings to bosons and fermions and free floating branching ratio to invisible particles (any process with decay string hinv is scaled by this). By setting the options doX=1, the process specified will be included as its own process and scaled by the appropriate coupling modifiers. By default, the $H\to \mu \mu$, $H\to cc$, $H\to Z\gamma$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Ratios of coupling modifiers	L1	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	lambda_WZ,lambda_Zg, lambda_bZ,lambda_gamZ,lambda_tauZ,lambda_muZ,lambda_tg,kappa_gZ	Ratios of coupling modifiers ${\lambda }_{WZ}={\kappa }_W/{\kappa }_Z$, ${\lambda }_{Zg}={\kappa }_Z/{\kappa }_g$, ${\lambda }_{bZ}={\kappa }_b/{\kappa }_Z$, ${\lambda }_{\gamma Z}={\kappa }_{\gamma }/{\kappa }_Z$, ${\lambda }_{\tau Z}={\kappa }_{\tau }/{\kappa }_Z$, ${\lambda }_{\mu Z}={\kappa }_{\mu }/{\kappa }_Z$, ${\lambda }_{tg}={\kappa }_t/{\kappa }_g$, ${\kappa }_{gZ}={\kappa }_g{\kappa }_Z/{\kappa }_H$, where ${\kappa }_H$ is the total width modifier. By default, the $H\to \mu \mu$, $H\to cc$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.

The next models are constrained models to study a limited set of ratios of couplings. These are particularly useful to study models such as 2HDM that modify the SM Higgs couplings in a specific way. The models are implemented in the python file HiggsCouplings.py.

You can produce the model by including the following option in the text2workspace.py command:

-P HiggsAnalysis.CombinedLimit.HiggsCouplings:model

	model	--PO	POIs	Description
Ratios of up/down fermion couplings	lambdadu	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	lambda_du,lambda_Vu,kappa_uu	Ratios of coupling modifiers ${\lambda }_{du}={\kappa }_d/{\kappa }_u$, ${\lambda }_{Vu}={\kappa }_V/{\kappa }_u$, ${\kappa }_{uu}={\kappa }_u^2/{\kappa }_H$, where ${\kappa }_H$ is the total width modifier. By default, the $H\to \mu \mu$, $H\to cc$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Ratios of lepton to quark couplings	lambdalq	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	lambda_lq,lambda_Vq,kappa_qq	Ratios of coupling modifiers ${\lambda }_{lq}={\kappa }_l/{\kappa }_q$, ${\lambda }_{Vq}={\kappa }_V/{\kappa }_q$, ${\kappa }_{qq}={\kappa }_q^2/{\kappa }_H$, where ${\kappa }_H$ is the total width modifier. By default, the $H\to \mu \mu$, $H\to cc$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Ratios of fermion to vector boson couplings	lambdafv	--PO dohmm, --PO dohzg --PO dohcchgluglu --PO BRU --PO higgsMassRange=x,y	lambda_FV,kappa_VV	Ratios of coupling modifiers ${\lambda }_{fV}={\kappa }_f/{\kappa }_V$ ${\kappa }_{VV}={\kappa }_V^2/{\kappa }_H$, where ${\kappa }_H$ is the total width modifier. By default, the $H\to \mu \mu$, $H\to cc$ are tied to other processes or fixed to their SM values. Set BRU=1 to include the Higgs branching ratio uncertainties directly into the calculation of the partial widths, instead of just using the uncertainties in the datacard. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.

Outdated couplings modifer models

These models were used early in the Higgs discovery, but are now considered outdated. They are still available for backward compatibility and for simple studies, but are generally not recommended. The models are implemented in the python file HiggsCouplings.py.

You can produce the model by including the following option in the text2workspace.py command:

-P HiggsAnalysis.CombinedLimit.HiggsCouplings:model

	model	--PO	POIs	Description
Custodial Symmetry Model	cWZ	--PO higgsMassRange=x,y	Cz,Cwz	Ratio of couplings to W bosons and Z bosons. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Couplings with universal up or down-type fermion couplings	c5udHiggs	--PO universalCF, --PO higgsMassRange=x,y	Cg,Cv,Cglu,Cu,Cd	Treat photon, vector-boson and gluon coupling as independent couplings. Up-type and down-type fermions have independent couplings. include universalCF to replace Cu and Cd with universal fermion coupling Cf. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.
Couplings with universal lepton or quark couplings	c5qlHiggs	--PO universalCF, --PO higgsMassRange=x,y	Cg,Cv,Cglu,Cq,Cl	Treat photon, vector-boson and gluon coupling as independent couplings. quark and lepton fermions have independent couplings. include universalCF to replace Cq and Cl with universal fermion coupling Cf. Include the higgsMassRange option with range $x<m_H<y$ to allow the Higgs boson mass to float in this range.