H-COUP Version 2: A program for one-loop corrected Higgs boson decays in non-minimal Higgs sectors,☆☆

https://doi.org/10.1016/j.cpc.2020.107512Get rights and content

Abstract

We present the concept of H-COUP_ver 2, which evaluates the decay rates (including higher order corrections) for the Higgs boson with a mass of 125GeV in various extended Higgs models. In the previous version (H-COUP_1.0), only a full set of the Higgs boson vertices are evaluated at one-loop level in a gauge invariant manner in these models. H-COUP_ver 2 contains all the functions of H-COUP_1.0. After shortly introducing these extended Higgs models and discussing their theoretical and experimental constraints, we summarize formulae for the renormalized vertices and the decay rates. We then explain how to install and run H-COUP_ver 2 with some numerical examples.

Program summary

Program title: H-COUP Version 2

CPC Library link to program files: http://dx.doi.org/10.17632/f88szmrj5x.2

Developer’s repository link: http://www-het.phys.sci.osaka-u.ac.jp/ hcoup/

Licensing provisions: GPLv3

Programming language: Fortran90

Journal Reference of previous version: Comput. Phys. Commun. 233 (2018), 134–144

Does the new version supersede the previous version?: Yes

Reasons for the new version: The previous version (H-COUP_1.0), which numerically evaluates the full set of one-loop corrected vertex functions for the Higgs boson with a mass of 125 GeV, does not automatically provide the decay rates, the total decay width and branching ratios. In addition, QCD corrections have not been included in the previous version.

Summary of revisions: Decay branching ratios and the total decay width for the Higgs boson with NLO electroweak and NNLO QCD corrections are added as outputs.

Nature of problem: Decay rates for the Higgs boson and the total decay width are numerically evaluated at NLO for electroweak and NNLO for QCD in the Higgs singlet model, four types (Type-I, Type-II, Type-X, Type-Y) of two Higgs doublet models with a softly-broken Z2 symmetry and the inert doublet model.

Solution of method: Electroweak and QCD corrections to the decay rates are computed by the improved on-shell scheme and the MS¯ scheme, respectively.

Additional comments including restrictions and unusual features: All functions of the previous version are included in H-COUP_ver 2.

References:

[1] S. Kanemura, M. Kikuchi, K. Sakurai, K. Yagyu, Comput. Phys. Commun. 233 (2018) 134-144 [arXiv:1710.04603 [hep-ph]].

[2] S. Kanemura, M. Kikuchi, K. Mawatari, K. Sakurai, K. Yagyu, Nucl. Phys. B 949 (2019) 114791 [arXiv:1906.10070 [hep-ph]].

[3] S. Kanemura, M. Kikuchi, K. Mawatari, K. Sakurai, K. Yagyu, Phys. Lett. B 783 (2018) 140-149 [arXiv:1803.01456 [hep-ph]].

[4] S. Kanemura, M. Kikuchi, K. Sakurai, K. Yagyu, Phys. Rev. D 96 (2017) 035014 [arXiv:1705.05399[hep-ph]].

[5] S. Kanemura, M. Kikuchi, K. Yagyu, Nucl. Phys. B 907 (2016) 286-322 [arXiv:1511.06211 [hep-ph]].

[6] S. Kanemura, M. Kikuchi, K. Yagyu, Nucl. Phys. B 917 (2017) 154-177 [arXiv:1608.01582 [hep-ph]].

[7] S. Kanemura, Y. Okada, E. Senaha, C. Yuan, Phys. Rev. D 70 (2004) 115002 [hep-ph/0408364].

[8] S. Kanemura, M. Kikuchi, K. Yagyu, Phys. Lett. B 731 (2014) 27-35 [arXiv:1401.0515 [hep-ph]].

[9] S. Kanemura, M. Kikuchi, K. Yagyu, Nucl. Phys. B 896 (2015) 80-137 [arXiv:1502.07716 [hep-ph]].

[10] S. Kanemura, M. Kikuchi, K. Sakurai, Phys. Rev. D 94 (2016) 115011 [arXiv:1605.08520 [hep-ph]].

Introduction

By the discovery of the Higgs boson at the LHC, exploring details of the scalar sector, which is responsible for the electroweak (EW) symmetry breaking, has become one of the most important subjects of high energy particle physics. The current situation clarified by collider experiments can be summarized by two important things, (i) properties of the discovered Higgs boson are consistent with those of the Standard Model (SM) Higgs boson within theoretical and experimental uncertainties, and (ii) other new particles have not yet been observed. These current experimental results can be explained within the minimal Higgs sector assumed in the SM, which is composed of one isospin scalar doublet.

On the other hand, the Higgs sector of the SM does not have any principle to determine its structure, differently from the gauge sector. Thus, non-minimal forms of the Higgs sector should also be considered as well, unless they are excluded by the current data. In addition, non-minimal Higgs sectors are often predicted in various new physics models which have been proposed to solve problems of the SM; i.e., the hierarchy problem as well as the existence of phenomena which cannot be explained in the SM such as neutrino oscillations, dark matter and baryon asymmetry of the Universe. Because the structure of the Higgs sector can strongly depend on each new physics scenario, exploring the shape of the Higgs sector is a key to determine the direction of new physics beyond the SM.

When additional Higgs bosons are discovered at future collider experiments, it provides direct evidence for a non-minimal Higgs sector. The structure of the non-minimal Higgs sector is then narrowed down by properties of additional Higgs bosons; e.g., electric charges, masses, couplings and so on. However, even if the second Higgs boson is not directly discovered, we can indirectly determine the structure of the Higgs sector by measuring deviations in observables for the discovered Higgs boson from the SM predictions such as couplings, the width, branching ratios and production cross sections. Currently, these observables are not sufficiently measured with enough accuracy for indirect searches for additional Higgs bosons [1], [2]. However, they are expected to be precisely measured at future experiments, such as the high-luminosity LHC (HL-LHC) [3], [4], [5], the International Linear Collider (ILC) [6], [7], [8], [9], the Future Circular Collider (FCC) [10], the Circular Electron Positron Collider (CEPC) [11] and the Compact LInear Collider (CLIC) [12]. Measurements of the Higgs boson properties at these future colliders have been summarized in Ref. [13]. For example, couplings of the discovered Higgs boson are expected to be measured with one percent level or better at the ILC with the center of mass energy of 250 GeV. Therefore, accurate calculations of the Higgs boson observables with radiative corrections are necessary to compare with their precisely measured values.

There have been many studies on radiative corrections to the vertex functions and decay rates of the Higgs boson h(125) in various non-minimal Higgs sectors and new physics models in addition to the SM, where h(125) represents the discovered Higgs boson with the mass of 125 GeV. In Table 1, we summarize previous studies on one-loop corrections to the hff̄, hVV (V=W,Z) and hhh vertices as well as the decay rates for hff̄, hVV in the SM, MSSM, NMSSM, two Higgs doublet models (THDMs) with a softly broken Z2 symmetry, the Higgs singlet model (HSM) and the inert doublet model (IDM). One can numerically evaluate these vertex functions and decay rates with higher order corrections by using several public tools. For the SM and MSSM (next to MSSM), HDECAY [67], [68], FeynHiggs [69], [70], [71], [72] and HFOLD [73] (NMHDECAY [74], [75], NMSSMCALC [76] and NMSSMCALCEW [48]) can compute decay width and branching ratios of Higgs bosons with EW corrections and QCD corrections. Regarding the extended Higgs models, 2HDMC [77] and sHDECAY [78] can give decay rates and total width, and branching ratios of Higgs bosons with QCD corrections in THDMs and the HSM. Also, 2HDECAY [79] can provide the decay rates and branching ratios with both EW corrections and QCD corrections in THDMs. Apart from these public tools, as a first tool to observables for h(125) with one-loop EW corrections in various non-SUSY models with extended Higgs sectors, H-COUP_1.0 [80] had been published.

In this article for the manual, we present H-COUP_ver 2, a fortran program for numerical evaluation of decay rates of the discovered Higgs boson h(125) with next-to-leading order (NLO) EW and scalar loop corrections, and next-to-next-to leading order (NNLO) QCD corrections in a variety of extended Higgs models such as the HSM, four types (Type-I, Type-II, Type-X, Type-Y) of THDMs with a softly-broken Z2 symmetry, and the IDM. H-COUP_ver 2 can also evaluate decay rates of h(125) in the SM with the same accuracy. We have confirmed that numerical values for the decay rates of hff̄ in the THDMs with the EW and scalar loop corrections at NLO are in good agreement with those computed by 2HDECAY. In the previous version (H-COUP_1.0), a full set of vertices for h(125) can be evaluated at one-loop level in the improved on-shell scheme for NLO EW in these models. By extending the H-COUP_1.0 functionalities, we completed the calculations of all the decay rates of h(125) as H-COUP_ver 2. Therefore, H-COUP_ver 2 contains all the functions of H-COUP_1.0.

Physics results obtained by preliminary version of H-COUP _ver 2 have been presented in Refs. [60], [61] where NLO EW and NLO QCD corrections were implemented. We note that, with a process to make a public version of the H-COUP_ver 2 program, we added NNLO-QCD corrections to the hqq̄, gg, γγ modes. We also added hμμ for the completeness of the list of the decay modes.

This article is organized as follows. In Section 2, we briefly review the extended Higgs models, and define input parameters for each model. In Section 3, we discuss renormalized vertices and decay rates of h(125) based on Refs. [21], [51], [52], [53], [60], [61], [62], [63], [65] which are implemented in H-COUP_ver 2. In Section 4, the structure of H-COUP_ver 2 is explained. In Section 5, the installation and how to run H-COUP_ver 2 are described with some numerical examples. Summary of this manual is given in Section 6.

Section snippets

Models and constraints

In this section, we define the Higgs sectors of the HSM, the THDMs with the CP-conservation and the IDM. In particular, we uniformly and compactly introduce mass eigenstates of the scalar fields and free input parameters in each model. Since all the models are exactly the same as those in H-COUP_1.0, see the manual of Ver.1 [80] for details of definitions and descriptions about the models such as Lagrangian and some formulae.

In the all models covered in this manual, mass eigenstates of scalar

Renormalized vertices and decay rates

In this section, renormalized vertex functions for the discovered Higgs boson hff̄, hVV (V=WorZ) and hhh at one-loop are defined. Subsequently, analytical expressions of the decay rates with higher order corrections are described, i.e., hff̄,hVVVff̄,hgg and hVγ (V=γorZ). These quantities are output parameters of the H-COUP_ver 2. In H-COUP_ver 2, the decays into extra Higgs bosons, e.g., hHH, hAA, are not contained.

Here, we outline the renormalization scheme for calculations of

Structure of H-COUP_ver 2

The structure of H-COUP_ver 2 is schematically shown in Fig. 1. Differently from H-COUP_1.0, the model and the order of calculations are specified from the command line interface (see Section 5). H-COUP_ver 2 then reads the model independent (global) and model dependent input parameters, where the former is the SM inputs and the squared momenta of the renormalized form factors, which are commonly used in all the model files. The SM parameters and their default values are summarized in Table 4.

Installation and how to run

In order to run the H-COUP program, users need to install a Fortran compiler (GFortran is recommended) and LoopTools [109] in advance. One can download the LoopTools package from [109], and see the manual for its installation.

One can download the H-COUP program on the following webpage

In the following, we describe how to run H-COUP_ver 2 in order.

  • 1.

    Unzip the HCOUP-2.X.zip file:

    Then, the HCOUP-2.X directory (HCOUP-2.X/) is created. In this directory, one can find 3 files (Makefile, README,

Summary

In this paper, the concept and the manual of H-COUP_ver 2 have been presented, which is a set of fortran programs for numerical evaluation of decay rates of the Higgs boson with a mass of 125 GeV and the decay width with higher order corrections (NLO for EW and scalar loop corrections, and NNLO for QCD corrections) for various models of extended Higgs sectors. In H-COUP_ver 2, in addition to the SM, the Higgs singlet model, four types of two Higgs doublet models with a softly-broken Z2 symmetry

CRediT authorship contribution statement

Shinya Kanemura: Supervision, Conceptualization, Formal analysis, Writing - review & editing. Mariko Kikuchi: Software, Formal analysis, Writing - original draft, Writing - review & editing. Kentarou Mawatari: Software, Formal analysis, Writing - original draft, Writing - review & editing. Kodai Sakurai: Software, Formal analysis, Writing - original draft, Writing - review & editing. Kei Yagyu: Software, Formal analysis, Writing - original draft, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported in part by the Grant-in-Aid on Innovative Areas, the Ministry of Education, Culture, Sports, Science and Technology, Japan, No. 16H06492 and No. 18H04587 [S.K.], JSPS, Japan KAKENHI Grant No. 18K03648 [K.M.], JSPS, Japan KAKENHI Grant No. 18J12866 [K.S.], and Early-Career Scientists, Japan , No. 19K14714 [K.Y.].

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