Status of the aligned two-Higgs-doublet model confronted with the Higgs data

Imposing the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data, flavor observables and the non-observation of additional Higgs at collider, we study the implications of available Higgs signals on a two-Higgs-doublet model with the alignment of the down-type quarks and charged lepton Yukawa coupling matrices. Compared to the four traditional types of two-Higgs-doublet models, the model has two additional mixing angles θd and θl in the down-type quark and charged lepton Yukawa interactions. We find that the mixing angle θd can loose the constraints on sin(β − α), tan β and mH ± sizably. The model can provide the marginally better fit to available Higgs signals data than SM, which requires the Higgs couplings with gauge bosons, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ u\overline{u} $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ d\overline{d} $\end{document} to be properly suppressed, and favors (1 < θd< 2, 0.5 < θl< 2.2) for mh = 125.5 GeV and (0.5 < θd< 2, 0.5 < θl< 2.2) for mH = 125.5 GeV. However, these Higgs couplings are allowed to have sizable deviations from SM for (mh = 125.5 GeV, 125.5 ≤ mH ≤ 128 GeV) and (125 GeV ≤ mh ≤ 125.5 GeV, mH = 125.5 GeV).


I. INTRODUCTION
The CMS and ATLAS collaborations have announced the observation of a scalar around 125 GeV [1,2], which is supported by the Tevatron search [3]. The properties of this particle with large experimental uncertainties are well consistent with the SM Higgs boson, which will give the strong constraints on the effects of new physics.
One of the simplest extension of the SM is obtained by adding a second SU(2) L Higgs doublet [4]. The two-Higgs-doublet model (2HDM) has very rich Higgs phenomenology, including two neutral CP-even Higgs bosons h and H, one neutral pseudoscalar A, and two charged Higgs H ± . Further, the couplings of the CP-even Higgs bosons can deviate from SM Higgs boson sizably. Therefore, the observed signal strengths of the Higgs boson and the non-observation of additional Higgs can give the strong implications on the 2HDMs.
In this paper, we focus on a two-Higgs-doublet model that allows both doublets to couple to the down-type quarks and charged leptons with aligned Yukawa matrices ( A2HDM) [24,28]. Also there is no tree-level FCNC in this model. Compared to the above four types of 2HDMs, there are two additional mixing angles in the Yukawa couplings of the downtype quarks and charged leptons. This model can be mapped to the four types of 2HDMs for the two angles are taken as specific values. There are also some works on the Higgs properties in the A2HDM after the discovery of Higgs boson [24,25,[29][30][31][32][33][34]. After imposing the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data, flavor observables and the non-observation of additional Higgs at collider, we study the implication of the latest Higgs signals data on the A2HDM.
Our work is organized as follows. In Sec. II we recapitulate the A2HDM. In Sec. III we introduce the numerical calculations. In Sec. IV, we discuss the implications of the available Higgs signals on the A2HDM after imposing the theoretical and experimental constraints.
Finally, we give our conclusion in Sec. V.

II. ALIGNED TWO-HIGGS-DOUBLET MODEL
The general Higgs potential is written as [35] We focus on the CP-conserving model in which all λ i and m 2 12 are real. Further, we assume λ 6 = λ 7 = 0, which also facilitates the comparison to the four traditional types of 2HDMs.
The two complex scalar doublets have the hypercharge Y = 1, Where v 1 and v 2 are the electroweak vacuum expectation values (VEVs) with v 2 = v 2 1 + v 2 2 = (246 GeV) 2 . The ratio of the two VEVs is defined as usual to be tan β = v 2 /v 1 . After spontaneous electroweak symmetry breaking, the physical scalars are two neutral CP-even h and H, one neutral pseudoscalar A, and two charged scalar H ± . These scalars are also predicted in the Higgs triplet models [36][37][38].
The Yukawa interactions of the Higgs doublets with the SM fermions can be given by where Q T = (u L , d L ), L T = (ν L , l L ), and Φ 2 = iτ 2 Φ * 2 . y u , y d and y ℓ are 3 × 3 matrices in family space. θ d and θ l parameterize the two Higgs doublets couplings to down-type quarks and charged leptons, respectively. Where a freedom is used to redefine the two linear combinations of Φ 1 and Φ 2 to eliminate the coupling of the up-type quarks to Φ 1 [24].
The tree-level couplings of the neutral Higgs bosons can have sizable deviations from those of SM Higgs boson. Table I shows the couplings of neutral Higgs bosons with respect to the SM Higgs boson. According to Table I, the A2HDM can be mapped to the four traditional types of 2HDMs via the angles θ d and θ l specified in Table II.

III. NUMERICAL CALCULATIONS
We have employed the following four codes to implement the various theoretical and experimental constraints. We require the A2HDM to explain the experimental data of flavor observables and the electroweak precision data within 2σ range.
• 2HDMC-1.5 [39]: The code is used to implement the theoretical constraints from the vacuum stability, unitarity and coupling-constant perturbativity. Also the oblique parameters (S, T , U) and δρ are calculated and the corresponding experimental data are from [40]. δρ has been measured very precisely via Z-pole precision observables to be very close to 1, which imposes a strong constraint on the mass difference between the various Higgses in 2HDMs. In addition, the code 2HDMC-1.5 [83] which calculates the Higgs couplings and the decay branching fractions, provides the necessary inputs for the following three codes.
• SuperIso-3.3 [41]: The code is used to implement the constraints from flavor observ-  [73] and D0 [74] collaborations as well as the four Higgs mass measurements from the ATLAS and CMS h → γγ and h → ZZ * → 4l analyses, which are listed in the [50]. In our discussions, we will pay particular attention to the surviving samples with χ 2 − χ 2 min ≤ 6.18, where χ 2 min denotes the minimum χ 2 . These samples correspond to the 95% confidence level regions in any two dimensional plane of the model parameters when explaining the Higgs data (corresponding to be within 2σ range).
In our calculations, the inputs parameters are taken as m 2 12 , the physical Higgs masses (m h , m H , m A , m H ± ), the vacuum expectation value ratio (tan β), the CP-even Higgs mixing angle (α), and the mixing angles of the down-type quark and charge lepton Yukawa couplings (θ d , θ l ). We fix respectively m h and m H as 125.5 GeV, and scan randomly the parameters in the following ranges: Where h i denotes h, H and A.m s is the mass of signal s and ∆m s is the experimental mass resolution of the analysis associated to signal s. However, if the χ 2 contribution from the Unlike the heavy CP-even Higgs, the right panel of Fig. 1 shows that the CP-odd Higgs A does not give the very visible effects on χ 2 around 125.5 GeV compared to the other mass ranges. m A is required to be larger than 63 GeV, and the on-shell decay h → AA is kinematically forbidden, which hardly affects the observed Higgs signals.
In GeV.
The contributions of the heavy CP-even Higgs boson to χ 2 can be sizably suppressed for m H ≥ 128 GeV. Therefore, we classify the surviving samples into groups: 125.5 GeV ≤ m H < 128 GeV and 128 GeV ≤ m H ≤ 900 GeV. In Fig. 3, the two groups of surviving samples are projected on the planes of mixing angles (sin(β −α), tan β, θ d and θ l ). Fig. 3 (a) shows that tan β can be over 20 for sin(β − α) is close to 1. Fig. 3 (b) shows that, for m H > 128 GeV, the mixing angle θ d can loose constraints on sin(β − α) visibly. For example, for  Here m 2 12 is taken as various values, the strong correlations still exist but the latter region becomes slightly wider than [16]. The main reason is from the constraints of ∆ρ, which is also studied in detail in [75]. Since there is small mass difference between  Thus m A is allowed to vary from 70 GeV to 700 GeV for m H ± around 100 GeV.
Similar to scenario A, Figs. 8 (d) and (e) show that, although the surviving samples favor 1 < tan β < 7, the value of χ 2 can be smaller than SM for a large tan β when θ d and θ l have the proper large values. Even for tan β = 41, the value of χ 2 can be smaller than SM for θ d = 0.7 and θ l = 2.1. Fig. 8 (f) shows that the samples with smaller than SM are in the range of 0.5 < θ d < 2 and 0.5 < θ l < 2.2. The minimal value of χ 2 (81.5) appears at θ d = 1.8 and θ l = 1.1.
In Fig. 9, the surviving samples with 20 GeV ≤ m h < 125 GeV are projected on the planes of Higgs couplings. Similar to scenario A, for the HV V coupling with the small absolute value, the Hbb coupling by suppressed properly is required to obtain enough large Br(h → ZZ * ) and Br(h → γγ). The constraints on hττ is much more weaken than huū and hdd. For the samples with smaller χ 2 than SM, there is the same sign for the heavy CP-even Higgs couplings to fermions and gauge bosons. Compared to SM, the HV V , Huū and Hdd shows that the theoretical constraint from perturbativity disfavors a large tan β much more visibly than Ref. [25]. In our analysis, we consider the 73 Higgs signal strengths observables from ATLAS, CMS, CDF and D0 collaborations as well as the four Higgs mass measurements from ATLAS and CMS, which are more than Refs. [24,25,31]. The HiggsSignals-1.1.0 is employed to takes into account the signal efficiencies, experimental mass resolution and uncertainties. Our paper shows that the Higgs couplings to gauge bosons and fermions are not more strongly constrained than Refs. [24,25,31,33]. Refs. [24,31] focus on the constraints of the Higgs signals on the Higgs couplings to gauge bosons and fermions. In addition to these Higgs couplings, we also give the allowed parameters spaces in detail, including tan β, sin(β − α), θ d , θ l , the neutral and charged Higgs masses, and show explicitly that the proper θ d can loose the constraints on sin(β − α), tan β and m H ± sizably. An interesting finding is that when θ d and θ l have the proper large values, the value of χ 2 can be smaller than SM for a large tan β (even tan β = 41), although the 2σ Higgs data and the relevant theoretical and experimental constraints favor a small tan β.

V. CONCLUSION
In this note, we studied the implications of the latest Higgs signals on a two-Higgs-doublet model with the alignment of the down-type quarks and charged lepton Yukawa coupling matrices. In our analysis, we consider the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data, flavor observables and the non-observation of additional Higgs at collider.
We obtained the following observations: decreases with m h in principle. The light CP-even Higgs can be allowed to be as low as 20 GeV for -0.25 < sin(β −α) ≤ 0. The constraints of the observed Higgs signals on the opening decay H → hh require tan β to be larger than 4 for m h < 60 GeV. Similar to scenario A, the mixing angle θ d can loose the constraints on sin(β − α), tan β and m H ± sizably. For m h < 125 GeV, θ d around π 2 can allow sin(β − α) to be in the range of −0.5 ∼ 0.44. Although the surviving samples favor 1 < tan β < 7, the value of χ 2 can be smaller than SM for tan β > 40 when θ d and θ l have the proper large values. m H ± is allowed to be below 100 GeV for the absolute value of tan(β − θ d ) is smaller than 2.5, and the samples with the smaller χ 2 than SM favor -0.5 < tan(β − θ d ) < 0 for the large m H ± .
(iii) The model can provide the marginally better fit to available Higgs signals data than SM. For m h = 125.5 GeV, the absolute values of hV V , huū and hdd couplings are respectively allowed to be as low as 0.94, 0.90 and 0.83, and θ d and θ l are favored in the ranges of 1 ∼ 2 and 0.5 ∼ 2.2. For m H = 125.5 GeV, the HV V , Huū and Hdd couplings are respectively allowed to be as low as 0.94, 0.86 and 0.77, and θ d and θ l are favored in the ranges of 0.5 ∼ 2 and 0.5 ∼ 2.2.