Two-Higgs-doublet models with Higgs symmetry

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1 Two-Higgs-doublet models with Higgs symmetry Chaehyun Yu a a School of Physics, KIAS, Seoul , Korea Abstract We investigate two-higgs-doublet models (2HDMs) with local U(1) H Higgs flavor symmetry which distinguish one Higgs doublet from the other. These models provide a natural resolution of the Higgs mediated flavor-changing-neutral currents problem, which exists in 2HDMs with Z 2 parity. We consider the Higgs phenomenology in Type-I 2HDMs with the U(1) H symmetry, where the SM fermions are not charged under U(1) H as the simplest case. Various constraints such as vacuum stability and perturbativity as well as the electroweak precision observables and collider search bounds on charged Higgs boson are taken into account. We find that the allowed Higgs signal strengths are much broader than those in the ordinary Type-I 2HDM and our model could be distinguished from the ordinary 2HDM in a certain parameter region. However, if the couplings of the new boson discovered at the LHC turn out to be close to those of the Higgs boson in the SM, the distinction would be nontrivial. Keywords: Higgs boson, 2HDM, U(1) H 1. Introduction The new boson discovered at the Large Hadron Collider (LHC) opens a new era in particle physics [1]. The property of the new boson is consistent with those of the Higgs boson in the Standard Model (SM) [2]. The most updated values of couplings of this boson to the SM particles indicate that this new boson is a Higgs boson in the SM, but we could not exclude the possibility that this boson is one of Higgs bosons in an extended model, which might be motivated by supersymmetry or grand unified theories, etc. Two Higgs doublet model (2HDM) [3] which adds an extra Higgs doublet to the SM Higgs sector or chiral U(1) models which might reconcile experimental anomalies in the top-quark forward-backward asymmetry at the Tevatron and R(D ( ) ) at BABAR [4]. The 2HDM is one of the simplest extension of the SM Higgs sector. In general, the models with many Higgs fields suffer from flavor changing processes. In order to avoid the flavor-changing-neutral-current (FCNC) problem, an ad hoc Z 2 symmetry is commonly assigned [5]. In most cases, a softly broken discrete Z 2 symmetry is address: chyu@kias.re.kr (Chaehyun Yu) Preprint submitted to Hepmad13 December 3, 2013

2 imposed to avoid the domain wall problem, which appear in the case that a discrete symmetry is spontaneously broken. However the origin of the soft breaking is not clear at all. This could be resolved by replacing the Z 2 symmetry by a local U(1) H gauge symmetry, which is the origin of the Z 2 symmetry when it is spontaneously broken [6]. In this work, we investigate phenomenology of the 2HDM with the U(1) H gauge symmetry in light of the discovery of a SM-like Higgs boson at the LHC. We focus on the Type-I case for simplicity and compare our results with those in the ordinary Type-I 2HDM. 2. Models There are many different ways to construct a Type-I 2HDM with U(1) H symmetry. In this work, we consider anomaly-free cases, some of which are shown in Table 1. Type U R D R Q L L E R N R H 2 (u+d) 3(u+d) U(1) H charge u d 2 2 (2u+d) (u+2d) q H2 = (u d) 2 q H U(1) B L 1/3 1/3 1/ U(1) R U(1) Y 2/3 1/3 1/6 1/ /2 Table 1: Charge assignments of an anomaly-free U(1) H in the Type-I 2HDM. In anomalous cases like U(1) B or U(1) L models, extra chiral fermions should be introduced. Among various scenarios, the first case in Table 1 is interesting because the U(1) H gauge boson Z H does not couple to the SM fermions. The Z H boson is fermiophobic and the SM fermions are U(1) H singlets. The scalar potential is fixed by local gauge invariance and renormalizability: V scalar = ˆm 2 1 ( Φ 2 )H 1 H 1+ ˆm 2 2 ( Φ 2 )H 2 H 2 ( m 2 3 (Φ)H 1 H 2+ h.c. ) + λ 1 2 (H 1 H 1) 2 + λ 2 2 (H 2 H 2) 2 +λ 3 (H 1 H 1)(H 2 H 2)+λ 4 H 1 H 2 2 +m 2 Φ Φ 2 +λ Φ Φ 4, (1) where H 1 and H 2 are two Higgs doublets andφis a complex singlet with U(1) H charge q Φ, which contributes to the U(1) H breaking. It should be noted that in this potential theλ 5 terms in the ordinary 2HDM do not appear. More detail discussion on the model can be found in Ref. [7]. After electroweak and U(1) H symmetry breaking, one can have a pair of charged Higgs boson H ±, a pseudoscalar boson a, and three neutral Higgs bosons h, H, h (mixtures of h 1, h 2 and h Φ ), where h is the lightest Higgs boson discovered at the LHC. A pair of charged Goldstone boson and two neutral Goldstone bosons are eaten by the SM gauge bosons W ±, Z and the U(1) H boson Z H. The existence of h Φ and Z H is different from the ordinary 2HDM and they can change Higgs phenomenology from the ordinary 2HDM. 2

3 3. Constraints There are many theoretical and experimental constraints on our model. First, we consider three well-known theoretical constraints, vacuum stability of the Higgs potential, perturbativity of the Higgs couplings, and unitarity of the scattering matrix elements. Secondly, we take into account the constraints on the charged Higgs boson. In the LEP experiments, the lower bound on the charged Higgs boson is about 80 GeV [8] and we also impose the recent bound coming from the top quark decay from the LHC experiments [9]. The bound from the b sγ is tanβ 1 in the Type-I 2HDM [10]. Thirdly, we consider the constraints from the electroweak precision observables (EWPOs), which is useful in the case that new physics has no direct couplings to the SM fermions. The ordinary Type-I 2HDM is exactly this case. In our model, this can be achieved by assuming that the Z H boson is heavy enough to be decoupled from the electroweak scale. In the non-decoupling limit we consider the fermiophobic case as shown in the previous section. In this case the Z H boson can couple to the SM fermions only through the mixing between the Z and Z H boson, but the mixing angle is strongly constrained by search for the dijet resonance and Drell-Yan experiments at the LHC. Finally, we note that the search for the SM-like Higgs boson at the LHC also constrain the heavy Higgs boson. In high mass region m H 200 GeV, the main search channel is h ZZ 4l and the constraint on the signal strength isµ ZZ gg [11]. We also consider the constraints from the SM-like Higgs boson search in the region m H 200 GeV. 4. Phenomenology In this section, we discuss phenomenology of our model, focusing on the SM-like Higgs boson. There are 10 parameters in the potential when the Z H boson effects are neglected. One of them is fixed by the SM-like Higgs boson mass m h 126 GeV. We scan the other 9 parameters in the following ranges: 1 tanβ 100, 126 GeV m A 1 TeV, dm H +,H 200 GeV, 0 α,α 1,2 2π, 126 GeV m h 1 TeV, 0 GeV v Φ 3 TeV, respectively, where dm H +(dm H )=m H +(m H ) m A. The signal strengthµfor each decay mode i with the production tag j is given by j µ i j =σ(pp h) 2HDM Br(h i) 2HDM σ(pp h) j SM Br(h i). (2) SM In this work, we consider two distinct cases. First, we consider the Type-I 2HDM with U(1) H by assuming that Z H boson is decoupled. Then the extra contribution comes from only h Φ. Secondly, we consider the Type-I 2HDM with U(1) H, but the Z H boson is fermiophobic. The Z H contribution to the EWPOs are limited by the small mixing angle which is required from the Drell-Yan experiments. We show the scattered plot forµ γγ gg andµ ZZ gg in Fig. 1 in the Type-I 2HDM with h Φ. The red points are allowed in the ordinary Type-I 2HDM, while the blue points are allowed in the Type-I 2HDM with h Φ. The skyblue and green regions are consistent 3

4 Type-I 2HDM with h Φ ordinary ZZ γγ Figure 1:µ γγ gg vs.µ ZZ gg in the ordinary Type-I 2HDM (red) and Type-I 2HDM withφ(blue). The skyblue and green regions are the allowed ones at CMS and ATLAS in the 1σ level Type-I 2HDM with Z H ordinary ZZ γγ Figure 2:µ γγ gg vs.µ ZZ gg in the ordinary Type-I 2HDM (red) and Type-I 2HDM with Z H (blue). The skyblue and green regions are the allowed ones at CMS and ATLAS in the 1σ level. with the data at CMS and ATLAS, respectively, in the 1σ range, where both data are consistent with each other in the 2σ level. The SM predictsµ γγ gg=µ ZZ gg = 1, which is consistent with the CMS data, but the ATLAS data are consistent in the 2σ level. As shown in Fig. 1, the region ofµ ZZ gg 0.4 is not allowed in the ordinary 2HDM. Our model could be distinguished in this region. However, if it turns out that the signal strength is close to the SM prediction, it would be non-trivial to distinguish our models from the ordinary 2HDM as well as the SM. In Fig. 2, we depict the scattered plot forµ γγ gg andµ ZZ gg in the Type-I 2HDM with the fermiophobic Z H boson by assumingα 1 =α 2 = 0, whereα 1,2 are the mixing angles between h 1, h 2 and h Φ. In this case we choose the following parameter ranges for the U(1) H gauge boson mass m ZH and U(1) H gauge coupling g H : 0 g H 4π and 36 GeV M ZH 1 TeV, respectively. The red points are allowed in the ordinary Type- I 2HDM, while the blue points are allowed in the Type-I 2HDM with Z H, respectively. As shown in Fig. 2, the 2HDM with Z H seem to have broader allowed regions, but 4

5 there is no essential difference between two models. However, in case of the general mixing between 1, h 2 and h Φ, we might be able to distinguish the 2HDM with Z H from the ordinary 2HDM like in the case of the 2HDM with h Φ. As in the previous case, if it turns out that the signal strengths are close to the SM prediction, it would be non-trivial to distinguish our models from the ordinary 2HDM as well as the SM. In this case, it would be crucial to discover new extra scalars and Z H boson in order to tell one from the other. 5. Conclusions In this work we considered the Type-I 2HDM with the local U(1) gauge symmetry, which is the origin of the typical Z 2 symmetry. We performed the detailed phenomenological analysis for the model by taking into account various theoretical and experimental constraints. We find that our models might be distinguished in a certain parameter region. However if the Higgs couplings to the SM particles are close to the SM couplings or the signal strengths are consistent with the SM prediction, the distinction of our models from the ordinary 2HDM with Z 2 symmetry or the SM would be non-trivial. In this case, it would be essential to search for the Z H boson and/or extra scalar bosons to distinguish our model from the ordinary 2HDM and the SM. References [1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716, 1 (2012); S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716, 30 (2012). [2] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 110 (2013) [arxiv: [hep-ex]]; ATLAS Collaboration, ATLAS-CONF , CERN, Geneva Switzerland (2012). [3] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher and J. P. Silva, Phys. Rept. 516, 1 (2012). [4] P. Ko, Y. Omura and C. Yu, Phys. Rev. D 85, (2012); JHEP 1201, 147 (2012); Eur. Phys. J. C 73, 2269 (2013); JHEP 1303, 151 (2013). [5] S. L. Glashow and S. Weinberg, Phys. Rev. D 15 (1977) [6] P. Ko, Y. Omura and C. Yu, Phys. Lett. B 717, 202 (2012). [7] P. Ko, Y. Omura and C. Yu, arxiv: [hep-ph]. [8] G. Abbiendi et al. [ALEPH and DELPHI and L3 and OPAL and The LEP working group for Higgs boson searches Collaborations], [arxiv: [hep-ex]]. [9] G. Aad et al. [ATLAS Collaboration], JHEP 1206, 039 (2012); S. Chatrchyan et al. [CMS Collaboration], JHEP 1207, 143 (2012). [10] T. Hermann, M. Misiak and M. Steinhauser, JHEP 1211, 036 (2012). [11] ATLAS Collboration, ATLAS-CONF , CERN, Geneva Switzerland (2012). 5