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Revista mexicana de física

versión impresa ISSN 0035-001X

Rev. mex. fis. vol.69 no.2 México mar./abr. 2023  Epub 05-Nov-2024

https://doi.org/10.31349/revmexfis.69.020803 

High Energy Physics

Flavor changing flavon decay ϕ→tc(ϕ=HF, AF) at the high luminosity large hadron collider

M. A. Arroyo-Ureña* 

A. Fernández-Téllez** 

G. Tavares-Velasco** 

* Centro Interdisciplinario de Investigación y Enseñanza de la Ciencia, Benemérita Universidad Autónoma de Puebla, 72570, Puebla, Pue., Mexico. e-mail: marcofis@yahoo.com.mx

** Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, 72570, Puebla, Pue., Mexico. e-mail: afernand@fcfm.buap.mx; gtv@fcfm.buap.mx

Abstract

We present a study of the flavor changing decays ϕ→tc(ϕ=HF, AF) of the CP-even and CP-odd scalar flavons at the large hadron collider and its next stage, the high-luminosity large hadron collider. The theoretical framework is an extension of the standard model that incorporates an extra complex singlet and invokes the Froggatt-Nielsen mechanism with an Abelian flavor symmetry. The projected exclusion and discovery regions in terms of the model parameters are reported. We find that AF could be detected at the LHC by considering a reasonable scenario of the model parameter space. As far as HF is concerned, we also found promising results that could be verified experimentally at the high-luminosity LHC.

Keywords: Flavon; flavor changing neutral currents; high luminosity large hadron collider

1 Introduction

It is well known that the standard model (SM) has been successful in predicting results experimentally tested to a high accuracy, culminating with the recent discovery of a new scalar boson compatible with the SM Higgs boson [1,2]. However, despite its success, some issues remain unexplained by the SM: the lack of a dark matter candidate, the hierarchy problem, unification, the flavor problem, etc. This encourages the study of SM extensions. In the framework of the SM there are no tree-level flavor changing neutral currents (FCNC), which are, however, predicted by several SM extensions, being mediated by the Higgs boson or other new scalar or vector boson particles. In the context of these models, it is worth studying any signal that could give clues for new physics (NP), such as the widely studied process ϕ→τμ, with ϕ a CP-even or CP-odd scalar boson [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. FCNC signals can also arise from the top quark decays t→cX (X=ϕ,γ,g,Z,H)[18,19,20,21,22,23,24,25,26], and from the less studied decay of a new heavy scalar boson into a top-charm quark pair [27], which could be searched at the LHC and the future high luminosity LHC (HL-LHC). The latter aims to increase the LHC potential capacity by reaching a luminosity up to L=3000 fb-1 around 2035 [28]. In this work we present a study of the ϕ→tc decay in a SM extension that incorporates a complex singlet SF via the Froggatt-Nielsen (FN) mechanism, which assumes that above some scale ΛF a symmetry (perhaps of Abelian type U(1)F) forbids the Yukawa couplings with the SM fermions charged under this symmetry; however, the Yukawa couplings can arise through non-renormalizable operators. The scalar spectrum of this model includes both a CP-even Flavon HF and a CP-odd Flavon AF. The former can mix with the SM Higgs boson when the flavor scale is of the order of a few TeVs. A detailed study of the Flavon phenomenology can be consulted in Refs. [29,30,31,32,33]. Our study not only could serve as a strategy for the Flavon search, but it can also be helpful to assess the order of magnitude of flavor violation mediated by this particles, which is an indisputable signature of physics beyond the SM.

The organization of this paper is as follows: in Sec. 2 we describe the most relevant theoretical aspects of the Froggatt-Nielsen singlet model (FNSM), which are necessary for our study. In Sec. 3 we obtain the constraints on the model parameters from the most recent experimental results on the Higgs boson coupling modifiers κi[34], the full decay width of the Higgs boson [35], anomalous magnetic dipole moment of the muon [36] and the perturbative limit. In addition, we include the current bound and the projections at the future colliders on BR(t→ch) in order to constrain the gϕtc coupling. Section 4 is devoted to study the signal pp→ϕ→tc(t→lνlb) and the potential background as well as the strategy used to search for the ϕ→tc decay at the LHC and the HL-LHC. Finally, the conclusions are presented in Sec. 5.

2 The Froggatt-Nielsen complex singlet model

We now focus on some relevant theoretical aspects of the FNSM. In Ref. [37] a comprehensive analysis of the Higgs potential is presented, along with constraints on the parameter space from the constraints on the Higgs boson signal strengths and the oblique parameters, including a few benchmark scenarios. Also, the authors of Ref. [11] report a study of the lepton flavor violating (LFV) Higgs boson decay h→lilj in the scenario where there is CP violation induced by a complex phase in the vacuum expectation value (VEV) of the complex singlet.

2.1 The scalar sector

In addition to the SM-like Higgs doublet, Φ, a FN complex singlet SF is introduced. They are given by

Φ=G+12v+ϕ0+iGz, (1)

SF=12(u+s+ip), (2)

where v is the SM VEV and u is that of the FN complex singlet, whereas G+ and Gz are identified with the pseudo-Goldstone bosons that become the longitudinal modes of the W+ and Z gauge bosons.

We consider a scalar potential that respects a global U(1) symmetry, with the Higgs doublet and the singlet transforming as Φ→Φ and SF→eiθSF. In general, such a scalar potential admits a complex VEV, namely, 〈SF〉0=ue-iα, but in this work we consider the special case in which the Higgs potential is CP conserving, i.e. we consider the limit with vanishing phase. Such a CP-conserving Higgs potential is given by:

V=-12m12Φ†Φ-12ms12SF*SF-12ms22SF*2+SF2+12λ1Φ†Φ2+λsSF*SF2+λ11Φ†ΦSF*SF, (3)

where ms22 stands for a U(1)-soft-breaking term, which is necessary to avoid the presence of a massless Goldstone boson, as will be evident below. Once the minimization conditions are applied, the following relations are obtained:

m12=v2λ1+u2λ11, (4)

ms12=-2ms22+2u2λs+v2λ11. (5)

In this CP-conserving potential, the real and imaginary parts of the mass matrix do not mix. Thus, the mass matrix for the real components can be written in the (ϕ0, s) basis as

MS2=λ1v2λ11uvλ11uv2λsu2. (6)

The corresponding mass eigenstates are obtained via the standard 2 × 2 rotation

ϕ0=cosαh+sinαHF,

s=-sinα h+cosαHF, (7)

with α a mixing angle. Here h is identified with the SM-like Higgs boson, with mass mh=125 GeV, whereas the mass eigenstate HF is the CP-even Flavon.

As for the mass matrix of the imaginary parts, it is already diagonal in the (Gz,p) basis:

MP2=0002ms22, (8)

where the physical mass eigenstate AF=p is the CP-odd Flavon. Both HF and AF are considered to be heavier than h.

2.2 Yukawa sector

The model, in addition to the new complex scalar singlet, also invokes the FN mechanism [38]. The effective FN U(1)F-invariant Lagrangian can be written as:

LY=ρijdSFΛFqijdQ-LiΦdRj+ρijuSFΛFqijuQ-LiΦ~uRj+ρijlSFΛFqijlL-LiΦlRj+H.c., (9)

which includes terms that become the Yukawa couplings once the U(1) flavor symmetry is spontaneously broken. Here qijf(f=u, d, l) denote the charges of each fermion type under some unspecified Abelian flavor symmetry, which help to explain the fermion mass hierarchy; ρijf are dimensionless couplings seemingly of O(1), ΛF represents the flavor scale and

Q-LiT=(uLi, dLi),

L-LiT=(νLi, lLi), (10)

Φ~=iσ2Φ*.

We now write the neutral component of the Higgs field in the unitary gauge and use the first order expansion

(SFΛF)qij=u+s+ip2ΛFqij≃u2ΛFqij1+qijs+ipu, (11)

along with Eqs. (2), (7) and (10). We also define Yijf=ρijf(u/2ΛF)qijf, M~f=(v/2)Yijf, rs=v/(2u). In order to diagonalize the mass matrix M~f, the electroweak fields are redefined as

FL→ULfFL, fR→URffR⇒Yf=ULf†YdiagofURf, (12)

where Ydiagof=l=(2/v)diago(me, mμ, mτ)=(2/v)Ml, analogously for the case of quarks. Thus, one gets the following Yukawa Lagrangian for the Higgs- and Flavon-fermion interactions:

LY=1vU-MuU+D-MdD+L-MlL(cαh+sαHF)+rsU-iZ~uUj+D-iZ~dDj+L-iZ~lLj(-sαh+cαHF+iAF)+H.c., (13)

where sα≡sinα, cα≡cosα. A fact to highlight is that the intensity of the flavor violating (FV) couplings are encapsulated in the Z~ijf=ULf†ZijfURf matrices. In the flavor basis, the Zijf matrix elements are given by Zijf=ρijf(u/2ΛF)qijfqijf, which remains non-diagonal even after diagonalizing the mass matrices, thereby giving rise to FV scalar couplings. In addition to the Yukawa couplings, we also need the ϕVV(V=W, Z) couplings for our calculation, which can be extracted from the kinetic terms of the Higgs doublet and the complex singlet. In Table I we show the coupling constants for the interactions of the SM-like Higgs boson and the Flavons to fermions and gauge bosons.

Table I Couplings of the SM-like Higgs boson h and the Flavons HF and AF to fermion pairs and gauge boson pairs in the FNSM. Here rs=v/2u. 

Vertex (ϕXX) Coupling constant (gϕXX)
hfif-j cαvMijf-sαrsZ~ijf
HFfif-j sαvMijf+cαrsZ~ijf
AFfif-j irsZ~ijf
hZZ gmZcWcα
hWW gmWcα
HFZZ gmZcWsα
HFWW gmWsα

3 Constraints on the FNSM parameter space

To evaluate the decay widths and production cross-sections of the Flavons HF and AF, we need the bounds on the parameter space of our model, they are:

  • The mixing angle α.

  • The VEV of the FN complex singlet u.

  • The matrix element Z~tc.

  • The Flavon masses mHF and mAF.

3.1 Constraint on the mixing angle α and VEV of singlet u

It turns out that these parameters can be constrained via the Higgs boson coupling modifiers κj(j=W, Z, g, b, τ, μ)[34], which are defined for a given Higgs boson production mode i→h or decay channel h→j as

κi2=σi/σiSMorκj2=Γj/ΓjSM, (14)

where σiSM(ΓjSM) stands for the pure SM contributions, whereas σi(Γj) includes new physics contributions.

Figure 1a) shows the cα-u plane, where each colored area represents the allowed regions by κj considering the expected results at the HL-LHC at a confidence level of 2σ. Besides, in the same plot, the intersection of all kj's is included, which coincides with κτ since the latter is the most restrictive. Meanwhile, we present separately in Fig. 1b) the intersection of all kj's and the allowed region by both the perturbative limit applied on the parameter of the potential λs=(mAF2+cα2mHF2+mh2sα2)/(2u2)≤4π and the current discrepancy between the experimental measurement and the SM theoretical prediction [36] of the anomalous magnetic dipole moment given by

Δaμ=(25.1±5.9)×10-10,

ΔaμFNSM≈mμ16π2∑ϕ=h, HF, AF‍∑l=μ, τ‍mlgϕμl2mϕ×2ln[mϕ2ml2]-3. (15)

Figure 1 a) Allowed regions by all κj coupling modifiers in the cα-u plane, where V=Z, W; b) Only intersection of kj's and excluded zone by perturbative limit. 

We notice in Fig. 1b) that cα is close to unity, this is to be expected because the dominant term of the ghfif-i coupling in Table I is proportional to cα. When cα=1, the SM case is recovered. As far as the VEV of the FN complex singlet is concerned, it is a lower limit imposed by the perturbative limit; the most stringent is when mAF=mHF=1000 GeV, u≥281 GeV. The exploration of the muon anomalous magnetic dipole moment help us to find a upper limit on u≤1100 GeV, in addition to imposing a lower limit on cα≥0.995. We also explored the total decay width of the Higgs boson in order to find additional constrains on the mixing angle α and u, however this observable is not restrictive.

3.2 Constraint on Z~tc

So far, we only have considered the bound on the diagonal couplings; however, we need a bound on the Z~tc matrix element in order to evaluate the ϕ→tc decay. To our knowledge, there are no processes from which we can extract a stringent bound on Z~tc, but we can assess its order of magnitude by considering the upper limits BR(t→ch)<1.1×10-3[35]. We also consider the prospect for the branching ratio BR(t→ch)<4.3×10-5 searches at the FCC-hh [39]. This is shown in Fig. 2.

Figure 2 Allowed region in the u-Z~tc plane from the current bound on BR(t→ch)<1.1×10-3 (blue color) and the projection at the FCC-hh (orange color). 

As for the bounds on the Z~ll diagonal matrix elements, we use those obtained in Ref. [14]. We summarize in Table II the values of the FNSM parameters used in the evaluations; while in Table III we define three benckmark points to be used in the Monte Carlo simulation.

Table II Model parameter values considered in the numerical analysis. 

Parameter Value
cα 0.999
u 600 and 1000 (GeV)
Z~tt 0.5
Z~bb 0.1
Z~tc 0.05, 0.2 and 0.45
Z~ττ 0.1 [14]
Z~μμ 10-3[14]
Z~τμ 0.35
mAF 0.2 — 1 (TeV)
mHF 0.2 — 1 (TeV)

Table III Benckmark points used in the Monte Carlo simulation. 

Benchmark points (BMP)
BMP1: Z~tc=0.45, u=600, 1000 GeV
BMP2: Z~tc=0.2, u=600, 1000 GeV
BMP3: Z~tc=0.05, u=600, 1000 GeV

4 Search for ϕ→tc decays at the HL-LHC

4.1 Flavon decays

We now present the behavior of the branching ratios of the main Flavon decay channels, which were obtained via our own Mathematica package so-called SpaceMath [40], that implements the analytical expressions for the corresponding decay widths. A cross-check was done by comparing our results with those obtained via CalcHEP [41], in which we implemented the corresponding Feynman rules via the LanHEP package [42]. In Fig. 3 we show the branching ratios of the CP-odd Flavon AF as functions of its mass mAF; we use the parameter values of Table II. As AF does not couple to gauge bosons at tree-level, its dominant decay modes are AF→tt-, AF→τ-μ+, and AF→tc-, with a branching ratio at the O(0.1) level for masses of the Flavon AF in the 200≤mAF≤1000 GeV. Other interesting channels such as AF→gg and AF→bb- search a branching ratio of O(10-3)-O(10-2).

Figure 3 Branching ratios of the two-body decay modes of a CP-odd flavon as a function of its mass for the parameter values of Table II ( u=1000 GeV and Z~tc=0.45). 

As far as the CP-even Flavon HF is concerned, the branching ratios for their main decay channels are presented in Fig. 4, for the same parameter values used for the AF decays. We observe that the dominant HF decay channels are HF→τ-μ+ and HF→tc- for mHF≤2mtop, with branching ratios of order O(10-1). Another important channel is HF→hh(h→γγ, h→bb-) which was studied by one of the authors of this project in Ref. [43]. Conversely, when mHF≥2mtop, the dominant channels are HF→tt-, W+W-, ZZ and τ-μ+. Other decay modes such as HF→bb-, HF→τ-τ+, HF→γγ and HF→gg have branching ratios ranging from 10-6 to 10-3, whereas the decays HF→Zγ and HF→μμ are very suppressed.

Figure 4 Branching ratios of the two-body decay modes of a CP-even flavon as a function of its mass for the parameter values of Table II (u = 1000 GeV and Z~tc=0.45). 

4.2 Events

In this section we now present a Monte Carlo analysis for the production of both the HF and the AF Flavons at the LHC via gluon fusion gg→ϕ(ϕ=HF, AF), followed by the FCNC decay ϕ→tc. We apply realistic kinematic cuts and consider tagging and miss tagging efficiencies. We then obtain the statistical significance, which could be experimentally confirmed.

We present in Fig. 5 the number of events produced σ(gg→ϕ→tc (t→lνlb))×L(≡Nϕ), where L=300 fb-1 is the integrated luminosity at the final stage of the LHC. For this computation, we use CalcHEP [41] with the CT10 parton distribution functions [44]. We note that for both Flavon masses mϕ, Nϕ is similar in the 400≤mϕ≤1000 GeV interval. Meanwhile, for masses in the range 200≤mϕ≤350 GeV, NAF≈3NHF. These results are encouraging since similar statistical significance will be obtained, despite different kinematic behaviors.

Figure 5 Number of events produced for the process gg→ϕ→tc (t→lνlb) as a function of the Flavon mass mϕ at s=14 TeV with an integrated luminosity of L=300 fb-1. 

4.2.1 Kinematic cuts

We now turn to the Monte Carlo simulation, for which we use Madgraph5 [45], with the corresponding Feynman rules generated via LanHEP [42] for a UFO model [46]. To perform shower and hadronization we use Pythia8 [47].

The signal and the main background events are as follows:

  • SIGNAL: The signal is gg→ϕ→tc→blνlc with l=e, μ. We generated 105 events scanning over mϕ∈[200, 1000] TeV and considered the parameter values of Table II.

  • BACKGROUND: The dominant SM background arises from the final states Wjj+Wbb-,tb+tj and tt-, in which either one of the two leptons is missed in the semi-leptonic top quark decays or two of the four jets are missed when one of the top quarks decays semi-leptonically.

In Fig. 6 we present the kinematic distributions generated both by the background processes and the decay of AF for mAF=200 GeV, namely, the transverse momentum of the particles produced by the decay of the top quark: (a) leading b-jet, (b) the charged lepton, (c) the missing energy transverse (MET) due to the neutrino in the final state are displayed. The transverse momentum of the leading jet is shown in (d). Finally, the transverse masses of the top quarks and CP-odd Flavon are depicted in (e) and (f). Meanwhile, in Figs. 7, 8, 9 is shown the same as in Fig. 6 but only for the signal to mAF=200, 400, 900 GeV.

Figure 6 Normalized transverse momentum distributions associated to the top decay: a) leading b-jet, b) leading charged lepton; c) tranverse missing energy due to undetected neutrinos; d) transverse momentum distribution of the c-jet; e) top quark transverse mass (mblνT) and f) CP-odd Flavon transverse mass (mblνcT) considering mAF=350 GeV. 

Figure 7 Normalized distributions generated by the decay of AF for mAF=200, 400, 900 GeV. Transverse momentum of a) leading b-jet and b) leading charged lepton. 

Figure 8 Normalized distributions generated by the decay of AF for mAF=200, 400, 900 GeV. a) Transverse missing energy due to undetected neutrino, b) transverse momentum distribution of the c-jet. 

Figure 9 Reconstructed CP-odd Flavon mass for mAF=200, 400, 900 GeV. 

The kinematic cuts imposed to study a possible evidence of the ϕ→tc ( mϕ=200 GeV) at the LHC are as follows:

  1. We requiere two jets with |ηj|<2.5 and pTj>30 GeV, one of them is tagged as a b-jet.

  2. We require one isolated lepton ( e or μ) with |ηl|<2.5 and pTl>20 GeV.

  3. Since an undetected neutrino is included in the final state, we impose the cut MET > 30 GeV.

  4. Finally, we impose a cut on the transverse masses mblνcT and mblνT as follows:

  • 0.8mAF<mblνcT<1.2mAF,

  • 0.8mtop<mblνT<1.2mtop.

The kinematic analysis was done via MadAnalysis5 [48] and for detector simulations we use Delphes [49]. As far as the jet reconstruction, we use the jet finding package FastJet [50] and the anti- kT algorithm [51]. We include also the tagging and misstagging efficiencies b-tagging efficiency ϵb=90% and to account for the probability that a c-jet is miss tagged as a b-jet we consider ϵc=10%, whereas for any other jet we use ϵj=1%.

We now compute the signal significance S=NS/NS+NB, where NS(NB) are the number of signal (background) events once the kinematic cuts were applied. We show in Figs. 10, 11, 12 the contour plots of the signal significance as a function of mAF and the integrated luminosity for the BMP1-BMP3, respectively, as shown in Table III. The results for the case of the CP-even Flavon HF, as well as the MadGraph files, will be shown upon request.

Figure 10 Contour plots for the signal significance as a function of the integrated luminosity and the CP-odd flavon mass, mAF. 

Figure 11 Contour plots for the signal significance as a function of the integrated luminosity and the CP-dd flavon mass, mAF. 

Figure 12 Contour plots for the signal significance as a function of the integrated luminosity and the CP-odd flavon mass, mAF. 

5 Conclusions

We study an extension of the SM with a complex singlet that invokes the Froggatt-Nielsen mechanism with an Abelian flavor symmetry. Such a model predicts CP-even and CP-odd Flavons that mediate FCNC at tree-level and thus can decay as ϕ→tc(ϕ=HF, AF), which is the focus of our work. We found the region of the parameter space consistent with both experimental and theoretical constraints. Then, we define a few benchmark points to evaluate the ϕ→tc decays along with the flavon ϕ production cross-section at the LHC and its next stage, the HL-LHC. We present a Monte Carlo analysis of both the signal gg→ϕ→tc→blνlc and the main standard model background, focusing on integrated luminosities in the range 140 — 1000 fb-1, which allow us to assess the possibility that this channel could be detected at the LHC in the best scenario of the model parameters. However, with the advent of the HL-LHC operating to L∼1000 fb-1, it could be possible to detect the decays ϕ→tc for a reasonable scenario in the 200<mAF<700 GeV interval and 200<mHF<380 GeV. However, if one considers the expected integrated luminosity at the HL-LHC (3000 fb-1), the mass interval of the Flavons could be increased. We make available, upon request, the necessary files to reproduce the Monte Carlo analysis.

Acknowledgement

We acknowledge support from CONACYT (México). Partial support from VIEP-BUAP is also acknowledged. The work of M. A. Arroyo-Ureña was supported by Centro Interdisciplinario de Investigación y Enseñanza de la Ciencia (CIIEC).

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How to Cite. M. A. Arroyo-Ureña, A. Fernández-Téllez, and G. Tavares-Velasco, “Flavor changing flavon decay ɸ→tc (ɸ = HF, AF ) at the high luminosity large hadron collider”, Rev. Mex. Fís., vol. 69, no. 2 Mar-Apr, pp. 020803 1-, Mar. 2023.

Received: June 09, 2022; Accepted: July 28, 2022

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