Effective Natural Supersymmetry from the Yukawa Deflected Mediations

Liang, Tai-ran; Zhu, Bin; Ding, Ran; Li, Tianjun

doi:https://doi.org/10.1155/2017/1585023

Advances in High Energy Physics

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Research Article | Open Access

Volume 2017 | Article ID 1585023 | https://doi.org/10.1155/2017/1585023

Effective Natural Supersymmetry from the Yukawa Deflected Mediations

Tai-ran Liang,¹Bin Zhu,²Ran Ding,³and Tianjun Li^4,5,6

Academic Editor: Ning Chen

Received28 Apr 2017

Accepted13 Jun 2017

Published10 Jul 2017

Abstract

The natural supersymmetry (SUSY) requires light (≤1 TeV) stop quarks, light sbottom quark, and gluinos. The first generation of squarks can be effectively larger than several TeV which does not introduce any hierarchy problem in order to escape the constraints from LHC. In this paper we consider a Yukawa deflected mediation to realize the effective natural supersymmetry where the interactions between squarks and messengers are made natural under certain Froggatt-Nielsen charges. The first generation squarks obtain large and positive contribution from the Yukawa deflected mediation. The corresponding phenomenology and sparticle spectra are discussed in detail.

1. Introduction

Gauge Mediated SUSY Breaking (GMSB) [1] is an elegant framework. In its minimal form, the SUSY breaking hidden sector can be communicated with visible sector only through usual gauge interaction. It can be realized by introducing spurion field with and messenger fields and the corresponding superpotential is written asHere spurion couples to the SUSY breaking sector and parameterizes the SUSY breaking effects and are charged under the Standard Model (SM) gauge group. Since the mass matrix of scalar messenger components is not supersymmetric, the SUSY breaking effects from hidden sector can be mediated to visible sectors via messenger loops. Compared with gravity mediated SUSY breaking, GMSB has two obvious advantages: (i)Soft terms are fully calculable. Even in the case of strongly coupled hidden sector, the soft terms can be still expressed as simple correlation functions of hidden sector, namely, the scenario of General Gauge Mediation (GGM) [2].(ii)It is inherently flavor-conserving since gauge interaction is flavor-blinded and thus is strongly motivated by the SUSY flavor problem.

However, the status of minimal GMSB has been challenged after the discovery of SM-like Higgs boson with a mass of 125 GeV [3, 4]. In order to lift Higgs mass to such desirable range, it then implies that Higgs mass should receive significant enhancement either from radiative corrections via stop/top loops [5, 6] or from extra tree-level sources [7]. The first option can be achieved through extremely heavy and unmixed stops or through lighter stops with maximal mixing (large trilinear soft term of stops) [8–11], while in minimal GMSB, the vanishing trilinear soft term at the messenger scale makes maximal mixing be impossible. The second option requires the extension of Minimal Supersymmetric Standard Model (MSSM) and has been widely investigated [12–27]. In this paper, we consider the first option where large trilinear term is required to soften fine-tuning. In fact, if the messenger sector is allowed to couple with squark or Higgs, the problem is improved with trilinear soft terms generated by additional interactions. The interactions can be generally divided into two types, that is, Higgs mediation and squark mediation. However, Higgs mediation generates irreducible positive contribution and leads to large fine-tuning, which is the so-called problem. The situation is quite different in squark mediation since it does not suffer from such problem and it allows better control to fine-tuning. One compromise is that squark mediation reintroduces dangerous flavor problem since there is no prior reason to specify the hierarchy and alignment of Yukawa matrix of squark. In this direction, Froggatt-Nielsen (FN) mechanism [28] is adopted as a canonical solution. Here we take the same strategy for squark mediation. In a previous study, [29] considered the type of sfermion-sfermion-messenger interaction with FN mechanism. In this work, we extend the model to include sfermion-messenger-messenger interaction and to examine its phenomenology systematically.

The rest of this paper is layout as follows. In Section 2, we present our notation and model contents. The realization of FN mechanism in Supersymmetric Standard Models (SSMs) and models are reviewed in Section 3. In Section 4, the FN mechanism is extended to constrain the possible interactions between squarks and messengers. We show that a unique interaction can be obtained with appropriate charge assignment. In Section 5, we explore the phenomenology of this model with an emphasis on spectra and fine-tuning issues. The last section is devoted to conclusion.

2. Vector-Like Particles (Messengers) in the SSMs and Models

First, we list our convention for SSMs. We denote the left-handed quark doublets, right-handed up-type quarks, right-handed down-type quarks, left-handed lepton doublets, right-handed neutrinos, and right-handed charged leptons as , , , , , and , respectively. Also, we denote one pair of Higgs doublets as and , which give masses to the up-type quarks/neutrinos and the down-type quark/charged leptons, respectively.

In this paper, we consider the messenger particles as the vector-like particles whose quantum numbers are the same as those of the SM fermions and their Hermitian conjugates. As we know, the generic vector-like particles do not need to form complete or representations in Grand Unified Theories. In particular it does not need complete multiplets (GUTs) from the orbifold constructions [30–41], intersecting D-brane model building on Type II orientifold [42–44], M-theory on with Calabi-Yau compactifications [45–47], and F-theory with fluxes [48–57] (For details, see [58]). Therefore, we will consider two kinds of supersymmetric models: (1) the SSMs with vector-like particles whose charges can be completely different; (2) the models.

In the SSMs, we introduce the following vector-like particles whose quantum numbers under are given explicitly as follows:

In the models, we have three families of the SM fermions whose quantum numbers under are where for three families. The SM particle assignments in and are To break the gauge symmetry and electroweak gauge symmetry, we introduce the adjoint Higgs field and one pair of Higgs fields whose quantum numbers under arewhere and contain the Higgs doublets and , respectively.

We consider the vector-like particles that form complete multiplets. The quantum numbers for these additional vector-like particles under the gauge symmetry areThe particle contents from the decompositions of , , , and under the SM gauge symmetries areHere we have introduced two pairs of and , and we denote them as and with .

In this paper, we consider the messenger parity. We further consider the messenger parity, for example, discrete symmetry with . Under this symmetry, the vector-like particles and transform are as follows:where . Thus, the lightest messenger will be stable. If the reheating temperature is lower than the mass of the lightest messenger, there is no cosmological problem. This is indeed work in our models. Otherwise, we can break the messenger parity a little bit by turning on tiny VEVs for and/or .

In the gauge mediation, it is very difficult to obtain the Higgs boson with mass around 125.5 GeV due to the small top quark trilinear soft term unless the stop quarks are very heavy around 10 TeV. To generate the large top quark trilinear soft term, we introduce the superpotential term [59, 60]. In addition, we consider high scale gauge mediation by choosingThe point is that we can increase the magnitude of top quark trilinear soft term via RGE running. Another point is that the couplings between the spurion and messengers can be very small because .

3. Froggatt-Nielsen Mechanism via an Anomalous Gauge Symmetry

It is well known that the SM fermion masses and mixings can be explained elegantly via the FN mechanism, where an additional flavor dependent global symmetry is introduced. To stabilize this mechanism against quantum gravity corrections, we consider an anomalous gauged symmetry. In a weakly coupled heterotic string theory, there exists an anomalous gauge symmetry where the corresponding anomalies are cancelled by the Green-Schwarz mechanism [61–63]. For simplicity, we will not consider the anomaly cancellation here, which can be done in general by introducing extra vector-like particles as in [64–67].

To break the gauge symmetry, we introduce a flavon field with charge . To preserve SUSY close to the string scale, can acquire a VEV so that the D-flatness can be realized. It was shown [64, 65] thatwhere is the reduced Planck scale. Interestingly, is about the size of the Cabibbo angle. Also, the charges of the SM fermions and the Higgs fields are denoted as .

The SM fermion Yukawa coupling terms arising from the holomorphic superpotential at the string scale in the SSMs are given bywhere , , , and are order one Yukawa couplings, and , , , and are nonnegative integers:Similarly, the SM fermion Yukawa coupling terms in the models arewhere

In addition, we shall employ the quark textures for the SSMs and models in Table 1, which can reproduce the SM quark Yukawa couplings and the CKM quark mixing matrix for [64–66]. And the following lepton textures can reproduce the neutrino masses and PMNS neutrino mixing matrix:where is either 0, 1, 2, or 3, and satisfies . This neutrino texture requires some amount of fine-tuning as it generically predictsInterestingly, with as large as , the amount of fine-tuning needed is not that huge and this is shown in the computer simulations of [64–66] with random values for the coefficients.

To be concrete, we choose the charges for the SM fermions and Higgs fields in the SSMs as follows:with for the SM fermions .

Also, we take the following charges for the SM fermions and Higgs fields in the models:

4. Squark Mediation versus Higgs Mediation

Natural SUSY can be regarded as an effective SUSY scenario where only stop, gluino, and small term are required in the spectra. As a consequence, the fine-tuning remains a manageable level. One nice property of Natural SUSY is that the first two generations of squarks can be very heavy without introducing any fine-tuning, which also evade bounds of SUSY direct searches from LHC. In terms of squark mediation with squark-messenger-messenger interaction, squarks receive additional positive contribution; thus it is possible to construct Natural SUSY model.

The basic formulas to compute corresponding soft terms are given aswhere and is the sum of the quadratic Casimir of each field interacting through . In above expressions, we do not include the contributions from usual GMSB (thus is labeled by ) and all of indices are summed over except for and . Without the FN mechanism, there will be general interaction between , , and . The squark mediation is not automatically minimal flavor violation like Higgs mediation. The MSSM-MSSM mixing term gives rise to dangerous nonvanishing and nondiagonal soft masses; for example,The nondiagonal terms in (20) motive [68] to construct chiral flavor violation scenario where only single , , or is allowed to couple the messenger. As a result, the dangerous flavor violation term is suppressed naturally. However our situation does not belong to chiral flavor violation. In order to realize effective SUSY scenario, all the first and second generation squarks must be coupled to messengers in order to obtain large soft masses enhancement. It seems the nondiagonal term is inevitable in (20). The loop hole comes from the fact that the bound is greatly improved when the squarks are nondegenerate. In particular, the largest bound comes from the first generation squarks because of large PDF effect of first generation quarks. Therefore it strongly suggests us for considering the first generation squark mediation which is technically natural under FN mechanism. The FN natural model is free from MSSM-MSSM mixing and the formulas are reduced to

It is easy to demonstrate how FN mechanism makes the squark mediation flavor-blinded. The general squark-messenger-messenger interaction within the messenger sector being complete multiplets is divided into -type, -type, and -type mediations; here and denote and , respectively. In Table 2, we list the complete messenger fields and their charge assignment.

For the -type Mediation, the most general superpotential iswhere is family indices. Based on Table 2, the Yukawa couplings in -type mediation can be determined as follows:Terms with negative power of must be removed in order not to violate the holomorphic requirement of superpotential. While terms with positive order of can be ignored which is guaranteed by the smallness of . Therefore only is allowed under the consideration of FN mechanism and holomorphy. For now we only consider squark-messenger-messenger interaction; this is mainly because the squark-squark-messenger interaction under FN charges has been discussed in the literature [69]. Since only the mediation is allowed, there is no flavor-changing problem.

For the -type mediation the most general superpotential is

According to FN mechanism the coupling looks likeIt is similar to -type mediation; only is allowed. For -type mediation we haveSubject to the FN mechanism we obtain the couplings

Consequently the allowed Yukawa deflected mediation interaction for squarks is summarized as follows:From (28), we obtain the extra contribution to soft masses for the first generation squarks. In other words there is no desirable large trilinear term from (28) which motivates us to resort to Higgs mediation.

Based on FN mechanism the only allowed superpotential for Higgs mediation isIt automatically preserves minimal flavor violation (MFV). Using (21), we obtain following soft terms:The choice of Higgs mediation in (29) is crucial in reducing the fine-tuning:(i)The trilinear soft term has an overall factor 3 coming from the higher representation of . Thus it can give rise to large trilinear term compared with other Higgs mediation.(ii) has a negative contribution from gauge coupling. Such a large coupling can reduce the fine-tuning easily.

The parameter space is thus determined by the following parameters:

5. Phenomenology Analysis

In this section, we give a detailed discussion on the results from our effective supersymmetry model. In particular the Higgs mass, stop mass, gluino mass, and fine-tuning are given explicitly. In our numerical analysis, the relevant soft terms are firstly generated at messenger scale in terms of gauge mediation and Higgs and squark mediation. The low scale soft terms are obtained by solving the two-loop RG equations. For this purpose, we implemented the corresponding boundary conditions in (30) into the SARAH [70–74] package. Then SARAH is used to create a SPheno [75, 76] version for the MSSM to calculate particle spectrum. The tasks of parameter scans are implemented using package SSP [77].

The framework that we concentrate on is MSSM with Yukawa deflected mediation. Its input parameters are given in (31). The scan range we adapt is Other parameters are fixed to GeV, , and . For the parameters in squark mediation, we divide it into two scenarios:In the scan, various mass spectrum and low energy constraints have been considered and listed as follows:(1) The Higgs mass constraints:(2) LEP bounds and physics constraints: [78], [79], [79].(3) Sparticle bounds from LHC Run-II:(i) Light stop mass GeV [80, 81],(ii) Light sbottom mass > 840–1000 GeV [82, 83],(ii) Degenerated first two generation squarks (both left-handed and right-handed) > 1000–1400 GeV [83],(iv) Gluino mass GeV [81, 84].

Finally, Barbieri-Giudice measure [85, 86] is used to quantify the fine-tuning:where denotes the input parameters in (31).

In Figures 1–3, we display the contour plots of important mass spectra and fine-tuning measure in the plane. There are some notable features which can be learned from these figures and summarized as follows:(1)The Higgs Mass. The Higgs mass range is taken from 123 GeV to 127 GeV in our numerical analysis. For small , one expects Higgs mass simply growth with an increases of . When increases, the allowed parameter space is forced to shift to smaller region in order to obtain correct Higgs mass.(2)The Fine-Tuning Measure. For small values of and , is usually dominated by . Since in these regions the RGE effects are most important, the contribution to the fine-tuning of , which only affects the boundary conditions, is negligible. The important parameter thus is which sets the range of the RGE running. For moderate and , the contributions from and are almost comparable. When becomes large it is always the biggest contributor to fine-tuning measure independent of the value of .(3)The Squark and Gluino Masses. Both stop and gluino masses fall into multi-TeV range and therefore out of current LHC reach.

(a)

(b)

6. Conclusions

In this paper, we investigated the extended gauge mediation models where Yukawa interaction between messengers and matter superfields is made natural under the consideration of F-N symmetry. Because of Higgs mediation the large A-term is generated naturally which can be used to enhance the Higgs mass efficiently. Considering the additional quark mediation, it is found that first generation squarks get large positive contribution, thus escaping from dangerous LHC constraints. We further study the parameter space and phenomenology numerically. The results show that the model is still promising under the stringent LHC constraint.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was supported in part by the Natural Science Foundation of China under Grant nos. 10821504, 11075194, 11135003, and 11275246.

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Copyright

Copyright © 2017 Tai-ran Liang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

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