]>PLB34433S0370-2693(19)30095-410.1016/j.physletb.2019.01.065PhenomenologyFig. 1The RGE running of the couplings for cosζu=1 (left), cosζu=0.92 (right). From top to bottom, the couplings correspond to Yu33, Yd33 and Ye33.Fig. 1Fig. 2The bottom-tau mass ratio (mb/mτ)0 at MZ without the weak scale threshold corrections, assuming the Yukawa unification. The RGE running of Yd,e33 depends on Yu33=mt/(vucosζu), and thus the ratio depends on cosζu. For a reference value, the running bottom-tau mass ratio at Z boson mass scale is mb/mτ ≃ 1.63 [24].Fig. 2Yukawa unification with four Higgs doublets in supersymmetric GUTBhaskarDuttaaYukihiroMimurabcmimura@riko.shimane-u.ac.jpaDepartment of Physics, Texas A&M University, College Station, TX 77843-4242, USADepartment of PhysicsTexas A&M UniversityCollege StationTX77843-4242USAbDepartment of Physics, National Taiwan University, Taipei 10617, TaiwanDepartment of PhysicsNational Taiwan UniversityTaipei10617TaiwancInstitute of Science and Engineering, Shimane University, Matsue 690-8504, JapanInstitute of Science and EngineeringShimane UniversityMatsue690-8504JapanEditor: M. CvetičAbstractWe discuss the Yukawa coupling unification, which can emerge in the grand unified theory, in the context of scenarios with more than one pair of Higgs doublet since the current LHC constraint has become a problem for the Yukawa unification scenarios with just one pair of Higgs doublet. More than one pair of Higgs doublets can easily arise in missing partner mechanism which solves the doublet-triplet splitting problem. In such a scenario, the Yukawa unification occurs at a medium tanβ value, e.g., ∼ 30, which corresponds to much smaller threshold corrections compared to usual large tanβ scenario for t−b−τ unification in the context of SO(10) and b−τ unification in the context of SU(5) models. Further, we show that an additional Higgs doublet pair lowers the sensitivity of the radiative symmetry breaking of the electroweak vacuum.KeywordsSUSY GUTCoupling unification1IntroductionThe Standard Model (SM) is well established to describe the physics below the weak scale, and the SM particle content is complete after the discovery of the Higgs boson whose mass is 125 GeV. However, 27% abundance of the universe, origin of the electroweak scale, neutrino masses etc. are not explained in the SM. The minimal supersymmetric standard model (MSSM), one of the most elegant extension of the SM, with origin in a grand unified model, e.g., SO(10) [1], has answers for all these puzzles.However, there is no evidence of supersymmetry (SUSY) at the LHC so far and this has generated constraints on the colored SUSY masses, e.g., squarks, gluino masses need to be ≥ 2 TeV [2,3]. Similarly, the lower bounds on non-colored SUSY masses have been kept on increasing. This situation has impacts on scenarios with predictions for lighter SUSY masses. One such example is a scenario which possesses unification of third generation Yukawa couplings motivated by the grand unified theories [4–6]. This scenario is running into difficulty with the current LHC constraints on the sparticle masses [7–9]. Since the unification of third generation Yukawa coupling can emerge in the context of minimal SO(10) unification scenarios [10], one wonders whether there is a way to circumvent this problem.In addition, the little hierarchy is becoming more fine-tuned with the non-observation of SUSY. Since the SUSY breaking scale (QS) associated with stop mass is moving up, it becomes closer to the symmetry breaking scale (Q0) where the Higgs squared mass turns negative by renormalization group equation (RGE). QS is a dimensionful parameter while the smallness of Q0 compared to the Planck scale is due to dimensionless parameters. The closeness of these two unrelated scales defines the fine tuning of the little hierarchy which is elevating with the non-observation of SUSY particles [11–16].Both problems seem to be ingrained in the choice of number of Higgs doublets in the low energy theory.11The phenomenological implications of the multi-pair of Higgs doublets in the low energy SUSY models are discussed in [17,18]. In the context of SO(10) or SU(5) GUT models, more than one pair of Higgs doublets may exist in the full theory. The light pair of doublet arises by choosing smaller mass for one of the higher dimensional Higgs representations in the missing partner doublet-triplet splitting mechanism. However, more than one pair can easily be made light as well. We consider such a scenario and show that both problems can be solved, i.e., (i) Yukawa unification and (ii) less fine tuning in little hierarchy can be achieved in the context of 4 Higgs doublet (4HD) SUSY models arising from SO(10) or SU(5). We show that the Yukawa coupling unification can be realized for lower tanβ, for which the threshold corrections are quite small.This paper is organized as follows. In section 2, we discuss missing partner model to understand the existence of more than one pair of Higgs doublets. In section 3, we describe t−b−τ unification and in section 4, we discuss the Higgs potential and fine-tuning of little hierarchy. Section 5 contains our conclusion.2Missing partner mechanismThe 126+126‾ representations (Δ+Δ¯) in SO(10) have three colored Higgs triplet reps (3,1,−1/3) (and three anti-triplet reps) under SM, and two pairs of Higgs doublets (1,2,1/2)+(1,2,−1/2). If we adopt 210 representation Φ to break SO(10), there are one triplet and one pair of doublets. Assuming that there are four 10-dimensional Higgs representations Ha (a=1,2,3,4), we obtain the Higgs triplet and doublet fields as(1)HT=(ΔT(6,1,1),Δ¯T(6,1,1),Δ¯T(10,1,3),ΦT,HT1,HT2,HT3,HT4),(2)HT¯=(Δ¯T¯(6,1,1),ΔT¯(6,1,1),ΔT¯(10,1,3),ΦT¯,HT¯1,HT¯2,HT¯3,HT¯4),(3)Hu=(Δu,Δ¯u,Φu,Hu1,Hu2,Hu3,Hu4),(4)Hd=(Δd,Δ¯d,Φd,Hd1,Hd2,Hd3,Hd4), and the mass terms(5)(HT)i(MT)ij(HT¯)j+(Hu)i(MD)ij(Hd)j. The mass matrices are written as(6)MT=(AT(4×4)BT(4×4)CT(4×4)DT(4×4)),MD=(AD(3×3)BD(4×3)CD(3×4)DD(4×4)). The matrices AT and AD are determined by the masses of Δ and Φ and their GUT-scale vevs, which depend on the SO(10) symmetry breaking vacua.22The minimal missing partner SO(10) model used in the Ref. [19] uses 10, 120, 126, 126‾ and 210. We have more doublets and triplets arising from four 10s compared to one 10 and one 120 which causes the dimensions for the matrices in Eq. (6) to be different compared to the minimal model. However, the final conclusion is independent of the choice of a particular model. The matrices BT,D and CT,D depend on the Higgs coupling HaΔΦ and the GUT scale vevs. The matrices DD and DT are obtained by the mass term of 10-dimensional Higgs fields. If the mass of 10 are suppressed then one linear combination of the Higgs doublets remain light (at weak scale) while all the other linear combinations of doublets and triplets are massive at the GUT scale. The smallness of mass can be due to supersymmetry breaking which can arise out of a term 1010X/Mpl in the Kahler potential where X is a SM singlet. Now a non-zero 〈FX〉 allows us to get 1010〈FX〉/Mpl in the superpotential which leads to Ms1010 where Ms∼ weak scale. This is similar to the origin of the weak scale μ term [20]. The Yukawa interactions to generate the fermion masses are given as(7)WY=hijaψiψjHa+fijψiψjΔ¯. The charged fermion Yukawa matrices are given by a linear combination of ha since the mixing of Δ¯u,d in the light Higgs doublets are tiny under the assumption above. The left- and right-handed Majorana neutrino masses can be generated by the f coupling. By investigating MT−1, one finds that the f coupling does not contribute to the proton decay amplitudes and the dimension-five operators CL,Rijkl are the linear combination of hijahklb.33In the missing partner mechanism, either one or no triplet is light. In the case when one triplet is light while the others are heavy, which may emerge in the missing partner mechanism, the 126‾ triplet component vanishes in the lighter colored triplet field content [22]. Therefore, compared to the minimal SO(10) model, though the predictivity of the neutrino masses and mixings is lost, the proton decay suppression is easier to be realized (in type II seesaw) by choosing the hierarchy pattern in ha (e.g., h1 is a nearly rank-1 matrix, which gives top, bottom and tau Yukawa couplings, and 1st and 2nd generation masses and CKM mixings are generated by the other ha). Surely, in this naive choice, the Georgi–Jarskog relations are not obtained. Instead of requiring four 10 Higgs fields, by adopting one 120 representation (which contains two triplets and two pairs of doublets) and two 10 fields,44We note that the 120 contribution can violate the quark-lepton mass unification and the masses of charged-leptons and down-type quarks can be fit. However, observed up- and down-type quark masses cannot be fit if only one 10 and 120 couple to fermions by renormalizable terms [21]. In order to fit the charged fermion masses, one needs two 10's or non-renormalizable couplings [19]. one can realize the same situation where only one pair of doublets is light55More general description of the missing partner mechanism in SO(10) GUT can be found in Ref. [23]. and the Georgi–Jarskog relations can be realized [22].3t−b−τ UnificationIn the context of a minimal SO(10) model, the doublet-triplet splitting arises just by cancellation in the determinant of the doublet mass matrix, and one of the linear combination is fine-tuned to be light. In the missing partner doublet realization of the doublet-triplet splitting, on the other hand, the lightness of one pair of doublets is realized by the smallness of the mass of the 10 (and 120) Higgs representations, and in principle, there is no strong reason that only one pair of doublets is light since it just depends on the number of 10-dimensional Higgs fields. It is possible that multi-pair of Higgs doublets can be light in this scenario, which is true in the missing partner mechanism also in SU(5) and flipped-SU(5).Here, let us consider the possibility that two pairs of Higgs doublets (totally, four Higgs doublets) remain light. There are two possibility depending on the number of excess of the triplet (3,1,−1/3) compared to (1,2,1/2):1.Two pairs of doublets are light, and one triplet (and one anti-triplet) Higgs is light.2.Two pairs of doublets are light, and no triplet Higgs is light. In the case 1, to avoid rapid proton decay, the Yukawa interaction to the fermions of the Higgs triplet needs to be very tiny (by the discrete symmetry or anomalous U(1) symmetry). Then, the Yukawa coupling of one of the linear combination of the Higgs doublets is absent. In the case 2, both two linear combination of the doublets can couple to the fermions and there are new FCNC sources in the Yukawa interaction. Surely, in the case 2, the gauge coupling unification in MSSM is destroyed explicitly (though it can be restored by the GUT-scale or intermediate-scale threshold corrections).We consider the consequence of the case 1.66As we have mentioned, the proton decay suppression can be more easily realized if only one 10 Higgs coupling generates 3rd generation masses and the others generates the masses of 1st and 2nd generations and the generation mixings. If one chooses so, the following discussion can be the same even in case 2 in principle. In the case 2, the additional Higgs couplings to the 1st and 2nd generations can induce new FCNC, which can be a source of lepton flavor non-universality, in the similar way to the non-SUSY general (so called type III) two Higgs doublet model. Denoting that the linear combination of the Higgs doublets which couples to fermions as Hˆ1u and Hˆ1d and the other combinations as Hˆ2u and Hˆ2d (we call this as Yukawa-basis), we obtain the Yukawa terms (below the GUT scale):(8)W=YuijqiujcHˆ1u+YdijqidcjHˆ1d+YeijℓiejcHˆ1d. The μ-term and the SUSY breaking Higgs mass terms are given as(9)W=μˆijHˆiuHˆjd, and(10)Vsoft=(bˆijHˆiuHˆjd+c.c.)+mˆHu2ijHˆiu†Hˆju+mˆHd2ijHˆid†Hˆjd. Via RGE (with a large Yu33), mHu211 becomes negative and the electroweak symmetry is broken. Not only Hˆ1u,d0 but also Hˆ2u,d0 acquires vevs (denote them as viu and vid). We define a new basis (called as vev-basis):(11)(H1uH2u)=(cosζusinζu−sinζucosζu)(Hˆ1uHˆ2u),(H1dH2d)=(cosζdsinζd−sinζdcosζd)(Hˆ1dHˆ2d), where tanζu=v2u/v1u and tanζd=v2d/v1d, so that 〈H2u0〉=〈H2d0〉=0, 〈H1u0〉=vu, and 〈H1d0〉=vd. We denote vu=v1u2+v2u2 and vd=v1d2+v2d2. As usual, we define tanβ=vu/vd, and v=vu2+vd2 is fixed by the gauge boson masses. The Yukawa terms (in the vev-basis) are(12)W=Yuijqiujc(cosζuH1u−sinζuH2u)+Ydijqidjc(cosζdH1d−sinζdH2d)+Yeijℓiejc(cosζdH1d−sinζdH2d), and the fermion mass matrices are(13)Mu=Yuvucosζu,Md=Ydvdcosζd,Me=Yevdcosζd. We find that the RGE running of the top, bottom and tau Yukawa couplings (whose description is easier in Yukawa-basis) for cosζu≃1, tanζd∼1 and tanβ∼30 resembles the running in MSSM for tanβ≃50. In other words, for tanβ≲35 in the MSSM, the bottom Yukawa coupling is small and the RGE running is governed by the loop diagram arising from the gauge interaction yb2≪g32. On the other hand, since yb=Yd33cosζd, Yd33 can be ∼1, the Yukawa interaction can contribute to the RGE evolution of bottom mass even if yb is small. This freedom can make the top, bottom and tau Yukawa unification possible for tanβ∼30 if the weak scale threshold correction is small.We plot the RGE running of the couplings Yu,d,e33 in Fig. 1 for different values of cosζu, assuming that the third generation Yukawa couplings are unified at MU=2×1016 GeV. In Fig. 2, we plot the bottom-tau mass ratio at MZ leaving out the weak scale threshold corrections as a function of cosζu.In the MSSM, it has been discussed that the bottom and tau unification is possible if tanβ∼2 or tanβ∼50. For tanβ∼2, the top Yukawa coupling is large and it can contribute to the RGE running of bottom Yukawa coupling, but, at present tanβ∼2 is excluded due to the 125 GeV Higgs mass. For tanβ∼50, the finite corrections and the TeV scale threshold corrections are large and it is difficult to realize the bottom-tau unification for the current bounds on the SUSY mass spectrum. Actually, the finite correction of q3bcHu⁎ is important for large tanβ:(14)mb=ybvd(1+X(μ,At,mt˜,mg˜,mb˜)tanβ). Naively, for a stop mass ∼2–3 TeV, At has to be large (for the 125 GeV Higgs) which makes the chargino contribution is large (Xχ˜±≃λt216π2μ(At−μcotβ)mt˜12−mt˜22I(μ2,mt˜12,mt˜22)), and the gluino contribution is large if mg˜ is large (Xg˜≃g3212π2mg˜(Abcotβ−μ)mb˜12−mb˜22I(mg˜2,mb˜12,mb˜22)).In 4HD case, there are additional contributions to X compared to MSSM if μ12 (in vev-basis) is not zero. In the chargino loop (Higgsino component), μ12 can directly contribute in the Higgsino propagator. In the gluino loop, there is a term yb(μ11−μ12tanζd)q˜3b˜cH1u⁎ in the F-term, |∂W/∂Hid|2. Therefore, if μ12 is small, the contribution to X is similar to MSSM and the finite correction is not sizable for tanβ which is not so large.In summary, in the context of MSSM with 2HD, RGE running is important for the bottom-tau unification for large tanβ but the large finite correction associated with the non-observation of SUSY masses destroys the realization of the bottom-tau unification. In 4HD, however, the suitable RGE running can be realized even for tanβ which somewhere in the middle where the finite corrections are not sizable, and as a result, top, bottom and tau Yukawa unification is possible in a simple manner. In the missing partner mechanism for the doublet-triplet splitting, the existence of two pairs of Higgs doublets with masses around the weak scale is not at all unnatural.4Minimization of the Higgs potentialIn 2HD case, the Higgs potential of the neutral Higgs vevs is(15)V=m12vd2+m22vu2+2m32vdvu+gZ28(vd2−vu2)2, where m12=mHd2+μ2 and m22=mHu2+μ2. The Z boson mass (at tree-level) is written as(16)MZ22cos22β=−(sinβcosβ)(m22m32m32m12)(sinβcosβ). The other minimization condition gives(17)m32=−12(m12+m22)sin2β. The symmetry breaking condition (which is equivalent to MZ2>0) is m12m22−m34<0. For a large tanβ, we obtain MZ2≃−2m22 and a cancellation between μ2 and −mHu2 is needed (if |mHu2| is large for a given boundary condition of SUSY breaking). It is often said that a smaller μ is preferable for “Natural SUSY” due to the tree-level relation. However, the Higgs mass parameters run by RGEs, and it is still unnatural if the RGEs give a large logarithmic correction to the mass parameters near the minimization scale (where the 1-loop correction of the scalar potential ΔV gives small derivatives ∂ΔV/∂vu≈∂ΔV/∂vd≈0). For example, if mHu2 runs rapidly, the radiative electroweak symmetry breaking is still sensitive to the SUSY breaking parameters (even if one tunes |mHu2| to be small at a scale). Such a situation can be expressed by equations as follows: By Tailor expansion around the scale Q0, the Z boson mass relation can be expressed as(18)MZ22cos22β≃(sinβcosβ)(dm22dlnQdm32dlnQdm32dlnQdm12dlnQ)(sinβcosβ)lnQ0QS, where Q0 is the symmetry breaking scale satisfying m12m22−m34=0, and QS is the minimization scale, which is roughly same as the geometric average of the stop masses. The RGEs of m22, m12 and m32 are given as(19)(4π)2dm22dlnQ=6(yt2(mq˜3L2+mt˜R2)+At2)+6yt2m22−6g22M22−2g′2M12+(6yb2+2yτ2−6g22−2g′2)μ2,(20)(4π)2dm12dlnQ=6(yb2(mq˜3L2+mb˜R2)+Ab2)+2(yτ2(mℓ˜3L2+mτ˜R2)+Aτ2)+(6yb2+2yτ2)m12−6g22M22−2g′2M12+(6yt2−6g22−2g′2)μ2,(21)(4π)2dm32dlnQ=(3yt2+3yb2+yτ2−3g22−g′2)m32+6g22M2μ+2g′2M1μ+6μAtyt+6μAbyb+2μAτyτ. One can find that lnQ0/QS to needed to be tuned to be small (irrespective of the smallness of μ) if the stop masses and At are large.Let us examine the “naturalness” of the little hierarchy in the case of 4HD. The Higgs potential in 4HD (in the Yukawa-basis) is given as(22)V=(v1uv2uv1dv2d)M02(v1uv2uv1dv2d)+gZ28(v1u2+v2u2−v1d2−v2d2)2, where(23)M02=(mu112mu122bˆ11bˆ12mu122mu222bˆ21bˆ22bˆ11bˆ21md112md122bˆ12bˆ22md122md222), and(24)mu112=(mˆHu2)11+μˆ112+μˆ122,(25)mu122=(mˆHu2)12+μˆ11μˆ21+μˆ12μˆ22,(26)md112=(mˆHd2)11+μˆ112+μˆ212, and so on. The minimization conditions of the tree-level potential can be written as(27)MZ22(−cos2β)(v1uv2u−v1d−v2d)=−M02(v1uv2uv1dv2d). We note that MZ2(−cos2β)/2 is an eigenvalue of the matrix: diag.(−1,−1,1,1)M02, and the corresponding eigenvector is (v1u,v2u,v1d,v2d). The Z boson mass can be written as(28)MZ22cos22β=−(v1uv2uv1dv2d)M02(v1uv2uv1dv2d)1v2. The symmetry breaking condition is detM02<0. In this case, a large tanβ (and cosζu∼1) can be obtained by small mu122, bˆ11 and bˆ12. The symmetry breaking can arise when the determinant of the sub-matrix (M02)ij(i,j=2,3,4) is negative, and it is not necessarily true that a cancellation in mu112 between −(mHu2)11 and μˆ112+μˆ122 needs to occur to obtain the little hierarchy. Surely, a cancellation is needed to make the magnitude of the determinant of M02 small for the little hierarchy. The cancellation happens radiatively at Q0 (by definition) and the important tuning quantity is the size of lnQ0/QS. In 4HD case, we obtain(29)MZ22cos22β≃(v1uv2uv1dv2d)dM02dlnQ(v1uv2uv1dv2d)1v2lnQ0QS. In the Yukawa-basis, d(M02)11/dlnQ and d(M02)33/dlnQ are positive due to the Yukawa interaction. The size of the term d(M02)(11,33)/dlnQ is governed by the stop mass. (M02)11 and (M02)33 are smaller at the lower energy side as happens in the 2HD case. However, the other component of d(M02)ij/dlnQ can be negative.77A careful treatment is needed since the signs of the off-diagonal elements depend on the signs of μij and bij (under the convention 0<ζu,ζd,β<π/2). In fact, due to the absence of Yukawa coupling (in the Yukawa-basis by definition), d(M02)22,44/dlnQ is negative, and thus, (M02)22,44 becomes larger at the lower energy. This can make to keep detM02≈0 for a wider range of QS compared to 2HD case. Roughly speaking, for a lighter stop mass ∼2–3 TeV, if the heavier Higgsino mass is O(10) TeV, one finds that the sensitivity for lnQ0/QS is relaxed, and the little hierarchy is much less fine-tuned compared to the 2HD case.In order to illustrate the above statement, let us rewrite Eq. (29) using a bold approximation. We neglect the terms which depend on cosβ, and gaugino masses M1 and M2. We also neglect the terms which depends on μˆ12 and μˆ21, assuming that the Higgs mixing ζu is mainly generated by SUSY breaking term, (mˆHu2)12, and that the dominant contribution from 2HD case is proportional to μˆ222. Then, we can write approximately as(30)12MZ2≃116π2(cos2ζu(6yt2(mt˜L2+mt˜R2)+6At2)+sin2ζu(−6g22−2g′2)μˆ222)lnQ0QS. For example, suppose that mt˜L=mt˜R=2 TeV and At=5 TeV. In 2HD case (which corresponds to sinζu=0), we obtain lnQ0/QS≃0.003, and it means that m12m22−m32≈0 is satisfied only in a narrow range, and QS needs to be fine-tuned and to be very close to Q0. The approximate relation tells us that detM02≈0 can be satisfied in a wide range if the heavier Higgsino mass is chosen to be(31)μˆ222∼cot2ζu6yt2(mt˜L2+mt˜R2)+6At26g22+2g′2, and electroweak symmetry breaking can happen “naturally”. One can find that μˆ22∼20,30,50 TeV for cosζu=0.92,0.96,0.98, respectively.We note that the wino, bino and one of the Higgsino (and one of the charged Higgs (as well as the CP-odd neutral Higgs)) can be light (∼1 TeV) in the 4HD scenario, while the other one needs to be heavy to relax the sensitivity which appears in the 2HD case.5ConclusionThe doublet-triplet splitting problem is one of the major issue in the grand unified models. The missing partner mechanism is known to provide a solution to the problem. In principle, the number of the pairs of Higgs doublets is a free parameter in this mechanism, though one pair of Higgs doublets is the minimal choice and it is preferable for the gauge coupling unification which can have additional contributions from GUT thresholds and intermediate scales. In this paper, we have investigated the possibility that two pairs of Higgs doublets (i.e., four Higgs doublets, 4HD) remain at the TeV scale. In 2HD, the bottom-tau unification, which is one of the major implication of GUTs, does not appear to be successful after including the current experimental constraints from LHC. In fact, for a suitable parameter region of tanβ where the RGE runnings allows us to generate bottom-tau unification, large threshold corrections from SUSY breaking are generated which ruin this unification. In 4HD, on the other hand, we find that the threshold corrections can be small even if the tree-level Yukawa coupling associated with bottom and tau are unified by RGE. This happens due to the freedom of the Higgs mixing terms at the TeV scale. It is possible to choose two pairs of Higgs doublet to be light and a linear combination of these two pairs acquire the vacuum expectation values by the minimization of the Higgs potential. The top–bottom-tau and bottom-tau Yukawa unifications are also implied in the context of SO(10) and SU(5) models respectively in this scenario. We also discuss the merits of 4HD compared to the 2HD choice for the little hierarchy between the SUSY breaking masses and the Z boson mass. The additional Higgs pair at O(10) TeV appears to relax the sensitivity of the radiative electroweak symmetry breaking.AcknowledgementsThe work of B.D. is supported by DOE Grant de-sc0010813. The work of Y.M. is supported by grant MOST 106-2112-M-002-015-MY3 of R.O.C. Taiwan, and Scientific Grants by the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 16H00871, 16H02189, 17K05415 and 18H04590).References[1]H.GeorgiC.E.CarlsonParticles and FieldsAIP Conf. Proc.vol. 231975575H.FritzschP.MinkowskiAnn. Phys.931975193[2]A.M.SirunyanCMS CollaborationEur. Phys. J. C77102017710arXiv:1705.04650 [hep-ex][3]M.AaboudATLAS CollaborationPhys. Rev. D97112018112001arXiv:1712.02332 [hep-ex][4]T.BanksNucl. Phys. B3031988172M.OlechowskiS.PokorskiPhys. Lett. B2141988393[5]B.AnanthanarayanG.LazaridesQ.ShafiPhys. Rev. D4419911613[6]S.DimopoulosL.J.HallS.RabyPhys. Rev. Lett.6819921984G.W.AndersonS.RabyS.DimopoulosL.J.HallPhys. Rev. D471993R3702arXiv:hep-ph/9209250[7]I.GogoladzeQ.ShafiC.S.UnJ. High Energy Phys.12072012055arXiv:1203.6082 [hep-ph]Q.ShafiS.H.TanyildiziC.S.UnNucl. Phys. B9002015400arXiv:1503.04196 [hep-ph]A.HebbarG.K.LeontarisQ.ShafiPhys. Rev. D93112016111701arXiv:1604.08328 [hep-ph]A.HebbarQ.ShafiC.S.UnPhys. Rev. D95112017115026arXiv:1702.05431 [hep-ph][8]Z.PohS.RabyPhys. Rev. D9212015015017arXiv:1505.00264 [hep-ph][9]M.YamaguchiW.YinPTEP201822018023B06arXiv:1606.04953 [hep-ph]W.YinN.YokozakiPhys. Lett. B762201672arXiv:1607.05705 [hep-ph]T.T.YanagidaW.YinN.YokozakiJ. High Energy Phys.18042018012arXiv:1801.05785 [hep-ph][10]L.J.HallR.RattazziU.SaridPhys. Rev. D5019947048arXiv:hep-ph/9306309H.MurayamaM.OlechowskiS.PokorskiPhys. Lett. B371199657arXiv:hep-ph/9510327N.N.SinghS.B.SinghEur. Phys. J. C51998363T.BlazekR.DermisekS.RabyPhys. Rev. D652002115004arXiv:hep-ph/0201081M.BadziakMod. Phys. Lett. A2720121230020arXiv:1205.6232 [hep-ph]M.Adeel AjaibI.GogoladzeQ.ShafiC.S.UnJ. High Energy Phys.13072013139arXiv:1303.6964 [hep-ph][11]B.DuttaY.MimuraPhys. Lett. B6482007357arXiv:hep-ph/0702002 [hep-ph]B.DuttaY.MimuraD.V.NanopoulosPhys. Lett. B6562007199arXiv:0705.4317 [hep-ph][12]B.DuttaY.MimuraarXiv:1608.07195 [hep-ph][13]G.F.GiudiceR.RattazziNucl. Phys. B757200619arXiv:hep-ph/0606105[14]P.W.GrahamA.IsmailS.RajendranP.SaraswatPhys. Rev. D812010055016arXiv:0910.3020 [hep-ph][15]H.BaerV.BargerP.HuangA.MustafayevX.TataPhys. Rev. Lett.1092012161802arXiv:1207.3343 [hep-ph]H.BaerV.BargerP.HuangD.MickelsonA.MustafayevX.TataPhys. Rev. D87112013115028arXiv:1212.2655 [hep-ph]K.J.BaeH.BaerV.BargerM.R.SavoyH.SerceSymmetry722015788arXiv:1503.04137 [hep-ph][16]H.BaerV.BargerM.SavoyH.SercePhys. Lett. B7582016113arXiv:1602.07697 [hep-ph][17]Y.SakamuraMod. Phys. Lett. A141999721arXiv:hep-ph/9903247[18]N.EscuderoC.MunozA.M.TeixeiraPhys. Rev. D732006055015arXiv:hep-ph/0512046[19]K.S.BabuI.GogoladzeZ.TavartkiladzePhys. Lett. B650200749arXiv:hep-ph/0612315[20]G.F.GiudiceA.MasieroPhys. Lett. B2061988480[21]L.LavouraH.KuhbockW.GrimusNucl. Phys. B75420061arXiv:hep-ph/0603259[22]B.DuttaY.MimuraR.N.MohapatraPhys. Rev. Lett.942005091804arXiv:hep-ph/0412105[23]K.S.BabuI.GogoladzeP.NathR.M.SyedPhys. Rev. D852012075002arXiv:1112.5387 [hep-ph][24]M.TanabashiParticle Data GroupPhys. Rev. D9832018030001