Natural Supersymmetry from the Yukawa Deflect Mediations
NNatural Supersymmetry from the Yukawa Deflect Mediations
Tai-ran Liang, Bin Zhu, Ran Ding, and Tianjun Li
4, 5, 6 School of Physics and Electronic Information,Inner Mongolia University for The Nationalities, Tongliao 028043, P. R. China Department of Physics, Yantai University, Yantai 264005, P. R. China Center for High-Energy Physics, Peking University, Beijing, 100871, P. R. China Key Laboratory of Theoretical Physics and Kavli Institute forTheoretical Physics China (KITPC), Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing 100190, P. R. China School of Physical Sciences, University of ChineseAcademy of Sciences, Beijing 100049, P. R. China School of Physical Electronics, University of Electronic Scienceand Technology of China, Chengdu 610054, P. R. China
Abstract
The natural supersymmetry (SUSY) requires light stop quarks, light sbottom quark, and gluinoto be around one TeV or lighter. The first generation squarks can be effectively large which doesnot introduce any hierarchy problem in order to escape the constraints from LHC. In this paperwe consider a Yukawa deflect medation to realize the effective natural supersymmetry where theinteraction between squarks and messenger are made natural under certain Frogget-Nelson U (1) X charge. The first generation squarks obtain large and postive contribution from the yukawa deflectmediation. The corresponding phenomenology as well as sparticle spectrum are discussed in detail. PACS numbers: a r X i v : . [ h e p - ph ] A p r . INTRODUCTION Gauge Mediated SUSY Breaking (GMSB) [1] is an elegant framework. In its mini-mal form, the SUSY breaking hidden sector can be communicated with visible sector onlythrough usual gauge interaction. Which can be realized by introducing spurion field X with (cid:104) X (cid:105) = M + θ F and messenger fields Φ. Corresponding superpotential is written as W = X Φ ¯Φ . (1)Here spurion X couples to the SUSY breaking sector and (cid:104) X (cid:105) parameterizes the SUSYbreaking effects, Φ are charged under the Standard Model (SM) SU (3) × SU (2) × U (1) gaugegroup. Since the mass matrix of scalar messenger components are not supersymmetric, theSUSY breaking effects from hidden sector can be mediated to visible sectors via messengerloops. Compared with gravity mediated SUSY breaking, GMSB has two obvious advantages: • 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]. • It is inherently flavor-conserving since gauge interaction is flavor-blinded, thus isstrongly motivated by the SUSY flavor problem.However, the status of minimal GMSB has been challenged after the discovery of SM-like higgs boson with mass of 125 GeV [3, 4]. In order to lift higgs mass to such desirablerange, it then implies that higgs mass should be received significant enhancement eitherfrom radiative corrections via stop/top loops [5, 6] or from extra tree-level sources [7]. Thefirst option can be achieved through extremely heavy and unmixed stops, or through lighterstops with maximal mixing (large trilinear soft term of stops) [8–10]. While in minimalGMSB, the vanishing trilinear soft term at the messenger scale leads to maximal mixing isimpossible. The second option requires the extension of Minimal Supersymmetric StandardModel (MSSM) and has been widely investigated [11–26]. In this paper, we consider the firstoption where large trilinear term is required to soften fine-tuning. In fact, if the messengersector is allowed to couple with squark or higgs, the problem is improved with trilinearsoft terms generated by the additional interaction. This type of interactions relevant togenerate large trilinear terms can be generally divided into two types, i.e., higgs mediation2nd squark mediation. However, higgs mediation generates irreducible positive contribution δm H u ∼ A H u and leads to large fine-tuning, which is the so-called A/m H u problem. Thesituation is quite different in squark mediation since it does not suffer from such problemthus has better control on fine-tuning. As a price, squark mediation reintroduces dangerousflavor problem since there is no prior reason to specify the hierarchy and alignment ofyukawa matrix of squark. In this direct, Froggatt-Nielsen (FN) mechanism [28] is adoptedas a canonical solution. Here we take the same strategy for squark mediation. In a previousstudy, Ref. [29] considered the type of sfermion-sfermion-messenger interaction with FNmechanism. In this work, we extend the model to include sfermion-messenger-messengerinteraction and exam its phenomenology systematically.The rest of this paper is layout as follows. In section II, we present our notation and modelcontents. The realization of FN mechanism in Supersymmetric Standard Models (SSMs)and SU (5) models is reviewed in section III. In section IV, The FN mechanism is extendedto constrain the possible interactions between squarks and messengers. We show that aunique interaction can be obtained with appropriate charge assignment. In section V, weexplore the phenomenology of this model with emphasize on spectra and fine-tuning issues.The last section is devoted to conclusion and discussion. II. VECTOR-LIKE PARTICLES (MESSENGERS) IN THE SSMS AND SU (5) 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 Q i , U ci , D ci , L i , N ci , and E ci , respec-tively. Also, we denote one pair of higgs doublets as H u and H d , which give masses to theup-type quarks/neutrinos and the down-type quark/charged leptons, respectively.In this paper, we consider the messenger particles as the vector-like particles whosequantum 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 SU (5) or SO (10)representations in Grand Unified Theories (GUTs) from the orbifold constructions [30–37],intersecting D-brane model building on Type II orientifolds [38–40], M-theory on S /Z withCalabi-Yau compactifications [41, 42], and F-theory with U (1) fluxes [43–52] (For details,3ee Ref. [53]). Therefore, we will consider two kinds of supersymmetric models: (1) TheSSMs with vector-like particles whose U (1) X charges can be completely different; (2) The SU (5) Models.In the SSMs, we introduce the following vector-like particles whose quantum numbersunder SU (3) C × SU (2) L × U (1) Y are given explicitly as follows XQ + XQ c = ( , , ) + ( ¯3 , , − ) ; (2) XU + XU c = ( , , ) + ( ¯3 , , − ) ; (3) XD + XD c = ( , , − ) + ( ¯3 , , ) ; (4) XL + XL c = ( , , − ) + ( , , ) ; (5) XE + XE c = ( , , − ) + ( , , ) . (6)In the SU (5) models, we have three families of the SM fermions whose quantum numbersunder SU (5) are F i = , f i = ¯5 , (7)where i = 1 , , F i and ¯ f i are F i = ( Q i , U ci , E ci ) , f i = ( D ci , L i ) . (8)To break the SU (5) gauge symmetry and electroweak gauge symmetry, we introduce theadjoint Higgs field and one pair of Higgs fields whose quantum numbers under SU (5) areΦ = , H = , H = ¯5 , (9)where H and H contain the Higgs doublets H u and H d , respectively.We consider the vector-like particles which form complete SU (5) multiplets. The quan-tum numbers for these additional vector-like particles under the SU (5) × U (1) X gauge sym-metry are XF = , XF = , Xf = , Xf = . (10)The particle contents for the decompositions of XF , XF , Xf , and Xf under the SM gaugesymmetries are XF = ( XQ, XU c , XE c ) , XF = ( XQ c , XU, XE ) , (11) Xf = ( XD, XH u ) , Xf = ( XD c , XH d ) . (12)4hen we introduce two pairs of Xf and Xf , we denote them as Xf i and Xf i with i = 1 , Z n symmetry with n ≥
2. Under this Z n symmetry, the vector-like particles X Φ and X Φ c transform as follows X Φ → ωX Φ , X Φ c → ω n − X Φ c , (13)where ω n = 1. Thus, the lightest messenger will be stable. If the reheating temperatureis lower than the mass of the lightest messenger, there is no cosmological problem. This isindeed work in our models. Otherwise, we can break the messenger parity a little bit byturning on tiny VEVs for XL and/or XL c .In the gauge mediation, it is very difficult to obtain the Higgs boson with mass around125.5 GeV due to the small top quark trilinear soft A t term unless the stop quarks are veryheavy around 10 TeV. To generate the large top quark trilinear soft A t term, we introducethe superpotential term XQXU c H u [54, 55]. In addition, we consider high scale gaugemediation by choosing (cid:104) S (cid:105) ∼ G eV , F S ∼ G eV . (14)The point is that we can increase the magnitude of top quark trilinear soft term via RGErunning. Another point is that the couplings between the spurion and messengers can bevery small because F S / (cid:104) S (cid:105) ∼ − . III. FROGGATT-NIELSEN MECHANISM VIA AN ANOMALOUS U (1) X GAUGESYMMETRY
It is well known that the SM fermion masses and mixings can be explained elegantlyvia the FN mechanism, where an additional flavor dependent global U (1) X symmetry isintroduced. To stabilize this mechanism against quantum gravity corrections, we consider ananomalous gauged U (1) X symmetry. In a weakly coupled heterotic string theory, there existsan anomalous U (1) X gauge symmetry where the corresponding anomalies are cancelled bythe Green-Schwarz mechanism [56]. For simplicity, we will not consider the U (1) X anomalycancellation here, which can be done in general by introducing extra vector-like particles asin Refs. [57–60].To break the U (1) X gauge symmetry, we introduce a flavon field A with U (1) X charge −
1. To preserve SUSY close to the string scale, A can acquire a VEV so that the U (1) X . ≤ (cid:15) ≡ (cid:104) A (cid:105) M P l ≤ . , (15)where M P l is the reduced Planck scale. Interestingly, (cid:15) is about the size of the Cabibboangle. Also, the U (1) X charges of the SM fermions and the Higgs fields φ are denoted as Q Xφ .The SM fermion Yukawa coupling terms arising from the holomorphic superpotential atthe string scale in the SSMs are given by −L = y Uij (cid:18) AM P l (cid:19) XY U ij Q i U cj H u + y Dij (cid:18) AM P l (cid:19) XY D ij Q i D cj H d + y Eij (cid:18) AM P l (cid:19) XY E ij L i E cj H d + y Nij (cid:18) AM P l (cid:19) XY N ij L i N cj H u , (16)where y Uij , y Dij , y Eij , and y Nij are order one Yukawa couplings, and
XY U ij , XY D ij , XY E ij and XY N ij are non-negative integers: XY U ij = Q XQ i + Q XU cj + Q XH u , XY D ij = Q XQ i + Q XD cj + Q XH d ,XY E ij = Q XL i + Q XE cj + Q XH d , XY N ij = Q XL i + Q XN cj + Q XH u . (17)Similarly, the SM fermion Yukawa coupling terms in the SU (5) models are −L = y Uij (cid:18) AM P l (cid:19) XY U ij F i F j H + y DEij (cid:18) AM P l (cid:19) XY DE ij F i ¯ f j H + y Nij (cid:18) AM P l (cid:19) XY N ij ¯ f i N cj H , (18)where
XY U ij = Q XF i + Q XF j + Q XH , XY DE ij = Q XF i + Q X ¯ f j + Q XH ,XY N ij = Q X ¯ f i + Q XN cj + Q XH . (19)In addition, we shall employ the quark textures for the SSMs and SU (5) models in Table I,which can reproduce the SM quark Yukawa couplings and the CKM quark mixing matrixfor (cid:15) ≈ . Y E ∼ (cid:15) c (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) , M LL ∼ (cid:104) H u (cid:105) M s (cid:15) − (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) , (20)6 ukawa The SSMs SU (5) Models Y U (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) Y D (cid:15) c (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) c (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) (cid:15) TABLE I: The quark textures in the SSMs and SU (5) models. where c is either 0, 1, 2 or 3, and tan β ≡ (cid:104) H u (cid:105) / (cid:104) H d (cid:105) satisfies (cid:15) c ∼ (cid:15) tan β . This neutrinotexture requires some amount of fine-tuning as it generically predictssin θ ∼ (cid:15) , ∆ m ∼ ∆ m . (21)Interestingly, with (cid:15) as large as 0 .
2, the amount of fine-tuning needed is not that huge andthis is shown in the computer simulations of [57–59] with random values for the coefficients.To be concrete, we choose the U (1) X charges for the SM fermions and Higgs fields in theSSMs as follows Q XQ i = (3 , , , Q XU ci = (5 , , , Q XD ci = ( c + 1 , c, c ) ,Q XL i = ( c + 1 , c, c ) , Q XE ci = (3 , , , Q XH u = Q XH d = 0 , (22)with Q Xφ i ≡ ( Q Xφ , Q Xφ , Q Xφ ) for the SM fermions φ i .Also, we take the following U (1) X charges for the SM fermions and Higgs fields in the SU (5) models Q XF i = (3 , , , Q X ¯ f i = ( c + 1 , c, c ) , Q XH = Q XH = 0 . (23) IV. SQUARK MEDIATION VS HIGGS MEDIATION
Natural SUSY can be regarded as an effective SUSY scenario where only stop, gluinoand small µ term are required in the spectra. As a consequence, the fine-tuning remains amanageable level. One of nice property of Natural SUSY is that the first two generation7quarks can be very heavy without introducing any fine-tuning, which also evade boundsof SUSY direct searches from LHC. In terms of squark mediation with squark-messsenger-messenger interaction, Squarks receive additional positive contribution thus is possible toconstruct Natural SUSY model.The basic formulas to compute corresponding soft terms are given as [27], A ab = − π d ija ∆ (cid:0) λ ∗ aij λ bij (cid:1) Λ , (24) δm ab = 1256 π (cid:32) d cBa d deB λ ∗ acB λ bcC λ deB λ ∗ deC + d cBa d dCc λ ∗ acB λ beB λ cdC λ ∗ deC + d cBa d dCb λ ∗ acB λ ceB λ ∗ deC λ bdC − d cda d fBc y ∗ acd y bde λ cfB λ ∗ efB + 12 d cBa d efc y cef y ∗ def λ ∗ acB λ bdB + 12 d cda d efc y ∗ acd y cef λ bdB λ ∗ efB + 12 d cBa d efB λ ∗ acB λ efB y bcd y ∗ def − d cBa C acBr g r λ ∗ acB λ bcB (cid:33) Λ , (25)where Λ = F/M , and C ijkr = c ir + c jr + c kr is the sum of the quadratic Casimirs of each fieldinteracting through λ ijk . In above expressions, we do not include the contributions fromusual GMSB (thus is labeled by δm ab ) and all of indices are summed over except for a and b . Without the FN mechanism, there will be general interaction between Q i , U i and D i .The squark mediation is not automatically minimal flavor violation like higgs mediation.The MSSM-MSSM mixing term gives rise to dangerous non-vanishing and non-diagonal softmasses, for example, m Q Q ∼ λ q λ q Λ . (26)The non-diagonal terms in Eq. (26) motives Ref. []to construct chiral flavor violation scenariowhere only single Q i or U i , D i is allowed to couple the messenger. As a result, the dangerousflavor violation term is suppressed naturally. However our situation does not belong tochiral flavor violation. In order to realize effective SUSY scenario, all the first and secondgeneration squarks must be coupled to messengers in order to obtain large soft massesenhancement. It seems the non-diagonal term is inevitable in Eq. (26). The loop holecomes from the fact that the bound is greatly improved once the squark are not degenerate.In particular, the largest bound comes from the first generation squarks because of largePDF effct of first generation quarks. Therefore it strongly suggests us to consider the firstgeneration squark mediation which is technically natural under FN mechanism. That is the8asic motivtion for us to consider FN mechanism in squark mediation. The FN naturalmodel is free from MSSM-MSSM mixing and the formula is reduced to A a = − π d cBa λ acB Λ ,δm a = 1256 π (cid:32) d cBa d deB | λ acB | | λ deB | + d cBa d dCc | λ acB | | λ cdC | + d cBa d dCa | λ acB | | λ adC | − d cda d fBc | y acd | | λ cfB | + 12 d cBa d efc | y cef | | λ acB | + 12 d cda d efc y ∗ acd y cef λ adB λ ∗ efB + 12 d cBa d efB λ ∗ acB λ efB y acd y ∗ def − d cBa C acBr g r | λ acB | (cid:33) Λ . (27)Let us demonstrate how FN mechanism makes the squark mediation flavor blinded. Thegeneral squark-messenger-messenger interaction within the messenger sector being SU (5)complete multiplets is divided into Q -type, U -type and D -type mediations, here U and D respectively denote ¯ u and ¯ d for short. In table II, we list the complete messenger fields andtheir U (1) charge assignment. Messenger (XQ , XQ c ) (XU , XU c ) (XL , XL c ) (XD , XD c ) (XE , XE c ) XS U (1) Charge (3 , −
3) ( − ,
5) (2 , −
2) (3 , −
3) (0 ,
0) 0TABLE II: Complete list of messenger fields and their U (1) charge assignment. For the Q-type Mediation, the most general superpotential is W Q = λ q i Q i XQ c XS + λ q i Q i XD c XL + λ q i Q i XU c XL c + λ q i XQXD , (28)where i = 1 , ..., λ q i ∼ (cid:26) , (cid:15) , (cid:15) (cid:27) , λ q i ∼ (cid:26) (cid:15) , (cid:15), (cid:15) (cid:27) ,λ q i ∼ (cid:8) (cid:15) , (cid:15) , (cid:15) (cid:9) , λ q i ∼ (cid:8) (cid:15) , (cid:15) , (cid:15) (cid:9) . (29)Terms with negative order of (cid:15) must be removed in order not to violate the holomorphyrequirement of superpotential. While terms with positive order of (cid:15) can be ignored which isguaranteed by the smallness of (cid:15) . Therefore Only λ q is allowed under the consideration ofFN mechanism and holomorphy. For now we only consider squark-messenger-messenger in-teraction, this is mainly because the squark-squark-messenger interaction under FN charges9as been discussed in the literature. Since only the Q mediation is allowed, there is noflavor-changing problem. For the U -type mediation the most general superpotential is W U = λ u i U i XU XS + λ u i U i XD c XD c + λ u i U XQXL c + λ u i U i XEXD . (30)According to FN mechanism the coupling scales like λ u i ∼ (cid:26) , (cid:15) , (cid:15) (cid:27) , λ u i ∼ (cid:26) (cid:15) , (cid:15) , (cid:15) (cid:27) ,λ u i ∼ (cid:8) (cid:15) , (cid:15) , (cid:15) (cid:9) , λ u i ∼ (cid:26) (cid:15) , (cid:15) , (cid:15) (cid:27) . (31)It is similar with Q-type mediation, only the λ u is allowed. For D-type mediation we have W D = λ d i D i XQXL c + λ d i D i XQ c XQ c + λ d i D i XD c XU c + λ d i D i XE c XU . (32)Subject to the FN mechanism we obtain the couplings λ d i ∼ (cid:8) (cid:15) , (cid:15) , (cid:15) (cid:9) , λ d i ∼ (cid:26) (cid:15) , (cid:15) , (cid:15) (cid:27) ,λ d i ∼ (cid:8) (cid:15) , (cid:15) , (cid:15) (cid:9) , λ d i ∼ (cid:26) , (cid:15) , (cid:15) (cid:27) . (33)All in all the allowed yukawa defelect mediation interaction for squarks are summarizedas follows W = λ q Q XQ c XS + λ u U i XU XS + λ d D i XE c XU . (34)From Eq. (34), we obtain the extra contribution to soft masses for the first generationsquarks. In other words there is no desirable large trilinear term A t from equation 34which motivates us to resort to higgs Mediation. Based on FN mechanism the only allowedsuperpotential for Higgs mediation is W H = λ h H u XD c XQ . (35)It is automatically preserves minimal flavor violation (MFV). Using Eq. (27), we obtain10ollowing soft terms A t = − λ h π δm H u = Λ (cid:16) λ h − (cid:16) g + g + g (cid:17) λ h (cid:17) π ,δm Q = − λ h y t π ,δm U = − λ h y t π ,δm Q = Λ (cid:16) λ q − (cid:16) g + g + g (cid:17) λ q (cid:17) π ,δm U = Λ (cid:16) λ u − (cid:16) g + g + g (cid:17) λ u (cid:17) π ,δm D = Λ (cid:16) λ d − (cid:16) g + g (cid:17) λ d (cid:17) π . (36)The choice of higgs mediation in Eq. (35) plays a crucial role in reducing the fine-tuning: • The trilinear soft term has a overall factor 3 coming from the higher representationof SU (5). Thus it can give rise to large trilinear term compared with other higgsmediation. • The m H u has a negative contribution from SU (3) gauge coupling. Such a large couplingcan reduce the fine-tuning easily.The parameter space is thus determined by the following parameters { Λ , M, λ q , λ u , λ d , λ h , tan β, sign ( µ ) } (37) V. PHENOMENOLOGY ANALYSIS
In this section, we give a detailed discussion on the numerical results for our effectivesupersymmetry model. In particular the higgs mass, stop mass, gluino mass as well asfine-tuning are given explicitly. In our numerical analysis, the relevant soft terms are firstlygenerated at messenger scale in terms of gauge mediation and higgs, squark mediation. Thelow scale soft terms are obtained by solving the two-loop RG equations. For this purpose,we implemented the corresponding boundary conditions in Eq. (36) into the Mathematica11ackage
SARAH [61–65]. Then
SARAH is used to create a
SPheno [66, 67] version for theMSSM to calculate particle spectrum. The tasks of parameter scans are implemented bypackage
SSP [69].The framework that we concentrate on is MSSM with yukawa deflect mediation. Its inputparameters are given in Eq. (37). The scan range we adapt isΛ ∈ (6 × , × ) GeV ,λ h ∈ (0 , . . (38)The other parameters have been fixed to M = 10 GeV, tan β = 10 and sign ( µ ) = 1. Forthe parameters in squark mediation, we divide it into two scenarios:Degenerated squark: λ q = λ u = λ d = 0 , Non-degenerated squark: λ q = λ u = λ d = 1 . . (39)During the scan, various mass spectrum and low energy constraints have been consideredand listed at below:1. The higgs mass constraints: 123 G eV ≤ m h ≤
127 G eV , (40)2. LEP bounds and B physics constraints:1 . × − ≤ B R ( B s → µ + µ − ) ≤ . × − (2 σ ) [70] , . × − ≤ B R ( b → sγ ) ≤ . × − (2 σ ) [71] , . × − ≤ B R ( B u → τ ν τ ) ≤ . × − (2 σ ) [71] . (41)3. Sparticle bounds from LHC Run-II: • Light stop mass m ˜ t >
850 GeV [72, 77], • Light sbottom mass m ˜ b > − • Degenerated first two generation squarks (both left-handed and right-handed) m ˜ q > − • Gluino mass m ˜ g > F T ≡ max { ∆ a } where ∆ a ≡ ∂ log m Z ∂ log a . (42)where a denotes the input parameters in Eq. (37).In Fig. 1-3, We display the contour plots of important mass spectra and fine tuningmeasure ∆ F T in the [ λ h , Λ] plane. There are some notable features can be learned fromthese figures and summarized at below:1.
The higgs mass:
The higgs mass range is taken from 123 GeV to 127 GeV in ournumerical analysis. For small λ h , One expects higgs mass simply growth with anincreases of Λ. With the increasing of λ h , allowed parameter space is forced to shiftto smaller Λ region in order to obtain correct higgs mass.2. The fine tuning measure:
For small values of Λ and λ h , ∆ F T is usually dominatedby Λ. Since in these regions the RGE effects are most important, the contribution tothe fine tuning of λ h , which only affects the boundary conditions, is negligible. Theimportant parameters thus is Λ which sets the range of the RGE running. For moderateΛ a and λ h , the contribution from µ and Λ are almost comparable. Finally, if λ h becomes large it is always the biggest contributor to fine tuning measure independentof the value of Λ.3. The squark and gluino masses:
Both stop and gluino masses fall into multi TeVrange and therefore out of current LHC reach.
VI. CONCLUSIONS
In this paper, we have investigated the extended gauge mediation models where yukawainteraction between messengers and matter superfields are made natural under the consid-eration of F-N U (1) symmetry. Because of higgs mediation the large A-term is generatednaturally which can be used to enhance the higgs mass efficiently. Considering the additionalquark mediation, it is found that first generation squarks get large positive contributionthus escaping from dangerous LHC constraints. We also study the parameter space andphenomenology numerically. The results show that the model is still promising under thestringent LHC constraint. 13 Λ h (cid:76) (cid:72) T e V (cid:76) m h FIG. 1: Distribution of higgs mass in [ λ h , Λ] plane. Λ h (cid:76) (cid:72) T e V (cid:76) m t (cid:142) (cid:76) (cid:72) TeV (cid:76) Λ h m g (cid:142) FIG. 2: Distributions of stop (left-panel) and gluino mass (right-panel) in [ λ h , Λ] plane. Λ h (cid:76) (cid:72) T e V (cid:76) (cid:68) FT FIG. 3: Distribution of fine tuning measure in [ λ h , Λ] plane.
Ackownoledgement:
This research was supported in part by the Natural Science Foundation of China undergrant numbers 10821504, 11075194, 11135003, and 11275246.15
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