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JHEP07(2012)155 e,f Springer July 12, 2012 July 16, 2012 July 25, 2012 June 11, 2012 , : : : : Revised 5) TeV and of . Accepted Received Published (0 10.1007/JHEP07(2012)155 O doi: and Stefan Pokorski e Published for SISSA by [email protected] , , Marek Olechowski c,d Emilian Dudas, 1205.1675 a,b Phenomenology It is shown that MSSM with first two generations of squarks and sleptons much [email protected] 3) TeV. The LSP can be either or bino or a mixture of both and it can − (2 [email protected] [email protected] Institute of Theoretical , Facultyul. of Ho˙za 69, Physics, PL–00–681 University Warsaw, of Poland TUM-IAS, Warsaw, Technische Universitat Munchen, Lichtenbergstr. 2A, D-85748 Garching, Germany E-mail: Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3CPhT, 0HE, Ecole United Polytechnique, Kingdom 91128 Palaiseau, France Department of Physics, Theory Division,CH-1211, CERN, Geneva 23, Switzerland Department of Applied MathematicsUniversity and of Theoretical Physics, Cambridge, Centre forWilberforce Road, Mathematical Cambridge Sciences, CB3 0WA, United Kingdom O b c e d a f Open Access Keywords: ArXiv ePrint: of the RG evolution,Higgs with vanishing is (or genericallyscenario, small) motivated heavy, trilinear by in coupling the supersymmetric the atbased FCNC the vicinity on problem and high of horizontal models symmetries, scale. 125 GeV. for the- mass The masses In of the thisbe lightest inverted stop a hierarchy is good dark candidate. Abstract: heavier than the third one naturally predicts the maximal stop mixing as a consequence Marcin Badziak, Inverted mass hierarchymass and in the the Higgs MSSM boson JHEP07(2012)155 17 18 2 13 19 5 – 1 – 16 16 − 1 µ 20 + µ sγ → s → b B In this paper we investigate the predictions for the lightest mass in the On the other hand, it has very early been observed that the supersymmetric FCNC In supersymmetric (SUSY) models, MSSM in particular, it has been appreciated from 4.2 4.3 4.4 MSSM spectrum and LHC phenomenology 3.1 Inverted hierarchy models: Abelian flavor symmetries 4.1 Dark matter models based on horizontalthe symmetries, hierarchical fermion the masses. sfermion(IH) The mass of predicted spectrum the pattern sfermion has is masses. been the linked so-called inverted to hierarchy MSSM with inverted hierarchy of sfermion masses. Due to 2-loop effects, heavy first two are rather lightgeneration but . says nothing about the massesand of CP the violation first problems can andsfermions be are. the substantially second eased Thus thelead the together heavier concept to the the of first-two-generation expectation naturalness of a and split sfermion the spectrum. FCNC Furthermore, supersymmetric in fermion problem mass the beginning of thespectrum is supersymmetric concerned phenomenology by the that naturalnesssfermion only argument, masses namely part and , of the thirdparticles the (and generation to whose a masses muchvia lesser enter extent loop the other effects, Higgs ). enhanced potential Those by either are large the at couplings. the Naturalness tree argument suggests level that (higgsinos) those or theoretical ideas going beyond theretical Standard argument. Model. However, if This onethe is abandons a LHC. it, qualitative there If and is one onlythe no takes a LHC reason it theo- or to too even expect literally, at new new LEP. physics particles at should have already been observed at 1 Introduction The issue of naturalness of the Higgs potential has for long been a driving principle for 5 Conclusions 3 The Higgs boson mass in IH model 4 More phenomenology Contents 1 Introduction 2 The Higgs boson mass in the electroweak scale MSSM JHEP07(2012)155 4 in (3) 0 (2.1) SUSY ) that m SUSY /M ≤ | 2.1 t M 0 X , denotes the | A we perform 6. . A 3 ]. Our findings  √ 5 5 = 2 t 2 SUSY where X being SUSY breaking M SUSY t Z 12 A M , the value of ] data. This is because the /M − | t 4 1 ,  X 3 . It follows from eq. (  | with SUSY A ]. Our predictions for the Higgs β M m 5 2 t SUSY 2 SUSY X tan M /M we discuss the implications of the low t µ/ + 2 X − ] and CMS [ ] versus 2-loop (in our case) calculation of  t 5 2 , A 1 2 t – 2 – 2 ≡ SUSY m t M X . However, the tree-level upper bound on the Higgs  | β ln  are the eigenvalues of the stop mass matrix at 4 t 2 W (3) being the scale of the 3rd generation sfermion masses. cos 2 . It follows from the above formula that sizable corrections 0 i | m ˜ t m 2 Z 2 m g m π ( 3 M SUSY 8 2 ˜ t M + m β 1 ˜ t 2 ]. One can then show that, for fixed 2 m = 0, with 6 ) was derived under the assumption of a relatively small mass splitting √ 0 cos 2.1 A 2 ≡ Z M , this can be traced to the 1-loop [ ]: 6 ≈ 3 SUSY renormalization scheme) and 2 h M m Equation ( The paper is organized as follows. In section Various phenomenological aspects of the inverted hierarchy of the sfermion masses and DR Higgs boson mass are quitethe sensitive maximal to contribution the from ratio stop mixing is obtained for between the stops. The generalizationfound of e.g. this in formula to ref. the [ case of a large splitting can be where the top trilinear coupling at to the Higgs bosonthe mass top can . be Sincesignificant, obtained the the when contribution precise to the values the stops of Higgs are the boson substantially stop mass heavier from masses than stop required mixing to may obtain be a given value of the CP-odd scalar, the Higgsgiven boson by mass [ corrected by the dominant one-loop contribution is It is well knownis that bounded at from the above treeboson by level the mass mass is ofare uplifted the taken at lightest into Higgs the boson account.properties quantum in of level the The the when MSSM magnitude stop the of sector. effects the of In loop the (soft) corrections decoupling SUSY depends limit, breaking mainly on the other phenomenological constraints andbenchmark implications points for are the presented. LHC Our conclusions are are discussed. presented in Several 2 section The Higgs boson mass in the electroweak scale MSSM energy MSSM spectrum onreaching the large Higgs values boson ofa mass. the detailed study Higgs A of bosonreview crucial the there mass role predictions some of is of for the the the emphasized. theoretical Higgs ideas stop leading boson In mixing to mass the in section IH in of the sfermion IH masses. scenario. In section We also its impact on theare Higgs mass in have a also qualitative beenboson agreement discussed mass with in are the a oftenof recent results a paper couple section of of [ ref. GeV [ the higher Higgs and, mass as and we to discuss the in not more fully detail overlapping range at of the the end investigated parameter space. seems to be favoured bymaximal the stop recent ATLAS mixing [ isand obtained even from with the RGThe lightest evolution stop effects, is predicted with toheavy. be initial The in the model 500–1000 GeV is mass less range fine-tuned and gluinos than are CMSSM. 2-3 TeV generations play significant role in reaching the Higgs mass in the region of 125 GeV which JHEP07(2012)155 , ) ]. S 15 [ DR /M t t ] which A X 10 scale where ]. decreases and in 9 ) is defined using The data used S 2 2.1 SUSY M between 2 and 2.5, M | the Higgs mass is en- S ]. In the case of CMSSM ] results). The Higgs are quite similar in most scale. 8 t 4 , ]. The original version X /M t 3 SUSY 14 X SUSY – | increases as M for various values of M 11 and introduced in eq. ( SUSY S M SUSY up to 5 TeV while keeping fixed all M U M ). Notice also that even though the SUSY ] and CMS [ scale. and m M 2 S 2.1 , Taking this into account the Higgs bo- , for the positive = 1 t M 1 for technical reasons. In SOFTSUSY it is possible Q SUSY X scale. It is clear from this figure that the sce- ]. S m 7 M M = – 3 – SUSY S scale. Such a procedure leads to excluding some M M Z . This asymmetry arises due to SUSY threshold effects 1187. M t . are the running soft masses of the third generation left- X ) U is obtained as a result of an iteration procedure. ) = 0 ( Z Q scale, even if there are no at the m M ( SUSY Z s M α M and U is defined using the soft masses while while m S S Q M M m we plot the Higgs boson mass versus ) does not depend on the sign of √ 1 3 GeV and . 2.1 ≡ S M = 173 In figure In our numerical studies we use a modified version of SOFTSUSY v3.2.4 [ There are theoretical uncertainties in the prediction of the Higgs boson mass. They The dominant 3-loop contribution to the Higgs mass hasThe been parameter calculated in [ 2 1 pole t it is positive and of the order ofthe 1–3 GeV eigenvalues with of precise the valuepart running depending of stop on parameter mass the space. matrix. softsome The terms cases The relative [ may difference values reach between of to 10%. fix In the some value figures of we use Higgs mass of 125 GeV.in The largest agreement Higgs with mass the isexpression obtained leading ( for one-loop formulahanced ( more than for the negative on the top Yukawa coupling which depend on the product of the gluino mass and nario with vanishing or veryof small about stop 125 mixing GeV is (suggestedboson incompatible by mass with of recent the 120 ATLAS GeV Higgs [ may bosononly be mass for obtained very in the heavy absencemass stops. of from the On the mixing stop the in mixing other the is stop hand, large, sector when stop but masses the of contribution about to 1 the TeV may Higgs be boson consistent with the where handed squark doublet (right-handed up-typein squark) this at plot the were obtainedother by MSSM scanning parameters defined at the of the parameter spacethis which part is of perfectly the viable parametermodified from space SOFTSUSY the is in theoretical important such point a forSUSY of way the corrections that view. studies the to in Since pole the the massesany SM present are negative parameters paper used squared and we in running have the the masses tachyons calculation at are of the the signalized only if there are of SOFTSUSY refuses tosquared calculate masses the at spectrum the ifthe there Higgs potential are is anyparameters minimized. negative are running The ( used reasongauge to for or this compute Yukawa is the couplings) that at SUSY in the corrections SOFTSUSY the to running the SM parameters (such as The estimated uncertainty isson about masses 3 GeV in [ tation the of range the 122–128 GeV excessesm are observed consistent by with the LHC the experiments. 125 GeVemploys Higgs In the interpre- the two-loop present formulae paper for we the use Higgs boson mass [ of this maximal correctionrunning increase stop with mass the matrix. splitting between the twooriginate eigenstates from of unknown the higher orderedge corrections and of from the the SM limited parameters, experimental mainly knowl- the top mass and the strong gauge coupling constant. giving the maximal correction from stop mixing to the Higgs mass, as well as the value JHEP07(2012)155 . U 2 /m Q m = 10 (top) β = 0. Analogous τ A and tan = S b A /M t the local maxima of the X U m = shows that the bigger stop mass 2 Q scale) are fixed to be 2 TeV except for 5. Moreover, the value of the Higgs m & U SUSY M /m Q for various values of m – 4 – SUSY 2 the positions of these maxima move towards the . M 2 in the case of large stop mass splitting may be larger ≈ is plotted there for various values of the ratio = 1 TeV. While for max | S S max S | 2 the mass splitting between the stops tends to suppress the exceeding 3 for S M /M /M t t . = 0 (to ensure that a is the LSP), /M X | 1 X t max | | S M S 1 TeV are very similar. X | − /M t /M = t X | µ X | = 1 TeV, A m . The Higgs boson mass versus = 50 (bottom). The solid (dashed) lines correspond to the negative (positive) values of = β µ The dependence of the Higgs mass on the stop masses splitting is shown in figure = . All the other MSSM parameters (defined at the 2 t mass corresponding to by several GeV as comparedsplitting to is the the unsplit bigger case.that maximal Figure Higgs for mass a may given beHiggs mass. obtained. It is also interesting to note The Higgs masskeeping versus fixed the valueHiggs of mass occur at larger values of or tan X M plots for negative Figure 1 JHEP07(2012)155 ]. 16 (also = 10) keeping 1 β U 0 since this /m Q < 3 m = 10. This can are the same as in β µM are very similar to µ SUSY . M β . In UV models, the values of is not present in figure β 122 GeV. The soft trilinear term SUSY & , especially when M ˜ τ h m m are very similar to those for tan β 1 TeV and a big contribution from the stop |  for various values of the ratio µ & S | is chosen there to be smaller than the sbottom – 5 – | /M t µ | SUSY X = 50 is slightly larger than for tan . These effects have been recently discussed in [ M and/or β b ˜ β m = 10. All other MSSM parameters at for which the bottom and Yukawa couplings are of the β |  µ β | is 2 to 3 times bigger than | t A | presented in these figures. As a matter of fact, for our choice of the µ . which maximizes the Higgs mass (for fixed other parameters). Typically, 1 max | the (not shown) plots for large tan 2 . The Higgs boson mass versus = 1 TeV assuming tan and the stop mixing at the EW scale depend on the pattern of soft terms fixed at a S SUSY M For large values of tan /M at the EW scale should not be much different from its optimal value corresponding to t SUSY t X such optimal value of M (usually high) scale of supersymmetry breakingpaper mediation we and are on interested the RG inwith evolution. the the In prediction inverted this hierarchy for of the squark lightest masses, Higgs motivated boson by the mass naturalness in arguments the and scenario 3 The Higgs bosonAs mass discussed in in the IH previousmixing model section, to the HiggsA mass is necessary| to obtain and the stau masses.those for For positive the sameparameters reason the the Higgs mass resultsbe for for attributed tan negative to the tree-level contribution which grows with tan typically leads to the enhancementcorrections of the important bottom for Yukawa coupling largeHowever, due tan to such SUSY reduction threshold offor the figure Higgs mass atwhich large is a tan consequence of the fact that same order as thesectors top may Yukawa also coupling be theand significant. loop become quite corrections large These from for corrections the tend sbottom to and reduce stau the Higgs boson mass Figure 2 fixed the case of figure JHEP07(2012)155 . , . . ) is 0 2 2 β U / / ). | A 1 1 0 m (3.2) (3.3) (3.1) ]. 3.3 = 10, M A Q 2) is a | /M , 0 β 18 m )–( ,  ( (1 m / 0 0 17 2 t 3.2 , . m m A 2 2 2) 2) , , (3) = 3 TeV and 0 . For (1 (1 ) does not depend 0 0 0 m m 3.1 m m 03 02 . . and 0 0 is approximately given by that ratio has to be about 2 t / − − 0 in eq. ( 1 A 2 2 t m M in the expressions ( A (3) (3) ≈ 2 2). However, as was pointed out . 0 0 , 2 0 2) m m / (3). , (1 1 A ). In consequence, a 125 GeV Higgs ]. The reason a rather large 0 | 0 65 35 0 (1 . . M 35 m 20 0 m . A | m + 0 + 0 + 0 ) = 2 0 2 0 d 2 A A / 2) = 10 TeV ( H 1 , ( 04 07 0 . . – 6 – M 5 and for (1 0 0 . 6 0 m . 3 1 − − m 1 for small 2 2 ) = / / ≈ − . 1 1 u ≈ − ) shows that, as long as the 2-loop effect is negligible, e.g. 2 H t M M / ( 1 0 0 0 at the EW scale in terms of the GUT scale values of the A 3.3 5 TeV and the gauge and Yukawa coupling at the GUT . A A 2 SUSY m 1 2 U is relatively small because the is heavy. It goes to /M . . )–( 0 0 m /M = 1 A 2 t A 3.1 + 0 + 0 3 TeV, the scalar mass of the third generation , respectively), the EW scale value of A 2 2 0 Q / / − and depends on the relative magnitude of 2 2 at the EW scale can be obtained. Due to the RGE running, the 1 1 A is a linear combination of the high energy scale masses and 0 = | Q M M t A 0 1 3 m . . A and ) is valid at the 2-loop RGE level. For the sake of definiteness we give A 3 2 2 one needs SUSY / 3.1 ≈ ≈ 1 2 / /M 1 2 U 2 Q M t 2 is required, with negative sign more effective for not too large a ratio m m M A |  ≈ ± 0 0 = 700 GeV, ], for very large scalar masses of the first two generations it may lead to tachyonic stops An inspection of eqs. ( The values of Equation ( Since the large stop mixing at the EW scale is crucial for the successful prediction for m 2 / 19 /m 1 4. These conclusions agree with a recent study [ 0 For − needed is that the RG evolutionis of correlated the (leading dividend to and ofboson the requires divisor a in heavy the spectrum ratio and significant cancellations in the Higgs potential. in [ due to the (small) negative coefficient in front of in CMSSM, ”maximal” stop mixing canThe be needed value obtained of only forA sufficiently large values of The dependence of the 3rd2-loop generation effect squark and masses it at is the negligible EW for scale small on values the of on the latter). Insoft most masses of at the the paper, GUT unless scale otherwise stated, we alsosoft take terms universal are Higgs given by: in this paper allcomputed the at coefficients obtained the fromscale scale the consistent RG with running radiativeM electroweak (unless symmetry stated breaking otherwise) (REWSB)that for of tan the first and second generation The precise values of the coefficients incouplings, the so above implicitly equation (among depend on otherThe the parameters) gauge coefficient on and in the Yukawa front values of of zero the when top the mass top and quark tan mass approaches its infra-red quasi-fixed point value [ low scale value of trilinear terms. In the caseparameters of ( the universal high energy scale boundary conditions for these model. The Higgs bosonthe mass soft is terms calculated at for the a GUT given scale. set ofthe the Higgs boundary boson conditions mass, for values before of going to the IH scenario, it is useful to discuss when large by the flavour models based on horizontal symmetries. We shall not refer to any specific JHEP07(2012)155 = 2) , β (1 0 2). One m , (1 0 m can be decoupled t (1,2) [TeV] 0 no REWSB A m 2. Increasing ≈ between zero and about 0 (3), the stop masses, as well 125 0 A several slices of the plot from SUSY tachyonic stop m . Very similar predictions are 4 3 /M | are needed for obtaining the Higgs 124 t 0 X | 2 TeV. The yellow “tachyonic stop” and A − . 123 = the Higgs mass initially increases reaching | 1000 0 0 A A | (3), the RG evolution of 0 2). In consequence, the logarithmic correction SUSY – 7 – , m 123 500 (1 /M | 0 1 TeV and ”maximal” mixing follow quite naturally t  2000 m X ≈ | 2) (3). For a given value of ]. , 0 3000 2) corresponding to = 1 TeV and 2 TeV is shown in figure 21 (1 that IH scenario predicts large values of the Higgs boson m , between 0.5 and 2 TeV and 0 SUSY 2 − 3 / (1 2 m 1 0 / M = 1 0) regions are excluded. In the dark green region the relic density of M 1288 [ m . 0 M 0 < 122 A 2 is taken with smaller < µ because the stop-mixing correction is close to its maximal value and 2 2 5 10 15 20 25 = 10, / h CMSSM 1 h β m M DM by gluino contribution to the RG running, without enhancing the stop t A 0, tan , decrease with increasing = 1 TeV and . Contours of the Higgs boson mass (black dashed line), the lighter stop mass (solid green 1 6 5 4 3 2 µ > 2 for three fixed values of / 5.5 4.5 3.5 2.5 1.5 1 3

SUSY

It can be seen from figure An example of the predictions for the Higgs boson mass in the IH scenario, for tan In the IH scenario, with

0 M m (3) [TeV] (3) M 4 TeV, if larger as to the Higgs mass decreasesrection while increases the polynomially one with from stopa mixing maximum increases. for Since a the valuefurther latter of decreases cor- − mass. In order to better illustrateparticularly the near dependence the of tachyonic the region, Higgsfigure mass we across present parameter in space, figure gluino mass 2-3 TeV. Thus, from the RG evolution. Moreover,smaller the than cancellations e.g. in in the the Higgs potential CMSSM are focus significantly point. 10, obtained for a range of from the evolution ofcan stop enhance masses because themasses, former due does to not thegenerations. depend negative In 2-loop on consequence contribution no to largemass initial the in values stop the of masses 125 GeV from range, the with 1st the lighter and stop 2nd mass in the range 500–1000 GeV and the the grey “no REWSB” ( gives Ω Figure 3 line) for JHEP07(2012)155 3 and (3.4) 2 / 1 2) for a becomes , . M 2 2 (1 which gives 0 µ = 122 (125) 2) 2) may drive , m , (3) is not able to h 0 (1 max (1 (3), m 0 ) m 0 0 m m m SUSY = 0, 006 . (3) below some critical 0 0 0 /M | A m t 2) the stops become light − , 2 at the EW scale is generated X . Even though it is negative | t (1 2 0 (3) A 0 m (3) becomes negative. This effect is 0 m 2 m 01 µ . 0 − 0 becomes more and more negative as the A 2 2 / 1 (3) , increases. On the other hand, the very small – 8 – 0 M m . = 0. In such a case 35 . 0 SUSY 4 0 15 TeV the lightest Higgs is necessarily heavier than A -terms. We found that for M − A > that the largest Higgs masses correspond to the largest 2 0 3 3 A 2) is always negative due to the specific structure of the two- 15 TeV implies that the lightest Higgs mass has to be not 1 , . 2 before the tachyonic stop is signalized. (1 > 0 2) + 0 , the stop-mixing correction also starts to decrease resulting in a m 2) 2 / , (1 SUSY 2 1 0 (1 M 2) reaches the value corresponding to ( 2). 0 m M , , SUSY 3 . m (1 (1 1 0 (3), as seen in figure 0 /M 0 | ≈ t m m 2). Therefore, a heavier Higgs prefers the regions of parameter space where . The “maximal mixing” can be realized only for m u , X | 3 2 H demonstrates that in the IH scenario the stop-mixing correction to the Higgs (1 0 m 5 (500) GeV and m O ≈ − 2 Figure It is also evident from figure Non-trivial constraints on the IH scenario follow from the requirement of proper µ has to be large enough to ensure that by increasing A sharp cut-off of some curves is partly due to the fact that SOFTSUSY for large negative. In order to protect proper REWSB the positive contribution from on the soft terms defined at the GUT scale which is approximately given by: 3 0 2 2 boson mass can be maximized evenentirely if radiatively by the gaugino masses.than This in requires the gaugino masses case somewhat of heavier non-vanishing reach very small values of smaller than about 123at GeV. least More generally,about we 122 GeV. found thatlarger This if values lower of the bound lighter on stop the mass Higgs is mass becomes even more stringent for the first and second generationto sfermions the are FCNC decoupled problem. which makes Thisof plausible also the the can flavor solution be problem seen reliesHiggs from on the mass the opposite perspective. is decoupling ofthe If expected the the requirement to first solution of two be generations large. of sfermions the In particular, for the parameters used in figure negative before the maximal stop-mixing correction tothe the reason Higgs for mass. the Constraintslarge from lack values REWSB of of are maximum also in a dependence of thevalues of Higgs mass on µ A enough to realize “maximalseen mixing” in scenario figure before value which in this case is smaller than 5 TeV. For larger values of (which influence the GUTto scale note values that of gauge theHiggs and potential coefficient minimization Yukawa in couplings). scale, frontcoefficient It in of is front of important loop RGEs. Even though this coefficient is very small, large values of Notice first the smallnessin of the the above coefficient formula in wecoefficients front should are of emphasize extracted and that to its some sign extent depends on on the the boundary conditions scale for at the which soft the terms large enough rapid decrease of the Higgs mass. REWSB. The origin of theseµ constraints can be understood by inspecting a dependence of its increase cannot compensate the decrease of the logarithmic correction. Moreover, for JHEP07(2012)155 (3) 0 m for several fixed values of 3 – 9 – , respectively). SUSY /M t X or . Slices of the part of parameter space shown in figure SUSY M given in TeV on themass, plots. The solid (dashed) lines correspond to the Higgs mass (the lighter stop Figure 4 JHEP07(2012)155 (3). (3), , the 0 0 from 8 2 m m 6 µ . the plot 7 ) = 1 d shows that the = 0. H ( 125 5 0 are more stringent 0 no REWSB (1,2) [TeV] This is because the = 0 is qualitatively ) constraint on the 0 A 2 m 0 4 − m µ ). . In figure µ ) (which is now larger A 3 d β + . tachyonic stop (3). = 50 as compared to the (3), (3) is excluded because it µ H 0 0 0 6 ( β 0 1000 m = 10, as seen in figure 500 m m → 2) for m 5 TeV and β , . s (1 ) = 124 B 0 u = 1 m 2 H / ( . Since the tau Yukawa coupling is 1 0 2 2000 123 µ M m . Second: β = 50 is presented. In addition, the splitting 123 β but for – 10 – 3 -terms, as seen in figure A 2) set by the condition of positive 900 (1500) GeV. Notice that in this example the Higgs , & 2) to avoid tachyonic stops. Also figure (1 but for tan , 0 2 (3) to be arbitrarily small because otherwise the stau would be lighter 3 = 10 the tachyonic stau is also present in some part of parameter space / (3) (outside of the range of the plot in figure 0 m (1 However, it can be seen that in spite of these constraints the 1 0 0 β m m 122 M 5 m is qualitatively similar to that for tan β 5 10 15 20 25 . The same as in figure CMSSM (3) and 0 5 TeV is large enough to generate stop masses radiatively. Smaller values m . is smaller for larger values of tan = 1 2 0 Figure 5 / 3000 A 1 = 50. There are two reasons for that. First: the positive contribution to 1 (3)) gives larger negative contribution to 6 5 4 3 2 M 0 β 5.5 4.5 3.5 2.5 1.5 2) for large tan and (3) require smaller m

,

0

The IH scenario can be also realized for large values of tan

2 0 m (3) [TeV] (3) One cannot, however, take As a matter of fact, for tan / (1 m 4 5 1 0 Higgs boson mass may reach even slightly larger values for tan than the lightest neutralino. but for much smaller values of for tan M than now of the samemasses order and as some the part top ofleads Yukawa parameter it to space gives a at large smaller tachyonic values negative stau. of contribution to the stau between the soft Higgsis masses introduced at the in GUT orderparameter scale, space. to Even reduce though them a impact dependence of of the theupper Higgs bounds BR( on and the lighter stop masses on requirement of maximal mixing andDependence of proper of REWSB the may Higgs putsimilar and an to upper the bound the lighter on one stop with mass non-vanishing on analogous to that from figure GeV can be obtainedmass for of 124 GeV canvalue be of obtained even for veryof small values of JHEP07(2012)155 are (3). 0 | 0 m A | and/or 2 / (1,2) [TeV] 1 0 m . We should, however, M | 0 (3). The region below the 0 A | = 0 the Higgs boson mass m 0 6 . A and for several fixed values of = 1 2 5 / d 1 H M no REWSB tachyonic stop m 125 500 1000 = 50 and 800 (1300) GeV. tachyonic stau β – 11 – & 124 2 ) at 95% C.L. The orange region is excluded because it / 1 − = 50. In particular, for µ M + β µ 123 but for tan → 3 s 2000 B CMSSM 122 2 4 6 8 10 12 14 16 18 20 . The same as in figure . Slices of the part of parameter space shown in figure 1 6 5 4 3 2 5.5 4.5 3.5 2.5 1.5 = 10 case. Moreover, gaugino masses required to obtain a given value of the Higgs

The examples presented above were designed in such a way that the Higgs mass of

0 β (3) [TeV] (3) m mass are somewhat smaller forof tan 122 (125) GeV can be reached if 125 GeV is obtained with the smalleststress possible that values of in the IH model larger Higgs masses can be reached if purple line is excludedpredicts by a BR( tachyonic stau. tan Figure 7 Figure 6 The solid (dashed) lines correspond to the Higgs mass (the lighter stop mass). JHEP07(2012)155 2 7 h . / 1 2 m (3). / 0 1 (3.5) /M m 0 ∆. As / A /M = 0 the = 1 TeV = 50 the 0 0 2 A . It can be β / A 2 1 / 1 M 6 M and = 10 and 0 , where: A ]. β } 2 TeV and a = 0 the Higgs mass up to 23 − ∆ , { 0 22 = A for several fixed values of 0 7 max A ≡ (150). Similarly, for tan . 2 / . 1

∼ O M h 5 TeV and a . m ln ln ∂ = 2 ∂ . For a given point in parameter space proper 2

/ – 12 – µ 1 ≡ ) that from the naturalness point of view neither (250) but for e.g. M a 3.4 ∆ ∼ O (150). is needed to obtain a given value of the Higgs mass. In other 0 A ∼ O is the best choice. We found that for tan 0 A ]. The focus point in the CMSSM gained a lot of interest since heavy stops when defining the measure of fine-tuning, see e.g. refs. [ stands for any soft term or 24 [ Z a 2 M / 1 . Slices of the part of parameter space shown in figure M is, the smaller value of It is also interesting to note the existence of a generalized “focus point” region. We One of the reasons why the “maximal mixing” generated by IH is interesting is that it 2  In the case of large loop corrections to theNotice quartic that Higgs a coupling, given it value is of more the appropriate Higgs to mass refer can to be obtained only for the values of the ratio of / 6 7 1 0 recall that in the CMSSMm the “focus point” refers to the region of parameterrather space than where in some finite range whose size is controlled by the value of large nor vanishing Higgs mass of 125 GeVthe requires Higgs ∆ mass of 125125 GeV GeV can is be reached reached with with ∆ ∆ explained before, in IHM scenario with the “maximalwords, the stop same Higgs mixing” boson the massThe bigger can level be the of obtained value fine-tuning for various of stronglyinferred values of depends from the on ratio the the coefficients relative in values of eq. ( The index REWSB requires cancellation between the parameters with the precision of order 1 chosen to be larger.about For 127 GeV example, can for be obtained. requires less fine-tuning than e.g.to CMSSM quantify to this obtain we the define same the Higgs fine-tuning boson parameter mass. ∆ In order Figure 8 The solid (dashed) lines correspond to the Higgs mass (the lighter stop mass). JHEP07(2012)155 ] 0 5 A ] is 5 with u ] which 2 H 10 m , the virtues 2 ]. Somewhat / 5 1 3 is emphasized (3) are typically / ˜ q  ] the computation . In SOFTSUSY only 1 5 m Z b ˜ > M M reported in ref. [ m ], under which first two = h (3) + 0 are included in the threshold 2 30 m Q ˜ t – m Z m M 28  + close to the EW scale. Such 1 ] can be reconciled with small ˜ t 2 ] as a way to ease the FCNC and 2) µ , 25 m 31 (1 – 0 28 For example for the benchmark points m 8 (3) = ˜ larger by 0.5–2 GeV. Secondly, in ref. [ q h m ], because of our generalized focus point. m 5 – 13 – ] are due to the fact that in ref. [ 5 )). In the focus point region of the CMSSM the LEP bound ] we find values of ], while we use the routines adopted in SOFTSUSY [ 3.4 5 27 reported in ref. [ (3), without any reference to potential models of such hierarchy. We to the Higgs potential and keeping 0 result from the cancellation of the gaugino contribution to h 0 2 m m m µ (3) in the range 1–1.5 TeV the upper bound on ˜ q  m 2) ]. In the IH parameter range, by taking , (10 TeV). 26 (1 0 O m Inverted hierarchy was proposed some time ago [ Our results are in a qualitative agreement with the results of ref. [ There is also another difference between ISASUGRA and SOFTSUSY. In ISASUGRA the heavy 8 sfermions of the firstmass, two while generations SOFTSUSY are decouples decoupled allleading from the logarithms the SUSY particles of RGEs at at the acorrections a ratios common to scale between scale equal the the to gauge heavy-sfermionISASUGRA the masses and effectively heavy-sfermion and Yukawa accounts couplings. for the On resummationfrom the of the the non-leading other logarithms. logarithms, hand, which Simple theof is estimate order missing decoupling of in procedure the SOFTSUSY, contribution adopted gives few in percent for the sfermion masses generations transform as a doublet, whereasmodels the do third generation explain is the atherefore singlet. difference can between Whereas accommodate U(2) the a firstscalars, hierarchy two they between generations do the not and first actually the predict two third it. and one To the our and third knowledge, the generation first of class of models in which would like now tosymmetries. recall briefly its link to models ofCP fermion constraints masses in based supersymmetric onsymmetries models. for horizontal explaining Early fermion ideas mass did hierarchies, like invoke U(2) horizontal [ non-Abelian for the benchmark points of table 13.1 of ref. [ Inverted hierarchy models:So far, Abelian flavor we symmetries havewith discussed the predictions for the Higgs boson mass in the IH scenario, as the one thatabove satisfies 1 simple TeV naturalness (because constraints. ofthe Our the average values masses of ¯ of the124 ¯ GeV, heavier quite stop close and toour the our parameter lighter result range, sbottom) of although and 125–126 GeV. with for heavier We third also generation notice spectrum, that the is fine similar tuning to in that of the Higgs bosonthe mass ISAJET is package performed [ take at into one-loop account all level relevant two-loop usinglisted corrections. ISASUGRA in program table from 1the of region ref. of light [ (below 1 TeV) average mass ¯ because in this partis of large parameter [ space theof stop the mixing focus is point strongly125 remain suppressed, GeV but unless for in the addition Higgs one mass obtains is large easily reachable. stopsmaller mixing values and of the region of contribution of small values of that of scalars (seecan eq. be ( satisfied withoutcontext of introducing the large 125 GeV fine-tuning Higgs of the the focus EW point region scale. of the However, CMSSM in is the much less attractive required to lift the Higgs mass above the LEP bound [ JHEP07(2012)155 . ) i D are 3.9 (3.9) (3.6) (3.7) (3.8) m 2 (3.10) ) . = F i 1, where ]. i m U )=0 43 ) and (  3 m – , l 3.8 38 = 3 /M d i i ( ), ( Q Φ , h with respect to the m , 3.7 , whereas ( 3 = i ]). We would like also e )=0  Q 2 > d 35 , l , , 2 2 d d h ( 33 , + , > d j 32 d , 1 + 2 i q ) . )=1  F i 1 ]. These models contain an additional i , d , l m D ∼ 34 1 ] are supersymmetric generalizations of 3 , respectively). d m d ( D ij 33 + ( H 6= , > u , predicted to be inverted i i 32 2 U D , h and h m charges of the left-handed (right-handed )=0 – 14 – i u 3 u > u h e 6= Q X ], to be positive and, in certain circumstances, to + , e H i j 1 ]) 3 u Q = 37 + 35 , , u i m 3 q 2 i , u q  36 under which the three fermion generations have different ( 3 m , X ∼ > q U ij 2 )=2 h 2 , e > q 2 ) denote the U(1) d 1 , u q 2 , h q u ( , , h i are D-term contributions for the scalar of charge i , d i )=3 D u 1 h ( i i e , e Q q 1 From the perspective of our present paper, the inverted hierarchy models do generically Whereas Abelian models naturally predict the inverted hierarchy, they do not gener- A successful fit of the experimental data requires larger charges for the lighter , u is the Planck scale or more generically the scale where Yukawa couplings are generated. 1 q ( tional splitting A relevant question is thereforeby what relaxing changes the are hypothesis expectedSince of in the degenerate the first first results two two presented generations generations so and are far of very heavy, we could expect large RGE effects. The be analyzed in someto details point (for previous out workshierarchy, that based see recently on e.g. geometric there [ localization were and various non-Abelian other family models explicitpredict [ realizations also a of splitting the between inverted the first-two-generation sfermions as well as intragenera- that the hierarchy ofhierarchy the of masses fermion of masses. scalars is ically predict approximate degeneracyAbelian among cousins. the first This two generations, leads unlike to their possible non- tension with FCNC constraints, which have to where F-term contributions. D-termleast) contributions in were effective string arguedbe models to dominant [ be over the naturally F-term generated contributions. (at It is then clear from ( Scalar soft masses in Abelianflavour entries flavor are models relevant are for typically our of present the discussion) form (only the diagonal in generations one simple example being (see e.g. [ Quark mass matrices for example, in such models are given, order of magnitude wise, by where up-quarks, right-handed down-quarks, Abelian flavor models of the Froggatt-Nielsen typeAbelian [ gauge symmetry U(1) charges (therefore the name horizontal orenergy flavor symmetry), scale spontaneously by broken at the aM vev high of (at least) one scalar field Φ, such that the inverted hierarchy was really predicted [ JHEP07(2012)155 | ) is S | 2 3.8 µ ) and (3.13) (3.14) (3.11) (3.12) 3 is quite Q . ( 2 0 2 is positive. (10TeV) it µ ) m 3 , S ] vanishes then E i ), ( ∼ O 2 E u 0 S S m H (1) coefficients of ]) m ( √ 0 O + 44 i m 025 2 L . m + 0 − 2 i ) to the EW scale soft scalar contributes to the EW scale 3 2 D and compensates the negative L S m S ( 2 0 ) S + 3 m i U . 2 U ( 035 . 0 i m 0 025 . m S, 2 D 0 f h . Since this contribution is negative one ≈ − Y )) so for the values of 25 ) S . − i 2 U e Q 05 2 2 Q 05 is negative but relatively small. The largest . 3.4 ) . m Y 0 3 + 0 m 0 [ S 2 − D . In particular, – 15 – ) ( 3 f )) which is crucial for obtaining the maximal stop 3 =1 0 i = X 008 ≈ − . Q m 2 f ( 0 3.3 = Tr( + 2 E 0 m d m m S 2 H 025 . ≈ − m typically result in tachyonic staus. Therefore, we conclude 35 . ). The individual contributions from the scalars to 2 Q + 0 − S m ] and therefore our conclusions concerning the running of soft i.e. of the same order as the first two generation soft masses. 2 3.9 u + 0 ) i 2 H d 2 46 ) , (compare with eq. ( D m H u h ( 45 0 S H ( -term contribution to the first and second generation squarks. m 0 is received by 025 ) = D . m 2 S 0 charges of are not chosen in such a way that 6 025 . . ) has to vanish (or to be very small) for phenomenological reasons, as ar- 0 0 X e Y m Q gives positive contribution to − ≈ − Y u S ≈ − 2 H is the of fermion 2 0, = Tr( m µ f enters RGEs at the one-loop level its effect on the RG running of soft scalar masses Y S S Let us also briefly comment on the effect of the mass splitting within the third gen- If the U(1) S > is generically of order = 0 and the prediction for the Higgs boson mass are almost identical to those presented For universal soft scalarinsensitive masses, to the the scalar overall mass contribution mainly from because the the contributions scalars from to is smaller than the eration of sfermions.the Such splitting diagonal may F-term be inapproximately present eq. given due by: ( to arbitrary two-loop effect (see coefficients inmixing. eq. ( The contribution to contribution from can expect that large values of that in IH models the maximal stop mixing consistent with REWSB is possible only if where value of is the dominant contribution implying thatFor proper REWSB is possible only if S Since (at least for non-colored scalars)from would generically heavy be first much two largermasses than generations. is the determined two-loop The by effect the contribution hypercharge from assignment and is approximately given by: gued in various papers [ terms and the fine-tuning remainS unchanged. In particular, for thein charge the assignment ( previous plots with degenerate first two generations. tion until now, is zeroD-term at dominance high-energy. of Interestingly the enough, type in put Abelian forward flavor in models this with section, the quantity S isHowever, equal Tr( to the Higgs scalars depend at 1-loop level on the combination (see e.g. [ where the trace is over the whole spectrum of MSSM states and which, under our assump- RGEs of all scalar soft masses and in particular of the third generation of squarks and of JHEP07(2012)155 9 & → s for ) . In B u 1 1 ]. The H M ( 0 48 ), BR( m sγ → b consistent with the 2 h 2) close to the boundary . , DM (1 2) and typically requires an 0 , SUSY µ a m 2). If the Higgsino is the LSP (1 ]. It is interesting to note that , 0 . This is because bino is the LSP (1 3 48 m [ 0 2) where the splitting between the − can become smaller than , 2 0 and tachyonic stop, respectively). m | h (1 µ | 0 < DM , 2 m 0 µ m 2) close to the boundary of the region where , are obtained not only due to large values of 2) from the REWSB constraint more stringent , (1 – 16 – | . WMAP bound can be accommodated [ 0 µ (1 | 1 0 m σ m 0. This resembles the focus point scenario in the CMSSM < at the GUT scale, the scalars give negative contribution to 2 = 50, respectively. 2 2) with a precision of order 10 ) µ β ] to compute the relic abundance of the LSP, as well as BR( , 3 U 47 (1 ( 0 0 m m 4 . + 0 2 ) = 10 and tan 3 β Q (3) but also because of even larger values of ( 0 0 ) and universal third generation scalar masses. ) approximately cancel out. Therefore, it is rather clear that splitting between u and the yellow regionsThe (corresponding corresponding to benchmarktan points are given as Points B and D in table stop-coannihilation region and doesHowever, the not large require stop veryHiggsino mixing precise LSP correction to is choice the present ofstop Higgs only parameters. are mass in light in some simultaneously. In the partlight our region in of plots the with it part the the of where Higgsino the and the dark the green Higgsino lighter region and stop in the are the vicinity both lighter of the border between the grey where for appropriatelythe large values present of casem small values of its relic abundancestate usually of turns bino out andregion to Higgsino with be the a 2 significant too component small of Higgsino but in if the the LSP is LSP much is larger a than the mixed correction to the Higgscase mass is is given as maximized. a A Point A benchmark inHiggsino point LSP table or illustrating mixed such Higgsino-bino LSP a of for values the of region where stop NLSP andWMAP the bound neutralino is LSP obtained foradjustment masses of very is small range small. of which usually Ω leads tothe too stop-coannihilation large region values often of coincides Ω with the region where the stop-mixing Stop-coannihilation for values of stops are tachyonic. TheIH scenario region for of some stop-coannihilation intermediate is range generically of present in the 3 m ) and SUSY contribution to anomalous magnetic moment, 6 H U − We use MicrOMEGAs [ • • . which makes the upper bound on ( ( 9 µ 0 0 0 2 + µ In the IH scenario therecompatible are with two the distinctive cosmological ways observations: to make the relic abundance of the LSP m 4 More phenomenology 4.1 Dark matter these threep scalar masses may substantiallyµ change the overallunless picture. gauginos are heavier. If stop In mixing the opposite may case, be the realized inverted for hierarchy lighter and the gauginos maximal than in the case of degeneracy between m JHEP07(2012)155 (4.1) 9 − 4 11 − − 10 10 10 × × × 61 1 . 1 3 . 4 9 4 − − 13 − − 10 10 10 10 × × , × × 4 66 07 . . below the experimental central 5 − 2 3 09) . 10 σ 0 × ± 4 9 − − 13 24 23) . . − 10 10 0 0 10 × × ± ± × 89 07 55 15 . . 7 ) is about 1 – 17 – . . 2 3 sγ 4 9 → ) = (3 ) = (3 − − 12 b sγ sγ − 10 10 1 1 1 1.6 10 → 10 10 10 50 × × → 888125 698 125 452 125.1 457 125.3 3700 3400 3800354135413542 3300 3154 3154 31552465 3477 3477 3478 3530 3487 3487 3488 3466 3545 3107 2432 3480 2367 1000 1500 1500 1000 0.111 0.118 0.021 0.116 -2000 0 0 -2000 b b 17690 21070 22500 14500 17680 21068 22495 14481 × ( ( Point A Point B Point C Point D 92 07 444, 813891, 940812, 647, 940 707 722, 1284 700, 1284 448, 461 677, 1286 455, 1286 419, 467 483, 869 457, 869 . . 476, 1801 699, 1581 505, 1632 979, 1274 1 1784, 2926 1555, 2717 1610, 29333467, 3580 1176, 1584 3108, 3257 3481, 3645 1853, 2368 2 3 SM exp 17675, 17675 21116, 21119 22526,17675, 22532 17685 14531, 21116, 14510 21120 22526, 22533 14531, 14541 17681, 17686 21069, 21068 22495, 22497 14482, 14528 ] for BR( BR BR ) 49 − ) µ (3) 0 + 2 sγ 2) µ 2 2 4 2 2 2 2 2 h , , , β , ± , , , , 3 / ˜ g ± 1 0 1 0 3 h 0 1 /m 1 A 1 1 ˜ H ν L,R (3) L,R L,R → 1 ˜ ˜ t ˜ ˜ ˜ ˜ b H τ ν ˜ ) ˜ χ χ χ µ ˜ ˜ e d 0 u → (1 A m m d m SUSY µ b m m 0 DM m m M m m m tan s m m m m m m m a H Ω sγ m B ( 0 ]: BR( . Several benchmark points with the inverted scalar mass hierarchy characterized by large → m 50 b BR( The SM predictionvalue [ [ the bino LSP andcharacterized the by mainly lighter Higgsino stop. LSP. Points B and D have a mixed higgsino-bino4.2 LSP. Point C is Table 1 stop-mixing contribution to the Higgs mass. Point A is an example of small mass splitting between JHEP07(2012)155 0. > . In (4.2) (4.3) (4.4) (4.5) (4.6) (4.7) (4.8) t β ]. The µA = 10 the 51 ) so strictly β 2 µM ) is even more − sγ ]. 0 because the sign 52 S, ) in addition to the → 2 1 > g b sγ 3 3 5 . ., → + 9 µM L . − τ b , the CP-odd Higgs mass is , BR( e X β 10 β , , , 2 τ 2 b 2 τ 2 t h × , A A A − 2 Z 2) . + + b + at 95%C 0 M e d 9 d below the experimental central value u since the dominant MSSM contribu- X − 2 H 2 b 2 H ± 2 H − σ ) in the region of parameter space with h β ]: 2 m m 10 u m 3 . and maximal stop mixing in IH scenario ]: sγ 2 H 53 + + × + − 54 10 m 3 3 t 3 5 below the experimental value. → and 3 ]. At large tan . 2 E ), 2 D 2 U e 4 t X − b ) is [ σ ) = (3 σ 2 t m m m d – 18 – − 56 − h < , 2 H µA µ µ + + + ) + 55 + 3 3 m 3 − [ µ 2 L µ 2 Q 2 Q µ ) = 3 ≈ 4 A m + m u m → → 2 A µ 2 H 0. It is also important to add that the main s = s = = m m ) is about 5 t b τ B β/m → B < ( e e e 6 s X X X − sγ t d B SM A tan 2 H → t b m BR at one-loop level is given by: A BR( ( t should be understood as the soft masses at the low scale. The RG u d d 2 H = 50. In this case BR( u 2 ) is typically between 1 H π m β 8 ) probes the region of large tan sγ m − − − µ d µ → + 1 TeV, BR( 2 H + µ and b µ m ≈ d = 10. The largest deviation from the experimental central value occurs for the → . This discrepancy can be relaxed to some extent if the Higgsino is heavier but H µ → σ s β with the Higgsino-bino LSP the discrepancy between the theory and experiment is m B s 1 Since the chargino contribution is proportional to tan B There is also part of the chargino contribution which has the same sign as sgn ( 10 speaking the chargino contribution may beA negative detailed also in discussion some on part the of the sign parameter of space the where chargino contribution can be found e.g. in [ where tion is proportional to given by: where running of which is now very close to the SM prediction [ This leaves veryBR( little room for contributions from the new physics. In the MSSM, even for 4.3 The LHCb upper limit for BR( restrictive for tan the “maximal mixing” is fartable below the experimental value.about For 8 the benchmark point D in can be obtainedcontribution only is for maximized forthe the maximal region stop of mixing parametermixing and space BR( grows with linearly the withfor maximal tan tan correction to thepoints Higgs with mass the lightest from Higgsino. stop SM ones: the chargedformer Higgs one always contribution increases and the the SMcharged model chargino-squark Higgs prediction. contribution is [ In far thechargino above IH contribution TeV scenario so for is tan this negative contributionof (with is respect this negligible. to contribution the is On SM) the the for other same hand, as the sgn ( In the MSSM there are two important contributions to BR( JHEP07(2012)155 ) u 35, . H (4.9) ( 1 TeV 0 = 0 ≈ . b 2 > m . However, h ± ) 2) d ˜ , χ . In addition, SUSY b H 56, (1 1 . ( M 0 300 GeV in some 0 → m ˜ t m . = 0 2) so they are much ˜ t , 005 t . m h 0 (1 ] that the existing LHC 0 − m 23 2 11 (3) 0 m 2 . + 0 2 0 A 5 TeV is given by: . 03 . = 1 ). We omitted terms proportional to the first – 19 – + 0 Q = 50 (and the other input parameters as specified /Q 2 / β in 1 3 TeV and other gauginos are correspondingly lighter, M M − 0 ln( A - not much below 1 TeV (in order to get 02 ≡ . β t 0 at the scale u − 2) increases. 2 H , 2 / 2 1 m (1 ) and 0 M − ) can easily be brought to phenomenologically acceptable values by m 6 the spectrum of the third generation is more compressed. In such a d . − 3.11 0 2 H µ . As explained earlier, higgsino mass may be in the range 200–400 GeV. β 2 + m / ≈ 1 µ u )) M 2 H → ] if bino is the LSP. Moreover, as stated before no official limits on direct stop m 3.1 s 23 − B ] the ATLAS constraints on the direct stop pair production have been presented in a particular 51. From the above formula it is clear that the CP-odd Higgs mass is driven to d . 57 2 H For large tan Gluino masses are in the range 2 If gluino is much heavier than the lighter stop, the stop pair production dominates BR( m In [ = 0 is given by eq. ( 11 τ as preferred by thesbottoms 125 GeV are Higgs expected mass), to be see in benchmark the point TeV range. D in Constraining direct table simplified production model of (motivated sbottoms bychain gauge in mediated such SUSY a breaking) model with differs a very much LSP from but those the typical for stop the decay IH scenario. this limit is highly modelfound dependent in and [ e.g. no lowerpair mass production limit for from right-handed the stop LHC was experiments are available yet. case the stop masslarger than splitting for is moderate smaller tan so the lighter stop mass is expected to be a bit much weaker because the stopsmaller pair than production that cross-section is ofproduction several the orders have gluinos of with not magnitude the beensearches same with presented mass. jets so and The far.particular missing LHC cases energy when limits the It may on Higgsino have is is the the already direct argued LSP excluded and stop in a main [ decay mode is heavier than sfermions of the third generation. for universal SUSY production cross-section at the LHC. In such a case the limits on the stop mass are In the IH scenario with “thecolored maximal sparticle, mixing” the in lighter stop theeffect is of range expected the to from heavy be first 500 thecoupling GeV two lightest generations so to on they 1 the TeV. are stauand typically masses The heavier is second than controlled magnitude generations by the of the are stops. weak the set gauge Masses two in of loop the the first sfermions of approximation the by first splitting the soft Higgssince masses such at splitting makes the the GUT pseudoscalar scale Higgs in heavier. 4.4 such a way MSSM that spectrum and LHC phenomenology The corresponding Yukawa couplingsh at thesmaller GUT values scale when equal: and second generation Yukawa couplingsYukawa couplings which give the are negative contribution negligible. tobecomes the Since very RG the running, light the or bottom pseudoscalar even and Higgs of tachyonic the tau when same the order. top, In bottombelow particular eq. and for ( tau tan Yukawa couplings are S JHEP07(2012)155 1 TeV. ≈ sbottoms 2 β / 1 M ]. 58 2 TeV it is enough to have − = 0 – 20 – A -terms at the GUT scale. It can be substantially A is assumed, e.g. for 0 A This article is distributed under the terms of the Creative Commons 5) TeV and assuming proper REWSB the Higgs boson is necessarily heavy, easily in From the above discussion it should be clear that the IH scenario is very weakly . (0 GA-2009-237920 UNILHC and bygrant the DEC-2011/01/M/ST2/02466. National Science Centre in PolandOpen under research Access. Attribution License which permits anyprovided use, the distribution original and author(s) reproduction and in source any are medium, credited. thank B. C. AllanachSlavich for for useful helpful correspondence. discussions, TheAdvanced as present Investigator research well was Grant as supported no. in T.TeV part Scale” Hahn, by (MassTeV), 226371 the S. by ERC “Mass Heinemeyer theTAPDMS Hierarchy and ANR-09-JCJC-0146. contract and P. PITN-GA-2009-237920 S.P. acknowledges and partial by Physics support the at by French the the ANR contract PITN- Acknowledgments This work has beenand partially R. supported Ziegler by for STFC. We useful would discussions like on to thank inverted G. hierarchy Gersdorff models. MB would like to smaller if negative This scenario is only moderatelycandidate, fine-tuned. particularly The when LSPdegenerate it remains with an has the interesting LSP a dark toparameter matter strong the range extent considered higgsino which in allows component this for paper or efficient looks stop-coannihilations. the like The stop a good NLSP bet is for the MSSM. the range 122-127 GeV. In particular,above if 15 TeV, the the masses above of conditions the122 first-two-generation GeV place sfermions a and are lower the bound boundsfermions on becomes the increase. Higgs more The boson stringent Higgs mass asto boson of the mass be about masses of about of 125 GeV the 1.5 requires TeV first-two-generation the for universal gaugino vanishing mass putting stronger lower limitsstops on and the sbottoms, masses addthat of some this attractiveness the scenario to predicts first-two-generationvanishing this large squarks or stop idea. than small mixing on In A-terms asO this at a paper consequence the of we high the have scale. RG shown evolution, For with the lightest stop mass to be at least 5 Conclusions The idea that the first twobeen generations promoted of sfermions in are the much heavierviolating past than the as the naturalness third a one principle. way has to to Also, the ease the fermion the sfermion masses supersymmetric mass in FCNC spectrum models problem, can based without then on horizontal be symmetries. linked The early LHC results, may be discovered (or ruled out)masses before above the about stops. 400 Nevertheless, GeV for are the consistent time with being the sbottom constrained experiment at [ the moment. is experimentally less challenging than that of stops so in IH scenario at large tan JHEP07(2012)155 , , ]. ] ] TeV ] SPIRE = 7 ] IN s ][ ]. √ Reconciling Comput. Phys. , , SPIRE hep-ph/0112177 [ IN , hep-ph/9609331 ][ ]. [ ]. (2012) 26 hep-ph/0305127 [ ]. two loop corrections to the hep-ph/0001002 [ ) hep-ph/0406166 ]. SPIRE 2 t SPIRE [ α IN B 710 (2002) 195 IN ( Precise determination of the SPIRE ][ ][ O (1997) 539 IN SPIRE of pp collision data at ]. (2003) 144 ][ IN 1 (2000) 29 Light MSSM Higgs boson mass to − B 631 ][ ]. hep-ph/0105096 C 75 (2004) 044 [ On the SPIRE Phys. Lett. TeV with the ATLAS detector at the LHC A 125 GeV SM-like Higgs in the MSSM B 672 IN 09 , B 580 ][ SPIRE = 7 IN TeV s Z. Phys. Approximating the radiatively corrected Higgs Natural supersymmetry: LHC, dark matter and ][ hep-ph/0212132 , √ JHEP Nucl. Phys. arXiv:1005.5709 (2001) 403 [ Combined results of searches for the standard = 7 , , [ – 21 – On the neutral Higgs boson masses in the MSSM for s arXiv:1112.3336 On the two loop Yukawa corrections to the MSSM Combined search for the Higgs boson Nucl. Phys. [ √ arXiv:1203.5539 Nucl. Phys. , [ , B 611 (2003) 333 (2010) 104 arXiv:1202.1408 ]. ]. 08 (2012) 014 hep-ph/0104145 [ Two loop corrections to radiative electroweak symmetry breaking in (2012) 109 (2012). B 657 03 An update to the combined search for the Standard Model Higgs boson SPIRE (2012). Nucl. Phys. 05 SPIRE , IN Combination of SM, SM4, FP Higgs boson searches of pp collision data at JHEP IN (2012) 49 [ , [ ][ 1 − JHEP , (2002) 305 JHEP SOFTSUSY: a program for calculating supersymmetric spectra , Nucl. Phys. rate B 710 143 , Three-Loop Calculation of the Higgs Boson Mass in Supersymmetry collaboration, G. Aad et al., ]. ]. ]. ]. γγ collaboration, S. Chatrchyan et al., collaboration, SPIRE SPIRE SPIRE SPIRE IN IN IN IN arXiv:1202.1488 the two loop diagrammatic andCP-even Higgs effective field boson theory in computations[ the of MSSM the mass of the lightest and the the MSSM Higgs boson masses at[ large tan beta arbitrary stop mixing neutral Higgs boson masses in[ the MSSM arXiv:1111.7213 Commun. 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