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JHEP06(2020)154 . inp 2 can M − Springer g June 8, 2020 May 23, 2020 June 25, 2020 , : : : January 25, 2020 : Revised Accepted Published Received 2 anomaly while the third − d g 0 at a certain energy scale, < d . In the setup, squarks, sleptons, and Published for SISSA by https://doi.org/10.1007/JHEP06(2020)154 2 H m ' u 2 H [email protected] m , and Norimi Yokozaki c 2 explanation in originally proposed Higgs-anomaly mediation Wen Yin Higgs-anomaly mediation − g ]: level when Higgs mediation becomes important at the intermedi- a,b . GeV. The scenario predicts light SUSY that can be fully 2 3 σ , in Higgs-anomaly mediation 1 12 10 2 GeV is slightly disfavored by the latest LHC data, the 0 at the intermediate scale. 2001.02672 The Authors. 16 ∼ < − c d Supersymmetry Phenomenology 10

A simple model for the explanation of the muon anomalous magnetic moment inp 2 H , g ∼ m [email protected] M ' inp u M 2 H m Daejeon 34141, South Korea Department of , Tohoku University, Sendai, Miyagi 980-8578, Japan E-mail: [email protected] T.D.Lee Institute and School ofShanghai Physics 200240, and China Astronomy, ShanghaiKavli Jiao IPMU Tong (WPI), University, UTIAS,Kashiwa, The Chiba University 277-8583, of Japan Tokyo, Department of Physics, Korea Advanced Institute of Science & Technology (KAIST), b c d a Open Access Article funded by SCOAP of Keywords: ArXiv ePrint: is consistent with thethat, radiative although the electroweak muon symmetrywith breaking. In thisstill paper, be we explained show atate 1 scale, covered by the LHC and future collider experiments. We also provide a simple realization The masses arefects, radiatively and generated masses by are anomalysmuons solely mediation and determined and by bino Higgs-loop anomaly aregeneration mediation. ef- light Consequently, the are enough heavy toscenario enough explain avoids to the the explain SUSY muon the flavor observed problem Higgs as well mass. as various The cosmological problems, and Abstract: was proposed byric the standard present model authors [ within are the massless at context tree-level, butmetry of the (SUSY) Higgs the doublets breaking get minimal masses large negative squared supersymmet- soft supersym- Muon Tsutomu T. Yanagida, JHEP06(2020)154 ] 11 EXP µ – (1.1) a 8 ]), and 5 , 4 ]. 18 – , 14 2) is one of the important 10 − − ] can suppress the dangerous g 10 3 13 2 , × ] (see also refs. [ − 12 3) 3 . g 7 2 [  4 − . g , should be charged under some symmetry Z = (27 8 7 – 1 – SM µ a GeV GeV In addition, to avoid the cosmological disaster, the 9 − 16 12 0 11 12 1 < 10 3 EXP µ = 10 ]. Importantly, new physics models to explain the muon d a ∼ 2 H 7 , inp = 6 m µ inp M a ' M ∆ u 2 H 2 with m 1 − 2 with g − is the SM prediction of the muon g µ SM a Among the new physics models, the minimal supersymmetric (SUSY) extension of the 2 anomaly should guarantee the suppression of flavor-changing neutral current (FCNC) One can also consider other flavor-safe mediation mechanisms e.g. refs. [ 2.1 Review on2.2 a simple explanation Muon of the muon 1 − sequestering between the SUSY breaking sectoror and Nambu-Goldstone visible (NG) sector hypothesis in of variousgravity contexts the [ sfermions mediated [ sfermion masses. Polonyi problem, the SUSY breaking field, (large) and unificationFCNC of problem, the masses fundamental for forces.gravity squarks mediation, To and avoids which sleptons the is shouldassume SUSY believed not that the be to squarks dominantly induce andare generated slepton the are by generated FCNC. massless by at The the flavor-safe simplest high mediation possibility energy mechanisms scale is and of to their SUSY masses breaking. It is known that is the experimental valueg [ processes and avoidance of cosmological problems. SM (MSSM) is one of the promising candidates since it also provides a solution to the indications for the existence ofdiscrepancy new is physics given that by couples to the (SM). The where 1 Introduction The discrepancy of the muon anomalous magnetic moment ( 5 Conclusions and discussions A A model with PQ symmetry 3 Muon 4 A model for Contents 1 Introduction 2 Higgs-anomaly mediation JHEP06(2020)154 ]. 23 , (1.3) (1.2) Note 22 3 (10) TeV can O & 2 / , renormalization 3 m 2 anomaly is known inp , the SUSY breaking − M ] or the split-SUSY [ g inp 21 M . = . inp RG µ = 0 , , sfermion masses also feel Higgs- Then, the gaugino masses can be ˜ 2 e 2 / β, M 2 2 3 m inp m = M h 2 anomaly can be also explained in a similar tan -term leads to the splitting of the light spectrum c ˜ 2 L , − D , are determined by the conditions of the is charged under some symmetry and thus − , m g µ, 4 Z ], minimal-split SUSY [ = Bµ = 0 = ] or gauge mediation. In the latter case, it is = 0 d ˜ 3 2 d 20 sign , e – 2 – 2 H 24 M m , A 19 , and m 2 9 / | = = 3 = = µ 2 | ˜ 2 u ], where and multiplets are sequestered d u M A m 2 2 H , m , 1 m = = = 0) 1 ˜ u . 2 Q > 2 ( A M -terms and gaugino mass terms. Above / m h 2 3 c A ]: e.g. the gaugino spectra are different from those predicted in anomaly m 26 h c − 2 discrepancy is difficult to be explained in a simple setup (see e.g. = − d are real parameters. and the Higgs doublets, the mass, the ratio of VEVs of the up g 2 H Z m Bµ = is assumed to be positive. At the tree level, the other soft SUSY breaking u and 2 H h . c ]). Therefore, we consider the sequestering scenario with anomaly mediation. µ m 4 25 In summary, we define Higgs-anomaly mediation with five free parameters: the cou- One of the simplest sequestering scenarios to explain the muon This condition is needed, otherwise the non-vanishing This kind of cosmological safety with alleviation ofIn the the gravitino problem NG with hypothesis of the sfermions the muon 4 2 3 manner, but one should takea into compact account the K¨ahlermanifold sigma-model [ mediation. anomaly mediation If if the the lowthe NG energy conclusion modes NG-modes is arise do the from not same induce as the this sigma-model paper. and anomaly cause mediation the in tachyonic scalars somesection by setup one-loop effects. We will provide a simple realization of the condition in hereafter, we assume the CPThen, symmetry is only violated by the Yukawa interactions of SM. be found in the pure-gravity mediation scenario [ define The parameters in theelectroweak Higgs symmetry sector, breaking (EWSB), once the five parameters are given. Here and follow the anomaly mediationloop trajectories. effects. Below pling between and down type Higgs doublets, the sign of the mass parameter and the scale to We notice again that the SUSYone breaking can field not have tree-level group runnings of the gaugino masses, the scalar trilinear couplings and sfermion masses where parameters are to be Higgs-anomaly mediationfrom [ the SUSY breakingdirectly. Then, sector, at but the Higgs renormalizationmasses group for doublets (RG) the couple scale, Higgs to doublets are the generated SUSY as breaking field only generated by anomalyknown mediation that [ the ref. [ that the tachyonic slepton problem can be solved as we will discuss soon. with a suppressed vacuum expectation value (VEV). JHEP06(2020)154 K (2.2) (2.1) 2 can ]. Since − 2 g ] Here, ∆ is taken to ]. Notably, : 9 . 1 , Z P inp 8 level by taking M M . ]. On the other 2 σ / 3 36 – m 3 32 + h.c. (1) from Higgs-loops at √ , d GeV. We show that, in GeV. The last section is O # H 2 anomaly based on Higgs- 16 16 u is a MSSM chiral superfield. 2 | ' K − i H Z 10 lives. The important thing is − φ g , we provide a simple example ]. The Higgs-loop effects with F  | g . + ∆ Z 4 2 2 27 P | i ]. The light squarks can be checked φ Z inp M | † i 2 P b φ 28 M c , M 1 3 + . ) + , we point out that the muon † µ c 3 With the heavy stops, the observed Higgs  GeV Z,Z , is taken to be 10 ( 5 – 3 – 12 ) can not be explained at the 1 ) + f GeV. In section inp 2 | d − 1.1 12 M 1 H 10 | " explanation of the muon + ∼ ln 0 and 10 σ 2 are negative and large [ 2 | P u < inp M u,d H d 3 M | 2 H 2 H ( 2 anomaly and the unification of bottom- or top-bottom-tau − 2 2 P | m m − = Z 2 discrepancy ( M | g ' GeV is the reduced Planck mass, and , breaks SUSY spontaneously with h ] for applications of Higgs mediation. K − u c Z 18 g 2 H 31 level for F – = 10 m , σ is called Higgs mediation. × 28 K Z , 4 ]. . ∆ 2 26 u,d , 28 1 2 H ' m P GeV, the muon -term of M 16 F In this paper, we study the 1 Although the sfermions are massless at the tree-level, radiative corrections lead to See refs. [ 5 The contains direct couplings of the Higgs multiplets to the SUSY breaking field that the Higgs multiplets live in the bulk. The K¨ahlerpotential then takes [ where 2.1 Review onLet a us simple review the explanation setup ofof of Higgs-anomaly the Higgs-anomaly mediation mediation muon is in a more brane-worldbrane detail. scenario, ( where One brane). of and the The (SUSY-breaking realizations live matter brane), in brane one where is the geometrically SUSY separated breaking from field the other brane be explained at 1 model to explain devoted to discussions and conclusions. 2 Higgs-anomaly mediation anomaly mediation in detail.the We first compactification review scale, the scenario asthis based case, well on the the as muon brane-worldinto where account the latest LHC data. In section be 10 Yukawa couplings can be simultaneously explained [ at the LHC when thethe wino CKM dark matrix is matter an issuppressed only compatible [ source with for thermal flavor leptogenesis violations, [ the dangerous FCNC processes are hand, Higgs loop effects atfirst the two generations one-loop are level small to duedetermined the to by the masses tiny anomaly for Yukawa couplings. mediation squarks and and Theby masses Higgs sleptons taking are mediation of essentially into the at account theanymore. the two-loop level The Higgs [ gaugino mediation masses effects,that, are the in solely a slepton determined brane-world masses by scenario, anomaly are where mediation. the not compactification It tachyonic scale was as shown well as broad SUSY mass spectra.are It significantly has enhanced been duethe shown to that one-loop the masses large level, for Yukawa when negative coupling third of generation sfermions boson mass of 125 GeV is consistently explained from stop loops [ JHEP06(2020)154 , ) inp 1.2 ]. If (2.8) (2.5) (2.6) (2.7) (2.3) (2.4) M 37 ∼ would induce 2 P GeV [around the may not be too far 16 /M j inp φ † i are the gauge couplings M φ = 10 3 2 | g /L Z . Le. and 2 , × | d / 2 2 3 1 H g , RG are derived. Here, the universal e − m , , 2 X ) µ y X 1 2 2 2 . The gaugino mass, on the other g / m − (  L dγ 2 3 X log . 2 2 P , i GeV m ) at the compactification scale 2 HM d 2 π i i g µ Qd δ g M g β 16 c d 2 16 × 1.2 2 + π / H  2 + 3 d / 2 X y 3 2 2 3 2 2 = 10 P m m – 4 – m − 1 L = /M − i ∼ − AM 2 | ' GeV, c) the scale should not be too high otherwise δ Qu L M = Z u ˜ µ 16 , = F inp ] and the references therein). This setup leads to ( , is composed of two sources of radiative corrections: | 2 X H L b ˜ 2 e u 2 X c m X M 28 y m − m : AM , respectively.) 2 X δ AM 3 − = C δ m W Bµ HM δ and . Since the Higgs doublets directly couple to the matter multiplets, the and SU(3) 2 4 / 3 L GeV. from the view-point of the UV theory, b) the gauge coupling unification and GeV is chosen from the following considerations: a) m µ P 16 16 c is assumed for simplicity. A possible model to explain the universal coupling M is the anomalous dimension of sfermion h = c is the beta function of the gauge coupling , SU(2) = 10 X i Y µ γ β inp (1) Anomaly mediation has a notorious tachyonic slepton problem. For instance, a left- The sfermion and gaugino masses are generated by the aforementioned quantum cor- M U of handed selectron/smuon acquires a negative mass squared at two-loop level where hand, is purely given by the anomaly mediation where and Higgs loop effects, sizable FCNC processes (see ref.at [ rections. The massanomaly of mediation, sfermion, the Higgs doublets to theof sfermion around masses 10 becomes important.away from The compactification scale stability the scale isthe above breaking 10 of the sequestering of order (16 grand unified theory (GUT) scale], the input scale should be below which the four dimensional description starts and SUSY breaking mediation from This is the ultra-violetmodel (UV) should realization not from be the calledis brane-world a quite scenario. “UV non-trivial completion” However, because to the thetheory have UV higher a or dimensional UV field M-theory. fixed theory point.we Alternatively, take the Nonetheless, the it conformal brane-world may scenario sequestering be with should derived compactification also from scale string- work 1 [ where coupling is given in section Yukawa interactions can be given in the usual way as The resulting mass spectra at the tree-level is ( JHEP06(2020)154 , ) inp 2.7 (2.9) M -term (2.12) (2.11) (2.10) µ = ) and ( RG µ 2.5 scale by using the 2 / 3 , . m  . 2 /  = inp 3 2 / inp m M 3 RG  100 GeV µ m M , 2  / which says at a rough estimation, log 2 explanation. In summary, we get 2 3 . This is contrary to the ordinary |  | 2 2 u log / u − m / 2 3 2 2 H 3 8 2 H . g / 2 2 m 2 3 m m / m | h 3  c m 2 ∼ h m  2 | 3 π c 2 b h g |  | 2 y c ) 2 16 RG 2 4 2 – 5 – µ + 1, and µ  g π This scenario is favored for the explanation of the 2 t 6 + & | ∼ | y ∼ u µ (16 ˜ β 2 q | 2 H 2 . 2. m ∼ π m 2 | − L (1) 16 ˜ AM µ g , O δ are negative and large, the EWSB requires a large L ∼ ˜ 2 e . d L m ˜ 2 t 2 H h c m m HM δ HM δ The contribution from the RG running via Higgs loops is dubbed as and ]. The negative contributions decrease the smuon masses, enhancing 1 u 2 H 1) which is disfavored in the muon are the top and bottom Yukawa couplings, respectively, and we have taken . m b (0 2. An important property is that anomaly mediation formulae ( y O − g Since 2 anomaly due to not only the small smuon and gaugino masses but also the large > and h t − β. c y g To sum up, although we have the universal sfermion mass conditions at A similar mass hierarchy holds in the slepton sector: the staus are much heavier than tan | µ | to have correct electroweak scale: This condition can be derived for tan flavor-safe mediation scenarios, whereThe splitting the spectrum low-energy is spectrain quite SM natural are is in also known some almost to sense be because universal. splitting. Radiative the EWSB and mass muon spectrum muon successfully solves the tachyonic sleptonmass squares problem. are Another of implication thewith same is the order that gravitino of the mass the smuon if gaugino mass and are loopthe suppressed SUSY compared mass spectrum is splitting at need to consider thesmuon/selectron Higgs acquires mediation at the two-loop level. For instance, the left-handed Here, we use again the leading logarithmic approximation. This positive contribution unless the mass hierarchy between the first two generation andthe third smuons generation and squarks. selectrons. To discuss the slepton masses for the first two generations we the leading logarithmic approximation.the On first the two other hand, generationand the squarks, thus, one-loop are are contributions proportional to highlydominantly to generated suppressed. due the to For tiny the those Yukawa anomaly coupling first mediation, squares, two generation squarks the masses are Higgs mediation. Higgs mediation. For instance, the contribution to a left-handed stop mass is where order but positive [ the muon do not change withsensitive. different renormalization Thus scale, one can i.e.formula estimate with the the the anomaly couplings contribution mediation also at is at e.g. UV this in- scale. This problem will be solved by taking account of the Higgs loop effects, which is same JHEP06(2020)154 2 2 µ µ ] + + GeV [ (2.15) (2.13) (2.14) u u RG μ 2 H 2 H also play m m β term. Also, ) only when 11 ), respectively, . Point III | d 10 with vanishing are also shown d , the successful 2 H | Bµ 2 H d 2.13 d , 1 m 2 H m | ) H ! | 9 2 τ m and tan q R y 2 10 1 | ˜ = 2 µ | | d u µ | + 2 2 H H M while both of | m m m u and | | and 2 b , , | y 2 H ] ] u u d μ 2 7 L | 2 2 2 u H H 1 μ + ˜ m m 2 H 2 µ (6 [ [ u 10 + 2 H 2 H d ]. In figure [right panel]. The red and green 2 2 H m M m sign m sign m m π | 1

28 III , q 16 ( 5 f , the radiative corrections to the . 2 | 10 0 / ' β 2 26 3 , ] µ d 1 > m 3 0 2 H 1 TeV enhance the bino-smuon loop contribu- + 40 20 20 40 tan [ u -axis is the sign of the argument. - - | d m y 2 H M µ ∼ β 2 H µ 2 µ is demonstrated. The detail of analysis as m m | m Note that the large d 1 RG (10). This is because a non-tachyonic CP-odd − tan log 2 . µ q 2 1 d O π d µ – 6 – g | ] 2 H 8 = (10) 3 5 , GeV m and ] [ u | β [left panel] and Point O RG  in table 2 μ 2 H ' 41 I µ – = m µ 2 A 2 t 15 + 38 III QED m y β 10 Point I u δ 6 2 H (green solid line) are positive at higher energy scales. This 2 0, one finds that the corrections lead to ( − 13 π m 1 + ∆ and 2 1 | 1 10 µ I < 16 q  + d 11 ' ' d 2 H is driven to be negative at around 10 TeV 10 | | u 2 H 2 given as [ d u m 2 2 2 H H 2 H m m | | m µ − 9 2 m ] ] u d 10 SUSY μ 2 g 2 2 + H H μ ) + µ m m [ [ u + This means tan 2 u H µ d 2 H m sign sign a 7 . m 2 H d 0 and ( 2 t log 10 m y , which are the diagonal components of the Higgs mass matrix, are represented. d < 6 2 5 µ u & 10 2 H ] + . The radiative EWSB of Point d 2 τ m 0 TeV y 2 H 40 20 20 40 [ - - The light smuons and bino with large The successful EWSB requires tan m + 2 b y tions to the muon We find that (Red solid line) and clearly shows that thethere EWSB is is no deeper broken vacuum radiatively inVEVs the with of flat the a direction sfermions. of small thein For enough Higgs comparison red field the and RG green runnings dashed of lines, respectively. 6 an important role inradiative Yukawa EWSB coupling for unifications Points [ well as data points willand be discussed soon. In the figure, the RG runnings of the corrections are estimated by using the RG equations: Given implies Since this condition shouldSUSY be breaking masses satisfied for at the Higgs doublets are needed to be considered. The radiative Figure 1 solid (dashed) lines represent by varying the renormalization scale. The sign of the JHEP06(2020)154 ] , | of h 44 c I [ The | . or ], but is 2 / level with 1181 54 3 . The second m σ 2 theoretical 2 is correct if 7 − ) = 0 − g Z g SuSpect 2.4.3 m ( s α GeV corresponds to the 0 due to the vacuum stability ). In fact, the variation of 16 < to be large enough by hand µ τ 2.11 y are two-loop corrections given = 10 2 anomaly at the 1 and inp ) or ( QED ], is slightly below the measured − b δ M y g 53 ], ii) the selectrons should be heavier 2.7 0 and 1 + ∆ – level. 45 and 46 σ [ µ µ < 6 ]. Here, ) is satisfied. We take, throughout the paper, ]; ∆ 2 2 at 1 , ) appears at the scale. In fact, this sample point ) is around the GUT scale, and thus the MSSM – 7 – 41 1 ) is the mass of the left-handed (right-handed) 2.13 − 2 can not be increased by decreasing R /L 1.2 ˜ µ g ] based on the simplified model can not be directly − GeV m 55 g ( 16 2 anomaly with L (10), which is hard to achieve in Higgs-anomaly mediation. ˜ − µ 2 and the mass spectrum is shown in the sample point g = 10 m − GeV as in [ −O 1). In particular, the sign of the muon . g FeynHiggs 2.14.0 = 16 inp 2. This can be found from the facts that i) the current LHC 34 GeV and QCD coupling constant as (0 µ . M O − = 10 g 2, we perform the numerical simulation by using = 173 inp with t − M 2 ]. This means that the brane-world scenario with compactification scale M g 5 − g ) is a loop function given in [ GeV is driven into a corner and is excluded if we take the is the muon mass; 16 x, y ] which are of it is disfavored from the null result of indirect detection experiments [ ( µ ]. The exception is ∆ 0 which we assume here and hereafter. ]. Therefore, the explanation of the muon f 8 GeV can not explain the muon by taking m 30 43 28 causes the split between the selectron masses, and thus it also leads to the selectron , = 10 16 1 Before ending this section let us make a few discussions. We notice that the Higgs µ > β 42 It is difficult to explain the muon We thank Sven Heinemeyer forThe useful thermal communication. abundance is not enough to compose the dominant . We need non-thermal 6 7 8 inp bound [ production of the dark matter e.g. from the gravitino decays. not excluded. Although we havesearch light with and zero-lepton squarks, in the current theapplied result LHC since of [ the our multi-jet spectrumand is then too the different. subsequent decay Inbut produces particular, beyond leptons. most the A squarks scope detail decay of collider to the simulation the present is bino paper. important boson mass, estimatedvalue 125 by GeV. The Higgsa boson few mass, however, GeV hasdominant from a uncertainty theoretical the comes uncertainty measured from largerdiscussion than top the is resummation quark on of mass thematter, the and wino-like sbottom higher loops). order LSP. If loop the corrections wino (the composes the dominant dark LSP [ M value from ref. [ at 10 bound on the wino-likethan neutralino the mass wino 460 GeV to [ two realize conditions the imply wino-like that neutralino thewhich as muon decreases wino the mass lightest or selectrontan masses (LSP). from The ( numerical result of the muon table case where the compactification scalewith (1 the SUSY breaking parameters ofalmost ( maximizes the To estimate the with appropriate modifications: in particular,at we the take early stage ofthe iterations such top that mass ( as smuon; in [ sign 2.2 Muon where JHEP06(2020)154 , . 2 ). ∼ . 58 inp /L − GeV. inp g inp M 2.15 2470 12 M M . In this GeV and 10 2480 inp × 2 in ( 12 56 (blue band) : the SUSY M − 10 σ = 3 inp g 2490 . × M inp 4 level with ). Thus, by choos- = 3 σ ,M  54 tanβ 2.11 inp 2500 M GeV 16 at an intermediate scale. In 2510 = 146 TeV 52 10 2 (red band) and 2 u,d 2. The contours of the Higgs boson / 3 H ∼ σ − -term and thus larger muon m | m 2520 g µ and thus the gaugino masses are also | /L , 2 50 /

3

0.09 0.08 0.07 0.06 0.10 h c m ), which enhances the muon ∼ 2 can be explained at the 1 58 – 8 – 2.12 RG GeV − )). However, one can increase the slepton masses µ g 12 , the smuon and selectron masses decrease due to the 2.11 10 h c 56 ∼ GeV, however, it is questioned whether the brane-world 16 [blue] regions of the muon 125 inp σ 10 has a UV completion. On the other hand, there is a possibility M for fixed 2, the contours of Higgs boson mass (left-panel) and the averaged 54  /L tanβ 124 − inp would effectively lead to larger g inp 129 M M [red] and 2 but large compactification scale, 1 2 with , which enlarges positive contributions from e.g. ( inp 123 | -term is increased due to ( σ 128 h | 52 , we show the numerical results of the 1 M c − | inp µ | 2 , one can (almost) fix the smuon and gaugino masses while decreasing g M h . For at the intermediate scale is theoretically possible. For not too small 127 c )). To see this, let us fix the gravitino mass. This means the anomaly mediation . The 1 inp inp 126 M 50 2.15 M GeV, which implies the dynamical generation of GeV, we can still have the brane-world scenario with compactification scale, 1

In figure A smaller

0.07 0.06 0.08 0.10 0.09 h c 12 16 ing larger Importantly, regions of the muon left-handed squark mass (right-panel) in first two generations for (see ( contribution is almost fixed atfixed. the scale (Remember that weity.) can If use we the decrease anomalysmaller mediation formulae logarithmic due factor to (see UVby e.g. insensitiv- increasing ( scenario with a small 1 with small breaking masses for the Higgssection, doublets we are take dynamically this generated possibility. at A around possible UV model is given in section In this section, we show10 that the muon fact, 10 being gray region the LSP is not the wino-like neutralino. We take 3 Muon Figure 2 mass [GeV] and theleft left-handed and squark right mass panels [GeV] respectively. in Black region first may two be generations excluded are due also to shown the in vacuum the decay. On the JHEP06(2020)154 . 2 t III A (4.1) + 2 and µ 0. With 3 II > → , respectively. ]. ) 2 5 S ˜ t 3 ˜ 2 u m M 1 m ˜ t III + m 2 . 3 06 √ . ˜ 2 Q 0 at the intermediate 146 123 0 12 11.3 31.2 2.25 3050 51.00 m , the average of the up and 549, 614 579, 667 < Point and 463, 1340 13.6, 14.0 14.6, 14.3 8.60, 12.2 2540, 2520 2320, 2320 2430, 2420 5( , 1) Mass (GeV) , . d d (2 2 H inp H ˜ ], 7 Q u m M 56 H 2 ' II is a free parameter, which can be / 3 u 06 S . 2 H m 124 0 12.5 11.5 31.8 2.06 3110 2 149.0 51.00 M 2 is enlarged. Sample points m c 550, 483 598, 584 Point are set at 472, 1370 14.1, 14.6 15.0, 15.7 8.91, 12.7 − 2580, 2560 2350, 2350 2460, 2460 + Mass (GeV) g β ¯ 2 if we adopt the result of ref. [ S becomes too large to satisfy it. We find that S ]. However, the purpose here is completely different. − | . For the mass of S g 57 µ I 1) – 9 – | , M and tan (2 + ˜ h X 0401 0 123 . 16.0 10.1 2.03 c d 3020 145.2 50.67 24.59 0 9 Point H 469, 465 526, 574 < 460, 1330 12.3, 12.6 12.9, 13.5 8.22, 11.7 u 2500, 2480 2290, 2290 2400, 2400 Mass (GeV) d otherwise 2 H SH , S explanation of the m λ σ GeV since a symmetry recovers in the limit = ' GeV range of the muon GeV] 16 µ / u σ 12 β 1) 2 1) 1) W , , , , h 2 H (TeV) δα 0 1 ˜ g inp L,R (TeV) (TeV) (2 (TeV) (TeV) 10 L,R c (TeV) 9 (2 (2 ˜ χ 2 ˜ ˜ ˜ e ˜ µ SM-like ˜ d . u tan 2 2 m 2 Q /  M , , ,  2 & 10 h [ 3 1 1 1 Particles 1 ˜ χ ˜ ˜ H t b τ ˜ 10 Parameters m inp are gauge singlet superfields. Here, log M ¯ S is out of the 1 I -parity violation is assumed. The black region may be excluded by the vacuum and R . Mass spectra for some model points. On all the points the wino is the LSP. We denote S = 146 TeV are shown. The wino (gluino) mass is around 463 GeV (3060 GeV). In the 2 This superpotential is the same as that in ref. [ / 9 3 where naturally smaller than 10 down type squark masses is taken. Here, 4 A model for We consider a simplescale. example The model superpotential is to given generate by Table 1 the second and first generation squarks by (small) decay to a color/charge breaking one,This setting restricts a constraint [ the parameter region of the 1 are shown in table The Point m gray region, the wino is not the LSP and the scenario is cosmologically inconsistent unless JHEP06(2020)154 , ) ). = 3 as S 2 − − 2 S (4.4) (4.5) (4.6) (4.2) (4.3) / GeV, 3 M (10 can be (10 16 m , O ∗ O ]) with the 10 # = 0 M 61 ∼ 2 K is also expected c ¯ S − /L 1 live in the visible c 0. The soft SUSY d . > H u,d + h.c. + ∆ 2 S H ] (see also ref. [ S 1) and d m . m 0 -1 and 60 H M (0 – u u , can be roughly regarded as O With this charge assignment, 58 S H , H 2 1 / ∗ S = c M 3 0 2 11 . 2 M M + m c -term are 2 ¯ , . 2 S. 2 P ln | B 2 2 + S , / / ¯ d 1 S 2 S 2 M 3 2 3 | | 0 0 c M 3 H m 2 S m m is generated. For instance, + | / ) ) 2 is a chiral multiplet of right-handed . | 2 3 2 2 2 2 2 P | 2 S | ¯ S c c π u N m are negative with (10), 0 0 8 λ Z S m M 3 | | | H + − c O S 1 1 + u,d c c c – 10 – + = i ¯ 2 H 1 0 S ' − φ = S β † i m d 0 . Charge assignment. = ( = ( S φ ξ 2 H 0 2 S K -term and Higgs µ m µ = , and a non-tachyonic soft SUSY breaking mass for ∆ Bµ ) + d -term is a common problem in scenarios with † ' H W B being one. Here, u Table 2 u ¯ S R ¯ 2 H N ), the Z,Z ( m SH (1) (1) (10). f S 4.3 U and U ). Note that O λ − Symmetry = inp 1 " is generated with the the K¨ahlerpotential: β M can live either in the bulk or the visible brane. In the former case, ) and ( ln S ¯ ln( S 2 P 4.2 Q, u, d, L, e ∼ M 3 ) (1). The setup can be justified in a brane world scenario with 1 S − , the soft SUSY breaking masses for the Higgs doublets are generated at O 2 being the the energy scale where M lives in the bulk and the MSSM fields including = / From ( 2 3 0 of ∗ S m 10 S K charges for M c : ln( The consistent charge assignment is given in table ∼ R The singlet field This charge assignment is consistent with the seesaw mechanism [ inp 2 S (100) TeV and tan 10 11 (1) to have a soft SUSY breaking mass, which doesU not affect the generation of This fine-tuning forO the small we may also have From the conditions of EWSBshould with tan be satisfied: to explain the correct weak scale, we need a fine-tuning of with where brane. where with identified as the GUT scale.M The SUSY massbreaking parameter, mass for m the Yukawa interaction, JHEP06(2020)154 and is the 2 . / 2 3 S θ , one can 2 F ¯ S m / ). With the 3 ) , the mass ) when the 3 (1) m A S c and U Bµ S − 2 0 are generated S 2. Moreover, the calculation of the 100 TeV. and < − /M 2 in Higgs-anomaly µ & S g d . The masslessness of ξ − 2 ( 2 H / g inp 3 m is generated through the m M i ' ' S u,d h FeynHiggs level explanation of the muon H u while keeping the sequestering 2 H m 12 σ d (and hence is used, where Φ = 1 + m i H are charged (see appendix u S u F h.c. H h , we provide a simple model to realize SH S 4 ) + λ and ¯ S and S ¯ S i , M S 2 S h / 3 1), are satisfied: – 11 – . m explanation of the muon 2 (0 Φ σ 3 O c < + 3 S c S ξ 2 GeV. This implies that 13 and . 12 by hand. The detailed study will be discussed elsewhere. 2 + Φ 2 S / 10 ¯ 2 3 S inp M S m ∼ S ) M 1) . 3 M c (0 inp (Φ + θ O 2 M 2 S d 0 at the intermediate scale using < R are suppressed but still one can have successful EWSB with the VEVs of is set at < S /M ξ 2 S = d d , ξ 1 2 H 2 H c ( L m m − ' ' = 2 suggests The wino is the LSP in our scenario with the mass in the sub-TeV range. This wino can We have found that, from the latest LHC data, the 1 i These conditions are required to explain the correct EWSB. Alternatively, insteadHere, of u u S 2 H 2 H − 12 13 F Start-Up Project and the JSPS Grant-in-Aid forconsider Scientific the Research Peccei-Quinn No. symmetry,symmetry, under 16H02176, which and conformal compensator field. Acknowledgments We greatly thank SvenHiggs Heinemeyer boson for mass. communication T. on T. Y. is supported in part by the China Grant for Talent Scientific spectrum of MSSMm particles may be slightly different frombe that tested in at the thedark LHC scenario matter by where may looking be for testedvarious by disappearing light indirect charged detection sfermions tracks. experiments which in are Alternatively, a the fully few wino covered years. at There LHC are and also future collider experiments. g dynamically at the intermediatem scale. In section scale to be aroundrenormalization the group GUT evolution scale. from the We GUT note scale that, to since the SUSY mass for third generation sfermions significantly, which explainssolves the the observed tachyonic Higgs slepton boson problem in mass, the and The originally smuon proposed anomaly and mediation bino scenario. gravitino masses problem are is small greatly enough relaxed to due enhance to the the muon heavy gravitino (Remember that thebreaking squarks field and is assumed sleptons tothis live carry case, in some gaugino conserved masses a charge are toby also same anomaly avoid vanishing GUT at the mediation. the Polonyi multiplet.) The tree problem. masses levelanomaly for In and mediation The squarks they and and are SUSY sleptons solely Higgs-loop are determined effects. radiatively generated The from Higgs loop effects increase the masses for mediation. In Higgs-anomaly mediation, squarksat and a sleptons high are massless energy atative scale the SUSY such tree breaking level as masses the squaredsquarks GUT at and scale a sleptons while arising certain the from energytant Higgs the scale, assumption doublets sequestered to get K¨ahlerpotential is large avoid a the and simple SUSY neg- and flavor impor- problem while respecting the GUT symmetry. conditions, h 5 Conclusions and discussions In this paper, we have explored the 1 The above terms do not generate too large JHEP06(2020)154 , (A.2) (A.1) -term µ ] . Note that S ¯ . As in the model , M/M ]. 2 ¯ 0 at the intermediate term. With the PQ ¯ M S = , ¯ 0 1 2 d M < : a new data-based 2 / ) ∼ κS 2 3 k H d 2 , Z SPIRE u 2 H 2 S in Higgs-anomaly mediation m + S 1 / arXiv:1608.06618 M IN ) 0 3 2 ( m ¯ 2 [ M − S M ][ SH α k m − ¯ 1 , and ' ) M ]. g 2 k 2 2 u 2 / 2 / k / 3 and 2 H 3 1 3 2 0 , and − k 2 m m m m 2 2 1 SPIRE − PQ k (2016) 086 + IN − g 3 d ¯ and -term. However, they are generated by 2 S 1 (1) ][ 0 0 − 09 µ k H ( S κ U κ S B (3 κ Muon ), one can obtain the desired sizes of M u + 2 0 3 arXiv:1802.02995 2 Nambu- Hypothesis for Squarks + − H + JHEP − / [ – 12 – 2 3 2 , / 0 are generated by S 3 m 2 (10 1 S . Charge assignment. ) ¯ 0 S < m 2 − O M ) k -term and 1 2 d = k µ k 2 H + 2 2 S 2 1 + m − arXiv:1607.05705 . The superpotential is ), which permits any use, distribution and reproduction in k k d Table 3 1 [ ( 3 k ' + (2018) 114025 H ( Splitting mass spectra and muon u 1 u R k PQ 2 H SH i ' − i ' (1) m D 97 (1) S S S . By minimizing the potential, we obtain , U (2016) 72 h λ U F S CC-BY 4.0 h Symmetry 4 F = 1) and are spurious fields breaking . This article is distributed under the terms of the Creative Commons ¯ (0 W M and B 762 O S Phys. Rev. ]. = , and 2 k S -term. SPIRE M ∼ µ IN 1 and Sleptons in Pure[ Gravity Mediation analysis Phys. Lett. B k T.T. Yanagida, W. Yin and N. Yokozaki, A. Keshavarzi, D. Nomura and T. Teubner, W. 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