Analysis of the Tev-Scale Mirage Mediation with Heavy Superparticles

JHEP11(2017)189 Springer October 17, 2017 : November 21, 2017 November 28, 2017 : : Received Accepted Published , Published for SISSA by https://doi.org/10.1007/JHEP11(2017)189 b and Yuji Omura . 3 a 1710.03412 The Authors. c Supersymmetry Phenomenology

We discuss effective models derived from a supersymmetric model whose me- , [email protected] Kobayashi-Maskawa Institute for theNagoya Origin University, of Nagoya Particles 464-8602, and Japan theE-mail: Universe (KMI), [email protected] Department of Physics, UniversityTokyo of 113-0033, Tokyo, Japan b a Open Access Article funded by SCOAP ArXiv ePrint: direct and indirect searches.and the We 2HDM also in discuss the bottom-up the approach. difference betweenKeywords: our effective model Then, the effective modeldistinguishable is a with two namely Higgs type-IIstudy doublet 2HDM the model mass which (2HDM) spectrum is with ofphenomenology widely higgsinos, SUSY in and discussed. particles the it and In effective is thethe extra model. this LHC Higgs paper, We fields, and we survey and the the summarizeout dark the the current matter expected experimental experiments mass bounds as scale from well of as the SUSY the particles flavor and physics. reveal Then, the future we prospects point for the Abstract: diation mechanism of supersymmetrythis (SUSY) model, breaking light istroweak higgsino namely scale, mass, mirage is that achieved mediation. bylow is the In scale. required unification of by Besides, the the we soft natural find SUSY realization breaking that parameters extra of at Higgs the the fields elec- are also possibly light in some cases. Junichiro Kawamura Analysis of the TeV-scale mirageheavy mediation superparticles with JHEP11(2017)189 ]. 7 , 6 ]. In this mechanism, ] indirectly constraints 3 10 ] are compatible, and the – 8 15 , 14 ]. A specific mass ratio of wino 5 , 4 In the Minimal Supersymmetric Stan- 1 GeV) [ 9 16 10 – 1 – 6 ∼ ] and the anomaly mediation [ 8 13 ] – 13 2 , 2 10 1 11 4 11 1 16 On the other hand, it is true that the relation between the SUSY scale and the realiza- See for a reviews, e.g. [ 3.5 DM physics 3.1 Electroweak symmetry3.2 breaking Direct LHC3.3 search Precision Higgs3.4 coupling measurement Flavor physics 1 to gluino can realizethe the strong EW bounds scale from naturally, theThe even direct if SUSY mass search gluino ratio and is is explaindicted heavy. the non-trivial, by 125 Then, GeV but a we Higgs it mediation mass canthe is [ mechanism: evade moduli known mediation namely that [ mirage such mediation a [ unique mass spectrum is pre- tion of the EW scalemodels is not that so are simple able in toof the MSSM. be the In consistent EW fact, with we scale thegaugino can naturally. experimental find masses some results at One explicit and the simple SUSY explain unification way the scale is origin ( to consider the MSSM with non-universal voted to discover the new particles.search, however, The show latest that LHC results SUSYnario. on particles In the do supersymmetry addition, not (SUSY) the existthe Higgs SUSY below discovery scale, around a since the few the 125lower TeV MSSM GeV than in predicts mass 125 that a [ GeV the simple without mass largeSUSY sce- of radiative scale a corrections. is neutral Then, Higgs much particle higher we is might than much conclude the that EW the scale. One elegant explanation for thesymmetric origin extension of of the the electroweak (EW) Standarddard scale Model Model is (SM). given (MSSM), by the thedivergence superpartners super- is of canceled the out SMscale in particles predicts are the the introduced Higgs superpartners and mass to quadratic squared. be The the natural EW-scale, realization so of that the a EW lot of efforts have been de- 1 Introduction 4 Numerical analysis 5 Conclusion 3 Phenomenology Contents 1 Introduction 2 Mirage mediation JHEP11(2017)189 (2.1) (2.2) (2.3) (2.4) , where ijk y , are given by ijk 2 U p / A 3 M , M m ln α + h.c. ) ]. The mirage mediation k i ]. φ φ 23 ( j – a 2 φ i 22 , C 19 φ 2 a g , 2 20 ijk , y a 2 2 X 19 p / p / ijk 3 3 − M A M m , l m 1 6 c ln ln run over the MSSM gauge groups and the 2 + p / α i α 2 3 i,j,k | 2 X M i = l l m π φ γ | – 2 – 2 | Q and i 2 i ln 16 a m ln α ijk dγ − 2 0 y 1 2 d | l g c 2 2 + π a π 1 j,k a X b ] and after the discovery [ 32 λ 16 1 4 i,j,k a 18 X λ = − – l a i 2 0 1 + c 16 1 π M are gauginos in vector supermultiplets and scalar fields in chiral 4 M 2 1 2 0 0 i ]. φ − + has been also studied in refs. [ M M = 24 2 and soft ) = ) = ) = U U U a λ −L M M M ( ( ( 2 i a ijk m M A is a Yukawa coupling. The indices In the mirage mediation, the soft parameters at the unification scale This paper is organized as follows. The mirage mediation is briefly reviewed in sec- In this paper, we reconsider the mirage mediation and discuss the phenomenology based In the last few years, the LHC run-II excludes light SUSY particles (sparticles); es- See for a review, e.g. [ 2 ijk are determined. supermultiplets. In our notation,y we factorize scalar trilinearscalar couplings fields, as respectively. The mirage mediation ismediation mechanism a of mixture the of supersymmetryterms, breaking the given is by modulus specified, and the soft anomaly SUSY mediations. breaking Once the tion 2, and phenomenologyof of numerical the analysis mirage are mediation shown is in discussed section in 4. section Section2 3. 5 The is results devoted to Mirage conclusion. mediation tested by the direct LHCboson search, couplings flavor and experiments, precision darkpoint measurements matter out of the (DM) the expected Higgs searches.for mass the Based scale direct of on and themodel the indirect and SUSY integrated searches. the particles research, 2HDM and We we in also reveal the the discuss bottom-up future the approach. prospects difference between our effective Therefore it is worth toble study with the the scenarios natural that explanation heavy of colored the sparticles EW can scale. on be the compati- latest experimentalthe results. Higgs field Even (higgsino), ifand are the the much higgsino sparticles, heavier become except than lighter for the than the TeV LHC scale superpartner reach, in the of our extra scenario. Higgs The bosons light particles can be the anomaly-mediation. Phenomenology of thethe mirage Higgs mediation boson have been discoveryin studied [ before the Next-to-MSSM pecially, colored sparticles, namely squarks and gluinos, have to be heavier than 2 TeV. renormalization-group (RG) correction of the moduli-mediation contribution is canceled by JHEP11(2017)189 , . . i 0 i α c ≡ g Q φ (2.7) (2.8) (2.9) (2.5) (2.6) is an ], but i ]. Note SUSY γ 28 27 M – depends on and each = 25 i mirage scale 0 c mir M ]. An important M . 2 0 30 , M i c 29 , 9 , ) = 8 . The size of is the gravitino mass. This . 0 mir 2 | 2 M / M vanishes at the leading order if 3 ( ijk 2 i y to , m | , ) i 2 is discrete in the string models. 2 φ / , m j,k ) comes from both of the mediation i X α/ 3 , 0 ) c is EW-scale even when the other scalar 1 2 2 2.4 M / /m u 2 U 3 = 1 ) is the quadratic Casimir for a scalar p − − / i 2 H 3 k ) M φ i c M m /m ( mirage scale m φ p a 2 ) = ( + ' – 3 – ). The unification scale, namely ln ( a C 2 M j ( 2 mir 0 c C | ]. Assuming that the moduli-mediation contribu- mir 2 a µ M M + = | g 10 ( at the and M i = 1 is realized in the original KKLT-setup [ and given by – c ≡ a 8 i u ijk U mir α X φ 2 H α are estimated as )[ M M m ,A 0 = 2 mir and compensate the loop suppression factors appeared in the with respect to the logarithmic of the renormalization scale i are soft masses for left-handed and right-handed top squarks, M i γ M 2 γ 3 u π GeV is the Planck mass and ) = 8 , m 18 mir 3 Q 10 M with the modulus. Note that ∼ O ( m ) shows that i × a ) φ 2 4 3) is the beta-function coefficients for the MSSM gauge couplings. M / . 2.9 mirage unification 3 2 could be determined by rational parameters, such as the winding number of − , α 1 /m ' , is a derivative of , where p 5 3 p u / Q M M 2, the mirage scale is around TeV-scale. In our analysis, we assume m ln 3 = 0 is satisfied. This means that Equation ( A remarkable feature of the mirage mediation is the unification of some parameters at We parametrize the ratio of the anomaly mediation to the modulus mediation by ∼ Q /d = (33 u i α m H a If √ respectively. c and the soft parameters at the anomaly-mediation contributionsmediation cancel contributions at out ais the given scale by RG ( corrections of the modulus- fact is that D-branes and the number of fluxes which generates modulithe potential. low scale ( tions satisfy where parametrization is motivated by the KKLT-type modulithat stabilization ln scenario ( [ anomaly mediated contributions. various rational values can be obtained in the similar setups [ and it is defined as b anomalous dimension for a scalar dγ mediation, respectively. Themechanisms. last We term parametrizedescribes in the the eq. overall ratio size ( of ofthe the modulus coupling scalar mediation of mass by is parameter the of unified gauge coupling at The first and second terms in these expressions correspond to the modulus and the anomaly JHEP11(2017)189 0 is M (3.1) (3.2) (3.3) u,d (2.11) (2.10) 2 H mirage m , 2 0 2 M = 0 has to be satisfied in ) = d H . c SUSY . 2 2 0 M -parameter are treated as input ( π , 2 i µ M 8 2 2 0 π . The size of modulus mediation = 0 M 8 , m d O 0 d , µ. 2 H is large and the bottom and tau Yukawa H . Note that A = M m c O β and the u,d = u,d , m ) = H A 2 H ) = 0 u and H m – 4 – u δm 2 H SUSY , c SUSY 2 β, M m when tan M / ), are much larger than the EW scale. If the ) = M ( 0 ( tan mir ijk M = 1 u,d ( A 2 H M Q ], the sub-leading corrections to the mass squared become O ( − c m 9 u,d , 8 2 H ) = m SUSY M ( mirage unification a M is satisfied and the A-term is not larger than the scalar masses for the top squarks, is for all scalar particles other than Q , higher-loop corrections in both the MSSM and UV-models, and sub-leading cor- c In this setup, all of sparticles, except for higgsinos, reside far above the LHC reach, As pointed out in refs. [ In our analysis, we assume need to be larger than about 7 TeV in order to explain the SM-like Higgs boson mass SUSY 0 parameters instead of softis parameters fixed to explain the SM-like Higgs boson mass. while the Higgs bosonsdirect are search for expected extra to Higgs be bosons around and the TeV-scale. higgsino One at collider promising experiments. way Besides, is the the This alignment is predictedsection. by We the have TeV-scale the mirage following mediation, parameters: as discussed in previous Note that the CP-odd Higgs boson mass and 3 Phenomenology In this section, we study phenomenology when the soft parameters are given by The sub-leading correctionM would come fromrections the in moduli fluctuation stabilizations. ofthe Those higgsino corrections the and are mirage the expectedare extra to scale expected Higgs be from to bosons small, be are so heavier below that than only sub-TeV, the while sub-TeV all scale. the other sparticles important for parameters thatsmall vanish but at not the vanishing at tree-level. the mirage Hence, scale: we assume that where order to realize the couplings are also sizable adding to the top Yukawa coupling. condition M as discussed later. Thus, thewhile 125 the GeV EW Higgs boson scale mass is and realized heavy without sparticles fine-tunings are in achieved, the TeV-scale mirage mediation. masses, which are estimated as JHEP11(2017)189 1068 1000 100 − – 5 – , flavor observables and DM observables at benchmark b,τ 15 45 30 10 1090 (a) (b) (c) (d) 3.39 3.41 3.40 3.38 2.97 1.92 3.08 3.02 κ 9896 6783 7905 26700 1477 1364 1429 1490 1477 1364 1429 1489 1485 1362 1431 1571 1117 1088 1022 105.4 7004 4767 5578 18975 7264 4980 5811 19465 285.8 274.3 240.5 2.405 524.6 255.0 341.1 3489 0.827 1.071 0.918 0.395 0.241 0.0806 0.156 4.20 0.801 0.872 0.854 0.609 0.125 0.126 0.141 0.0971 0.866 0.856 0.860 0.886 0.131 0.142 0.138 0.101 1.837 30.4 9.19 0.706 1.011 1.014 1.012 1.011 1.011 1.014 1.012 1.011 0.119 0.119 0.102 0.00116 0.614 1.41 2.11 0.152 0.769 1.96 1.52 8.97 − 125.09 125.09 125.09 125.10 0.0873 0.0946 0.105 3.95 9 s] / 10 4 3 ) ) [fb] ) × 10 ) ) b ) 2 tb [cm τν [pb] [pb] bb × ττ h − + 25 ) 8 µ 0 β 0 1 → 1 2 11 → h µ A b ˜ ˜ t t [GeV] → ˜ H τ χ → + M 10 H 10 sγ [GeV] [mm] κ κ 10 µ ∆ m m m m [GeV] m m + ∆ m H tan H/A 0 × H × H thermal H → × µ cτ m → M Ω b → =0 Parameters Mass [GeV] SD Br( ∆ SI s Br( v Br( Br( σ σ i B DM observables Degree of tuning pp Br( . Values of parameters, masses, widths, branching ratios, production cross section of ( Indirect observables σv Branch/cross section σ h Br( in association with a b-quark, Long-Lived Particle search points (a)–(d). Table 1 H/A JHEP11(2017)189 (3.8) (3.5) (3.6) (3.7) (3.4) ]. The 33 at a scale , because of ) u Q 2 H , ( mir u m u,d M 2 H 2 H = δm m . Q u ), the , + 2 2 H | + ∆ µ 2.10 u,d , δm mir − | Q 2 0 2 H u M m 2 H ,M ˜ 2 m ≡ | . ln i 2 µ t | y include corrections from the effective u,d 3 ' − gauge coupling are also vanishing in = H 2 − | u,d Y µ →h mir 2 1 2 H , a Q g

M u,d m − | ] interfaced by SUSY-HIT-v1.5a [ 3 2 Z 10 H a

β 32 m + 2 ln ln V u,d – 6 – ln 2 2 ) d ∆ 1 g d tan Q ∂

Q 3 2 ∂H ( − u u i ln 2 H 2 = H a β d ˜ m u max u,d dγ 1 H H − 1 2 ≡ γ tan h should be larger than about 6.8 TeV in order to explain the d 2 a − 2 H 0 ∆ ) ˜ + m M ] and SDECAY [ Q ] ( a u,d ]. = 31 ]: u 2 H and the decay of the 125-GeV Higgs boson. The higgsino becomes 27 H 39 2 Z . We calculated the mass spectrum of sparticles and their decays 40 γ 2 m – γ m 1 s 34 = ∆ = max 2 X 2 is related to the parameters of the MSSM as 0 π u,d Z M 4 → 1 is assumed in the last equality. ˜ 2 H m B ˜ m ) = , = 0. The RG effects through the U(1) is loop corrections to the effective potential. − Q β d ( µ V u H + c 2 H µ m = Let us discuss the sensitivity of the Z-boson mass with respect to the parameters in According to the assignment of the modular weights in eq. ( The mass spectrum and the values of observables at several benchmark points are → can be expressed as [ u s H the mirage mediation [ Note that the modulus contributionc to the Higgs bosonsour is setup absent of at the modulus mediation. Q where the anomalous dimension for the up-type Higgs boson is given by where ∆ where tan potential, 3.1 Electroweak symmetry breaking First of all, weZ-boson analyze mass the condition for the EW symmetry breaking. In the MSSM, the summarized in table by using SuSpect-v2.41 [ Higgs boson masses,FeynHiggs-v2.12.2 decays [ and couplings125 to GeV the Higgs boson SMthe mass, fermions LHC so are reach. that calculated superpartners by except using higgsino are much higher than B the lightest supersymmetric particleof (LSP) the in higgsino thissignificant is setup. bounds a on Hence good our the model. DM neutral candidate component and the direct and indirect DM searches give extra Higgs bosons lead deviations from the SM predictions in some processes such as, JHEP11(2017)189 u . . 2 H | 0 (3.9) µ M | δm (3.11) (3.12) (3.13) (3.14) (3.10) . If we ) requires SUSY 3.4 may be fixed M α , 100 when

= u , ≤ 2 Z 2 H

-parameter increases µ mir u m -parameter and µ δm 2 H 0 µ M

. m ). When we assume that 2 . 0 dM ∆ , ' 0 d 2.8 M 0 mir

M u ∼ + M M 2 Z 2 H 0 c -parameter. We see that ∆ − , m mir to satisfy µ increases as M 2 ) ≡ δm / 2 u µ M T 3 ln α π H ln 0 d m 4 γ mir + d c M

= T M through eq. ( 0 0 ≡ 2 Z and the T as 0 2. We see that the sensitivity is suppressed 2 2 when u M 0 m F p / α M 3 ln ( 2 H √ 3 T αM 2 ∼ M / / M ' − 3 m 0 K – 7 – δm + and the b-term because they are suppressed by

α 1 3 and = 2 m ∆ u M since the minimization condition eq. ( d 0 / 0 2 H 3 , H + u ln 8 and 14 TeV, respectively. ∆ = 2 . and 2 H 2 0 M 2 Z m | dM is ]. The degrees of tuning of the 6 / ] induced by the third-generation quarks and squarks. dm δm 0 µ 3 , -parameter is a fundamental parameter since it is an 2 m α | δm

moduli 0 mir 9 6 , µ . 2 m αM M 0 42 ∆ 8 K 2 Z , M M 4 = ' = ≡ M m ∼ 41 =

. 0 2 µ mir C 2 ' / 2 Z | 0 C 1 TeV where the thermal relic density of the higgsino saturates 3 relates to . F

µ dM m | gets non-zero F-term vacuum expectation value, the size of the 1 2 M dM 0 m 2 Z SUSY is important for the argument. ln ln ' /C T as a fundamental parameter that is independent of other param- m M implicitly depends on M 0 d d C µ u

ln ln . Using above relations, we obtain M F = 2 H mir d d ≡

Q M µ δm ∆ ), 1 because ∂K/∂T shows the degree of tuning of . ∼ 3.6 u 1 ≡ c 2 H T and expected to be small [ δm K β 250 and 1000 when ' Figure Therefore the sensitivity to We assume that some suitable mechanism ﬁxes In eq. ( , 2 2 | µ by the loop factor.Coleman-Weinberg potential In [ our numerical analysis, we evaluate the correction100 from the 1-loop 650 GeV. In the case where we choose where Note that the K¨ahlerpotential of the moduli is and only the modulus anomaly mediation consider the KKLT-like setups behindby the rational mirage parameters mediation, andmodulus the it mediation value is of irrelevant to this tuning argument. Thus the size of the where we treat eters. We alsounique assume supersymmetry preserving that parameter. the Then,quadratically. ∆ We see that ∆ | tan are given by Here we do not consider tuning of JHEP11(2017)189 0 = M ,µ 0 M ]. In our 2000 dominantly is small and 43 0 TeV at the . β 6 34%. Since the . H/A & 1500 ), where the Higgs 0 M ττ → 1 TeV. In these regions, data with the center of μ[GeV] . 1000 80% and sub-dominantly ) associated with bottom 1 1 − ∼ . H/A | H/A 10%. When tan µ 500 ]. We calculate the experimen- | 1GeV) for . Br( → ∼ 44 (0 × ) pp O 0 ( σ 800 600 400 200 H/A

1000

however give the most stringent bound on μ Δ → (right). The gray lines correspond to ∆ 0 TeV as we will see later, the tuning of ττ . µ pp 6 , but there are radiative corrections from SM ( – 8 – 0 → σ & ] obtained by 36.1 fb M 30 0 43 M H,A -parameter as long as (left) and 25 µ 290 and the degree of tuning is about 0 0 ' is smaller than about M µ 0 1 20 ˜ χ m [TeV] − 15 0 1 M ˜ χ m 10 get smaller for larger ≡ + + 5 m 1000 from bottom to top. m , =13 TeV. s . Degrees of tuning of 500 50 √ , 500 100

1000 5000

0 The higgsino can be also detected by the collider experiments. There are two neutral The experimental analyses constrain 250 Δ M , and two charged components inand the mass higgsino. differences Theircome are masses from tend smaller the to mixing than bedifference with sub-GeV mostly ∆ gauginos, degenerate in and decrease ourtree-level. as scenario. gaugino ∆ masses increase. The The mass mass differences bosons are producedanalysis, by we the calculate the gluonquark production fusion by cross using process section MadGraph-v2.5.4 ortal with b-associated limits 5-flavor scheme based process [ onenergy [ the result of ref. [ the bottom and the taupair Yukawa couplings of are top suppressed, quarks. the Higgstheir The bosons searches masses, also for since decay there toto a are quarks. large amounts of backgrounds for the Higgs bosons decaying 3.2 Direct LHCIn search this setup, the extra Higgscould bosons be are discovered expected by to the bedecay lighter LHC to than experiments. the a TeV The scale pairdecay neutral and of they to Higgs bottom a bosons pair quarks of with tau a leptons branching with fraction a branching fraction 125 GeV Higgs boson massbecomes requires severer than thatthe of electroweak the symmetry breakingThis occurs is much with better the than parameter other tuning scenarios with about sparticles 0.3%-level. heavier than about 5 TeV. Figure 1 100 the observed value of DM, ∆ JHEP11(2017)189 . The (3.15) (3.16) (3.17) (3.20) (3.18) (3.19) 1 is smaller 0 1 ) are shown ˜ χ . m , ! and the lightest 3.15 π , 4 − x ) + 1 − π . − ˜ χ 2 2 e, µ 1 r x m √ = √ and − r ≡ l 9 MeV is the pion decay 2 . ( µ 1 2 π − + 2 91 x p µν 2 ] , m 1 , ) 1cm) in our setup, so that the 350 MeV and would dominate l . − e , , ∼ − − ) 51 x 1 2 , (0 ∼ ( eν π r ˜ f χ Z O P 2 b, τ 3 tanh 50

/ , ) 2 l m m 2 = x + 2 W x 46 s f 4 m ]. We refer the most optimistic cases in − ( f Z − x 1 , 49 2 W 1 m (∆ + 2) ln 15 s 2 ¯ q 2 ff C √ Z 5 α SM h ]. Now we define a ratio of a coupling in the r θ 2 ) 2 m + 4( – 9 – /g 59 ' + 2 including the loop effect in eq. ( π ]. There are recent studies about the precision – m 4 α 8 − cos + π x 56 57 2 rad 2 π ¯ ff 4 – (∆ r = m f MSSM h m 3 2 F g 2 F − 52 p π rad G 2 G ≡ + 2 15 2 x m f is the Fermi constant, r 9 2 ∆ κ 2 F − ]. When the mass difference ∆ ) = ) = − l + G r lν π ]. The radiative correction for the mass difference is given by 49 , 0 1 , 0 1 ln ˜ + χ ˜ χ ) = 1 3 46 48 , x m r ( → → ∆ 45 P / + 1 + 1 χ χ ) = 2 l,π r Γ(˜ ( m Γ(˜ is the Cabbibo angle and f = C θ . The LEP experiment gives the most stringent bound on such degenerate hig- ]: the higgsino has to be heavier than about 90 GeV. l,π 1 47 x On the other hand, the expected signals are so weak that these are buried under deviated from the SMmeasurements of prediction the [ HiggsMSSM couplings to [ the one in the SM, the future collider experiments,the where second there layer of is a no pixel background detector events3.3 is and at the a location radius Precision of 3 Higgs cmThe coupling in measurement light the 33-TeV extra collider. and Higgs SM bosons particles; change especially, couplings the with couplings bottom between quark the and tau 125-GeV lepton Higgs can boson be largely The decay length of thefuture chargino hadron could collider be experiments longer wouldThe than give decay stronger lengths bounds calculated from thanexpected the the exclusion above LEP limits three experiment. at decay the modesnext HL-LHC are section, and shown referring the in the 33-TeV table hadron result collider shown are in shown ref. in the [ where constant, neutralino. The partial decay widths are given by [ the backgrounds in hadronthan collider experiments the and one theare at mass proposed limits the in could LEP. not refs. Recently,than be [ about the severer 0.6 higgsino GeV, the search chargino exploiting dominantly decays disappearing to tracks Thus the size ofthe the mass correction difference. is Thein ∆ values table of ∆ gsinos [ where gauge boson loops [ JHEP11(2017)189 τ – ]. for ∆ 66 76 [ 4 – , ] and b (3.22) (3.23) (3.21) (3.24) (3.25) γ − s 72 67 10 X × ]. The SM → ) and the SM 79 B 16) , h more precisely, 6 GeV [ . . β, 0 τ 1 78 κ , tan > 70 [ γ 32 . E 9 2 . , using FeynHiggs 2.12.2 − f , µ κ 2 , for = (3 10 c/a ˜ 2 t β 4 meson decays: × ln ) − , m exp a ] and the two-loop SUSY QCD 1 ) B cot ˜ 2 t ca 10 − 55) . h 60 . sγ f m + c β × α 0 )( ) by using micrOmegas-4.3.2 [ I → c t b/c cot ¯ − 23) ff. b . − µ f 1 + ∆ 00 h ln 0 . µA . We calculate b + ∆ ¯ 2 β ff bc µ )( 2 I t h π b ]. − β, y g + = (3 → 1 36 corrections [ 16 − 70 . [ = s b tan a – 10 – + 9 a/b ( B exp h ¯ ff ) × − β I h α ln = (3 2 3 ) − 10 2 µ cos ab sin −L + × ,M SM , µ ) 2 − µ 2 2 2 b ˜ sγ − 18) ) and Br( → ]. The HL-LHC will be able to measure . ,M , m ) = γ 0 1 = L s s → 2 b ˜ ˜ 2 τ 65 ]. If there is only one extra Higgs doublet that couples to the f B X , b m ]. The future sensitivity may reach a few % in the HL-LHC and m κ ( a, b, c 64 70 60 → ( , . 63 , comes from radiative corrections induced by sparticles. ∆ µI , I s µI f 2 69 3 [ B 62 M = (3 M − 2 s ] and Br( π µ α π ]. α 8 SM + 3 3 77 2 ) µ 71 ]. We have checked that the other couplings of the SM-like Higgs boson are = MSSM, SM) is the coupling between the 125-GeV Higgs ( ) is defined as − (10%) [ I µ 61 ( → O ' − ' ): + is a mixing angle between two CP-even Higgs bosons. The first factor comes f b s τ µ ¯ can be determined more precisely at the lepton collider experiments. ff a, b, c h B ∆ 6 GeV [ ∆ I ( h . b α → g I 1 κ s We calculate Br( In our supersymmetric model, there is also a superpartner of Higgs field, namely hig- > B are written as ] and γ f We adopt the experimentalE values as follows:predictions Br( we use areBr( Br( 68 right-handed down-type quarks asinvolving in charged Higgs the which type-II does 2HDM, not there depend on is tan angsino, below one-loop 1 correction TeV. Therehiggsino may loop be [ a cancellation between the charged Higgs loop and the 3.4 Flavor physics In our model, the flavormatrix. violating couplings Then, involving sparticles we are canstringent only bound evade given on by the this the strong kind CKM bounds of model from comes flavor from physics. the rare It is known that the very close to thethe SM LHC value. is The currentthe accuracy measurement of may the be Higgs moresuch coupling accurate as than measurements ILC 1% at and inwhile TLEP the [ future lepton collider experiments Note that these corrections are enhancedwhich by includes tan the re-summationcorrections of [ the ∆ where where from purely Higgs bosonmodel. mixing, and The then factor, itare ∆ also approximately exists given by in the type-II two Higgs doublet fermions ( κ where JHEP11(2017)189 , , 2 ξ 16 ]. In 86 , ]. In other 85 ]. This oc- 88 87 , ]. If the SUSY 45 001 [ 83 . , 0 82 is the higgsino density χ 1188 . ]. ]. Otherwise, the model should = 0 76 2 84 – h , where Ω ]. 72 DM 80 DM Ω / χ Ω ≡ ξ – 11 – (10) TeV and the higgsino mass is enough light O & 0 M ]. Hence, the production of the higgsino should be suppressed, 81 and the cross section for the indirect detection, which observes ξ There are several ways to produce the higgsino in the early universe. 3 , we consider the case that the higgsino dark matter is only thermally 2 is the total DM density. The cross section for the direct detection should be (100) GeV that the higgsinos produced by the late-time decays annihilate enough O DM ]. In the previous works, the size of modulus mediation is below sub-TeV, so that There are studies about the DM in the mirage mediation and other similar setups [ Note that the discussion about the DM in this subsection would become irrelevant, if In figure It would be possible that the relic density of the higgsino is explained by the usual If the mirage mediation is realized by the KKLT-like setup and the moduli and the . See for a review of the supersymmetric dark matter, e.g. [ 90 3 , χ 89 the 125-GeV Higgs boson massdirect can detections not now be realized. becomethan very Furthermore, the sub-TeV strong, constraints as so from far the that as the gaugino the masses higgsino should dominates be the heavier DM relic density. This situation is and Ω rescaled by the factor the cosmic rays originated fromwhen the our annihilation predictions of the are higgsinos, compared should with be the rescaled experimental by results. annihilation cross section by using micrOmegas-4.3.2 [ the observed DM relic densitythe is higgsino explained does by not sometions dominate particle(s) the are other dark relaxed than matter by the density, the higgsino. the rescaling limits If factor, from the DM observa- produced and saturates the observedcase, relic we density: study the Ω constraintsassuming that from the the observed direct relic andcalculate density indirect the is fully detections thermal occupied relic of by density the the of dark higgsino the matter, dark higgsino, matter. spin-independent We cross section and the thermal freeze-out mechanism, when thecurs higgsino if the mass gravitino is and about modulithe fields 1.1 TeV decay decay [ earlier widths than of theexpected higgsino the from freezing-out, gravitino although the and KKLT-like setups. themirage Another moduli mediation possibility should is is be realized thatscenario the larger by looks mass than some spectrum interesting the other from of mechanisms ones the the than naively bottom-up the point KKLT-like of setup. view. This plained by the higgsino produced bybe the non-thermal extended way [ to have anotherthis light case, supersymmetric the dark dark matter,higgsino matter such dark as is matter axino in no [ the longer other the cases. higgsino, while the dark matter could be the to overclose the universe [ or the produced higgsinobreaking should be scale diluted is by enough e.g.m thermal heavy inflation [ efficiently, the overclose problem could be circumvented and the relic density could be ex- The neutral component of the higgsinoin is our the LSP scenario. and a good candidate for the dark matter gravitino masses are below PeV-scale,gsino. late-time However, decays it of is these known particles that produce the the higgsino hig- dark matter produced in such a way tends 3.5 DM physics JHEP11(2017)189 , = pb 2 q   t 10 2 (3.28) (3.29) (3.26) (3.27) .   −   q q t T f Hχχ c,b,t λ X = u,d,s q ,   ] give the most = q q t TG | 94 , respectively. We f P µ β 2 c,b,t − 27 , X 2 W − | = 1). Besides, the light t q 1 + | − q = 1 µ M t TG q f T + 2 W − | and cos 2 . Thus the spin-independent TG f 2 t | 27 1 β f 2 β µ and drop all contributions from are the higgsino-higgsino-Higgs s M + corresponds to the relative sign ) ) = +1( u,d,s h q 1 − | 2 2 X , , t and = + 1 sin 2 2 1 q q m 2 | , i T Hχχ ). The heavy Higgs boson contribu- µ   M f . W N | | µM µM | θ β , λ µ 1 − | 2 A 3.28 ¯ qq Z c u,d,s 2 | q m X 2 W − | d, s, b tan = hχχ m t 2 h q , M 2 H m 1 λ | W = m   W m c M ) = +1. N θ ) 2 h q Z 2 h , 2 H – 12 – 1100 GeV. There are future experiments such as β + 1 2 m m ) m = | s ] and the PandaX-II experiment [ ∼ β for ) W µ q 2 2 µM − c N χ , T s β 1 93 β f , 1 − | 2 m c N 2 hχχ ) 92 -parameter. µM 2 m λ (1 , M µ 1 2 = tan     − ], where the phenomenology of the higgsino DM is studied pb for 2 q µM t TG TG − 91 9 are short for cos χ f f N − ] is that the sparticle masses are much heavier in our scenario, β 9 2 9 2 m m 2 (1 + sgn( χ N sgn( c 91 and + + 2 2 g g m m q q 1 + f f = = and 1 + by taking the decoupling limit u, c, t β 2 u,d,s u,d,s hχχ 2 W β Hχχ X X = = λ 4 N = 4 h , s λ 4 N m q q to 4 h m q m W m is the nucleon mass,     h m 100 GeV and 10     , t π 4 α N 2 π for g W × × ∼ g 16 4 m c β χ = ' The XENON1T experiment [ The higgsino-higgsino-Higgs boson couplings are originated from the higgsino-gaugino- The direct-detection experiments constrain a cross section of DM-nucleon scattering; m cot SI N σ Higgs boson contribution is proportionalbecomes to significantly 1 + large sgn( when sgn( severe bounds on the spin-independentfor cross section. The current limit is about 10 replaced the sparticles. Higgs boson couplings inby the the gauge-basis. gaugino masses Thistion as means becomes can that be constructive the read (destructive) couplings from when are eq. suppressed sgn( ( where where − of the gaugino massesboson and couplings, the especially, the spin-independent cross section gives stringentof bounds the on the MSSM. parameter space Thegiven by, spin-independent cross section for the higgsino DM is approximately in the Non-Universal Gauginoprevious work Mass in scenario. ref.because [ the The size most of importantand A-term is the difference fixed heavy with by top the Moreover, the squark there mediation are is mechanism relatively at required light relatively to exotic small explain Higgs values bosons. the Higgs boson mass around 125 GeV. similar to the one in ref. [ JHEP11(2017)189 ' → 0 M 32 (38) H/A & s, although Br( β / × 3 ) cm H/A 26 is chosen to realize is tighter for larger − 0 → is estimated as 1 TeV means that the A is satisfied, a higgsino 10 . M 1 0 m χ pp × ( 0 M m ' . ] show the upper limits on 2 1 µ prod ' = 50 while there is no limits 99 ∼ σ , A β 98 m is below the neutrino floor, the signals 001. In this case, the higgsino mass is . 0 SI ξσ 4 TeV for tan . -parameter is the same (opposite) as the gaugino 1 – 13 – ]. If 1188 µ . & 96 3%-level and the required tunings are comparable. 300 is satisfied above the line where tan . A = 0 ≤ 2 m 0 h χ M 250 from bottom to top, where 33% in this region. Note that . , ], would reach the cross section, 300 . An important fact is that these processes are independent , χ , the sign of the 100 2 m -parameter is opposite (same) to the gaugino masses. The degree 2 µ is about 0 = 400 ' 15. Note that the limits are not so changed, even if the higgsino mass pb from left to right. The exclusion limit for 0 0 ], XENON-nT experiment and so on. These experiments will probe wide 01 GeV and is shown by the background colors. The gray dashed lines 3 . A . M M 0 95 − m β 10 , 09 1 ] if the higgsino saturates the dark matter density. The future experiments, such . 6 TeV, respectively. ∆ − . ] which detects anti-protons. Analyses in refs. [ shows the observables in the case that the thermal relic density of the higgsino 8 91 for tan , 97 2 because of the larger production cross section and branching fraction to a pair of 4 A . is on the so-called neutrino floor [ The red region is excluded by the LHC direct search for the extra neutral Higgs bosons The current limit on the annihilation cross section comes from the AMS-02 experi- If the dark matter is dominated by the higgsino, we will observe cosmic rays originated = 125 7 β m , ) = 10 SI h 0 -parameter should be tuned about 0 . ττ tan tau leptons. Theon current limit is is different. 6 when the sign ofof the the tuning of µ decaying to a pair of tau leptons. The red lines correspond to saturates the observed value:about 1.1 Ω TeV. In figure masses in the right (left)m panel. The size ofcorrespond the to modulus ∆ mediation there is a large uncertainty due to the unknown profiles4 of the dark matter. Numerical analysis Figure ment [ the cross section, andcluded the [ higgsino mass lighteras than the about CTA 500 experiment GeV [ has been already ex- sizable, the higgsino-higgsino-Higgs bosonas coupling in is the suppressedtotal spin-independent by annihilation cross the process section, unless gaugino theWe so masses Higgs could boson that not mass observe these is suchanalysis processes at enhancement in the of can next resonance the region not section. annihilation precisely. cross dominate section the in our numerical a pair of W-bosonsthe and case of with Z-bosonsof through other the sparticles t-channel masses,indirect higgsino detections because exchange constrain except these the for are higgsinopair mass mediated annihilate itself. by into If the as-channel higgsino CP-odd pair Higgs itself. of boson bottom exchange. Thus quarks the Although this (sub-dominantly contribution tau potentially leptons) becomes through the parameter space as longξσ as the spin-independentof cross the section dark times matter the are buried rescaling under factor the neutrinofrom background. the higgsino annihilation. In most parameter region, a higgsino pair annihilates to LZ experiment [ JHEP11(2017)189 ) ] sγ ) = 20 15 10 30 25 2 TeV , [ 1 0 → M b -level, in 1 (+1) in µM σ − ) = pb is predicted. 2 , 1 3 . The gray region − 2 µM 10 . The meanings of the . The dashed gray lines < β 0 ) M ττ → is small. The measurement of 01 from left to right. Note that . 1 β =0.1188. sgn( , 2 H/A h 05 . χ pb. We see that the contribution from 1 Br( , 11 [pb] from left to right. The yellow region is -level from the current central value even × 10 − exclusion limits are also depicted by the green . 3 σ − σ 10 [pb] on the yellow lines. The black solid (dashed) prod H/A 10 = 1 × 11 σ ] , − 1 – 14 – b,τ planes with the fixed tan 30 25 20 15 10 − Out[1719]= κ 10 TeV [ A 0 × M 5 ) are deviated from the central values at 2 m . - − level. The 1- ) = 10 µ µ σ + ττ µ → 250 from bottom to top. The green and brown regions are excluded → [pb] and 2 , 01 from left to right. . s 1 at the 2 11 H/A , B 300 − , deviation from the SM prediction. The measurement of Br( sγ 05 . 10 Br( 1 σ , → × × 0 b . ) = 400 10 . 0 ) excludes the light charged Higgs boson and heavy higgsino region as far ) and Br( M = 1 and − = 1 H/A µ shows the results on sγ − SI + µ b,τ σ → 3 κ µ + → . Values of the observables in the case with Ω µ is large, and the deviation reaches the 1 is predicted since the deviations are mostly determined by the mixing between the pp b ( → τ β → κ s s Figure The yellow region shows that the spin-independent cross section is below the neutrino The black solid (dashed) lines show Br( prod B ' B σ 1 (+1). b − red, brown, green and yellowis regions excluded and lines by are the the charginoby same search the as at in AMS-02 the figure experiment LEP experiment. if the The purple higgsino region saturates is the excluded dark matter relic density. The floor. Thatdetections means even that if the the darkspin-independent yellow matter cross section is region in saturated is the bythe unit the very of heavy higgsino. Higgs difficult The boson to yellow exchange lines be reduces show (enhances) probed the the by cross section the when direct sgn( if the extra Higgs bosons are so heavy that κ Higgs bosons. The deviationsHiggs from bosons the are SM lighter predictions than are 1.5 TeV. more than 1% when the extra the brown and greenthe regions, uncertainties respectively. of The the uncertainties SMlines are prediction correspond and calculated to the by 1 experimental combining results.excludes the The brown light and charged green Br( Higgs boson regionas even tan tan below the neutrino floorsections of are the DMlines direct show detection. The spin-independent direct-detection cross left (right) panel.correspond The to ∆ color ofby the background denotesand the brown lines. size The of to red region is excluded by the LHC direct search and the red lines correspond Figure 2 Out[1718]= JHEP11(2017)189 ] ] 6.8 6.6 7.4 7.2 7.0 8.75 8.50 8.25 9.75 9.50 9.25 9.00 TeV TeV [ [ 0 0 M M ] 50. The meaning of the each 6.0 5.5 7.0 6.5 , TeV [ 0 40 M , 30 , 20 , = 10 β ] ] – 15 – Out[1452]= Out[1457]= 7.6 7.4 8.0 7.8 27.5 25.0 22.5 20.0 17.5 TeV TeV [ [ 0 0 M M . The gray and purple regions are excluded by the LEP experiment 2 Out[1461]= s. / 3 cm 25 − . Values of the observables in the case tan 10 × Figure 3 line is the sameand as the in AMS-02 figure experiment.unit of The purple dashed lines show the annihilation cross section in the Out[1454]= Out[1450]= JHEP11(2017)189 . - . µ | µ | . This s at / 3 ). cm increases, when 3.26 26 ) becomes severe. mirage condition A − − mirage scale m 10 µ + × µ 0 . → s 100 in the TeV-scale mirage B ≤ ), namely the µ 2.7 ). -parameter, which are relevant to the µ 2.10 . are expected to be below sub-TeV due to is near the TeV scale. DM 100 could be covered by the long-lived particle . Note that the 125-GeV Higgs boson couplings , µ Ω – 16 – and the β A / ≤ χ u m = 0 in eq. ( µ from the long-lived higgsino search at the HL-LHC 2 H µ m u,d = Ω 1)%-level. The event rate of the annihilation reduces H . ξ c mirage scale (0 O = 50, where the bound from Br( = 10, while whole region in the figures will be covered by the β β and the and require 4 U ) U M 10 TeV is satisfied, M at -parameter is . s. µ u,d / 0 H 3 c because of the lighter gaugino masses. M β cm 5 TeV. 25 . − 1 = 10. Most of the region with ∆ 10 A specific feature of the mirage mediation is that the RG effects for the soft parameters The annihilation cross section at zero-velocity limit is above 1 The yellow lines show the spin-independent cross section. The cross section is under When The expected upper bounds on . β We define 4 × is same (opposite) sign as the gaugino masses as can be read from eq. ( A 0 TeV, so that the future indirect detections could cover the region where the degree . Exploiting this unification feature, EW symmetry breaking, can bemediated smaller contributions than to the the otherunification soft Higgs scale parameters soft ( when parameters the are modulus vanishing at the gauge-coupling given by the modulus mediationbelow are the compensated unification by scale, thecancellation anomaly and also mediated both happens contributions contributions inif cancel the the out soft modulus at SUSY the mediation scalar respects masses the as condition well as eq. the ( gaugino masses, 5 Conclusion In this paper, wethe have EW studied scale the naturally TeV-scale without mirage conflict mediation with scenario the that current can experimental results. explain 1 of tuning the significantly as the abundance of theby higgsino a decreases because square the of event rate the is rescaled suppressed factor the neutrino floor atfuture tan experiment if theheavier higgsino Higgs boson is mass theµ significantly dark and matter. it increases The (decreases) as cross section depends on the parameter space comes fromparameter the region direct with search tan forThose the limits extra are highly Higgs dependent bosonsto on except tan the large bottom quarksm and the tau leptons deviate from the SM value at 1%-level when for the dark matterlong-lived search only is if crucial themediation. to higgsino Unfortunately, test the dominates the long-lived thelarger particle region tan dark search where matter could ∆ not density. probe Thus our the scenariothe for vanishing modulus mediation for the Higgs soft masses. The current limit on the of (the 33-TeV hadron collider)tan are described by thicksearch at (dashed) the red 33 TeV lines hadron in collider. the This panel region can with be covered by the indirect detections purple dashed lines show the annihilation cross section in the zero velocity limit in the unit JHEP11(2017)189 , pp (2010) 1 ]. 21 Phys. Rev. Lett. SPIRE , IN ][ ) and the decay of the sγ 10. The light higgsino also → b . β features allows us to control the ]. ), Br( − hep-ph/9709356 µ ]. + µ SPIRE IN increases. → ][ SPIRE β s IN (1998) 1] [ , but it also predicts small top squark mixing. B u – 17 – Adv. Ser. Direct. High Energy Phys. ][ 2 H , 18 m Combined measurement of the Higgs boson mass in mirage unification ), which permits any use, distribution and reproduction in TeV with the ATLAS and CMS experiments hep-ph/0312378 ) leads light extra Higgs bosons, and then the effective theory [ 8 leads small The soft supersymmetry breaking lagrangian: theory and applications 2.10 and arXiv:1503.07589 [ (2005) 1 3%-level. The CC-BY 4.0 = 7 . s This article is distributed under the terms of the Creative Commons A supersymmetry primer √ 407 and CMS collaborations, (2015) 191803 mirage condition Adv. Ser. Direct. High Energy Phys. Phys. Rept. ATLAS collisions at 114 [ D.J.H. Chung et al., S.P. Martin, We emphasize that the TeV-scale mirage mediation discussed in this paper still holds The assignment eq. ( The [2] [3] [1] any medium, provided the original author(s) and source are credited. References Scientific research from the MinistryJapan, of No. Education, 17H05404. Science, Sports, and Culture (MEXT), Open Access. Attribution License ( Acknowledgments The work of J. K. isPromotion supported of by Grant-in-Aid Science for No. Research Fellow of 16J04215. Japan Society The for work the of Y. O. is supported by Grant-in-Aid for soft parameters at low energycan and remain the below parameters the relevantmatter. TeV-scale. to In the The EW our extra symmetry scenario, Higgsthat breaking bosons the they higgsino and can the is be higgsinos a exploredindirect by are candidate the ways. expected for current to the and be upcoming dark experiments below in TeV-scale, both so the direct and 125-GeV Higgs boson, so thatThe these differences would are be getting different significant from as the tan predictions in themotivations 2HDM. of the low-scalethe supersymmetry. parameters The at EW 0 scale can be explained by tuning below the SUSY scale is likethe the type-II higgsinos. two-Higgs double model The (2HDM) apparentThe accompanied higgsino with difference could be from the the darkThe matter 2HDM and higgsino is can be the in detected existence bythe our the of hadron dark scenario the matter collider experiments. will higgsinos. exploitinginfluences be disappearing physical searched tracks observables such if by as tan not Br( only the lepton collider but also Then the top squarkHiggs. mass This fact should indicates be5 that TeV in all heavier our superpartners than scenario except and aboutwith the consistent color higgsino 5 with TeV at are the to the also stringent LHC. heavier bounds realize than on the masses 125-GeV of superpartners JHEP11(2017)189 ]. ]. , D ]. ] B 557 SPIRE SPIRE IN ]. 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