JHEP03(2016)143 Springer March 21, 2016 February 2, 2016 : February 29, 2016 , : November 21, 2015 : : Revised Published 10.1007/JHEP03(2016)143 Accepted Received doi: b,c Published for SISSA by [email protected] , and Ryosuke Sato a . 3 Matthew Reece 1511.00691 a The Authors. c Supersymmetry Phenomenology

We propose a framework of supersymmetric extensions of the Standard Model , [email protected] [email protected] Cambridge, MA 02138, U.S.A. Institute of Particle and Nuclear Studies,Tsukuba High 305-0801, Energy Japan Accelerator, Research Organization (KEK), Department of Particle PhysicsRehovot and 76100, Astrophysics, Israel Weizmann Institute ofE-mail: Science, Department of Physics, Harvard University, b c a Open Access Article funded by SCOAP ArXiv ePrint: particles and gravitinos withto simulate reduced this missing scenario energy.which and ameliorates find both We a of construct viable the parameter a major space simplified phenomenological of problems model specific withKeywords: benchmark supersymmetry. models butions to its mass.is New Yukawa not couplings are needed sizable toplings, and lift large these the supersymmetry fields breaking Higgs areHidden mass. charged Valley-like under phenomenology. To a avoid Theand new a ordinary Hidden gauge Landau sparticles Valley group, pole sector decay which for to is confines the exotic almost and new new supersymmetric leads Yukawa states cou- to which a decay back to Standard Model Abstract: that can ameliorate bothproblem. the New SUSY vectorlike Higgs matter fields mass couple problem to and the the Higgs missing and superpartner provide new loop contri- Yuichiro Nakai, SUSY Higgs mass andValley collider signals with a Hidden JHEP03(2016)143 15 16 ]: experimental searches 6 -terms or from very heavy [ 14 A ] and references therein for more 5 2 2 ˜ m 23 ˜ 9 m  26 ].) A flurry of literature has attempted to ∼ 18 > 2 ]. Experimental results pose two significant 12 2 1 – m 19 m 7 – 1 – 6 13 and 10 d 1 and λ 19 '  missing superpartner problem . As is well-known, in the MSSM a 125 GeV Higgs mass u d 3 8 23 λ λ ] for early references and [ 3 20 4 – 2 17 4 1 26 3.3.1 The3.3.2 case with The case with SUSY Higgs mass problem 5.1 Constraints on5.2 gluino and squark Comments masses on (s)quirk phenomenology 3.4 The LOSP3.5 decay The hidden3.6 glueball/gluinoball decays The decays3.7 of gluino-glue fermions The effect on Higgs decays 3.1 Phenomenological possibilities3.2 The Hidden3.3 Valley spectroscopy The simplified model of Hidden Valley phenomenology 2.1 New loop2.2 contributions The model2.3 The Coleman-Weinberg2.4 potential Avoiding Landau poles requires large loop contributions fromunmixed stops, stop either masses from (see large [ recent work). The secondhave is so the far failedsearches to for squarks find and a gluinos single includes superpartner. [ (A small subset of the powerful recent The Standard Modelfine-tuning Higgs puzzle. boson, Supersymmetry as remainszle, an a interesting despite weakly possible increasingly interacting resolution strong for scalarobstacles this constraints to particle, puz- [ weak-scale introduces supersymmetry asis a a the solution to the fine-tuning problem. The first 6 Discussions 1 Introduction 5 Collider phenomenology 4 RGEs and benchmarks 3 Phenomenology with the Hidden Valley Contents 1 Introduction 2 Raising the Higgs mass JHEP03(2016)143 ], ], u,d are 35 52 λ – u,d 47 λ -terms), ], but it doublets µ 35 L ] (a variation with ], compressed spec- in SU(2) , then the threshold 44 0 57 d , – ¯ Ψ 42 -parity violation [ 55 ]). As discussed in [ , , m, m u R 71 38 ] and by Martin [ , 30 35 , ¯ 30 Ψ. If the Yukawa couplings u Ψ d H d λ -terms in the MSSM is an interesting problem ], and theories with multiple invisible particles Ψ+ ]. However, when the Yukawa couplings – 2 – A d 69 – ¯ 32 Ψ [ u ], Stealth Supersymmetry [ 65 ]. It could also be solved by relaxing our fine-tuning H Y u is crucial to lift up the Higgs boson mass. For example, 20 54 , λ – u,d 53 U(1) 13 ⊃ 1 can be obtained naturally for several representation of ]. The new matter fields are Ψ λ × ∼ 46 W – L u λ 28 ]. But another possibility is that stops are not the only important singlets. Then they admit supersymmetric mass terms ( SU(2) 27 ]. The missing superpartner problem, on the other hand, is generally ¯ L Ψ, but (for appropriate hypercharge choices) they can also have Yukawa × – ] could all provide partial explanations for the absence of obvious signals Ψ 46 0 C 21 – 70 m 28 + d ¯ Ψ ], supersoft supersymmetry [ u ¯ Ψ in SU(2) 64 Ψ – m ] assumed that SUSY breaking in the Hidden Valley sector is of the same order with The large Yukawa coupling In this paper we explore a scenario that can ameliorate both the SUSY Higgs mass Most supersymmetric models beyond the MSSM that provide new interactions to lift 58 35 ⊃ introduce a new gauge interactiona to the new new spontaneously particles [ brokenthis gauge gauge group group confines wasof and considered [ leads in to [ athat Hidden in Valley-like the phenomenology. ordinary sector. The author Instead, we consider that the Hidden Valley sector is almost for collider searches. Martin pointed out that Ψ’s under SU(3) are larger than thatthese value, couplings we hits encounter a one Landau problem: pole immediately. renormalization A group possible running solution of to this problem is to couplings to the Higgs fields: fairly large, and alsoparticles the supersymmetry are breaking of contributions thecorrections to same the to order masses the as ofsignificant. Higgs the the All new quartic supersymmetric the induced masses new by particles are integrating near out the these weak scale, new and particles they can are interesting be targets the Higgs mass andvectorlike that matter fields superpartner that signals couplemass are to as absent the so Higgs studied and far. inand provide refs. new Ψ, The loop [ idea contributions isW to to its add new involve multiple modules that solve different problems. problem and the missingbeen superpartner previously problem. studied bydeserves This Babu, renewed way Gogoladze, of attention and lifting in Kolda the the [ Higgs current mass phenomenological has context in which we know the Higgs mass do notin dramatically a change the way superpartner that crossdecay can sections chains or evade to decay direct evade chains searches.lift the the missing Similarly, Higgs superpartner most mass. problem modelsattempts do that As to not alter a construct involve result, superpartner natural interactions these that SUSY two models problems that are usually agree treated with as all independent: existing data generally addressed by modifying the dominantsupersymmetric decays Hidden of Valleys [ superpartners. tra [ per decay chain [ in the data so far. interactions beyond the MSSM [ requirements; generating sufficiently large in its own rightloop [ contributions: vectorlike matteras beyond studied the in MSSM [ could help raise the Higgs mass, solve both of these problems. The Higgs mass problem could be solved with new tree-level JHEP03(2016)143 , ˜ t m 73 , we (2.2) (2.1) 5 , we conclude and 6 , we use the SARAH 4 , , 2 ˜ 2 t m  m M 4 ˜ 4 t t ] and gaugino mediation [ , we present our framework and ln m X 72 2
1 2 t 12 X − ], which is naturally realized by viable + 2 ˜ 2 t t R m X 56 ˜ 2 t , m + 55 ˜ t t + m m L ˜ 2 t – 3 – , Hidden Valley spectroscopy is firstly discussed. ln m 3  c c 2 2 N . This contribution is sizable when the stop mass π π N 2 t 8 β 4 t y 16 y cos ≈ ≈ − µ u u H − 2 H λ t m ∆ A ∆ ≡ t X = 3 and c N The rest of the paper is organized as follows. In section ]. Then, ordinary superpartners decay to exotic new states decaying back to Standard where is large. On theHiggs other potential, hand, the large stop mass generates a large quadratic term in the Higgs mass. To obtain the observedcorrection 125 GeV to Higgs the mass in Higgs the quartic MSSM, coupling we need from a top/stop significant loops, We plot a parameterpole space problem. which can explain the correct Higgs2.1 mass without a New Landau loop contributions The minimal supersymmetric extension of the Standard Model generally predicts a light 2 Raising the Higgs mass We here explain our frameworkpresent with specific models new and loop calculate contributions the Higgs to mass the from Higgs the Coleman-Weinberg mass. potential. Then, we code to givedemonstrate detailed that the numerical models results hide fromWe for also existing searches comment some by on showing phenomenology benchmark somecomment of exclusion models. on the curves. vectorlike future fields. directions In Ingauge including section groups. section the possibility of multi-fold replication of the SM the accelerated unification and naturallyinputs leads to in gaugino the mediation present as framework.which the respect SUSY-breaking From the this unification. background, we InWe then section consider present new a simplified vectorlike model fields discussions. for collider We phenomenology also which will analyze be the useful effect for later on Higgs decays. In section experimental searches. analyze the effect on thecan Higgs explain mass the in correct Higgs specific masslow models. without cutoff a We show Landau scale pole a compared problem. parameterbe to space We justified assume which the a by usual relatively considering scale multi-fold of replication the gauge of coupling the unification. SM gauge This groups can which realizes mechanisms of SUSY breaking74 such as gaugeModel mediation [ particles and gravitinossupersymmetry with at reduced the missingrelease LHC. energy. tools This based We is propose on essential a specific for simplified benchmark hiding model models to and simulate will this publicly scenario, which will facilitate supersymmetric, as in Stealth Supersymmetry [ JHEP03(2016)143 , . i 1 ¯ Ψ , (2.6) (2.5) (2.3) (2.4) i . is larger ]. ,Ψ ) . d u c 57 . ¯ λ Ψ – , 2. Generally, ]. If we could u / 55 ¯ + h f . f 2 Z 44 ¯ f φ ¯ φ M † f Mf ¯ f φ ] (for a review, see ¯ Ψ. Below the mass ≈ φ 2 f , + ˜ ¯ u M ¯ m j Ψ 76 b , 2 H ]. The scenario is also flavors; Ψ ¯ Ψ Ψ + 0 i m + f F 75 Ψ 71 j m − , , φ ¯ 0 ij φ 2 † f i , Ψ and + µ φ . m φ 54 d 35 while the quadratic coefficient , 2 f , − u, d singlets, and assume  ¯ Ψ + 4 2 t 3 m 53 u 30 0 m,ij d L g y b Ψ ¯ + ˜ Ψ 3 16 u j + m ¯ φ d Ψ † i − ¯ φ ¯ φ t m u ¯ y Ψ + 2 ij φ ∗ t + u ˜ ¯ y m i m ¯ Ψ Ψ in SU(2) 6 b ¯ d Ψ +  u increases as + – 4 – j H 2 i d 1 is the flavor index — enumerated from zero for Ψ φ t gauge theory with 5 + π u ¯ d † i φ λ y H − u φ 16 H H ]. As we will see in later sections, it is remarkable λ φ ) 2 ij are introduced to complete the SU(5) multiplets. The d d,i 81 ' N Ψ + m ¯ λ – H f d µ , t ¯ + ˜ ,...F Ψ + d,i 78 f 1 u d i ln A dy , ¯ φ d Ψ H † d d doublets and Ψ, + u so that the required tuning is relaxed. Then, if we have new ) imply a possible way to avoid this problem [ ¯ φ i λ ¯ = 0 Ψ 2 d L 2 t φ u i 2.2 y d = m ¯ H φ u + ˜ W u,i u H λ ∆ φ ) and ( u,i † u = φ A 2 u 2.1 VL are in SU(2) m + ( d W is a scale at which the stop mass is generated. This quadratic term has to be = ˜ where the dominant contributions to the running are given by ¯ , the quartic coefficient ∆ Ψ t t , y m (the lower index y u VL , only increases as ]). A similar logic has been considered before [ ¯ M f u 77 soft Without any other interactions, running of the new large Yukawa coupling hits a 2 H and m −L We also have new soft supersymmetry breaking terms for the new particles: f reasons that will becomeThe clear colored shortly). vectorlike particles The chargenew assignment superpotential is terms summarized involving in the table vectorlike particles beyond the MSSM are missing superpartner problem is ameliorated as in Stealth2.2 Supersymmetry [ The model We consider a supersymmetric SU( new gauge field onlyscale couples of to these the mattersupersymmetric new fields, version the matter of new fields, the gaugeref. Ψ dynamics Hidden [ finally Valley confines. scenariosimilar [ This to is the exactly ideathat the of ordinary superpartners “quirks” decay [ to exotic new states in the Hidden Valley sector and the The two terms innew the gauge right coupling hand is side somewhat of strong, the the equation Landau have pole opposite problem signs. can be Then, avoided. if the The scalars, which reduces fine-tuning. Landau pole immediately. A possibleinteraction solution to to the this new problemYukawa particles. is to We can introduce a illustrate new this gauge by considering the case of the top Higgs interactions such as where Ψ than the top Yukawa, we can lift up the Higgs mass without large soft masses of the new tuned away for the correct electroweak symmetrythe breaking, tuning is worse thancorrections a of percent ( even withoutincrease a large logarithm. However,∆ the radiative where JHEP03(2016)143 i 0 − ¯ Ψ F (2.7) (2.8) . and i ij . δ 2 2 0 . ˜ ¯ ˜ ¯ m m 0 i = ≡ δ d i i d f f u 2 ij 2 00 ¯ ¯ A ¯ ψ ψ ψ ψ ψ ψ ˜ ¯ ’s alone, this would ˜ ¯ m m λ = 1) diagonal symmetry. , d,i under which Ψ − ij , 2 δ F ) 2 2 0 ) representations of the full ˜ F ’s, it is an assumption about m m A ,A ,F = ˜ ≡ i i d f f u 0 ¯ SU( ¯ ¯ φ φ i φ φ φ φ 2 ij δ 2 00 1) symmetry. This ansatz for the × u ˜ 1 transform in the fundamental and ˜ m m 1 as different from the other Standard − A scalar name fermion name − ) ’s and 0 λ F , = F ¯ Ψ , ij Y 1) and (1 2 3 0 u,i δ 2 3 / / / / 0 0 ,...F 1 1 ¯ 0 m 0 m, F, 1 1 and are the only Standard Model singlets charged b b − − U(1) 0 0 which couple to the Higgs pair up through a = 1 ≡ = ¯ Ψ – 5 – i 0 L ,A 00 -terms and the Yukawa couplings to be aligned, ¯ Ψ 0 i 0 m,ij A 0 m, and δ terms, while the additional Yukawa couplings of Ψ with d ), implies an unbroken SU( 0 SU(2) i λ 2 ij and , b ¯ Ψ 2.7 m 0 = ij , b C δ 0 0 0 in the running. Alternatively, we could choose the special d,i and ¯ 3 1 2 m m ) respectively. i ¯ m F = ≡ SU(3) , 0 ij 0 00 , λ -terms) will arise in gauge or gaugino mediation, which guarantees b m H 0 m i from ˜ ) δ 2 0 N u ¯ ¯ ¯ N 1 2 N 1 2 N 3 1 N N 1 1 N 1 1 . We will take the λ symmetry is preserved by these terms: m 2 1) and (1 ) 2 SU( = that couple to the Higgs fields. (In the presence of the transform as spurions in the ( 6= 0 : F 1) F, H j u,i i i d u ) ¯ − VL f f λ ¯ ¯ Ψ Ψ Ψ Ψ SU( N W F × can split ˜ . The charge assignments. For convenience we also list the names we use to refer to the 1 0 6= 0 or SU( ) ¯ Ψ i Now that we have already singled out Ψ The couplings to the Higgs bosons inevitably break the symmetry: the Yukawa cou- F × if 1 UV completion. The fields Ψ antifundamental, respectively, of the unbrokensoft SU( masses (including universality of (for instance)and the ˜ This ansatz, taken together withIt ( assumes that thevectorlike two mass. fields This Ψ many assumption arbitrary is choices made of parameters largely to to consider, avoid although becoming one burdened could try with to too justify it in a Model singlets, let uswhile consider still an allowing ansatz these for two fields the to mass play terms a that possibly is different as role simple than as the others: possible In other words, we will assume thatunder Ψ SU( simply be a choice ofthe label; physics in of the SUSY presence breaking of — both made purely for simplicity.) plings in SU( which could be justified1) by gauge or gaugino mediation models. Then a global SU( This introduces a verying large assumptions. number of We have newtransform a as parameters, global ( so symmetry we SU( will make some simplify- Table 1 (scalar and left-handed Weylthat fermion) we components always of use eachthe daggers chiral field. for multiplet. complex conjugation, Notice, whereas in bars particular, are simply part of the name of JHEP03(2016)143 ] . , . 0 m      82 0 m, 2 † | b (2.9) = (2.10) u (2.11) m d 0 0 d H u H m µH λ d , | † u , and (the Higgs λ 2 λ m + † m µ + m b 2 + b | 0 0 , † u d m m | H † u A † u + , H , and A 2 d u † u 0 0 ˜ λ A m m . , , ) basis is: 2 2 , 2 d | † d 0† 0
 d ¯ † u φ d m m 2 3 m , H H d , ˜ , u H d † d 2 u † − d H λ µ | λ d , φ d 2 m H † 0 λ 2 , λ + 2 , ˜ ¯ m | φ u µ 2 2 0 + M | d , + λ 0 ˜ ¯ λ m d m m | φ , † u H log 2 0 − | d + H  u m 2 u A † u 4 λ ˜ H m to eventually decay to the lightest such † u M 2 | is neglected, all soft masses are ˜ F H H d m b , in which case the mass terms alone leave an ) 2 µ † u d | 2 1) H u N d H – 6 – ˜ ¯ − m λ λ † d µH ( | | λ † d = 0 λ + 2 + 2 0 X 2 2 0† m, | + m 0† 0 b ˜ ¯ 0 0 ˜ m 2 † m d Tr m , m π | H 2 2 u N † d 48 π + H 1 m A u 2 0 can be obtained by setting all of the SUSY-breaking param- 32 ≈ λ = ˜ ˜ ¯ -terms are zero, m 2 f b 2 0 = 2 | 0 0 ˜ M m u † d , m H † CW quartic d 0 m H u - and V V † b H λ µ A | † d u = λ 0 + λ 0 2 + 0 m, | + b 0 0 † 0 m, b u , a simple computation based on the 1-loop effective K¨ahlerpotential [ m m 2 | , H u to zero. Due to the large number of free parameters, we will not attempt to 0 ˜ u m + 1). H 2 s m A u 2 0 the mass matrix of the new particles. The new contribution to the Higgs mass − λ ˜  = M m 0 0 F 2      ) diagonal symmetry unbroken and only the couplings to the Higgs further break it M m m In the limit that Because our ansatz leaves a large symmetry group unbroken, it can lead to unwanted = F 2 s M gives give a complete analyticanalytic expression answers for for the some shift specialto in simplified illustrate the ans¨atzefor the the Higgs result. couplings, mass. and Here, also we some will plots present and The fermion mass matrix eters in will be proportional to SUSY-breakingIt soft will terms, also ˜ dependsuperpotential on mass). the The supersymmetric scalar mass parameters matrix in the ( result, with 2.3 The Coleman-Weinberg potential We compute the one-loop effect on the Higgs potential using the general Coleman-Weinberg equations. For phenomenologicalterms purposes, for we different flavors will that break assumein all small the remaining flavor variations fundamental symmetries in andparticle. representation allow the all of mass Such particles SU( anvariety approximate of symmetry UV that completions. is slightly broken could be produced in a SU( to SU( stable particles in theassumption theory. in discussing In the practice, Coleman-Weinberg then, potential we and will the renormalization use group this ansatz as a simplifying case JHEP03(2016)143 ) u ) 2 u λ and ) as ˜ m . We 2.6 2.11 m (2.12) d A . − λ 126 2 d 156 

m 2.4 132 2 2 and | | + ˜ 0 0 0 0 u 2 0 m m λ 2.2 , the measured m 148 u (with zero − | − | 120 (2 ˜ 2 H 4 140 2 2 . This shows that | | | 2 2.0 m we show the value m u m m | will play an important | | m λ

= ˜ 1 2 2 d 2 0 112 λ − + 1.8 ) + ≈ 13. The equation ( 2 2 m 2 u . | | 2 ˜ 0 0 0 0 0 m = ˜ m m m 1.6 2 0 | | − unless it is very large. At right, ≈ ˜ ¯ 2 d m + + d = 700 GeV λ ˜ λ m 2 2 3 = | | 1.4 115 ) =0 = 300 GeV stop 2 − 2 d d m m |  | | 2, and ˜ m λ μ= 200 GeV tanβ=20 m N=3 2 0 (fixing the SUSY breaking mass ˜ 0 0 m Higgs Mass Varying Vectorlike Mass with ˜ ¯ m m 1.2 ≈ m log = ˜ 4 + u |

3

− | 2 u

700 500 300 400 600 800

2 0 GeV m ] [ 2 H 2 , λ 2 m | | | | m 0 0 0 0 ( ˜ λ m 2 | m | m ( = 3 | 0 0 and ˜ ⊃ 2 – 7 – | − | m N | m 2 V 2.6 m 2 | | | 148 2 = m m | | 0 0 140

2.4 when m + λ ) + 5 2 132 ) 2 0 126 2 2 2.2 | ˜ | m 0 0 0 0 m − m | 05 to . 2 d 2.0 0 + u − | = 0 in this plot for simplicity, but a nonzero , the result is mostly insensitive to m λ 2 2 ˜ 2 β | d ≈ | 120 λ 1.8 m − m | | 2 0 ( ˜ ¯ m  ( 115 2 0 1.6 4 | 0 0 m = 700 GeV m | 112 1.4 + 2 ˜ Higgs Mass Varying Yukawas = 300 GeV  stop 4  m μ= 200 GeV tanβ=10 m= 500 GeV m N=3 | . We have set . The effect of hidden sector vectorlike matter on the physical Higgs boson mass. We u 2 u 1.2 . For a different perspective on the same result, in figure H ≈ π λ u 1.5

1.0 1 2.5 0.5 2.0 0.0

λ d 32 λ | Let us now be more quantitative. We have plotted the shift in the Higgs mass in N terms). In the plot at left, we fix all masses and vary the two Yukawa couplings quartic V gives a contribution of achieving a sizable effectin on the the superpotential. Higgs properties will require a largefigure Yukawa coupling These analytic approximations arepoints. mostly useful The to expressions highlightpreserving scale some mass as squared important terms. qualitative SUSY-violating Thusin mass the order squared SUSY-breaking to produce splittings terms a must dividedHiggs large not effect. be by mass too Recall SUSY- requires small, that, if a the quartic light Higgs coupling is mostly More general expressions can be derived,ing but the are not effective very K¨ahlerpotential enlightening; approximationthe for (i.e. various instance, masses retain- small to SUSY differ, breaking) one but finds allowing that the up-type Higgs quartic coupling is b see that, due towe large vary tan the supersymmetricwell vectorlike as mass parameter role later in the paper. Figure 1 plot contours of constantValley physical sector, Higgs with the mass simplifications as a function of various parameters of the Hidden JHEP03(2016)143 , λ stop m = 1.5 5 2.0 . 1100 450 stop = 1 t 280 /m t X 1.8 . Then we solve the u λ 2 1.6 ˜ t = 125 GeV,X m h 1 800 ˜ t m 1.4 √ ≡ =0 = 300 GeV d  μ= 200 GeV tanβ=20 m λ N=3 1500 2 can lift the Higgs to 125 GeV even with 1.2 was set to zero to give a simple illustration, SUSY > ∼ d

Stop Mass Form

700 500 300 400 600 800

u λ M GeV m ] [ λ = R – 8 – , which gives a good guide for the qualitative size µ 2.6 700 =0 1500 t are smaller. (In particular, notice that the horizontal axis SUSY 2.4 u M λ (taken to be the geometric mean of the stop masses) necessary 2.2 stop 300 m 2.0 = 125 GeV,X u λ h 2500 1.8 5000 ], for the discussion of phenomenology such as collider signals, the most 1.6 85 – 83 1.4 =0 = 300 GeV d  μ= 200 GeV tanβ=20 m λ N=3 8000 Stop Mass Form . The stop mass scale 1.2 code [

700 500 300 400 600 800

GeV m ] [ = 0), so when the Hidden Valley contribution is turned off the stop masses must be several t X we simply take one-loop correction and neglect this2.4 uncertainty. Avoiding Landau poles A new gauge interactionLandau keeps pole. the running The of new the gauge new dynamics Yukawa couplings finally from confines. hitting We a investigate a viable region of the effect. InColeman-Weinberg later potential. sections we Finally will letHiggs run us RGEs boson from comment mass. a on higherSARAH higher-order Although scale corrections and they on use could the theimportant be complete uncertainty calculated comes from thanks uncertainty to of recent confinement development scale. of Thus, in this paper, vectorlike matter fields, atone-loop an Standard RG Model scale RGphysical Higgs equation mass. to This runare approximation down important resums to at the the large leadingfixing large stop electroweak all logarithmic mass. scale soft terms masses and We that to have find be greatly equal a simplified at the spectrum in the plot by of the stop massnew needed vectorlike to matter. liftof To the the compute Higgs Standard the masscorrections Model Higgs to and Higgs mass, 125 the GeV boson we correction for to match from fixed the the the parameters SUSY quartic Coleman-Weinberg of potential prediction, coupling the involving including the stop new threshold ( TeV. Vectorlike matter at aunmixed few stops hundred at GeV 300 GeV. with in At right, which we case show the a scenario necessaryin with the values significant plot of stop at mixing right hasbut a will much smaller be range!) nonzero Again, in the remainder of the paper. Figure 2 to raise the Higgsfrom mass a to Hidden 125 Valley GeV, sector assuming with that the a contribution specified to parameters. the quartic At coupling left, arises we assume no stop mixing JHEP03(2016)143 at d λ (2.13) at the do not h u , g λ !! . The bound for simplicity 5 4 u , for example, λ 3 − M 2  = 1 2 = 300 GeV in the left m −
10 GeV for a cutoff scale = ) M 2 0 ∼ at the vectorlike mass scale > Λ = u m / λ 2 m = µ and the gauge coupling where the Landau pole problem 0 0 = GeV compared to the usual scale u ln( u
8 0 m , λ ) λ 7 2 , m ) 6 ln 2 Λ / = Λ  2 / 0 0

2 µ ) µ m GeV. This can be justified by considering 2 ln( Λ 16 ln( / 2 2 1 – 9 – ln b µ ( 1 4 = 3 in the lower two panels. The supersymmetric 2 0 2 b b 2 F ln 5. In the lower right panel of figure GeV (from left to right). The number of SM singlets . 4 0 − 1 6 b ]. Note that this expression is renormalization scheme 1 ∼ > = 2. To obtain the correct Higgs mass, a relatively large +

88 , 10 [ u ) = 500 GeV in the right panels. The Yukawa coupling 7 F 2 λ 2 Λ M N / , 10 2 8 π = µ 4 = 3 m ln( 1 b 0 = b 0 m ≈ and ) = µ π N 0 0 ( 4 shows the allowed (white) region of the coupling 2 ]. We ignore SUSY breaking and assume h m g 3 = 3 87 ≡ , 0 ) b 86 µ = 2 in the upper two panels and ( We have assumed a relatively low cutoff scale 10 Figure GeV. We will use these results in later sections. h = 3 is weaker than that for F 6 α In this section, spectroscopyto of specify the the Hiddencollider glueball Valley phenomenology and in with gluinoball the ourWe spectra. Hidden scenario analyze Valley how is which the We will discussed. lightest then neutralinopresented be and simplified present useful We the model. for a try Hidden We later Valley simplified also particles discussions. investigate decay model by the for using Higgs the boson decays. multi-fold replication of the SMas gauge the groups SUSY-breaking which inputs naturallypossibility in leads in the to the present gaugino final framework. mediation section We although will the further detailed comment analyses3 on are this left for Phenomenology future with work. the Hidden Valley Yukawa coupling is required, we can see that this10 is realized when the confinement scale is Λ of the gauge coupling unification around 10 the vectorlike mass scalebound is of assumed the to confinement be scaleis zero. Λ weaker as for From we a these lower fixed figures, thefields value UV we also of cutoff can contribute the scale. to know Yukawa coupling Smaller lowering aF supersymmetric the lower masses bound of of the the vectorlike confinement scale. The lower bound for and the confinement scale Λ where thehit Yukawa coupling a Landau pole untilis 10 masses of the vectorlikepanels fields and are taken to be where independent and enables us toscale. know the Then, value we of can the judgeuntil gauge if some coupling the UV at theory the scale withvectorlike vectorlike the when mass mass vectorlike we scale). fields fix hits a a Landau confinement pole scale or (and not a Yukawa coupling is avoided. Forcode numerical [ analyses, we considerof the the 2-loop analyses. RGEsSUSY by Yang-Mills After and using integrating the the out (canonical,vectorlike SARAH rather mass the than scale vectorlike holomorphic) at fields, gauge two-loop level coupling the is below effective given the by theory is pure of the confinement scale Λ and the Yukawa coupling JHEP03(2016)143 2.2 2.2 = 500 GeV 2.0 2.0 M = 1.8 1.8 m do not hit a Landau = h 0 u u g 6 λ λ 1.6 1.6 7 6 m 8 7 10 8 10 10 10 = 10 10 0 0 1.4 1.4 m = 3 in the lower two panels. F 1.2 1.2 at the vectorlike mass scale and the . However, the precise details of u 4 λ 1.0 1.0

0 0

80 60 40 20 80 60 40 20

GeV GeV ] [ Λ ] [ Λ and the gauge coupling u λ – 10 – 2.2 2.2 at the vectorlike mass scale is assumed to be zero. The d λ 2.0 2.0 = 300 GeV in the left panel while 1.8 1.8 = 2 in the upper two panels and M 6 7 8 F = . If SUSY breaking is mediated only weakly to states with no 6 u u 10 10 7 10 8 λ λ m 1.6 1.6 10 10 10 = 0 GeV (from left to right). The supersymmetric masses of the vectorlike fields 6 m 1.4 1.4 = , 10 0 0 7 m 1.2 1.2 , 10 8 . The allowed (white) region of the coupling 1.0 1.0

0 0

Stealth SUSY or not Standard Model charges — as in gauge or gaugino mediation via messengers that have 20 60 40 20 80 60 40 80

GeV GeV ] [ Λ ] [ Λ • one-loop interactions like thethe phenomenology one depend depicted onincluding: in several figure choices we can make in constructing the scenario, 3.1 Phenomenological possibilities The basic scenarioto we have cascade described decays of will supersymmetric always raise particles into the the Higgs dark boson sector, mass proceeding and through lead Figure 3 confinement scale Λ where thepole Yukawa coupling until 10 are taken to be in the right panel. Thenumber Yukawa of coupling the SM singlets is JHEP03(2016)143 ] 54 . The . Once h ˜ g 5 h g ) are bound 0 → ˜ S ( 0 χ ˜ S -parity odd particles into ) and R 0 S ( d S h ˜ that transform as fundamentals g H i 0 0 0 0 m ¯ Ψ Ψ , where × ˜ S u h Ψ → 0 × m . If the mass of the LOSP (lightest ordinary ]. χ – 11 – d ]. . If the particles Ψ 91 ¯ , Ψ 89 , or ˜ ˜ 90 S 0 . The simplest ways of mediating SUSY breaking treat φ Z charge — the hidden sector can be nearly supersymmetric. → h ) u h 0 ˜ g χ N H ), ˜ 0 ˜ S 0 S ( fundamentals or not ˜ h S ) and have no Standard Model charge are light, the confining hidden theory S N h ) → N 0 SU( χ . One of the microscopic interactions responsible for decays of all the Standard Modelof constraints flavors on equally. FCNCs,scenario but This we due is consider) to appealing it directvariation from could search pushes the consider bounds the models point on theoryfirst that squarks of into two, treat (even as view a the in in somewhat third Natural the generation fine-tuned SUSY [ differently regime. from the A of SU( can be QCD-like rather thanpion-like a bound theory states. of pure Onmasses, glue. the there In other will particular, hand, only there be if may bound all be states of light of theFlavor-blind hidden Ψ mediation gluons particles or and have not gluinos. weak scale the confinement scale of thee.g. hidden sector, ˜ the decay willstates involve of just a hidden few gluons particles, (see section 3.3). Light should think of itsemitted decays hidden-sector in gluinos and terms gluonsleading of to can the a then high-multiplicity unconfined radiate final theory, additional statethe parton hidden e.g. confinement shower gluons, as scale ˜ illustrated of in thea figure hidden large sector number is of bound reached, the states. many On partons the confine other into hand, if the mass of the LOSP is near energy can be dilutedor by some the regions number of of the particles, NMSSM as [ in HiddenParton Valley scenarios showers [ versus simplesuperpartner) decays is much larger than the confinement scale in the hidden sector, we SM charges but no SU( This gives a realization of Stealthto Supersymmetry. the Even hidden if SUSY sector, is bounds mediated directly on superpartners could still be weaker as the missing • • • higgsino to a hidden-sector gluon and gluino. Figure 4 the hidden sector. Replacing the Higgs boson by its VEV, this becomes a decay of the neutral JHEP03(2016)143 charges if we try h ) b b ¯ N ˜ + − G b ¯ b b b b b b ¯ ¯ ¯ τ τ b S 0 0 S S . Finally, because the mediation S S 6 ˜ S ˜ G b ¯ S b ˜ S S – 12 – h h ˜ g g 0 q ˜ χ . This scenario is the focus of our work in this paper. 0 S 0 q ˜ χ or fundamental fermions, we consider the case of a pure-glue S h ˜ q ) N ˜ q , again with a soft gravitino through the Stealth SUSY mechanism and with pairs of ˜ . This is an interesting scenario that we will defer studying until a future paper. G . A squark decay process in the scenario with a parton shower preceding confinement. 0 . A squark decay process in the scenario where the confinement scale is sufficiently large b ¯ χ bb ¯ b → 0 -jets reconstructing the scalar ˜ hidden valley. However,different we phenomenology. emphasize In that particular, it otheridea would realizing choices be Natural appealing in SUSY, to in model-building constructheavier. which a can stops It version are lead of would light this to also but first-generationshowers be squarks and very are jet interesting much physics to play consider a the role case in where the hidden-sector signals. parton flavor-blind scheme that mediatesSUSY. to the We work SM in and aLOSP not regime mass the that where hidden we the can sector, confinementthan approximate scale realizing the a is Stealth leading parton large decays shower. enough asscheme involving compared This we a to case few consider the is particles will rather illustrated tendto in to arrange figure produce for tachyonic light scalars with SU( SU( χ b In this paper we will consider one of the simplest possibilities: gaugino mediation gives a Figure 6 that we should think of the decay as directly into composite states. In this case, we obtain a decay mass of ˜ Figure 5 The vertical blue barlarge represents final-state multiplicities hidden-sector can hadronization. arise if As the in confinement Hidden scale is Valley sufficiently models, low very compared to the JHEP03(2016)143 . , , 6 1 1 0 . r MS 0 − − 0 0 r r Λ ) has 3 7 0 ≈ . . 2 r ]. The G MS 97 ], building , Λ ). On the 0 r 96 (or, account- 95 , 2.13 = 0 showing a 94 MS λ with mass 7 m − + with the central esti- . The next states have determined by the static MS MS r ; and 1 5Λ , has a mass of about 2 . 1 − 0 λλ r 3 . or the Sommer scale parameter and 5 and 11Λ σ ]. In the absence of such a matching MS MS 93 , translating to about 7Λ 5Λ 7Λ . . 1 − 0 MS scheme, as in equation ( and mass 6 = 1 supersymmetry depending on the rela- r 2 + . N − – 13 – ; 0 1 in the ) is the force at distance − 0 r ], with a reliable extrapolation to r 9, multiplying and dividing by 1.5 to capture possible ( . and the confinement scale Λ. The phenomenology of 8 MS . 0 F 102 λ 6 in both cases [ – . ≤ m 0 Λ. In this case we have a pure-glue Hidden Valley, either 98 MS ≈  Λ 0 state with mass 4 0 0 r . These translate to 4 65 where . This is an important point: even if the RGE estimate is that and mass 5 . 1 ≤ ++ , m − 0 0 MS r 4 ++ . 3 = 1 m . This requires a matching calculation that depends on the particular . 2 0 r MS . Again, there is an order-one matching uncertainty attached to these ) 0 Λ r 0 MS ( r ]. Given masses quoted in such a nonperturbative scheme, we need to know = 1 supersymmetric Yang-Mills spectrum has only recently begun to come Λ F 0 than to Λ 92 r N MS Notice that the glueball (and gluinoball) masses are, on a logarithmic scale, closer The We assume that the vectorlike fermions all have masses significantly larger than the numbers. to 10Λ the confinement scale ismasses significantly of below confined the states scale may of not be superpartner so masses, light. the actual If MSSM superpartners decay to hidden- mass-degenerate lightest supermultiplet asoverlaps the expected. multiplet containing This the “gluinoball”while supermultiplet, operator the which heavier mostly supermultipleta (mostly mass overlapping of themate about “glueball” operator for 3 Tr quantum numbers 2 Due to the numerouslarge closely number spaced of stable states glueballsYang-Mills with theory (in different to the quantum other absence numbers, light of particles there higher-dimension that operators are provide linking a decay the modes). under control on the lattice [ tive size of thenonsupersymmetric pure-glue gaugino Hidden mass Valleys hason been lattice discussed gauge in theory refs.lightest results [ glueball for is the a 0 spectruming of for pure matching Yang-Mills uncertainty, theory between [ about 4 broad LHC signatures inprecise a details of simplified the model masses framework, and rather couplings, this than order-one toconfinement uncertainty give is scale, numerically acceptable. nonsupersymmetric or with approximate theory in question.has For been QCD-like computed theories with andcalculation zero is for a or general twoas theory, flavors, we well the as will quantity a quote rangevariations masses in 0 based the on matching the for estimate non-QCD-like theories. Because our goal is to highlight the of a nonperturbative quantity likedefined the by string tension potential [ how to match to perturbationless theory, number for instance by knowing the value of the dimension- To estimate the spectrumfortunately, of lattice confined results states, are wecomparison not use to always results perturbation presented of in theory. latticetimate a computations. of By manner the solving Un- that confinement RGEs,other allows scale we hand, transparent can Λ the obtain lattice a can compute perturbative the es- spectrum of massive states of a theory in units 3.2 The Hidden Valley spectroscopy JHEP03(2016)143 2 θ by π (3.2) (3.3) (3.4) (3.1) 4 ∼ ). Here, 0 . We can 0 S κ S ˜ m components, 2 0  F S 0 0 and S S S m m ]). Then, it is im- ( , 1 2 0 ) S 2 103 + θ m 0 2 S S S m m ) and 1 2 S ), the supersymmetric mass pa- (1 + ˜ 0 ˜ + . m S 0 ) 3.3 0 ,  m S 2 . SS S is quite low. 0 Λ → / m ) 0 SS 5Λ ( MS S α S m ∼ W ]. m 0 + α S d 104 m W H – 14 – , m u ∼ ) Tr( 2 S θ SH ∼ m S S component. As in ( S λ m 2 + (cubic terms with θ + 3 d term and the second is the coupling between the Higgs and (1 + ˜ H mix significantly and thus we assume the mixed mass param- κS S u 0 µ 1 3 S m µH + → = and S S m as the gluinoball chiral superfield, originally come from the gluino mass. With these nonzero S 0 S simplified ˜ m W ). The effective description of the gluinoball and glueball supermultiplets is is of the same order. The coupling of the cubic term is estimated as ∼ 0 µν as the glueball chiral superfield whose lowest component is proportional to S F 0 SS m S µν m The hidden gluino mass induces SUSY-breaking mass splittings in the gluinoball and F components. Therefore, we here assume F where ˜ the squared masses of the singlet scalars are glueball supermultiplets. The smallcomponent gluino of mass the can holomorphic be coupling.morphic accommodated Since coupling, in the Λ terms confinement also scale oframeters gets depends the are a on determined the by holo- the confinement scale and they are expected to obtain nonzero sizes of the mass parameters as The two multiplets eter using Naive Dimensional Analysis (NDA) [ The first term isthe the Hidden usual Valley fields generatedwill see after below. integrating The out next theand three vectorlike terms glueball matter represent multiplets. the fields supersymmetric as masses From we of the the discussion gluinoball in the previous subsection, we assume the otic new states in decaysmodel of is ordinary given sector by particles. The superpotential of our simplified and Tr( still unclear although someportant to attempts note have that beensupersymmetric our known Yang-Mills simplified theory (see model after e.g. doesfor the [ not our confinement, mean purpose. but the this The effective treatment theory simplified is of model sufficient the is pure useful when there is no high multiplicity of ex- lightest supermultiplets, discussed above, containingThe the gluinoball simplified and model glueball has operators. roughly two identify SM singlet chiral superfields denoted as to produce high-multiplicity final states unless Λ 3.3 The simplifiedWe model now of present Hidden a simplified Valleynomenology phenomenology model which of will the be Higgs and useful Hidden for Valley later fields discussions. for collider Let phe- us concentrate on two of the sector particles that are confined, there may be relatively little room for a parton shower JHEP03(2016)143 d d ζζ λ 2 H m (3.5) (3.6) → , ˜ ∗ u h 2 H ; where m → 2 ˜ m ++  ). Note that one 2 coupling is sizable, m 3.2 d , . λ 2 ˜ ··· m state via 0 , , + ) ∼ ) > . u d ++ 2 . c . c ia ia . m + + + h + h . We now consider the decay of the d ··· ··· α µν and all soft masses of the vectorlike H F + + W u 0 0 α α α µν components into the other terms in the H m F W 2 F sin ∼ cos ˜ Tr m h h d ) Tr m − +  H µ – 15 – ( u 2 β β H m θ τ 0 0 2 sin cos d d v v λ ( ( u mm and Z 2 2 2 λ 1 1 2 d h 2 π π h √ √ to a pair of SM particles and compare the calculations in ), the decay amplitude of the 0 g λ ig 16 32 = = ' 3.5 ++ − − 0 0 u d u H H λ = = is the holomorphic coupling. Note that the Higgs fields enter into eff 2 h πi g 4 L + π YM 2 θ 1, and the soft breaking terms are not small, . Then, consider the following two cases: where the 2 term. Although we can introduce 246 GeV is the Higgs vev. First, consider the gauge theory calculation. Using  ) = m µ d µ b ' , and the soft breaking terms of the vectorlike fields are small, ( λ d v τ λ The interaction strength between the Higgs sector and the singlet chiral superfields can ' u where the dimension-six operator ( the expression with the holomorphicglueball/gluinoball combination scalar 0 terms of the gauge theoryof and the the neutral simplified components model. of the Here, Higgs we use fields, the standard definitions where theory depends on the Higgs vevsthe from which canonically we can normalized extract gauge the kinetic effectivethe interactions. term, hidden With the gauge coupling field between is the given Higgs by sector the and dimension-six operator, is tiny, 3.3.1 The caseTo with know the effective interactions between theout Higgs the fields vectorlike and fields the gauge supersymmetrically. fields, The we gauge integrate coupling of the low-energy effective presented simplified model. Forthe the Higgs sector gauge and theory thefields. side, new gauge the We fields effective are assume interactions generatedfields just between after are for integrating out simplicity ˜ the that vectorlike λ we assume that onefields, scalar there is are always the lighterand than usual the the soft gluino-glue termssuperpotential, fermion. such we as do For not the the consider quadratic Higgs them mass just parameters for simplicity. be ˜ estimated by comparing amplitude calculations in terms of the gauge theory and the scalar is heavier andthe the hidden other gluino is mass lighteris is than not much the larger appropriate. fermion thanconstituent in the However, is each confinement the almost scale, supermultiplet. determined mass by thisthe the of When spurion glueball, gluino the argument is mass lighter composite in than this which the case. gluino-glue contains fermion. Then, the at Therefore, least gluino in one the as scalar, following discussions, a we have ignored the second and third terms in the superpotential ( JHEP03(2016)143 , . . in c . ++ 3 0 S (3.7) (3.8) (3.9) (3.10) m m +h ∗ ) 06 to . d = 50 GeV, 0 coupling is H u S SS = 3 ++ λ 0 H , m ( 0 m ++ S 0 ++ 0 0 , F , decay constant and F 2 h 0, the masses of the SS ) and . · . g ++ c 2 m 2 0 . ++ S ++ = 1 m λ 2 0 1 d + h − m λ α 1 , we can write the following 2 h 4 ⊃ − = 50 GeV, the − W θ 5, is the 0 m . 2 h 2 α ++ . m m i · 0 ++ W 0 0 = 1 0 = (300 GeV) m ] tells us that i · F 2 u Tr SS 0 simplified , λ 2 · · · | 97 = m m L ++ ξ which corresponds to the hard breaking 0 0 0 0 D + 5, the masses of the vectorlike fields are · · · | ( F . ¯ u SS µν ξ + ξ 2 mm F H m ξ ¯ ξ † u = 1 y d ˜ m ξ | . On the other hand, in the simplified model, µν 2 λ ξ H u F u π y – 16 – ∼ > 2 ζζ λ | | ++ λ 2 0 0 32 2 h Tr · h 4 ζζ g θ ) u m m by comparing the calculations of the decay of the | 2 · h β 2 H = | ˜ ) m † u u + β S m H H | and λ α 06 GeV. Moreover, for the gluino-glue fermion, we find the † u + . 2 | 1 0 2 H unlike the previous case. We can estimate the size of the α u 0 = 300 GeV and . It is important to note that this coupling is proportional to π cos( λ ∼ S 3  u | 0 0 · 2 16 h − d H cos( v m g † λ 0 u · 10 ) is negligible but other interactions are generated after integrating θ = 0 0 H 4 SS v × d 3.5 d m 4 m . λ S Z mm 0 u λ 2 λ π ∼ 2 h in the simplified model. Note that the Higgs enters into the expression g S 32 to a pair of SM particles in terms of the gauge theory and the simplified λ u H is the superspace derivative. The coefficient has been estimated by NDA. This † ++ u is tiny and the soft breaking terms of the new vectorlike fields are not small, the is the Yukawa coupling of a SM fermion = 300 GeV, the soft breaking parameter is ˜ α d H ξ 0 0 0 y D λ is the mass of the lightest scalar 0 S m in this case. We concentrate on this case in the rest of the discussions of this section ++ denotes a SM particle) can be calculated as = 0 d ζ (dimensionful) coupling of glueball 0 model as before.m When we assume that this coupling is estimated as where operator includes the interaction term with the combination out the vectorlike fields.the glueball scalar. They include Byoperator the using at the a effective leading SUSY-breaking interaction order spurion between of the ˜ the soft Higgs breaking and parameter, although we briefly look at another case just below. 3.3.2 The caseWhen with effective interaction ( In the nonsupersymmetric case,When the we lattice assume result thisvectorlike value [ fields of are the decayestimated constant, as λ in the simplified modelthis Lagrangian. expression although We the canamplitudes, qualitative replace we result the obtain is mass unchanged. parameter Then, comparing these two the same decay amplitude can be estimated as where we have used the scalar trilinear interaction, where m ( JHEP03(2016)143 is i 0 1 plus ˜ S h ˜  χ h (3.12) (3.11) Z W ∗ + W dominates 0 ˜ ˜ H S → S  100 GeV. As a  χ have small mass → ˜ . H ∼ 0 0 2
. . This distinguishes χ χ but ˜ c models considered in and then the LOSP µ . π S d 0 1 λ i χ H + h ˜ S h u h α , and ˜ Z  1 + W SH , χ α TeV and 0 , ˜ ! W 0 1 ˜ 0 1 H 2 h ∼ ˜ χ χ 2 Tr m 2 m 0 α ˜ M H − D u 1 , H is estimated as

2 0 1 0 1 α ˜ v χ ˜ ˜ S χ ]. However, in our case there is an important 2 D S m κ † u m 57 will be the dominant decay process: it proceeds H π π – 17 – ], for which this decay is usually subdominant or ˜ → 2 S 2 S h S ˜ S λ λ 0 1 2 plus singlino. 16 16 57 | S χ – 0 0 4 ∼ ∼ W θ m 55 → | 2 ˜ ˜ [ S S 2 0 h and ˜ S | ˜ m κ χ 0 → pays the price of a small coupling → ˜ m S 0 1 . Details of such decays arising through a superpotential 0 1 | ˜ H ˜ h ˜ χ ˜ χ S 2 7 | Γ Γ 2  ]. u → π λ | W 0 1 2 16 h 105 χ g → are computed in ref. [ θ 4  , which may be 5–10 GeV for ˜ d S S d 2 χ H u Z /M 2 Z SH m S ˜ S λ ∼ i . Decays of the neutral higgsino to singlet plus singlino, higgs plus singlino, or h × h 0 The decay width of ˜ Higgsinos come in a nearly-degenerate multiplet: ˜ . This means that the decay ˜ ˜ H 3 splittings result, even the heavierthan states to in the the LOSP: multipleta ˜ three-body may decay decay that directly is to highly the phase-space singlino suppressed. rather through the higgsino-singlino mixingthe and decays then in a our coupling scenariothe of from past those order that in 4 had other smallat Stealth values most SUSY of an order-one fractionhas of been the studied decays. in However, ref. the [ case where ˜ decays to exotic new statessectors, through as the interactions depicted between in theinteraction Higgs figure and Hidden Valley difference: the composite statesκS are strongly coupled to each other through operators like 3.4 The LOSPIn decay our framework, wesupersymmetric assume particle low-scale (LSP) SUSYparticle is breaking (LOSP) the at is gravitino. 10–100 TeV, assumed and The to the lightest lightest be ordinary the supersymmetric higgsino-like neutralino ˜ Note that this operatorsponds also to does the not hard includeHiggs the breaking sector down-type term and Higgs the in Hidden or theparticles Valley higgsino fields at simplified and have the model. an corre- LHC. important The role in interactions hiding between supersymmetric the Figure 7 singlino, and of the charged higgsino to effective interaction with the Higgswe and can higgsino. write At the leading order of SUSY breaking, JHEP03(2016)143 0 ) + S + − − v η 0 (3.14) (3.13) SS coupling, m S S λ λ 5 MeV when ]. Then, the denotes 0 . − 1 0 S 107 = η ∼ . . The decay width c in the case that the b ¯ . , b = 30 [ ζζ = 300 GeV. The decay − + h , β A , µ ∗ → state is , the decay length of the ) ) ) + 3 m + d h − − ++ , µ 2 0 H ++ 2 0 − u m τ m ( H ( = 10 + decay to a pair of SM particles is ( 0 ζζ ζζ S S 0 → → λ ++ SM h MSSM A SS Zh, τ Γ Γ (100) GeV. Thus, the dominant decay 2 2 m O  . With a typical size of the  → S 0 + ˜ λ ∗ S is v 0 ++ v (the imaginary component − 0 2 0 = 100 GeV and tan 2 0 0 A 0 1 0 ˜ χ decays are the same with those of the CP odd S m SS m + SS ⊃ − ˜ S,S → − – 18 – m iη 0 + m − 0 − m S − + m, which is not so displaced to be observed at the + S 2 h ,S m 2 A λ 0 ]. Then, with 0 µ − λ m S ˜ and S m 1 1 nm where we have taken ξ = .  0 106  π 0 ∼ simplified = cannot decay through the dimension-six operator in the 4 ˜ ∼ S,S 0 ∼ ∼ L SS + mass. The interesting point of this expression is that the + S decays are the same with those of the Higgs boson decays. S − ∼ ], they are possible in the present supersymmetric theory m ζζ − 0 ζζ ++ → ++ 0 is the physical CP odd component of the two Higgs doublet 95 cτ → → ++ + cτ 0 1 ++ states, we have already estimated the amplitude in terms of the ). Then, the width of the 0 β − 0 χ 0 Γ = 50 GeV [ Γ 3.8 sin ++ d a ++ 2 GeV for 0 ) is the width of the SM Higgs boson decay + ∼ m ++ β 2 0 = m is assumed to be 0 ( cos is the lightest neutralino mass and the hidden gluino-glue mass is ignored. In κ u ζζ SS a 0 1 → ˜ χ m SM h , where we have defined = m states is estimated as A While the pseudoscalars 0 ··· + ++ Higgs boson decays. The totalstate width is of given the by CPdecay odd length Higgs is boson estimated as withinto the a mass of pair the of 0 discussed SM above. gauge bosons through loops of the vectorlike fermions is suppressed as by using the interactionA terms, and model. The branching fractions of the 0 nonsupersymmetric theory [ through the CP oddis Higgs estimated boson as as 0 0 LHC. The hidden glueball andthrough gluinoball loops scalars of can the decay vectorlike intoa fermions. a high However, pair since power of the of SM decay theis gauge width confinement subleading bosons is scale in proportional and the to present suppressedvectorlike scenario by masses. where the the vectorlike confinement masses, scale this is mode much smaller than the where Γ Higgs mass is givenbranching by fractions the of 0 the 0 The total width ofwe the take Higgs boson with the mass of the 0 Valley fields. For the 0 simplified model as in ( denoted as glueball/gluinoball scalar which decays back to SM particles3.5 as we will see The next. hidden glueball/gluinoballLet decays us nowSM consider particles. decays of They the decay hidden through glueball the interactions and between gluinoball the scalars Higgs to and a the pair Hidden of our setup, of the LOSP isthe given by decay is ˜ prompt.fermion becomes When offshell the in confinementsuppression. this scale decay process. is The large, produced In the this gluino-glue case, Higgs fermion the or decays width the to gets gluino-glue a the phase gravitino space and the lighter where JHEP03(2016)143 ). , 19 . 2 0 3.2 − (3.15) (3.16)  < are the 2 / ) 3 2 ˜ S 1 eV m ++ 0  4 , derived from and ++  . 0 c 1 . ˜ S → δm + h h ∗ 20 GeV , ) d ) where ˜ 2 S H  , the widths of the heavier u 3 ζζ from new exotic particles in δm H 1 − ˜ ( S ( ˜ S 2 ζζ . Particles with SM electroweak 0 m γγ S → 0 50 GeV → γγ SM h = 10 κ →  Γ ∗ S S → h h 2 λ λ 1 ) 1 2 h ˜ h 2 ˜ S 2 S 1 is the mass splitting between the scalar 4 mm m . → δm 1 is constrained by the global fit of the signal − ⊃ − 2 2 δm v 2 indirectly. Since we assume that the width of ˜ ' ˜ S S 2 2 S ++ are the lighter and heavier gluino-glue fermion ¯ λ 4 τ – 19 – 0 m ) 2 τ ( 2 ) 3 2 ˜ S ++ π π δm 0 simplified m ( (4 = 60 GeV and πF and ˜ S L , ]. The Higgs decay to two glueball or gluinoball scalars → 128 2 1 b ¯ ˜ m ˜ S S h ∼ 108 m m ' 4 ζζ 1 , ZZ, b ! ˜ S and ˜ − 2 S 2 S → 2 1 m m W ˜ ˜ S S ]. The decay width is given by + Γ − m 1 = 50 GeV, 56 − ,

1 2 . If there is some mass hierarchy between the two gluino-glue fermions, ˜ S 2 ˜ 55 S γγ, W Pl ˜ 5 S m m πF M → m 3 = 16 h is the SUSY-breaking scale and √ ˜ S = F F/ ˜ G √ δm S = Next, we look at the Higgs decay to a pair of (offshell or onshell) Hidden Valley par- → 2 ˜ S / 3 Γ ticles. The branching fraction of strength of the Higgs decay toshould SM be particles satisfied is at the 95%is C.L. same [ given as by that of the the interaction SM, terms, Br( quantum numbers coupling tothe the Higgs Higgs branching boson ratio potentiallyno to induce mass two measurable terms photons changes of through to theTherefore, their electrically there charged loop are vectorlike effects. no fieldsthe which important present However, depend setup. contributions there on to are the Higgs vev. two gluino-glue fermions is small and do not3.7 consider this decay The mode. effectDecays on of Higgs the decays SM-likeFirst, Higgs we boson consider the in Higgs our decay framework to may two photons, deviate from those of the SM. masses. We have usedWhen the we cubic take term ingluino-glue the decay to superpotential the gravitino of and the thethe lighter simplified heavier gluino-glue gluino-glue model are fermion of ( similar decays order.as to the the Therefore, lighter gravitino. one In with the a pair rest of of SM discussions, particles we as assume well that the mass splitting between the where where and the fermion, bothm of which suppress thethe decay width. heavier fermion The possibly gravitinothe decays mass to offshell is the given Higgs. lighter by lighter one The and and dominant heavier a mode fermions pair respectively. is of The SM decay particles width through can be estimated as Supersymmetry [ The lightest hidden gluino-gluegluinoball fermion scalar decays which to decayshidden the to gravitino gluino a LSP mass and pairthe is the of glueball small, glueball SM or or the particles gluinoballreduced, mass as supermultiplet which splitting discussed is contributes above. between also to tiny. the hiding When supersymmetry scalar In the at this and the case, the LHC the fermion as missing in proposed energy in is Stealth 3.6 The decays of gluino-glue fermions JHEP03(2016)143 5 − = as → − µ τ + 10 ++ ++ (3.19) (3.17) (3.18) 0 bµ ¯ 87 and 0 × . b m 7 ]. In this ]. ++ → . 0 ∼ ) and ) = 0 ) 109 111 − [ [ b → ¯ ++ 3 − is given by b µ 0 1 − h µ + − − + µ → ++ µ 0 bµ + ¯ = 10 → b ++ HDECAY bµ ¯ → S b → λ ++ h ]. The sensitivity to this , . h , → = 3000 fb 2 π ]. Due to smallness of the  110 h L [ Br(0 ++ 0 · 109 = 4 4 ++ [ h ) 0 0 − b ++ ¯ ++ m κ 0 b 0 m 10 2 → ++ h → .  0 ) → − HDECAY h − ++ + Γ 1 µ Γ are also possible, the present bound is not + mainly decays into a pair of bottom quarks s SM h = 50 GeV. Here, Br(0 2 Br(0 Γ | h bµ ¯ ++ · b v ++ 0 0 ) ++ κ – 20 – πm 0 ] with only SM charged messengers or low-scale . Then, we obtain Br( ) = → S ++ ++ at 14 TeV LHC with m 0 λ 17 when we take 16 72 h 0 ++ | . 5 ++ 0 0 0 − → decays are given by those of the Higgs boson decays ++ ∼ m ∼ and 0 10 h ++ ) 3 0 × ++ ++ are calculated by ), this is lower than the projected upper bound that could = 125 GeV which is calculated by → 0 − − 4 ++ h → h ++ µ 0 − 0 h m + 10 = 10 → Br( µ ++ , in the superpotential of the simplified model. The branching h 2 · 0 ]. We here focus on gaugino mediation from a relatively low scale, 0 S Br( × is denoted as Γ → λ ]. Therefore, we concentrate on the decay, 4 → . 74 , SS , ]. As the initial condition of SUSY breaking, we consider the situation ++ π h ++ 2) ) = 2 110 0 73 / − 0 87 , µ = 4 κ ) = 2 ++ 41 MeV for 0 0 + . − 86 20% [ κ µ bµ ¯ → + b . = 4 µ is onshell. The decay to offshell glueball or gluinoball scalars is too suppressed h ) → τ is possible but there seem to be no experimental searches for this mode. The 4 → SM h ++ h τ → 2 ++ Although these exotic decays of the Higgs boson are not yet very constrained by current b Br( h . However, there are large QCD backgrounds and no limits exist at present. The decay b where the Hidden Valleyrealized sector by low-scale is gauge supersymmetricgaugino mediation at mediation [ [ the mediationthat scale. is, we This assume canThe nonzero initial be masses gaugino masses for have the to MSSM be gauginos large enough and for vanishing the scalar scalar masses. superpartners of the SM complementary to direct searches for superpartners. 4 RGEs and benchmarks In this section we giveSARAH detailed codes numerical [ results for some benchmark models by using the branching ratio Br(0 be achieved with Run 1channel LHC is expected data, Br( to reach few data, they will be a very important probe of the scenario during the LHC’s Run 2 that is The branching fractions ofby the taking 0 the Higgswhen boson we mass take as Br(0 LHC multilepton searches weakly constrain theBr( branching ratio of thewhere Higgs decay 0 to 4 to be observed. Then, the branching ratio of the decay mode 50 GeV. Although direct probesso of strong. The glueball orvia gluinoball mixing scalar of 0 the SM Higgs4 boson. Therefore, the dominantto exotic mode 2 is given by Then, we obtain Br( fraction of where Γ expression, the decay rate of the Higgs to two onshell glueball or gluinoball scalars is the cubic term, ( JHEP03(2016)143 = 2 , (4.6) (4.7) (4.1) (4.2) (4.3) (4.4) (4.5)
) F 2 , , ˜ ¯ m ) ) 2 0 2 0 + ˜ ¯ m m 2 1 m + ˜ + 2 d 2 u 1)( ˜ m m , − + ˜ ) + ˜ 3 F d u 2 H 2 H M 2 3 + ( m m g ( ( 2 0 3 1, the above term becomes 2 2 c 2 d ˜ ¯ 2 u m π π λ λ + ˜  , 2 2 + 16 16 2 2 | d 2 0 1 λ M is taken to be 50 TeV and 100 TeV + + m 2 2 M 2 2 | g | | m 2 1 1 2 c ) + ˜ , , 2 M 1 π M M 2 d g ) ) | | . For these masses, the two-loop effect is + ˜ 2 0 2 0 16 2 2 2 m 1 ˜ ¯ 2 2 1 1 π π ˜ ¯ m m is some numerical constant. This two-loop m g g + ˜ 32 15 M c 16 16 + ˜ + 2 1 2 u coupling is 0.5. The confinement scale, which g − 5 5 6 6 2 d 2 u 1 m and – 21 – 2 d c | m m − − (˜ λ 2 3 2 2 2 + ˜ + ˜ | | m ) M 2 2 2 | d u 2 ) + 2( ˜ h 2 π . On the other hand, the one-loop beta function of the 2 H 2 H 2 f g M M 2 0 2 3 π | | ˜ ¯ g m m m 2 2 ˜ ¯ m (16 ( ( 2 2 2 2 16 π π 2 2 g g + 2 d 2 u 6 6 3 π π ' 32 16 16 λ λ 2 f 4 4 λ 16 16 m M 3( ˜ 2 ' ' − ' − ' − ' µ ˜ ¯ 2 0 2 0 2 d 2 u 2 f m 2 is large in our setup. In fact, if ) d ˜ ˜ ¯ ˜ ˜ ˜ ¯ µ m m = 2100 GeV. The m m m 2 log 4 h h µ µ µ π µ µ 3 d d g cg log d d d M d d d (16 log log log log log d d d d = d , we show four benchmark model points (A), (B), (C), (D) to study in more ' ' 2 2 2 ' ˜ M 2 f m is the hidden gauge coupling and ˜ µ = 3 for (C) and (D). The mediation scale ’s are some numerical constants. Thus, the hidden gaugino mass is generated from m = h i g µ c d 1 F log In table d M d There are also threshold corrections to the hidden gaugino mass from the vectorlike particles, which log 1 d while for (A), (C) and (B),are (D) respectively. The MSSM gaugino masses at theare mediation not scale larger than the running corrections. where ˜ the two-loop level but suppressed compared to the MSSMdetail gaugino at masses. colliders below. For (A) and (B), we take the number of the singlets as dominant in the RG equationhidden of gluino mass is proportionalthe to two-loop itself beta which function is includesgaugino zero the masses: at following term the which mediation is scale. proportional However, to the MSSM where contribution is included innegligible all because of the soft masses of the vectorlike scalar fields and is not important, while there is no such contribution to ˜ the hidden gluino massthe is hidden zero gluino at and the thegroup mediation new effects. scale. vectorlike scalar At The fields one-loop soft are level,Yukawa couplings generated SUSY-breaking the by give terms masses the dominant including of renormalization contributions the to MSSM gaugino the masses vectorlike or scalar the masses, new fermions to avoid the current LHC bound. The Hidden Valley sector is supersymmetric and JHEP03(2016)143 , , , | 3 1 ¯ u d 2 H M m , and 321 236 210 210 50 10 m , | 626 617 100 (D) | 1.42 3 1413 1413 2 0 − − − − 125.2 ¯ u . For all (the 2nd | q ˜ ¯ m 2 m | − 1 ¯ ˜ ¯ , d m | 3 p 311 220 193 103 46 10 50 q , the slepton m (C) 630 621 1.42 , 1411 1411 3 − − − − 125.2 | p ¯ , m d 2 0 , 1 = 700 GeV. The | ¯ u ˜ m 2 m 0 | , the scalar masses , m ˜ m λ 310 222 194 194 m 3 49 10 | (B) 621 612 100 , is taken to be 50 TeV , and the (tachyonic) ¯ p 1.42 u 1395 1395 | − − − − 124.9 1 M = p q 2 0 m , the scalar masses of m ˜ ¯ 0 0 m m λ , | , the (tachyonic) scalar M 3 m q f 302 208 180 180 M 45 10 50 p 625 615 (A) 1.42 1394 1394 ˜ ¯ = 700 GeV. m − − − − 124.9 , m | (the 2nd generation squark , the down-type Higgs soft | 2 0 , M u 1 f ˜ , the (tachyonic) scalar masses of ¯ m d | 2 H f = m m ˜ ¯ m p m | [GeV] [GeV] [GeV] [GeV] m , , 1 | | | | f u [GeV] [TeV] q ¯ u 2 0 2 0 2 2 [GeV] [GeV] [GeV] [GeV] [GeV] [GeV] λ m ˜ ˜ ¯ ˜ ˜ ¯ − m m m m λ d m h f f u m | | | | MS ˜ ˜ ˜ ¯ ˜ , m m m m m M M Λ p p p p 1 q − − − − m and triplets ˜ d 2600 GeV for (A), (B), (C), (D), respectively. The – 22 – , and triplets ˜ m , the (tachyonic) up-type Higgs soft mass 291 d 3 , ˜ 429 695 684 (D) 1497 1427 1577 1497 1515 1615 2422 2302 2259 − u m M 2800 , ˜ m , , u 2 m 117 , the 1st generation squark masses M 429 694 684 (C) d 1493 1437 1579 1493 1511 1611 2637 2527 2488 − 2550 , H 1 , m M = 3 for (C) and (D). The mediation scale 290 (B) 421 682 671 1469 1401 1548 1469 1486 1585 2380 2259 2216 − F = 2750 . The table also shows the hidden gaugino mass ¯ e 3 m M 121 , 421 682 672 (A) l 1467 1412 1552 1467 1484 1583 2593 2483 2444 − = m 2 = 2 while . The table also shows the hidden gaugino mass M ¯ e F = [GeV] m 1 | , , the 1st generation squark masses l u [GeV] d [GeV] [GeV] [GeV] [GeV] [GeV] [GeV] [GeV] [GeV] [GeV] M [GeV] [GeV] , the (tachyonic) up-type Higgs soft mass 2 H H d m . Four benchmark model points (A), (B), (C), (D). For (A) and (B), we take the number of 3 1 3 1 3 1 3 l 3 2 1 e q q d d u u H m m | m m M M M M m m m m m m m q , coupling is 0.5. The confinement scale, which determines the hidden gauge coupling at the 2 − d masses are almost the same),masses the 3rd generation squark masses the new vectorlike pairmasses of of the doublets vectorlike pair ˜ the of (tachyonic) SM scalar singlets masses which of couples the to the vectorlike pair Higgs of SM singlets without Higgs couplings determines the hidden gaugepoints. coupling at The the table low showsM scale, the is numerical results taken to ofmass be the Bino, 10 GeV Wino for and all gluino the masses the vectorlike pair ofscalar SM masses singlets of which the couplesthree vectorlike to cases, pair the the of correct Higgs SM Higgsgroup, singlets mass without we is Higgs obtained. take couplings the Toother avoid supersymmetric spontaneous supersymmetric mass breaking masses of parameters of the of the hidden the vectorlike gauge fields singlets are as also low scale, is takenBino, to Wino be and 10 GeV gluino forthe masses all down-type the Higgs points. softgeneration mass squark The masses table are showsthe almost the slepton the numerical masses same), results theof of 3rd the generation the new squark vectorlike pair masses of doublets ˜ Table 2 the singlets as and 100 TeV for (A),scale (C) are and (B), (D)λ respectively. The MSSM gaugino masses at the mediation JHEP03(2016)143 , 0 1 s m χ 3 (4.8) . We and ) where u 3.5 decays as , the new λ ). Then ˜ 4.6 0 1 decays into 2 χ 3.2 s in ( 3 S as well as the MSSM is a mixture of their 3) s s . Finally, κ/ , , 2 2 + ( 3.6   d . The neutralino ˜ H 2 u / 3 m m SH parameter, constraints on 500 GeV 500 GeV S and a fermion ˜ > m λ S   s s 2 4 as the lightest supersymmetric particle. ⊃ do not hit a Landau pole until at least   ˜ 2 2 G u u h . . > m g λ λ 1 1 1. They are within the experimental bound ˜ s parameters from the new vectorlike fields are = 500 GeV. The other supersymmetric masses ≈ 0   T – 23 – simplified β 3 3 m > m N N = 500 GeV. For all the points in table as discussed in section W 0 1   = ˜ and ˜ χ G M 0 0 × × m S m = and sin 13 02 ≡ . . 0 0 m 0 0 m ≈ ≈ LOSP = S T m ∆ ∆ m and the gauge coupling u is a mixture of the glueball and gluinoball and ˜ λ s . Due to the supersymmetric initial condition of the hidden gauge sector, emitting the gravitino | 2 s ] ˜ ¯ m | 32 by using the interaction term p ˜ s , s | 2 Let us comment on fine tuning for the electroweak breaking in the present scenario. GeV. The contributions to the ˜ → m 6 | 0 1 ˜ The lightest supersymmetric particle inand the the MSSM sector mass is ordering theχ is higgsino-like neutralino ˜ decays into the SM particles via mixing with the SM-like Higgs boson as discussed in section the Hidden Valley sector containssimulation, the it glueball is and enough gluinoball toparticles. supermultiplets. introduce a For collider scalar Here boson superpartners. We also introduce the gravitino 5.1 Constraints on gluino and squark masses mass whose absolute value at the electroweak scale is5 reduced. Collider phenomenology In this section, we discuss the present status of our scenario. As we have seen in section We have assumed a lowmasses mediation and scale the to MSSMvanishes. realize gaugino the While masses. mass the hierarchylarge As between tachyonic Bino the up-type the and scalar Higgs mediation Wino soft scale masses mass is give is larger, a driven the positive by hierarchy one-loop the contribution stop to mass, the the up-type Higgs where we have assumed at 95% C.L. If weare have more another relaxed. contribution to the 10 given by [ The SM charged vectorlike scalar massesgaugino always masses get at positive one-loop contributions fromTo level, the avoid Then, MSSM spontaneous the singlet breakingmass scalar of parameters masses of the are the hidden driven singletsof to gauge as the tachyonic. group, vectorlike we fields takeYukawa are coupling the also supersymmetric the hidden gluino massthe and the Higgs soft are scalar relativelybecause masses small, the of but new the Yukawa for new couplingscalar vectorlike all is soft fields sizable four masses coupling as cases, of to we thea the discussed vectorlike correct sum before. fields are Higgs rule However, tachyonic. some mass among This of is the can the obtained be scalar seen masses from of ( the vectorlike fields is satisfied at low energies. p JHEP03(2016)143 . s . ˜ s at to m  .A ˜ s T (5.2) (5.3) (5.4) (5.5) (5.6) (5.1) . For − W  E 3 δm ˜ s ) = 1 − ] W ˜ m G → ∼ s 57 because of ˜ s  1 . Although ≡ is dominant → ˜ s m χ  1 → . We neglect ˜ s s 2 s χ suppresses the  1 s /  δm ) m χ → 2 s W Br(˜ δm 0 1 m . Thus, the amount satisfies [ χ ˜ s → 2 to 5 GeV. Thus, for − δ is ˜  1 ˜ 2 s . In particular, in low ≈ /m , ∗ χ ˜ q 0 1 m ˜ q δ ˜ g, χ q = 50 GeV, . . However, for now we will m is ( 5 0 1 . The condition for decays s / ) = 1 0 1 χ 1 s ˜ s ˜ m and ˜ χ   to ˜ ˜ q ∗ q W  1 , ˜ W , , , . χ µ ˜ q ]. For → g 87 04 07 02 →  1 . . . . , ˜ 250 GeV 109 ˜ g χ [   1 g as, 5 χ / Br(˜ ) = 0 ) = 0 ) = 0 ) = 0 2  1 , the additional phase space suppression will ¯ b c ¯ ¯ τ  χ depends on the mass splitting b c gg τ 3 , ˜ W and the small mass splitting – 24 – 0 2 S T − HDECAY → → ˜ , → λ → χ in the rest frame of ˜ E . A subtle question is the decay of ˜ 10 s s ˜ s s s 0 1 δm ˜ s ) G  χ ˜ s Br( Br( Br( Br( ) = 1 ˜ s /m s ˜ q ]. At the LHC, SUSY particles are mainly produced by , the dominant decay mode for ˜ ˜ g, 20 GeV → are not the LOSP, in the higgsino multiplet these states are m can be estimated by the branching fraction of the SM Higgs 112 0 2 ( < ∼ [ 3.4 χ s  1 ]. This mechanism weakens the constraint from null results at δ ∼ χ Br(˜ 56 . The decay table and the mass spectrum for other MSSM particles , s decay promptly. The gravitino would be observed as missing and ˜ 55 [ 0 1 0 2 SUSYHIT mostly decays into , χ χ T that we consider are significantly smaller than those considered in previous . The momentum of 0 2 E s S is roughly χ λ and higgsino multiplets ˜ T ) = 1 , and ˜ ˜ s s E and s s , ˜ s s 1 to 2 TeV, typical splittings among the higgsino states are → . Also, ˜ . All this assumes that there is sufficient phase space for the decays ˜ 0 1 κ ≈  1 χ We show the present constraint on our models. For simplicity, we assume the branching As discussed in section χ 2 , 1 Br(˜ Mass dependence of theother branching decay fractions modes is of notare significant calculated for by a small pair production of coloredscale SUSY gaugino mediation, particles, squarks i.e. are mildly ˜ lighter than the gluino. Since gluino exchange The branching fraction of boson, which can be calculated by using If these are insteadlead decays to to the an dominant off-shell decayalways consider being scenarios a with transition sufficient within phase ˜ space for afraction two-body of higgsino ˜ decay. The values of work on Stealth SUSY.M Nonetheless, they are typicallythe not parameter space much smaller that we thanfor focus 10 on ˜ we can usually assume that ˜ directly to the singlinoare to suppressed dominate due to is small that phase the space, transitions i.e. within that the the mass higgsino splitting multiplet the LHC Run 1. large strictly speaking ˜ approximately degenerate.dominate Thus over there purely is MSSM the transitions potential like for ˜ the decays ˜ the LHC. However, thebetween size ˜ of missing typical Lorentz boost factor in theof laboratory missing frame is given by size of missing assume JHEP03(2016)143 0 1 ], χ 119 ]. We 7 Prospino CheckMATE . The produc- ∗ ˜ q makes use of the q . Thus we can see jet algorithm [ T t E ], and interface them 2200 as 10 GeV for solid lines k is more severe than the ˜ 114 q [ δm ] sets a somewhat weaker bound. CheckMATE < m are almost independent of the 122 2000 ˜ g , ˜ q m q ], the anti- 121 → ], whose internal name in m) = (150, 50, 30) GeV m) = (150, 50, 10) GeV m) = (250, 50, 30) GeV m) = (250, 50, m) = (150, 50, 10) GeV m) = (150, 50, , the jet multiplicity in SUSY events δ δ δ δ 7 118 g , , , , s , s s s s as 50 GeV and assume the Bino and Wino 1800 s , m , m , m , m PYTHIA 8.209 117 m [GeV] ]. Since the dominant decay product of ˜ and LOSP LOSP LOSP LOSP -jets from the decay of the LOSP. This gives h gluino (m (m (m (m b 120 gives the suppression of m , we used an independent code validated by one of the , we show the present constraint from the LHC – 25 – 1600 and the subdominant mode is ˜ 8 δm ˜ q q ], FastJet [ plane from an ATLAS large jet-multiplicity search [ CheckMATE ˜ q 116 1400 In figure m - ˜ g 2 m plane. We can see that the bound is weaker than the case of the ] to obtain the present constraint. collimates the four ˜ q ]. 1200 , the branching fractions of ˜ ˜ q 115 m 57 [ - ˜ g . In particular, the strongest bound is from the signal region with the . The constraint on the region with LOSP m -jets come from decays of > m 800 m a missing transverse momentum requirement [ b 1400 1200 1000 2000 1800 1600

˜ g

squark LOSP m [GeV] m prescription for setting limits [ m -jets larger than 2. s as 150 GeV for red lines and 250 GeV for blue lines and b without where . Constraints on the ]. We generate SUSY events by using CL b LOSP 113 + 4 m [ We have also checked that a different ATLAS multijet search based on counting events with high jet ˜ CheckMATE 1.2.1 2 G atlas_1308_1841 other side. If multiplicity Because this analysis isauthors not and included discussed in in [ MSSM mass spectrum becausethe smaller stealth SUSY scenariofigure. works A in smaller our setup.smaller jet Let multiplicity and us reduces comment thefor on efficiency a of other smaller the features cut, of which leads this to a weaker bound becomes large. Thus, we findjet that multiplicity with the missing most transverse stringentis momentum bound [ comes from anumber search of for large Run 1 data in the tion cross sections for2.1 these modes are calculatedto at the nextDELPHES leading detector order by simulation [ and the is are heavier than the gluino for simplicity of the analysis. diagrams give large contributions fordominant the mode squark of production SUSY in particles such is a mass ˜ spectrum, the Figure 8 take and 30 GeV for dotted lines. In this figure, we take JHEP03(2016)143 = W -jets at b state can and so on. f 0 ¯ d ψ ¯ ψ f + u ψ ψ → ) is more severe. ∗ ˜ q +( W preserve their own baryon < m become the dominant modes f ˜ g → ¯ ψ  1 m , pp f , ψ 0 d , tbχ -wave states. The dominant decays ¯ 2 ψ , S 0 u 0 1 ]. , ψ ttχ 34 − d ¯ ψ → + u g ψ , ˜ ˜ q – 26 – → ) ∗ < m ( ˜ g γ , m ) ∗ ( Z → pp , ] where the fermions charged under the new gauge group are called f ¯ 81 ψ 6= 0) to the superpotential and assuming the somewhat lighter singlet – f i ( ψ boson, the constraint on the region with 78 i ¯ → Ψ W u pp Ψ ` so that the colored quirks can decay [ 0 i i . On the other hand, for λ ¯ q ψ + i ¯ Ψ The colored quirk and squirk can be produced by the gluino decay when the gluino mass due to the ¯ df T i We have proposed a frameworkcan of ameliorate supersymmetric both extensions the of SUSYNew Higgs the mass vectorlike Standard problem matter Model and that fields theits missing couple mass. superpartner to problem. The the newto Higgs Yukawa lift couplings and are the provide sizable new Higgs and loop mass. large contributions SUSY to To breaking is avoid not a needed Landau pole for the new Yukawa couplings, these λ fermion 6 Discussions on the bound onOn the the gluino other mass hand, fromnumber in the and our gluino are models, decay completelywith to the the stable the colored standard colored without cosmology quirks if quirk anyHowever, they and we extension. are squirk. produced can in This easily significant extend might numbers during the be reheating. models incompatible by adding a renormalizable operator ∆ Valley fields decay tothe the LHC. SM particles, which might lead tois signals heavy with enough. many InRun the 1 present but scenario, is the produced heavy much more gluino at is Run hardly 2. produced In at this case, the we LHC should include a possible effect The heavier charged quirk fermions decaypairs to the are lighter neutral joined quirks. by1 The mm. quirk-antiquirk the These hidden bound states, gaugeemission the and flux quirkonia, radiation can strings of lose whose many energyalso soft via radiate lengths photons hidden soft are before glueball pions. or pair muchare They gluinoball annihilation. smaller finally the The annihilate than ones in to the the hidden glueballs or the gluinoballs. As discussed above, the Hidden fermions. Then, the squirkThe decays promptly direct to pair-production the rates quirktheir of fermion couplings the and to the SM the hidden SMof singlet gaugino. the particles scalars quirks are are is small. highly moreare On involved. suppressed given the The because by other direct hand, pair-production collider processes phenomenology for the quirk fermions discussed in refs. [ quirks. We mainly follow the discussionsof of the these works present and scenario. commentsquirks. on some The First, new electroweak features consider doubletDue the and scalar color to triplet superpartners the squirks of soft are quirks pair-produced scalar which at masses, we the call LHC. these squirks are heavier than the corresponding quirk because we assume theE LOSP is higgsino-like. Since the top quark5.2 is a source Comments of on missing (s)quirkLet phenomenology us briefly describe collider phenomenology of the new vectorlike fields. This has been flavor of JHEP03(2016)143 ], 125 GeV. 16 ]. 124 , 123 (1) eV, one possible candidate O -)jet multiplicity. Then, it is not b ]. The detailed analysis of this model 57 – 27 – -jets are produced in the decay chain, in particular from decays b ]. The SUSY-breaking source is separated from the gauge site to which 126 , and will resemble those discussed in [ 8 Another question in the present framework is a candidate for the dark matter in our We have assumed that the cutoff scale of the new Yukawa couplings and the hidden lightest neutralino or thescenario, gravitino, the depending lightestcorrect on supersymmetric abundance the particle of scale the istemperature gravitino of after assumed dark the SUSY matter inflation. to breaking. gives If be the aof gravitino severe the is the In as constraint dark light our gravitino, on as matter the but in reheating the the present model is the lightest hidden baryon. Since there is an so that the naturalbounds on SUSY squarks spectrum in such canin a scenario figure be are realized. significantly weakeris than those We left we expect for have future presented that work. the experimental universe. In the usual supersymmetric models, the dark matter can be explained by the sector fields, do notthe couple RG to effects. the The sourceto scale the and where mediation their the scale nonzero moose ofthe SUSY of soft breaking. 1st the masses and It SM are is 2nd gauge generated ansource. groups generations interesting by is of In (and natural) broken this quark alternative corresponds case, and that these lepton squarks multiplets are couple heavy while to the the 3rd SUSY-breaking generation squarks remain light the successful unification ofsignificantly the gauge lowered. couplings In is addition,SUSY maintained breaking this and [ the model unification nicely scalethe accommodates is matter gaugino fields mediation couple. of gauginos The get MSSM nonzero gauge fields masses can at couple tree-level to while the the source other and fields, the including MSSM our new strong gauge coupling is relativelyThis low compared can to be the justifiedis, usual by unification the considering scale moose multi-fold around (or replicationlink 10 quiver) of fields of the the to SM SM the gauge gauge ordinary groups. groups SM is That gauge spontaneously group broken at by some some low scalar scale. As discussed in ref. [ between the quirks and theand Hidden signals Valley particles, of theirappropriate supersymmetric decays produce to particles a use have parton a shower we large simplified need ( model to for developparticles, some collider possibly techniques simulations. building to on For deal LHC previous with work Run the done 2 parton in shower searches, Pythia of [ the Hidden Valley of the Hidden Valley particles,jets and at they the might LHC.ameliorates be observed both We as find of many a theLHC displaced viable major vertices Run parameter in phenomenological 2, space problemsquirks MSSM of with and specific gluinos supersymmetry. squirks benchmark can as modelsdecay At be well into which the directly SM as produced. particles the through ordinary the They sector Hidden partly particles. Valley fields. decay The Since to there produced (colored) is quirks a finally mass hierarchy like phenomenology. Suppressing themediation soft with masses a vanishing of hidden the gauginoValley mass new leads sector. vectorlike to scalars an Then, almost by supersymmetric ordinary gaugino Standard Hidden Model sparticles particles decay and gravitinos to withof exotic reduced this missing new energy. scenario, states As many which a striking decay feature back to fields are charged under a new gauge group, which confines and leads to a Hidden Valley- JHEP03(2016)143 ] ]. ]. ]. ]. SPIRE SPIRE IN IN [ ][ (2013) 126 SPIRE , SPIRE IN [ 02 IN (2014) 055 [ collisions with the arXiv:1308.1841 06 pp JHEP (1991) 1 , ]. TeV JHEP 85 , (1991) 1815 arXiv:1309.0528 arXiv:1112.3068 = 8 SPIRE , [ (2014) 109] [ s 66 TeV IN Mini-split √ ][ 01 = 8 s ]. √ ]. TeV with the ATLAS detector SPIRE (2012) 095007 IN TeV proton-proton collisions using the Prog. Theor. Phys. = 8 Implications of a 125 GeV Higgs for the MSSM [ SPIRE , Upper bound of the lightest Higgs boson mass in The supersymmetric Higgs for heavy Phys. 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Attribution License ( any medium, provided the original author(s) and source are credited. calculations. We are alsoand grateful Satoshi to Shirai Hitoshi forsearch Murayama, useful Abroad. Yasunori discussions. Nomura, The work Chris YN ofis Rogan MR is supported is supported supported by by in a part a JSPSby by JSPS Fellowship the the for Fellowship NSF National Young for Grant Science Scientists. PHY-1415548. Re- Foundation This RS under work Grant was supported No. in PHYS-1066293 part and the hospitality symmetry becomes stable.observational prospect It of this might hidden be baryon dark interesting matter. toAcknowledgments analyze the abundance and the We thank Ethan Neil for useful correspondence on the interpretation of lattice gauge theory unbroken baryon number symmetry in our model, the lightest particle charged under the JHEP03(2016)143 ] ] , ]. , , ]. SPIRE IN , , ]. SPIRE ][ IN GeV ][ , arXiv:1203.2336 SPIRE ]. [ arXiv:1503.08037 ]. IN [ ]. 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