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Title Hidden SUSY from precision gauge unification

Permalink https://escholarship.org/uc/item/6jr3g86b

Journal Physical Review D - , Fields, Gravitation and Cosmology, 88(3)

ISSN 1550-7998

Authors Krippendorf, S Nilles, HP Ratz, M et al.

Publication Date 2013-08-26

DOI 10.1103/PhysRevD.88.035022

License https://creativecommons.org/licenses/by/4.0/ 4.0

Peer reviewed

eScholarship.org Powered by the California Digital Library University of California PHYSICAL REVIEW D 88, 035022 (2013) Hidden SUSY from precision gauge unification

Sven Krippendorf,1,* Hans Peter Nilles,1,† Michael Ratz,2,‡ and Martin Wolfgang Winkler3,§ 1Bethe Center for Theoretical Physics and Physikalisches Institut der Universita¨t Bonn, Nussallee 12, 53115 Bonn, Germany 2Physik-Department T30, Technische Universita¨tMu¨nchen, James-Franck-Straße, 85748 Garching, Germany 3Deutsches Elektronen-Synchroton DESY, Notkestrasse 85, 22607 Hamburg, Germany (Received 10 June 2013; published 26 August 2013) We revisit the implications of naturalness and gauge unification in the minimal supersymmetric . We find that precision unification of the couplings in connection with a small parameter requires a highly compressed gaugino pattern as it is realized in mirage mediation. Due to the small mass difference between the and lightest supersymmetric (LSP), collider limits on the gluino mass are drastically relaxed. Without further assumptions, the relic density of the LSP is very close to the observed dark density due to coannihilation effects.

DOI: 10.1103/PhysRevD.88.035022 PACS numbers: 12.60.Jv

small parameter which (further) narrows down viable I. INTRODUCTION soft mass spectra. Remarkably, we are led to a highly Two key motivations for studying low-energy supersym- compressed pattern of gaugino and masses at or metry are the possibility for a natural solution to the below the TeV scale, while the scalar can be electroweak [1] and gauge coupling out of reach for the LHC experiment. As the LHC sensi- unification [2]. Given this input of a natural solution to tivity is drastically reduced in case of a small mass splitting the electroweak hierarchy problem and gauge coupling between the gluino and the lightest supersymmetric parti- unification, we analyze in this article their effect on the cle (LSP), PGU provides an attractive explanation of why spectrum of supersymmetric soft masses. Here we concen- SUSY has not been discovered so far. trate on the minimal supersymmetric extension of the The required spectrum of gaugino masses can be standard model (MSSM). accommodated in mirage mediation and as such is If one ponders the question whether or not gauge cou- directly connected to UV scenarios arising within string plings really unify in the MSSM, it turns out that there is a theory [9–13]. Fixing the ratio of gaugino masses with non-negligible dependence on the pattern of supersymme- PGU opens interesting windows towards explicit UV try breaking. In particular, in some of the most popular realizations of mirage mediation. scenarios, such as the constrained MSSM (CMSSM), Further, the problem of overproduction— gauge coupling unification is not precise given soft masses usually arising in SUSY models with a bino LSP—can around the weak scale. This refers to the fact that the strong naturally be solved by a compressed gaugino spectrum. We 2 coupling 3 ¼ g3=ð4Þ turns out to be about 3% smaller find that in mirage mediation, PGU is intimately linked to than 1 and 2 at MGUT, which is defined as the scale the occurrence of coannihilations. These allow for a con- where 1 and 2 unify. sistent explanation of dark matter in terms of the lightest Of course, this discrepancy of the couplings at MGUT . may originate from some thresholds at the high scale [3] This article is organized as follows: in section II we (see also S. Raby in [4]). However, here we would like to perform a model-independent analytical discussion of discuss precision gauge coupling unification (PGU) in the gauge coupling unification. In section III, we study absence of high-scale threshold corrections1 and determine whether or not PGU can be achieved in realistic SUSY the consequences for the spectrum of soft masses. models taking the CMSSM and mirage mediation as Several examples of spectra achieving PGU have been examples. Then, we turn to the LHC and dark matter discussed in the literature [5–8]. Most of these are now phenomenology of models with successful PGU in excluded by the nonobservation of superpartners at the section IV, before concluding in section V. LHC or by the relatively large mass of the Higgs . The consideration of naturalness leads us to the choice of a II. THE EFFECTIVE SUSY THRESHOLD SCALE The MSSM gauge couplings evaluated at the scale of *[email protected] †[email protected] grand unification can be written as [14] ‡[email protected] MSSM 1 1 b MGUT 1 §[email protected] ¼ i ln þ þ 1 2ð Þ 2ð Þ 8 2 2 i The size of these threshold corrections is ultimately set by the gi MGUT gi MZ MZ gi;Thr UV theory of choice. For a bottom-up analysis we take it as a UV parameter which we here assume to be vanishing. (1)

1550-7998=2013=88(3)=035022(10) 035022-1 Ó 2013 American Physical Society KRIPPENDORF et al. PHYSICAL REVIEW D 88, 035022 (2013) MSSM 0.02 where the bi denote the standard MSSM beta function coefficients, ðb1;b2;b3Þ¼ð33=5; 1; 3Þ, while 0.01 includes two-loop effects, threshold corrections related i 0.00 precision unification

to the heavy standard model fields as well as a possible 3 term required for the transition between renormalization 0.01 2 schemes—the gauge couplings g ðMZÞ are typically given i 0.02 in the MS rather than the DR scheme. The threshold tan 10 corrections within the MSSM read [14] 0.03 200 500 1000 2000 5000 10 000 1 X b M ¼ i ln TSUSY GeV 2 8 2 ; (2) gi;Thr MZ FIG. 1 (color online). Deviation from PGU as a function of where the sum runs over all sparticles and heavy Higgs TSUSY. The width of the band corresponds to the 1 experimen- tal error in ðM Þ. fields with mass M evaluated at the low scale and bi s Z denoting the contribution of the particle to the ith -function coefficient (cf. [15] for the exact expressions Turning to realistic SUSY models, despite the fact that 2 of bi in the MSSM). not all superpartners have a common mass, it is still To arrive at a consistent picture of unification, the gi are possible to define an effective SUSY threshold scale required to meet in a single point. Assuming the absence of TSUSY through the relation threshold corrections induced by heavy fields of a grand MSSM SM unified theory (GUT), this implies that the masses of the bi bi ln TSUSY MSSM fields must arrange such that their overall threshold 82 M Z to the gi allows for PGU. X bi M MSSM To get a first impression on the effect of soft masses on ln þðc1 þ c2b Þ (5) 82 M i gauge coupling unification, let us make the ad hoc assump- Z tion that all sparticles as well as the heavy Higgs doublet with the same ðTSUSY;c1;c2Þ for all three standard model have a common mass TSUSY which we call the SUSY gauge groups. Note that the term c1 accounts for an overall threshold scale. In this case, the overall threshold correc- shift of all g ðMGUTÞ, while the c2 term results in a change tion (2) to the gauge couplings takes a very simple form. i of MGUT. We find Therefore TSUSY has a very simple interpretation: a 1 MSSM SM SUSY spectrum with an effective SUSY threshold scale ¼ bi bi ln TSUSY 2 2 ; (3) TSUSY has the same effect on gauge coupling unification as g Thr 8 M i; Z a degenerate spectrum with all superpartners having this SM where bi stands for the beta function coefficients of the common mass, up to a change of MGUT and/or the unified standard model. Now we can determine the SUSY thresh- gauge coupling. old scale for which the gauge couplings meet exactly. To The effective SUSY threshold scale takes the form3 quantify the deviation from PGU, we follow [7,16] and 32 19 12 19 3 19 m = m = m = introduce ¼ W~ h~ H TSUSY 28 19 Xsfermion; (6) 2 2 = g ðMGUTÞg ðMGUTÞ mg~ ¼ 3 1;2 3 2 ; (4) g1 2ðMGUTÞ ; where mW~ , mh~, mH and mg~ denote the mass of the wino, the Higgsino, the heavy MSSM Higgs and the gluino, where we define MGUT as the scale at which g1 and g2 meet. respectively. The contribution reads 0 10 1 In Fig. 1 we depict 3 as a function of the SUSY 3 19 7=19 = m ð Þ Y m ð Þ ~ i threshold scale. For the determination of 3,wehave @ L~ i A@ QL A Xsfermion ¼ ; 3=19 2=19 5=19 (7) used Softsusy (version 3.3.2) [17], where we set the strong ¼1...3 m ð Þ m ð Þ m ð Þ i D~ i E~ i U~ i coupling strength to sðMZÞ¼0:1184 0:0007 [18] and tan ¼ 10. It can be seen that the three gauge couplings where the masses of the appear in a self- would exactly meet in a single point if all superpartners as explanatory notation. As we will show explicitly in the well as the heavy Higgs doublet had a common mass next section, Xsfermion ’ 1 whenever the sfermion masses TSUSY ’ 2 TeV. Note that the required value of TSUSY are universal within a SU(5) multiplet at the high scale has a very mild dependence on tan which only affects which is expected to hold in a GUT model. The mass the gauge coupling at the two-loop level. splitting of sleptons and squarks through renormalization

2Here we neglect two-loop contributions to the thresholds. 3A simplified version of this formula was discussed in [14].

035022-2 HIDDEN FROM PRECISION GAUGE ... PHYSICAL REVIEW D 88, 035022 (2013) group running does not affect this conclusion. Hence, the 1.4 m 1 2 500 GeV sfermions leave no direct effect on PGU. A0 0 Note that the insensitivity of gauge coupling unification tan 10 to the scale of sfermion masses is due to the completeness 1.2 of these GUT multiplets. Only split GUT multiplets give sfermion nontrivial contributions to TSUSY [cf. equation (6)]. This is X 1.0 also utilized in models of [19]. It is also interesting that the decoupling of complete genera- 0.8 tions of soft scalar masses, e.g. the first and second gen- eration, does not affect PGU, allowing for a realization of 0 1000 2000 3000 4000

‘‘natural supersymmetry’’ with a light third generation of m 0 GeV soft scalar masses. FIG. 2. Effect of sfermions on gauge coupling unification in III. GAUGE COUPLING UNIFICATION the CMSSM for varying m0. IN MSSM MODELS lead to ‘‘unnaturally’’ large fine-tuning as can be seen from As can be seen from equation (6), TSUSY mainly depends the mass of the Z boson which—at tree level—can be : 2 2 on the Higgsino mass and on the mass ratio mW~ mg~. In the written as M ’2m 2jj for tan 1. In the Z hu following, after discussing the case of uncompressed gau- case of a large Higgsino mass, severe cancellations gino masses, we shall show how a change in this mass ratio between m and are required. can lead to PGU. hu We will therefore now turn to a class of models in which PGU can be accommodated more naturally. A. Uncompressed gaugino mass spectra In models with gravity mediated SUSY breaking, the B. Compressed gaugino mass spectra gaugino masses are typically expected to unify at the GUT The effective TSUSY can be enhanced if one increases the scale MGUT. Taking m1 2 to be the universal gaugino mass = wino mass relative to the gluino mass. Specifically, we now at the GUT scale, the physical mass of wino and gluino can discuss the possibility of realizing PGU by nonuniversal be approximated as gaugino masses which can be accommodated in soft mass ’ 0 9 ’ 2 5 mW~ : m1=2 and mg~ : m1=2: (8) spectra arising from UV completions of the MSSM. To obtain nonuniversal gaugino masses, an obvious possibility is to use In turn the effective SUSY threshold scale reads anomaly mediated contributions. While in pure anomaly ’ 0 3ð 12 4 3 Þ1=19 mediation the hierarchy between the gluino and wino is TSUSY : m~ m1 2mH Xsfermion: (9) h = even larger than in gravity mediation, more compressed gau- In the limit where the sfermions are substantially heavier gino spectra can be obtained in schemes with mixed gravity/ than the gauginos, sfermion masses are only weakly anomaly mediation, also referred to as mirage scheme. affected by renormalization group equation (RGE) run- At first sight, having gravity and anomaly mediation at ning. As long as the sfermion masses are universal within similar strength appears as an ad hoc assumption. But note SU(5) multiplets at the high scale, we find Xsfermion ’ 1. that this naturally occurs in a wide class of string models Even if gaugino masses are non-negligible and the masses due to the interplay between moduli stabilization and of squarks and sleptons are split by RGE running, their SUSY breaking. Examples of such mixed mediation effect on gauge coupling unification remains small. This is schemes have been discussed in the context of type IIB illustrated in Fig. 2 where we depict Xsfermion in the string theory with moduli stabilization following Kachru, CMSSM for a fixed gaugino mass m1=2 and a varying Kallosh, Linde and Trivedi (KKLT) [9,10,12,20–22], in the scalar mass m0. It can be seen that Xsfermion never deviates context of heterotic string theory [13,23–25], and in the by more than a few percent from 1. context of G2 compactifications [26]. Taking Xsfermion ¼ 1, we can determine the Higgsino In mirage mediation, the gaugino masses at the high mass which is required to obtain PGU, i.e. TSUSY ’ scale can be written as 2 TeV m3 2 . We find ¼ = ð þ MSSM 2Þ Mi 2 % bi g ; (11) TeV 1=3 TeV 1=4 16 m~ ’ 20 TeV : (10) h where m3=2 denotes the mass and parametrizes m1=2 mH the gravity mediated contribution to the gaugino masses; Due to the small exponents of the last two terms, Higgsino in the limit of vanishing % pure anomaly mediation is ¼ Oð10 TeVÞ masses as large as mh~ are required for gauge recovered. Notice that jM3j < jM2j at the GUT scale coupling unification, even if we take m1=2 and mH in the unless for % & 0:5. The gaugino masses at the low scale multi-TeV range. As is well known, such heavy can be approximated as

035022-3 KRIPPENDORF et al. PHYSICAL REVIEW D 88, 035022 (2013)

m3 2 5 ’ 0 45ð þ 3 3Þ = m 50 TeV mB~ : % : 16 2 ; (12a) 3 2 2500 tan 10 m3=2 m ~ ’ 0:9ð% þ 0:5Þ ; (12b) W 162 4 2000 m3=2 m~ ’ 2:4ð% 1:5Þ : (12c) 1 g 2 m 1500 16 2 3 The gaugino spectrum is thus typically more compressed g g m PGU 1000 m than in models with gaugino mass unification. In the 0 8 & & 2 5 regime : % : the gluino is even the lightest 2 500 gaugino. In the context of mirage mediation, the scalar masses g LSP 0 and trilinear terms are model dependent. The former are of 1 500 the order of the gravitino mass unless in case of sequester- ing. The trilinear soft terms are typically suppressed com- pared to the gravitino mass and can thus be neglected. In 500 1000 1500 2000 this study we assume sfermion masses in the multi-TeV GeV regime as suggested by the KKLT and heterotic models ð Þ with F-term uplifting [12,13,27,28]. FIG. 3 (color online). Parameter scan in the ; % plane for fixed m3 2 ¼ 50 TeV. The region where the gauge couplings In order to avoid a naturalness problem, we should = unify precisely within the experimental error on the strong ¼ ð3Þ ¼ ~ð3Þ require that mhu;d m ~ mU approximately hold the QL coupling are shown in green. The red region exhibits a gluino 4 LSP. The dotted contour indicates where the mass ratio between GUT scale. In this case, the RGE trajectory of mhu exhibits the well-known focus point [29,30] such that gluino and LSP becomes 2. multi-TeV scalars are not unnatural. In the focus point scenario m is driven to a very small value at the low hu spectrum, i.e. a spectrum where the mass difference scale, while m is not considerably affected by RGE hd between gluino and LSP is small. For 1:1 <%<2:4, the ’ running. This implies mH mhd for the physical mass of gluino is the LSP, unless the Higgsino becomes even the heavy MSSM Higgs as well as a suppressed term lighter (shrinking of the red band at the left side in [29]. Therefore, the above assumption is equivalent to Fig. 3). The two regions in parameter space consistent ¼ ¼ mH m ~ð3Þ mU~ð3Þ up to subleading corrections. with PGU correspond to the two regions where the mass QL As the running of the gauge couplings depends on rather ratio of wino and gluino gives rise to the required effective than the Higgs soft masses this form of the input is more SUSY threshold scale. suitable for our purposes. To be specific we set There is only a weak dependence on the overall scale of gaugino masses which is set by m3=2. This is due to the fact 32 19 28 19 mH ¼ mi m0; (13) / = = that the SUSY threshold scale TSUSY mW~ =mg~ , i.e. the dependence on m3=2 almost cancels out. Therefore, where mi denotes the mass of the sfermion i at the high our results remain qualitatively unchanged for different scale. We are thus left with the five free parameters m3=2, %, choices of m3 2. Similarly, PGU only shows a weak m0, and tan . To avoid excessive fine-tuning we restrict = tan our attention to 2 TeV. Further, for any point in the dependence on . For illustration, we have included tan parameter space, we eliminate m0 by requiring that the scans with varying m3=2 and in the Appendix. mass of the light MSSM Higgs is mh ¼ 126 GeV, which 15 TeV typically leads to m0 . We should point out that IV. IMPLICATIONS FOR THE LHC our conclusions are insensitive to the assumptions in the AND DARK MATTER scalar sector as the latter hardly affect gauge coupling unification. Thus our discussions are also valid in schemes A. LHC discovery potential where some of the complete sfermion families receive a We can now turn to the implications of PGU for SUSY mass m3=2 which typically is larger than m0. searches at the LHC. As described in the previous section, We now can ask what constraints on the parameter space this naturally leads us to models with mirage mediation arise from imposing PGU. In Fig. 3, we present the where PGU can naturally be accommodated with a parameter region consistent with PGU for fixed m3=2 and small . tan . Precision unification clearly favors a compressed Within the mirage scheme, solid predictions on the spectrum can be made. While the scalar 4This is a very reasonable assumption as e.g. in the heterotic superpartners are typically outside the reach of the LHC, models, these fields have the same localization properties (see the gauginos and Higgsinos remain relatively light. discussion in [23,24]). We cannot predict the hierarchy among gauginos and

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Higgsinos, but there is a general trend that PGU prefers a ATLAS g qq 1 spectrum in which the mass difference between the gluino CMS g bb 1 and the lightest neutralino is small. ATLAS R Such compressed SUSY models are much more difficult 1500 g LSP to detect at the LHC than ordinary SUSY models like the CMSSM (see e.g. [31–33]). While there is still a strong 1000

gluino pair production, the subsequent decay of GeV

yields only a small amount of visible energy. In the 1

experimental searches, a sizable fraction of the potential m signal events is rejected due to too soft jets. In the case of 500 extreme compression, only events with initial state radia- tion can pass the event cuts, and the signal acceptance is 0 typically well below 1% [32]. 0 500 1000 1500 2000 If the gluino is the next-to-lightest supersymmetric m g GeV particle, the relevant gluino decay modes read FIG. 4 (color online). Parameter points with successful gauge g~ ! qq þ ~1; (14a) coupling unification (gray). Also shown are the constraints on g~ ! g þ ~1; (14b) the gluino mass for the decay modes g~ ! qq þ ~1 and g~ ! bb þ ~1 by ATLAS and CMS (see text). The yellow region where ~1 denotes the lightest neutralino. The first process features a gluino LSP which is constrained by the ATLAS search proceeds via an off-shell squark, the second via a / for stable R-hadrons. squark loop. Additional decay modes open up if further or are lighter than the gluino. It is instructive to determine the regime of gluino and strongly compressed spectrum where initial state radiation (lightest) neutralino masses preferred by PGU. For this is anyway required to pass the event trigger, the latter being purpose, we have generated a large data sample with insensitive to the gluino decay. Therefore, we believe that random choice of input parameters in the intervals at least the ATLAS limit can still be used as a reasonable estimate. The stronger CMS limit should not be applied, as 40–200 TeV we do not find a preference for b-jets in the final state % ¼ 0:5–30;m3=2 ¼ ; % (15) compared to light quark or jets. We have, never- ¼ 0:1–2 TeV; tan ¼ 10–50: theless, included it in Fig. 4 as the LHC gluon searches without b-tagging should reach apffiffiffi similar sensitivity once ¼ 8 TeV Note that the considered range of m3=2 corresponds to a the full data sample collected at s is analyzed. gravity mediated contribution to the gaugino masses of Therefore, the CMS constraint can be seen as a projection 0.25–1.25 TeV. of the current sensitivity of the LHC to gluinos. In Fig. 4, we provide a scatter plot of those parameter A small fraction of the benchmark points features a ð Þ sets which lead to successful PGU in the mg~;m~1 plane. gluino LSP. Apart from the fact that a gluino LSP is very To guide the eye, we have also included the present limits unfavorable from a cosmological perspective, stable glui- 985 GeV on the gluino massR from the ATLAS search for jets plus nos with mg~ < are excluded by the ATLASsearch 1 missing energy at dtL ¼ 5:8fb [34] and fromR the for R-hadrons [37]. This constraint is also depicted in Fig. 4. CMS search for b-jets plus missing energy at dtL ¼ We observe that more than 90% of the benchmark points 19 4fb1 5 0 5 : [35]. Both analyses are based on a simplified with PGU fulfill m~1 > : mg~. The strong compression of model with just the gluino and the LSP assuming 100% the spectrum implies that the limits on the gluino mass are branching of the process (14a). CMS additionally requires considerably weaker than in ordinary SUSY schemes like the final state to be bottoms. Both limits are not the CMSSM. In particular we find that a large fraction of strictly applicable as the considered decay modes do not the benchmark points with mg~ ¼ 500–1000 GeV is not necessarily dominate in the setup we consider. In particu- excluded by the LHC. Note that it is not a general feature lar, we may encounter longer decay chains if the gluino of mirage mediation that the collider limits on the gluino decay to heavier neutralinos/charginos is kinematically mass can be relaxed (see [24]). Only for % & 4 the con- accessible, leading to events with more and softer jets straints become considerably weaker which is exactly the than in the simplified model. As too soft jets typically parameter regime favored by PGU. fail the cuts performed in the ATLAS and CMS analyses, We should also point out that the gluino can be rather this can clearly affect the constraints. However, very soft long-lived in the scenario we consider. This is partly jets would mainly arise in parameter regions with a because of the phase space suppression due to the small mass difference between the gluino and neutralino, and 5See [36] for a similar analysis by ATLAS. partly because of the large mass of the squarks which

035022-5 KRIPPENDORF et al. PHYSICAL REVIEW D 88, 035022 (2013) mediate the gluino decay. The gluino decay rates in case of m~1 mg~ scale as (see e.g. [38]) m ð Þ5 1mm

m~ m~ 10 ð~ ! þ ~ Þ/ g 1 g qq 1 gaugino fraction 4 ; mq~ (16a) 3 2 ðm~ m~ Þ m ð~ ! þ ~ Þ/ g 1 t g g 1 Higgsino fraction 4 ; mq~ (16b) 16 14 12 10 8 6 4 2 log GeV where mt denotes the top mass and mq~ the mass of the 10 g squark in the intermediate state. In the setup we consider, FIG. 5. Distribution of the gluino decay rate within the bench- the squarks are in the range mq~ 15 TeV as implied by the mark sample. The vertical dashed lines indicate where the gluino requirement mh ¼ 126 GeV (see section III B). Note that the decay length c=~ reaches 10 m (roughly the LHC resolution) decay of the gluino into two quarks scales with the gaugino g and 1 mm respectively. fraction of ~1, as the Higgsino coupling to light quarks is suppressed, while top quarks in the final state are kinemati- cally inaccessible for m~1 mg~. The decay into the gluon and neutralino, on the other hand, scales with the Higgsino The gluino will, however, almost certainly decay within the inner pixel detectors of ATLAS / CMS. It is unlikely component of ~1. In our setup the mass splitting between left- and right-handed squarks is typically small, i.e. parity is that the gluino decay vertex is more than a few mm from approximately preserved in the squark sector. Therefore, the the initial collision vertex (see Fig. 5). While dedicated decay of the gluino into the gaugino and gluon—which searches for gluino decays with such tiny displacements do requires parity violation [39]—can be neglected. currently not exist, it seems feasible to employ similar We have systematically determined the total gluino methods as for the identification of b-jets. In particular one could study the distribution of the transverse impact decay rate g~ for the benchmark sample using the tool SDECAY 1.3 [40]; the corresponding distribution is shown parameter in events with jets and missing energy. One in Fig. 5.6 We find that for slightly more than 10% of the might worry that the jets arising from the gluino decays are too soft to be detected. However, we find that a decay benchmark points the decay length c=g~ exceeds 10 m which roughly corresponds to the LHC resolution. This length above the LHC resolution can be obtained for mass splittings m~ m ~ as large as about 100 GeV (depending suggests that, in a non-negligible fraction of the parameter g 1 ~ space, one might be able to observe displaced vertex on the composition of 1). We thus want to emphasize the signatures. Note that, in our approach, we assumed univer- importance to develop search strategies for gluinos with decays slightly displaced from the collision vertex. It is sal squark masses at the high scale and fixed mq~ such that the correct Higgs mass is obtained. There exist, however, also important to determine how b-tagging is affected if the theoretical uncertainties in the calculation of the Higgs superpartner spectrum contains gluinos with a decay length mass at the level of a few GeV [41]. As the squark mass similar to that of b-. Even if gluinos are too short-lived to give rise to dis- enters the loop corrections to mh only logarithmically this translates into an Oð1Þ uncertainty on the squark mass.7 placed vertices, the study of gluino decays is of high / 4 interest. This is because details of the superpartner sector Given that g~ mq~ , our calculation of the gluino decay rate can, thus, only be seen as an order of magnitude are encrypted in the gluino decay pattern. It will be difficult to distinguish the multijet decay modes of the gluino. estimate. For many benchmark points c=~ is at least close g However, as was pointed out in [42], it is feasible to to the LHC position resolution. Therefore, we believe that ~ ! þ ~ there is indeed a realistic chance to observe displaced identify the radiative mode g g 1 which typically vertices. Particularly long gluino lifetimes are obtained if gives rise to events with a low jet multiplicity. This particular decay mode is very sensitive to the Higgsino the LSP is gauginolike. In this case ~ is suppressed by the g component of the lightest neutralino [cf. (16)]. A large fifth power of the mass splitting (or the decay must proceed branching fraction in this mode would thus hint at a rela- through the subleading Higgsino admixture of ~1). tively small term. Of course, it will be challenging to determine the full set of high scale parameters just from the 6 The distribution was slightly smoothed. gluino decay. But in any case it is remarkable that gluino 7Note also that in the benchmark sample we have set tan ¼ 10–50.Fortan <10, larger squark masses are required in decays can in principle be used to learn about the spectrum order to obtain mh ¼ 126 GeV; i.e. the lifetime of the gluino of superpartners which are, in principle, outside the reach would be further enhanced. of the LHC.

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B. Dark matter 2 h As it is well known, the lightest neutralino is a very good DM candidate for the dark matter in the Universe. However, in the simplest realizations of gravity mediation, the lightest neutralino is either binolike or Higgsino-like. Considerable neutralino mixing does only occur in some narrow regions of parameter space. Due to its small annihilation cross section, the bino density from thermal production typically exceeds the observed dark matter density DM by far. The latter has recently been determined at high accuracy by the Planck Collaboration [43], 3 2 1 0 1 2 3 2 2 log h DMh ¼ 0:1196 0:0031: (17) 10 Higgsinos, on the other hand, undergo efficient annihila- FIG. 6. Distribution of the thermal neutralino relic density for tions into third generation quarks or gauge ; coanni- the benchmark sample with (solid) and without (dashed) requir- hilations with the charged Higgsinos further enhance their ing PGU. The observed dark matter density is indicated by the gray contour. cross section. Hence, the relic density of a Higgsino LSP is typically well below the dark matter density. In both cases one has to invoke a nonstandard cosmological history if the ¼ exp 2 mW~ mB~ LSP is to account for the observed dark matter. In case of B (18) TF the Higgsino, nonthermal production e.g. by the decay of a 20 heavy gravitino or modulus field is a viable option (see e.g. with the freeze-out temperature TF mB~= . Given [44–46]). For a bino LSP the situation is more unfavorable a splitting of 10% one finds B 0:01. This factor as, if its abundance is diluted by the decay of a heavy field, compensates for the large wino pair-annihilation cross binos are typically regenerated by the same decay, reintro- section, yielding a relic dark matter density consistent with ducing precisely the same problem [47,48]. observation. Another possibility to obtain the correct relic In mirage mediation, the gaugino masses are nonuniver- density is by mixing effects in the neutralino sector. sal at the high scale due to the anomaly-mediated contri- Turning to direct dark matter detection, we find that the butions. We have seen that if we require PGU, we are drawn cross section of the lightest neutralino with is into a region of parameter space where the gaugino spec- dominated by exchange of the light Higgs (as the other trum is highly compressed. This turns out to be very favor- scalars are in the multi-TeV regime). The coupling of the able for the dark matter density. We have determined the lightest neutralino to the Higgs scales with the gaugino/ 2 neutralino relic density h for a large benchmark sample Higgsino mixing angle; it vanishes in the limit of a pure using the boundaries (15) with the tool MicrOMEGAs 2.4.5 state. The neutralino cross section p for the bench- 2 [49]. In Fig. 6 we compare the distribution of h among mark points with PGU is shown in Fig. 7. For the determi- 8 the sample points with and without imposing PGU. nation of p we used MicrOMEGAs 2.4.5, but took the We find that without the requirement of PGU, the light- est neutralino is typically bino- or Higgsino-like, similar to 43 the models with gaugino mass unification. The distribution 10 of the relic density among the benchmark points has two 10 44 peaks corresponding to the bino and the Higgsino case

2 XENON 100 respectively. 10 45 If we include the requirement of PGU, the picture cm changes dramatically. Remarkably, as most benchmark p 10 46 points with PGU feature a compressed spectrum, the dis- tribution is now peaked close to observed dark matter 10 47 density. The reason is that in the parameter regions with 48 precision unification, the mass difference between bino and 10 10 20 50 100 200 500 1000 2000 wino is typically 10%, suggesting the occurrence of m GeV coannihilations. In particular in case of a bino LSP, wino 1 pair processes would still dominate the annihilation cross FIG. 7. Neutralino proton cross section for the benchmark section. These would be suppressed by a Boltzmann factor points with successful gauge coupling unification (gray). The current limit from the XENON100 direct dark matter search is 8For this figure we have disregarded benchmark points with a also shown. The latter is only applicable if the lightest neutralino gluino LSP. The distribution was again slightly smoothed. accounts for all dark matter in the Universe.

035022-7 KRIPPENDORF et al. PHYSICAL REVIEW D 88, 035022 (2013) updated nuclear quark form factors from [50] suggested amount of visible energy. The detection of gluinos by recent lattice QCD calculations (see also [51]). Note becomes far more challenging than in most of the standard that these form factors suggest a smaller SUSY models. In the case of extreme compression, initial contribution to the mass compared to earlier state radiation is required to trigger on the SUSY events computations [52]. They thus tend to give a smaller p. and the detection efficiency is strongly reduced. The gluino 48 2 We find that p scatters between 10 cm and is typically rather long-lived; its decay length may exceed 1043 cm2. While the XENON100 experiment [53] has the LHC resolution and lead to displaced vertices at the just begun to probe this regime of cross sections, the next level of m to mm. Even if displaced vertices are absent, generation of direct detection experiments will be able to interesting information on the superpartner spectrum can test a significant fraction of the depicted benchmark points. be obtained by studying the gluino decay modes. Still, there exist benchmark points with a binolike LSP Another virtue of compressed gaugino masses is that which have a strongly suppressed p. These may even be they generically lead to coannihilation effects in the early consistent with thermal dark matter production due to Universe. Cosmological problems related to the overpro- coannihilations. Consequently, there is no guarantee for a duction of dark matter which are present e.g. in the signal in direct dark matter detection. One should also keep CMSSM can easily be solved. Indeed, we find that in the in mind that the lightest neutralino must not necessarily parameter space with PGU, the relic neutralino density is account for the dark matter in the Universe such that direct expected to be close to the observed dark matter density. detection experiments would be doomed to fail. Finally, it is needless to say that measuring superpartner spectra that support PGU will provide us with invaluable V. CONCLUSIONS information on how the standard model is completed in the ultraviolet. This analysis is based on the hypothesis that PGU is not an accident. In general, imposing PGU reduces the dimen- ACKNOWLEDGMENTS sion of the soft supersymmetry breaking parameters by 1. Within the more ‘‘traditional’’ patterns of soft masses, We would like to thank Jamie Tattersall and Jan Hajer imposing PGU implies typically a large parameter, which for useful discussions. This work was supported by the is in conflict with usual ‘‘naturalness’’ arguments. On the SFB-Transregio TR33 ‘‘The Dark Universe’’ (Deutsche other hand, a particularly attractive pattern of soft masses, Forschungsgemeinschaft), the European Union 7th consistent with PGU, is the one of mirage mediation where network program ‘‘Unification in the LHC era’’ (PITN- the gaugino spectrum is compressed and the parameter GA-2009-237920), the Deutsche Forschungsgemeinschaft can be small. Such a spectrum can be realized in various (DFG) cluster of excellence Origin and Structure of string constructions which exhibit a ‘‘competition’’ between the Universe and the ERC Advanced Grant project gravity- and anomaly-mediated contributions to soft masses. ‘‘FLAVOUR’’ (267104). The similarity of gaugino masses at low energies has pro- found implications for collider and dark matter searches. APPENDIX: DEPENDENCE OF PGU By requiring PGU we are driven in a corner of the ON tan AND m3=2 MSSM parameter space with a nonstandard collider phe- nomenology. The small mass difference between gluino Figures 8 and 9 illustrate the dependence of PGU on and neutralino typically leads to events with a reduced tan and m3=2.

5 5 m 3 2 50 TeV 2500 m 3 2 50 TeV 2500 tan 30 tan 50 4 2000 4 2000

1 1 m 1500 m 1500 2 2 3 3 PGU g g g g

m PGU 1000 m m 1000 m

2 500 2 500 g LSP 0 g LSP 0 1 500 1 500

500 1000 1500 2000 500 1000 1500 2000 GeV GeV

FIG. 8 (color online). Same as Fig. 3 for different choices of tan .

035022-8 HIDDEN SUPERSYMMETRY FROM PRECISION GAUGE ... PHYSICAL REVIEW D 88, 035022 (2013) 5 5 m 3 2 30 TeV m 3 2 80 TeV 4000 tan 10 1500 tan 10

4 4 1 m 3000 2

1 g 1000 m m 3 2 3 2000

g PGU g

g m m m PGU 500 1000 2 2 g LSP 0 g LSP 0 1 1 1000 500 500 1000 1500 2000 500 1000 1500 2000 GeV GeV

FIG. 9 (color online). Same as Fig. 3 for different choices of m3=2.

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