PoS(DSU2015)026 http://pos.sissa.it/ would likely be a ) higgsino ( m 2 > s √ is natural. Ultimately, we expect detection of both a DFSZ 2 / 3 m  µ ∗ [email protected] axion and a Higgsino-like WIMP. LHC14sign can diboson probably and eke jet+soft out dilepton SUSY channels. signals The in ILC the with new same- Speaker. Guided by the twin pillarsnaturalness, of we simplicity find and regions naturalness, of and highlyscale upon natural top SUSY clarification squarks with of and light the gluinos higgsinos notion with andby of mass highly SUSY less mixed and than TeV- the 4 strong TeV. Thethe CP gauge Little and hierarchy Hierarchy problem SUSY is with mu solved problems are solved by SUSY DFSZ axions. Then Higgsino factory and usher in the era of the superworld. ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). The 11th International Workshop Dark Side14-18 of December the 2015 Universe 2015 Kyoto, Japan Howard Baer SUSY dark matter, axions, LHC and ILC Dep’t of Physics and Astronomy, UniversityE-mail: of Oklahoma, Norman, OK, 73019, USA PoS(DSU2015)026 ] ]. 9 µν A 3 re- , ˜ G 8 h A , m 7 µν problem G A in physics, 2 ) π ¯ Howard Baer θ 1 ( . 32 U 3 crisis strong CP problem QCD natural L 700 GeV– we see the fine- . This 10 < ∼ − R ˜ u 10 m < ∼ . The electroweak fine-tuning prob- ¯ θ h m ] (within the context of certain simplified mod- 350 GeV and 6 , < 2 ∼ 5 ˜ g : such a situation is dubbed as h m m 2 TeV[ > ]. In addition, recent limits on sparticle masses from LHC ∼ 4 125 GeV in the context of SUSY requires highly mixed TeV- ˜ q m ' h m 125 GeV while, at present, no sign of physics from beyond the SM ' h 8 TeV and . m to be present in nature. 1 > ∼ ˜ g both m . Such extraordinary fine-tunings are generally thought to be indicative of some sort h ] with mass Everything should be made as simple as possible, but not simpler The appearance of fine-tuning in a scientific theory is like a cry of distress from 2 m , 1 nature, complaining that something needs to be better explained While SUSY tames the quadratic divergence problem, log divergent contributions to The LHC experiments Atlas and CMS have discovered a very Standard Model (SM)-like Higgs There are two fine-tuning problems in the SM. One already mentioned occurs in the Higgs As a guide to physics beyond the SM, we will here be guided by two principles: simplicity while measurements of the neutronis elegantly EDM solved tell via the us introduction it of is Peccei-Quinn symmetry tiny: and its concommitant axion[ gluon field strength term seems required by ’tHooft’s theta-vacuum solution to the searches require While SUSY solves the gauge hierarchyeach problem of and these the solutions PQ also axionWe gives solves would rise the expect to strong dark CP matter problem, candidates: the SUSY WIMP andmain. the The axion. rather large value of scale top-squarks to bolster its mass[ naturalness with better than 3% fine-tuning– tuning problem potentially re-emerging. This hasand led has some spurred authors some to movement proclaim away a from SUSY as a solution to the hierarchy problem. In this els). Comparing these lower bounds with upper bounds from Barbieri-Giudice-Dimopoulos[ boson[ SUSY DM, axions, LHC, ILC 1. Introduction of pathology with, or missingmass link should within, be the what theory it underand some question. is negative, because are To put the less than it disparate or bluntly, contributions of the to order Higgs its squared mass, some positive occurs (aside from a slewconfirmation of or rejection anomalies– from larger especially data the sets).boson 750 This seems situation GeV is to diphoton especially be puzzling an mass since elementary the bump–divergent, Higgs spin-0 quantum awaiting excitation corrections which to its ought mass. to receive Sincesibility enormous, the of SM quadratically is fine-tuning renormalizable, parameters there to isvalue always whatever the accuracy of pos- is required so as to maintain the measured To this we add some direction from Weinberg sector of the model and involves quadratic corrections to and naturalness. Simplicity guidesthe our SM, search especially for with new poorly physics motivatedadvice extensions, in from the that more Einstein the likely is one further is one to strays be from wrong. Thus, the lem is solved once-and-for-all bybroken the SUSY introduction guarantees of cancellation supersymmetry of (SUSY) quadraticand into divergences is to the all the SM. orders Softly maximal intheory. perturbation extension theory The of other the fine-tuning problem set occurs of in spacetime the QCD symmetries sector that where undergirds the quantum field PoS(DSU2015)026 ]. ]. 125 11 11 (2.2) (2.1) ∼ 1 TeV. h ∼ m Λ . To guard Howard Baer 2 h 125 GeV. But m ∼ is independent of h 2 m is the superpotential of SUSY fine-tuning µ 2 . at the weak scale [ µ 2 3 TeV. 2 GeV. The onset of fine- ) . ) = < are minimized for TeV-scale ∼ 2 91 ) 1 ˜ t µ 2 tree , = ( m 1 ) are individually comparable to ˜ 2 h t − Z ( m u u 30. The main requirements for low β m 2.2 100 GeV over-estimates Σ ( 2 > ∼ in the MSSM leads to violation of the tan are given in the Appendix of Ref. [ 2 h ) ∼ − EW d d u u m ∆ Σ Σ . ]: 1 2 + 10 µ − u and 2 H − β u u 3 ) m 2 Σ ( k -boson mass and the weak scale SUSY Lagrangian ( can be freely tuned to maintain Z contributions to observables such as the better. u u tan − 2 Σ d d Z µ Σ m − is the ratio of Higgs field vacuum-expectation-values and u + d ] and occurs for 2 H d v 2 H m / 12 u m ]. This latter condition also lifts the Higgs mass to 2. If the RHS terms in Eq. ( v dependent / 11 ' − = 2 Z = m β 2 Z 2 m 30, the lighter top squarks are bounded by < ∼ contain an assortment of radiative corrections, the largest of which typically are squared soft SUSY breaking Higgs mass terms, 30) are easy to read off. ) d 300 GeV, the closer to compares the largest independent contribution on the right-hand-side (RHS) of j < 2 H ∼ EW ( − d d ∆ m EW Σ EW ∆ ∆ 100 and is driven radiatively to small negative values and When evaluating fine-tuning of contributions to some observable, it is not permis- u u | ∼ ) 2 H ) to the left-hand-side 2 H k µ m ( highly mixed top squarks[ (This part is called radiatively-driven naturalness.) The top squark contributions to the radiative corrections GeV. For m sible to claim fine-tuning of dependent quantities one against another u u 2.2 Here we cover three common measures of naturalness found in the literature. In supersymmetric models, minimization of the scalar potential to find the Higgs field vevs 2, then no unnatural fine-tunings are required to generate Σ •| • • / 2 Z Here, Higgsino mass parameter, tan the arise from the top squarks. Expressions for the Eq. ( The value of fine-tuning ( m SUSY DM, axions, LHC, ILC talk, we emphasize that this supposedwhich crisis arise arises only from due to not cancelling tuning is visually displayed in Ref. [ against this, we have articulated a Fine-tuning Rule[ As an example, in thethe SM, leading quadratic the divergences tree-level so Higgs that squared mass this then means the SMIn is contrast, likely analogous only reasoning valid applied as to an the effective theory case up of to energy scales 2.1 Weak scale fine-tuning in the MSSM leads to the well-known relation between the Fine-tuning Rule. Proper evaluationSUSY of might be fine-tuning hiding! in the MSSM then guides the way2. to Naturalness where clarified parameters: PoS(DSU2015)026 and (2.3) u . 2 H 1 m δ Howard Baer radiatively-driven natu- i.e. . ,
EW ] ∆ 2 SUSY 14 m / 2 Λ renormalization group equation (RGE). ln ) dt . This is different from the case of the SM. 2 t u / via RG contributions to the stop masses is u A 2 H 2 H ) m + 2 , δ 3 1 dm ˜ t itself: in fact, the larger the boundary condition 2 U ( 4 u u u m 2 H Σ + m 3 2 Q ]. m ( 2 2 12 t f , π 3 8 13 , ∼ − 11 4 TeV, possibly beyond the reach of LHC. u 600 GeV. This arises from requiring[ − 2 H 3 m < ∼ δ 1 < ∼ ˜ b , ˜ g 2 , 1 ˜ m t m Typical sparticle mass spectrum from SUSY models with low then the larger is the cancelling correction ) First and second generation squark andlittle slepton cost masses to naturalness[ may range as high as 5-20 TeV with required to be The gluino mass which feeds into the Λ It is common to hear that low fine-tuning in SUSY requires (several) light third generation A typical sparticle mass spectrum with radiatively-driven naturalness is shown in Fig. ( • • u 2 H The RGE actually contains dependence on squarks with mass 2.2 Large log fine-tuning not too big. Thetheir problem combined effect here must is be evaluated that using a the variety of intertwined large logs contribute to m Figure 1: ralness. SUSY models with these propertiesThe presence have of been a dubbed high radiatively-driven degreea natural of physical fine-tuning SUSY theory. generally or indicates RNS. a pathology or missing element in SUSY DM, axions, LHC, ILC PoS(DSU2015)026 µ (3.1) (2.4) ], one . For 17 can arise EW parameter 2 ∆ µ Howard Baer µ is generated. ]. Large soft ∼ to fundamen- hardly evolves P 19 2 Z BG m , µ ), then one must m / ∆ P 18 . A Little Hierarchy m 2 PQ P v . Since the axion mass or µ has been evaluated for m / λ BG ]. The Majorana neutrino ∼ SUSY GUT ∆ 20 m µ 2 hidden m ] but can occur more generally m  combine while 15 ∼ instead of where phenomenology 2 Z µ and the mu parameter 2 u P m
/ u 2 H 3 m . Such models contain solutions to the 2 H m nearly cancel. This condition occurs in m a 100 GeV[ f m u ∼ δ 2 H ∼ P m and the so-called SUSY mu problem: one µ m . In most cases, δ ) + measures the sensitivity of i / quantities, and are calculated in terms of more SUSY GeV. A value of | µ p Λ i d ( m p u H 11 and u 2 H 5 ) 10 H m log may range as high as Λ are again both requred to have weak scale values (as 2 ( ∂ ) ∼ u X from the superpotential and soft terms from the SUSY Λ / + 1. When PQ symmetry is spontaneously broken, then 2 H ]. µ 2 Z 2 µ λ + dependent PQ m 16 m µ v weak ( . By combining the dependent bracketed terms, and since ∼ u log ) 2 h 2 H (where ∂ | m m i Λ weak is that the soft terms such as ( , then the PQ scale sets the scale for the axion mass, the and u max 2 H ) PQ 2.2 ≡ v m . . For the case of pMSSM, the derivatives show that ∼ ≡ 1 so that the mu term is indeed forbidden. But the Higgs doublets couple i BG weak a p u carries PQ charge ∆ ( − f EW 2 H µ ∆ 20 TeV produce a small value of X . In this case, the soft term contributions to m 2 δ ' / − 3 5 m BG ) + then generates a visible sector Little Hierarchy of in terms of corresponding high scale ∼ ∆ Λ u ( u 2 H 2 H m hidden SUSY m ). Heavier stops are allowed when ( m m The BG measure A class of models exists with radiatively induced PQ symmetry breaking[ A crucial aspect of Eq. < EW ∆ develops a vev of order the PQ scale PQ terms mass scale is also generated and is comparable to PQ scale where the PQ field expects superpotential mass terms of order the Planck mass X to PQ scalars via the hyperbolic branch/focus-point region of the mSUGRA model[ from very different sectors of thebreaking theory: sector. This brings to bear the originrequires of it: at theappearing, weak then regenerate scale. it via some Toinvokes mechanism. solve the In the SUSY the SUSY DFSZ original Kim-Nilles axion mu mechanism[ both solution problem, carry to PQ one the charge must strong first CP problem. forbid mu The from MSSM Higgs multiplets 2.3 BG fine-tuning SUSY DM, axions, LHC, ILC Properly combining dependent contributions according to the Fine-tuning Rule leads to where hardly evolves, then in in models with non-universal soft terms[ tal model parameters models valid at some high scale This is in contrast to the SUSY particle mass scale v is also determined by and by naturalness the Higgs mass! fundamental entities. For example, for gravitygravitino mediation mass they are all calculated as multiples of the evaluate the multi-parameter effective theories where theparametrize multiple our parameters, ignorance assumed of to SUSYspecified, be breaking. then independent, However, the when soft the parameters are SUSY all breaking sector is well- so that again 3. The mu parameter and DFSZ axions PoS(DSU2015)026 4 TeV are Howard Baer − 3 < ∼ ˜ values and expect g a m f 3. , they can also be non-thermally > is large. i θ µ GeV, then dark matter tends to be axion- where 10 a f 10 underproduced < ∼ a 6 f ]. 24 ]. For low 23 and highly mixed TeV-scale top squarks and , µ 22 ]. The reason is that, inspite of a possible reduced local abundance of 25 which is allowed in each PQMSSM scenario for the RNS benchmark models (from a f decays produce dark radiation for which there are strong limits. One must also ]. Axinos are produced thermally while saxions are produced thermally or via co- ], where axions are mainly produced via coherent axion field oscillations. For higher aa 21 22 Range of → ]). Shaded regions indicate the unnatural range of s 24 In addition, ton-scale noble liquid WIMP detectors shoud probe the entire parameter space SUSY models with small The ADMX experiment will soon initiate a search over a wide range of The dark matter is then expected to be an admixture of a higgsino-like WIMP and a DFSZ ax- values, then axinos and perhaps saxions decay after WIMP freeze-out and augment the WIMP a f completely natural. However, the expected signaturesexpectations at such LHC as can in be the quite CMSSM/mSUGRA different model from where previous of natural SUSY models[ Figure 2: Ref. [ WIMPs, their coupling via Higgs exchange iscomponents never small: and it naturalness is requires a product both ofsmall. to gaugino times be Higgsino significant so the WIMP-Higgs coupling is never 5. Consequences for LHC searches abundance. If too many WIMPs or dark radiation are produced, then the model is excluded. produced from axino and/orduced saxion from decay late in axino/saxion theabundance[ decays, early universe. then they If may too re-annihilate many resulting WIMPs in are a pro- larger WIMP to reach sensitivity to the DFSZ axion[ herent saxion field oscillations. Saxion decaywhile to SM particles dilute any abundanceaccount already present for gravitino production andcoupled Boltzmann decay. equations[ The complete calculation requires solution of eight ion. While the Higgsino-like WIMPs are thermally SUSY DM, axions, LHC, ILC gauge hierarchy problem, the strong CPor naturalness problem, problem. the SUSY Awesome! mu problem and the Little Hierarchy 4. Consequences for axion and WIMP searches dominated[ PoS(DSU2015)026 1 e Z of m 1 − -jets and versus b ]. Cascade ) Howard Baer p ]. 27 1 , e Z 29 ( 26 SI 100 (blue). We also ξσ < 20 GeV would signal 3 TeV[ − 500 or 1000 GeV. Since EW ∼ 20 GeV[ ˜ ∆ g = 10 − s m < ] → √ 10 29 < ∼ 1 e Z 30![ reach of LHC14 with 1000 fb should be visible above BG for high (wino pair production) followed by m 2 TeV or < . . This SSdB signature has very small 1 4 − σ 1 e T Z e Z 2 e E 2 6 Z EW − signals appear to allow LHC14 to probe ∼ ` e ∆ j m W 2 + + 2 / ` − 1 e 30 (green) and 30 Z → 1 m W < e → Z − 2 pp 7 e Z EW W , which is produced in cascade decays, can decay ∆ 2 e Z or T where E 6 2 TeV so that LHC14 can probe only a portion of natural j + 2 ∼ e Z + ˜ 1 g e . The Higgsinos yield only soft tracks so these events look like W Z m − + . Thus, gluino pair events are expected to be rich in 1 j comes from initial state radiation and is in addition to a soft OS/SF → e W W e reach of LHC14 is to j W + ¯ b 1 pp t is bounded kinematically by is the reach of ILC for natural SUSY with − W ) 4 or − → ` i ]. The . The combined SSdB and 4 e Z + ¯ e t T Z ` 28 t ( E 6 m → and g 2 , 1 e Z where + ¯ Plot of rescaled higgsino-like WIMP spin-independent direct detection rate ` ` W 1 e Z Also shown on Fig. A qualitatively new signature arises from In addition, it appears For RNS SUSY, gluino pair production is still an important discovery channel where it is → → + 2 2 -jets. An important difference is that the e e dilepton pair plus virtually the entire natural SUSY parameter space with 6. How natural SUSY cries out for ILC SUSY parameter space via gluino pair production. Figure 3: from a scan over NUHM2 parameter space with decay events containing an OS/SF dileptonthe pair presence with a of bump light fromintegrated 0 Higgsinos luminosity within extends the to events. The 5 same-sign boson production: expected that ˜ SUSY DM, axions, LHC, ILC show the current reach from the LUX experiment and projected reaches of Xe-1-ton, LZ(10) and Darwin. backgrounds. The 3000 fb luminosity LHC14[ Z t W PoS(DSU2015)026 and 0 m 6 . , then the 1 2 , 1 − Howard Baer e Z channel is also = m j 0 2 A e Z 1 and e Z 1 e W m region of interest. We also show . In this case, the ILC would be | µ EW | ∆ 2 > ∼ s √ plane of NUHM2 model for in the low sets the mass scale for µ 2 . µ / 1 8 vs m 2 / 1 m should be open for 300 GeV and 2 e Z − 1 e Z 100 and ∼ − 1 µ 15. We also show the region excluded by LHC8 gluino pair searches (left of solid e contours (red) in the ] The light Higgsinos– so difficult to see at LHC– are easy to see above SM W + = 1 30 EW e β .[ W ∆ → − . e 2 / + Plot of 1 e m 5 . 5 TeV and tan 2 of integrated luminosity (dashed/dot-dashed contours). The LHC14 reach via the Guided by the twin pillars of simplicity (the further one strays from the SM, the more one is 1 = ' ˜ − Higgsino factory 0 g a likely to be wrong) andgated naturalness the (unnatural consequences models of naturalness are for likely futureof dark wrong naturalness matter models), finds and that we collider some experiments. have SUSY Clarification investi- models remain which are highly natural: those with light Hig- background at ILC. In addition,the a underlying variety SUSY model of and precision parameters. measurements Natural could SUSY be cries made out for to the pin ILC7. down to be Conclusions built! Figure 4: SUSY DM, axions, LHC, ILC blue contour), and the projectedfb region accessible to LHC14 searches via the SSdB channel with 300/3000 m shown, assuming it is insensitive to the choice of the reach of various ILCregion machines is for excluded by higgsino LEP2 pairm (LEP1) production searches (black for contours). chargino pair The production. blue (gray) To aid shaded the reader, we notein that RNS SUSY we have reactions PoS(DSU2015)026 collider − e , 115028 Howard Baer + e 87 , 57 (1986). , 161802 (2012); 1 [ATLAS Collaboration], 109 (2014) no.3, 037701. et al. 89 (2010) 214. (2012) 162. (2012) 30. (1998) 096004; J. L. Feng, K. T. Matchev 687 , 115019 (2014). 708 58 716 (2012) 1. 5 [arXiv:1207.7214 [hep-ex]]. (2012) 075010; A. Arbey, M. Battaglia, (2012) 035; C. Brust, A. Katz, S. Lawrence 89 , 095013 (2013); H. Baer, V. Barger, (2008) 3. 85 (1995) 573. 716 88 (2016) no.7, 075001. (2016) 3, 035016. (2014) 176; G. 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