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JHEP08(2009)080 ). e, ii e assump- M-preferred June 15, 2009 : August 20, 2009 August 12, 2009 : : utralino CDM. ). cold , i Received f cold axions, while the Accepted Published nents: ted at the LHC in the case th a very light of mass preferred in the case of neu- 10.1088/1126-6708/2009/08/080 doi: GeV) for many baryogenesis mech- 6 10 > ∼ [email protected] Published by IOP Publishing for SISSA , R T ). cold or warm thermally produced axinos. To iii [email protected] , problem is solved by the Peccei-Quinn mechanism. In this cas CP Supersymmetry Phenomenology We examine the minimal supergravity (mSUGRA) model under th [email protected] 100 keV. For mSUGRA with mainly cold DM (CDM), the most D SISSA 2009 Dept. of andNorman, Astronomy, OK University 73019, of U.S.A. Oklahoma, E-mail: c

anisms to function, weadmixture find of that cold and the warm bulk∼ axinos of should be DM rather should slight,parameter consist wi space o regions aretralino precisely DM. those Thus, which ratherof are different mSUGRA SUSY least with signatures mainly are axion expec CDM, as compared toKeywords: mSUGRA with ne sustain a high enough re-heat temperature ( warm axinos from decay, and tion that the strong Abstract: Howard Baer, Andrew D. Box and Heaya Summy Mainly axion cold darksupergravity matter model in the minimal the relic (DM) abundance consists of three compo JHEP08(2009)080 . 3 4 5 5 6 6 1 3 7 15 (1.1) is the scaled h to quadratic di- nd o dark matter tly measured to high e log divergence is soft ified theories (GUTS), the SM) of particle physics has divergences cancel between ing supersymmetry (SUSY) gences lead to scalar masses M does emerge naturally from ngle effective theory. In SUSY cle physics. , 006 . 0 ], for which an elegant solution was pro- ± 2 ], and which naturally predicts the existence 110 . 3 – 1 – = 0 ], which lately finds 2 problem [ 1 h CP CDM Ω . The axion turns out to be an excellent candidate particle a GeV), unless exquisite fine-tuning of parameters is invoked 16 ]. 5 10 × 2 ]: the axion ≃ 4 is the dark matter density relative to the closure density, a c GUT M ρ/ρ 2.3.3 Thermal production of axinos 2.3.1 Relic2.3.2 axions Axinos from neutralino decay The second problem — the gauge hierarchy problem — arises due The first problem is the strong 2.1 problem 2.2 Leptogenesis 2.3 Mixed axion/axino dark matter for CDM in the [ precision by the WMAP collaboration [ 1 Introduction The cosmic abundance of (CDM) has been recen 3 Preferred mSUGRA parameters with4 mainly axion CDM Summary and conclusions Contents 1 Introduction 2 The gravitino problem, leptogenesis and mixed axion/axin posed by Peccei and Quinnof many a years new ago particle [ [ vergences in the scalarblowing sector up of to the the SM.GUT highest The scale scale quadratic diver in the theory (e.g. in grand un The gauge hierarchy probleminto is the naturally theory. solved By byfermion including introduc and softly boson brokenenough SUSY, loops, that quadratic and vastly different only scales log remain stable divergences within remain. a si Th Hubble constant. No particleexactly present the in right properties the to Standard constitutetwo Model CDM. compelling However, ( CD solutions to longstanding problems in parti where Ω = JHEP08(2009)080 > of CP a gions GeV. /N ), and 6 -parity a x f ( R > m 10 . s ]. Related > ∼ eV ]. 2 12 R − s, and an even T 10 xion and axino the strong -parity even field, mainly axion cold ]. We will restrict R ]. Gravity-mediated both n ref. [ , we first discuss the 11 ibility of including a 6 urselves to examining 2 ]. In a SUSY context, 7 e [ for ]. n models with dominant rve as the lightest SUSY ose-Einstein condensate, ally produced neutralino on n the PQ solution to the Q breaking scale gravitino problem 14 ced axino dark matter. In tures, as well as generating red range 10 tralino decays. The favored sses. These models experi- . The axion supermultiplet weak scale. The axion mass genesis mechanisms: thermal ted with large scale structure order to do so, we will need to seful to invoke supersymmetric d dark matter [ to reach values . We then examine production IMP CDM candidate. The grav- n the early universe. In addition, problem [ element abundances produced by -parity even saxion field R CP is the next-to-lightest SUSY particle ], and is expected to lie in the general 9 0 1 χ ). The supermultiplet also contains an – 2 – axion supermultiplet x ]. The saxion, while being an ]. ( 8 [ a 15 a dark matter, we will be pushed into mSUGRA parameter space re GeV are needed, leading to the mSUGRA model with 12 cold 10 , but also with a small admixture of thermally produced axino Majorana field, the axino ˜ problem is also invoked. For definiteness, we will restrict o − 1 2 , we confront the mSUGRA model with the possibility of mixed a 11 3 CP eV. The axino mass is very model dependent [ We will be guided in our analysis also by considering the poss The remainder of this paper is organized as follows. In secti In this paper, we investigate supersymmetric models wherei Of course, it is highly desirable to simultaneously account 5 − contains a complex scalar field,whose whose imaginary real part is part the is axion the field odd spin- 10 (NLSP); the case with a stau NLSP has recently been examined i smaller component of warm axinoaxino dark matter mass arising value from is neu ofaxion order CDM 100 explore keV. We thewhich note possibility can here that allow recent work for axions o and the form the solution a cosmic of cosmic background several radiation B problems [ associa dark matter order 10 itino of SUSY theories is also a good super-WIMP CDM candidat theories, the lightest neutralino emerges as an excellent W SUSY breaking models includeence tension due with to weak-scale possible ma late overproduction decaying of gravitinos gravitinos i may disruptBig calculations of Bang light nucleosynthesis (BBN). This tension is known as the the axion field is just one element of an strong the paradigm minimal supergravityour (mSUGRA work or to CMSSM) cases model where [ the lightestprevious neutralino work ˜ on axino DM in mSUGRA can beviable found mechanism for in baryogenesis ref. in [ allow the for early re-heat universe. temperatures In after the inflationary epoch gravitino problem, and thenand examine non-thermal several leptogenesis possible and Affleck-Dinemechanisms baryo leptogenesis for axion andsection thermally and non-thermally produ range of keV to GeV. An axino in this mass range would likely se nonethless receives a SUSY breakingis mass constrained likely by of cosmology order the and astrophysics to lie in aparticle favo (LSP), and is also a good candidate particle for col that are very differentdark from matter. those In allowed addition, by we the find that case very of high therm values of the P problem and the gauge hierarchy problem.models In this which case, include it is the u PQ solution to the strong We will find that inpredominantly order to sustain such high re-heat tempera JHEP08(2009)080 , 2 / 1 is a and (2.1) m . m a f GUT , and find gauge and cale, M R T o dark , we present a . Here, 4 weak m scale gravitinos: the perature ∼ k matter. This has a HC. The requirement of y gluino pair production P l alization group equations gram of Isajet for spectra erHiggs mechanism. The he PQ breaking scale dden sector is chosen such models. The mSUGRA pa- SUGRA space most favored /M tor which is uncoupled to the In addition to a mass for the 2 os. In section most disfavored by mSUGRA rticle and Higgs boson masses. , ich serves as the gauge particle 1 ) m parameter is determined by the µ , the various sparticle and Higgs ( µ ∼ om all collider phenomenology. 2 GeV. to sustain at least non-thermal lep- / weak 3 is larger than the lightest MSSM mass m 11 R m 2 T / β, sign can be produced thermally in the early 3 m ˜ G tan , is the unified trilinear SSB term at 0 – 3 – 0 A , A are generated for all scalar, gaugino, trilinear and 2 , / 1 GeV favors rather heavy squarks and sleptons. Thus, ] as a template model for examining the role of mixed weak 6 GUT 11 , m m 10 0 M , at which point electroweak symmetry is broken radiatively m > ∼ R T weak m to GUT is the ratio of Higgs field vevs at the weak scale. The GUT scale ]. M d 16 ], a link is suggested between hidden sector parameters and t is the unified soft SUSY breaking (SSB) scalar mass at the GUT s /v 17 u 0 v m ≡ In all SUGRA scenarios, a potential problem arises for weak- matter β In ref. [ 1 hidden sector parameter assumed to be of order 10 we expect in this case that LHC signatures will be dominated b followed by 3-body gluino decays to charginos and neutralin togenesis favor a sparticle masswith spectrum neutralino which cold is darkby actually matter. neutralino Likewise, CDM thelarge regions are impact of least on m favored themainly sort by axion of mixed CDM SUSY axion/axino with signatures to dar be expected at L that parameter space regions with large enough common scenario is to postulateMSSM the sector existence of except a via hiddenthat gravity. sec supergravity is The broken, superpotential whichfor of causes the the the superHiggs gravitino hi (wh mechanism) to develop a mass 2.1 Gravitino problem In supergravity models, supersymmetry is broken via the sup cold and . We plot out contours of re-heat tem gravitino, SSB masses of order axion/axino dark matter in gravity-mediated SUSY breaking summary and conclusions. 2 The gravitino problem, leptogenesis and mixed axion/axin rameter space is given by We adopt the mSUGRA model [ bilinear SSB terms. Here, we will assume that where eigenstate, so that the gravitino essentially decouples fr gravitino problem. In this case, gravitinos Yukawa couplings, and the SSB(RGEs) terms from are evolved usingowing renorm to the large top quark Yukawa coupling. At is the unified gaugino mass at boson mass matrices are diagonalized toThe find magnitude, the physical but spa not the sign, of the superpotential EWSB minimization conditions. Wegeneration adopt [ the Isasugra subpro tan JHEP08(2009)080 ]. ], ]. 21 26 19 [ . (2.2) 2 2 ]. One / / is elec- 3 3 may be 18 ), a lower i m m 10 N ) to achieve weak − ≪ he early uni- e 120 GeV, and 0 m inflaton decay. 10 m , × asymmetry have < ∼ ∼ 9 . eff L is so heavy that its δ 0 h R . For more general 2 T ˜  − m G / ≃ nt). The late gravitino 3 B 3 chieved provided the re- m /s genesis invokes an alter- ν f recent evidence for neu- universe. In non-thermal e B m 05 eV = n ryon-antibaryon asymmetry . in SUGRA theories. nt abundances. The precise f te and only of order 0 to be in thermal equilibrium) hes for light top squarks [ value needed here apparently 0 ely low ses, but with 5 TeV is to maintain a value of into the cosmic soup threatens , with a long lifetime of order ropy ratio is calculated in [  of the universe. The produced m R < ∼  T l electroweak baryogenesis within 2 R 1 violating phase which may be of or- / T N φ 3 m m M CP 2 are presented recently in ref. [ R asymmetry is then converted to a T  L decays near the onset of BBN. In this case, ]. The high 5 TeV. In this case, the − ˜ R G – 4 – GeV 24 > ∼ B ]. In this scenario, heavy right-handed T 6 2 / 23 3 rules out many attractive baryogenesis mechanisms, 10 is an effective m  GeV [ R T 9 eff ]. The × δ 10 26 11 − ∼ 10 GeV are allowed. 9 × 2 . 8 exceeds ≃ R ]. The latter requirement is difficult (though not impossible 3) decay asymmetrically to leptons versus anti-leptons in t T B s 20 GeV may be inferred for viable non-thermal leptogenesis via − n ], it is possible to have lower reheat temperatures, since th 6 25 as large as 10 10 = 1 R i > ∼ is the inflaton mass and ( GeV. Such a low value of T φ i R 5 sec (due to the Planck suppressed gravitino coupling consta T 125 GeV [ N m 5 10 < ∼ An alternative attractive mechanism — especially in light o A related leptogenesis mechanism called non-thermal lepto In the simplest SUGRA models, one typically finds 10 < ∼ can then decay to various sparticle-particle combinations 1 ˜ t − R ˜ asymmetry via sphaleron effects as usual. The baryon-to-ent decays occur during or after BBN,to and destroy their energy the injection successfulconstraints BBN of predictions BBN on of the the gravitino light mass eleme and 1 troweak baryogenesis. However, calculations ofthe successfu MSSM context seem to require sparticle mass spectra with G been solved numerically in ref. [ generated via inflaton decay. The Boltzmann equations for th at a rate which depends on the re-heat temperature universe (even though the gravitinos are too weakly coupled m 2.2 Leptogenesis One possible baryogenesis mechanism that requires relativ where trino mass — is thermal leptogenesis [ We will not consider this possibility further. where it is found states Here for simplicity, we will assume degeneracy of scalar mas in the MSSM, and is also partially excluded by collider searc way to avoid the gravitino problem in the case where puts this mechanism into conflict with the gravitino problem native to thermal productionleptogenesis of [ heavy in the early values of der 1. Comparing calculation with data (the measured value o verse. The lepton-antilepton asymmetryvia is sphaleron converted effects. to Theheat a measured temperature ba baryon abundance can be a T lifetime is of order 1 sec or less, and the and so here instead we assume that SUGRA models, the scalar masses are in general non-degenera bound JHEP08(2009)080 e ), q cold QCD (2.4) (2.5) (2.3) is the at tem- det m P l t>t a ( ]. In this ns on, and f M are allowed 28 ∼ arg 8 + ) literally, and 10 θ r density to the rse, one gets an is the quark mass − 2.5 ]: = q 6 5 ¯ θ m 10 ine leptogenesis, along eq. ( would constititute ∼ ere with re-heat temper- asymmetry by sphalerons R iverse. Since their lifetime axion/axino DM scenarios alignment is plus-or-minus T ne: production via vacuum (where ] leptogenesis [ ies , coherent ion rate becomes comparable ton number asymmetry. The ial turn-on corresponds to the ity today [ 27 . ntropy production at /N 6 a / ) can have any value 7 ¯ , θf x i  ( ) − a t R ( , values of 2 eV T P l 2 2 a is inadvertently small, then much lower 6 /s h M i| a − ) i B ν t ) H m n ( t 10 m ( a |h 2 × m a 1 is identified in the scalar potential, which may – 5 – h 23 6 2 1 2  / ≃ ∼ 1 4 1 is the mass of the lightest neutrino and ) ) B i t s ν ( n ≃ a m ] find that the baryon-to-entropy ratio is given by Hℓ 2 n h violating Lagrangian parameter and 28 (to avoid overproducing gravitinos in the early universe), a Ω = (2 CP i /N a φ ) turns out to be longer than the age of the universe, they can b < f eV. γγ . As the temperature of the universe drops, the potential tur GeV. 7 8 − → GeV 10 10 QCD ]. In this mechanism, the axion field a 9 5 Λ − − 6 10 9 ≫ − is the Higgs field vev, 10 < ∼ T i 10 ∼ is the time near the QCD phase transition. Relating the numbe R H ∼ T t h R ν T A fourth mechanism for baryogenesis is Affleck-Dine [ Thus, to maintain accord with either non-thermal or Affleck-D m is the fundamental strong entropy density allows one to determine the axion relic dens can also lower the axion relic abundance. Taking the value of values of axion relic density could be allowed. Additional e Planck scale. To obtain the observed value of where have a large field value into the early the universe. SSB When terms, theoscillations expans the about field the oscillates, potential andlepton minimum since number asymmetry will the is develop field then aas carr converted to lep usual. a Detailed baryon number calculations [ dark matter. However, in the event that An error estimate ofa the factor axion relic of density three. from vacuum mis- Axions produced via vacuum mis-alignment 2.3 Mixed axion/axino2.3.1 dark matter Relic axions Axions can be produced via various mechanisms in the early un (they decay via comparing to the WMAP5 measured abundance of CDM in the unive approach, a flat direction for with constraints from thewith gravitino problem, we will aim for where the axion production mechanismmis-alignment relevant [ for us here is just o a good candidate foratures dark matter. Since we will be concerned h peratures the axion field oscillates and settles to its minimum at θ matrix). The difference in axionvacuum field mis-alignment: before it and produces after an potent axion number density JHEP08(2009)080 2 ]. − 001 . dark 31 (2.7) (2.6) GeV, axino , values values. 12 = 0 29 R , we will R e various 2 915. The 10 T R . T decay into h axion T ce to below warm × ˜ TP a  ˜ aγ 2 ], and is given (purple), 10 ]. Thus, in the . 1 1 MeV [ 4 31 30 . → GeV. We also see − , 0 < ∼ R GeV 0 1 hermal production, T 12 GeV) = 0 29 > ∼ 4 χ 6 ˜ a 10 = 10 /N r to achieve 10 a ypically in the range of ˜ m a − eV. If we take the axion f  10 GeV [ 5 rly universe, they can still also give more m  ined with smaller amounts 11 = 10 he constraints that plague − − to neutralino number density. the cosmic soup. The axino 1 ve high values of 10 R is the model dependent color 10 d in ref. [ ge factors of relic density. For /N ˜ a T < ∼ a ( es of ∼ > ∼ N f s m ˜ a 1 GeV g a . . We plot values of Ω m , 0 m 2 10 GeV, we usually get  and h /N 100 keV — give the largest 2 0 1 a − R ˜ χ f  ∼ T 1 Ω ˜ a will no longer be stable, and can decay via 0 1 ˜ < a = ∼ ˜ χ 0 1 m GeV χ ˜ a m 10 (as can occur in the mSUGRA model at m /N Q a m 11 f dark matter as long as – 6 – ∼ = 10 2 2 on the large side: h h 0 1 cold ˜ χ  /N a ˜ NTP a f s Ω 108 g . ]. The photon energy injection from ˜ 1 ]. The axino DM arising from neutralino decay is generally GeV, or a lower bound  29 18 11 ln 10 6 s g × 5 . 1 sec [ 5 5 100 GeV and Ω − < ∼ eV. ≃ ∼ 6 2 01 0 1 − . h ˜ χ /N 0 , we plot the re-heat temperature needed to thermally produc a 10 1 m ˜ a TP f ∼ × Ω ) 4 values) an axino mass of less than 1 GeV reduces the DM abundan ] using hard thermal loop resummation as is the strong coupling evaluated at . The relic abundance of axinos from neutralino decay (non-t ˜ aγ > ) is given simply by ∼ 0 s is the lightest SUSY particle, then the ˜ 31 g a ˜ aγ GeV, we will need values of a m → 6 m In figure The lifetime for these decays has been calculated, and it is t 0 1 → NT P 10 χ 0 1 (˜ ˜ > anomaly of the PQ symmetry, of order 1. We take e.g. thermally produced axinos qualify as ∼ where upper bound and 2.3.2 Axinos fromIf neutralino the decay ˜ DM from neutralino decay. 2.3.3 Thermal productionEven of though axinos axinos may notbe be produced in thermal thermally equilibrium via inthermally scattering the produced and ea (TP) decay relic processes abundance in has been calculate considered warm or even for cases with in ref. [ abundances of axinos versus the Peccei-Quinn scale mSUGRA scenario considered here, where that the purple curves — with lowest values of (green) and 1 GeV (maroon). We see from the curves that in orde since in this caseThe neutralino-to-axino the decay axinos offers a inherita mechanism to the case shed thermally where lar produced relic density a factor of three lower, then the bounds change χ or Of course, from the preceeding discussion, large values of WMAP-measured levels. τ the cosmic soup occursthe case typically of before a BBN, gravitino thus LSP [ avoiding t (solid), 0.01 (dashed) and 0.1 (dot-dashed), assuming valu large likely need to examine scenariosof with cold mostly and axion warm CDM, axinos. comb matter, independent of any other parameters. Thus, to achie JHEP08(2009)080 , 0. is 2 h 2 ∼ oop a h 2 in eV h (solid) 11, i.e. a ˜ a TP . a (purple), 7 esponding m 4 − = 0 2 h = 10 ˜ a en by the central ˜ NTP a m (dashes), 10 6 +Ω versus PQ breaking scale 2 M saturate the WMAP R h T = 10 green, and also the solid green ˜ TP a R ial evaluation at an optimized e Isasugra subprogram of the T . The abundance of Ω )., we plot the values of Ω 2 R +Ω a ]. T

needed to saturate the measured 2 = 0.001 = h 33

˜ a

2

a

h

a m ~ TP ]. Complete one-loop mass corrections

). in GeV units, along with

s considered in this section. ]. In their results, they always take Ω = 0.1 = Ω

b 2

h 32

12

a

~

TP

(GeV) +1) (where all mass parameters are in GeV Ω , /N a 10 f

, , where we examine the mSUGRA point with

] (to calculate the stau relic density, which is not handled

= 1 (GeV), (GeV), 1 = – 7 –

a 0 ~ 2

, 13 m , the value of 300 , /N = 0.001 (solid), 0.01 (dashed), 0.1 (dashed-dotted) = 0.001 (solid), 2

a (GeV) = 0.0001 (purple), 0.01 (green), 1 (maroon) (purple), 0.01 (green), 1 (GeV) = 0.0001 (GeV), 0.0001 =

h

a a ~ ~ f

under the assumption that a ~

TP m m Ω 6 GeV. For this point, the neutralino relic density computed . /N 9, so the point would be excluded under the assumption that generated in the stau NLSP region is always less than the corr a . f )) = (1000 R ]. Isasugra performs an iterative solution of the MSSM two-l T µ = 8 ( = 172 was recently examined in ref. [ 16 2 t 0 1 h ˜ χ 1 m 0 1 1e+09 1e+10 1e+11 1e+12 versus ˜ χ 001 (solid), 0.01 (dashed) and 0.1 (dot-dashed), and with

1000

2 0.001 .

β,sgn 1e+09 1e+06

R

(dashed-dotted) GeV (dashed-dotted) 10 10 10 10 10 8 10 10 10 10 10

. 10 m 2 100 keV, meaning the bulk of axino DM / exceeds 10 1 /N < a R f T ˜ a – 8 – m vs. m (dashed), 10 12 6 (a) 2 0 10 h m 2 h CDM . We see that for low values of 11 ~ a moves to values higher than 100 keV. At the highest TP Ω 2 (solid), 10 Ω 7 10 (GeV) , which wants to rise with increasing ˜ h a = 100 keV, /N 2 : for this case, the axino mass can drop below 100 keV into /N a m h ˜ a ~ a NTP a = 10 f R f 10 R Ω m T T ˜ a TP WMAP 2 10 h a overlap to within the line resolution). But comparing with f Ω 9 R 0 10 GeV regime, and in fact doesn’t even exceed 10 T -1 -3 -8 -5 -9 -7 -6 -2 -4 -10 6

10

10 10 10 10 10 10 10 10 10

10 h

Ω GeV, axion CDM dominates the relic abundance. In this case, , in contradiction to what is needed to generate large scale s 2 GeV, the DM abundance is dominated by Ω GeV versus PQ breaking scale 11 , we plot again the same quantities as in figure 8 is fixed, this means we can compute the needed value of 11 3 10 R 10 warm × T GeV so they yield consistent baryogenesis mechanisms. In ou < . Axion and TP and NTP axino contributions to dark matter dens ∼ 3 6 10 > ∼ /N In figure Next, we explore the mSUGRA a > needed for each value of = 1 MeV. In the case of ∼ GeV and 10 f /N 7 ˜ a R R )., we see for almost all of this range, a Figure 2 fixed to a value of 100 keV (solid) and 1 MeV (dashed), and we all 10 T of all three components of axion/axino dark matter, while fr to maintain the WMAP measured abundance of CDM. Frame drops. The regioncosmology with for mainly all axion choices CDM of is robust in that it gi the warm DM region, since now axinos will only be a small compo fixed mainly by requiring the total relic abundance saturate and since drop precipitously so that Ω is well below the 10 f m of the universe. An exception occurs in the case of thermal leptogenesis), where for all three cases of is actually approaches a maximum for the case of mainly axion dark matter b T JHEP08(2009)080 ∼ iate ˜ a , high value value m R T R R 003. We T T . = 100 keV old axions turate the ark matter ˜ a = 0 values, along m 2 R h T GeV. 12 ity for (b) ˜ a NTP 6 These values are far 10 05 GeV in the regions 10 . 3 = Ω 0 ∼ 11 ray region is excluded by 2 0. Using these values, we ld a high enough ion. h < 10 (GeV) tral blue regions of the plot ˜ a /N ˜ TP a GeV. In the case of lower , which allows for an increased a µ > 4 f 10 m 2 h 10 10 a ), and then calculate the required . The values range from 10 GeV in the stau co-annihilation > 2 ∼ ˜ a h 9 R at each point in mSUGRA space. We − m is much below T value: Ω 0 1 1 1 3 5 7 4 2 0 6 10 0 1 R ˜ χ

˜

2 NTP χ

T 10 10 10 10 10 10 10 10

R ∼ = 10 and h T (GeV) m R the color-coded regions of β T 4 GeV. While yielding a much higher CDM and 4 2 – 9 – (from Ω h 10 0 1 ˜ a 12 ˜ (a) χ > ∼ 2 10 m = 0, tan h 2 R = 100 keV (solid), 1 MeV (dashed) = 100 keV (solid), : we find ~ a 0 h T R m CDM 11 A ~ a TP T Ω Ω 10 (GeV) /N 2 a h f 10 . 2 h WMAP 10 a ~ a NTP is valid perturbatively only for /N ). We plot in figure Ω Ω . The lower right red region is excluded due to lack of appropr a 2 2 f R 9 h h T 0 10 ˜ -1 TP a -3 -8 -5 -9 -7 -6 -4 -2 -10 ˜ TP a 10

10 10 10 10 10 10 10 10 10 10

we see that the usual regions preferred for neutralino cold d

10 h GeV so that the measured dark matter density is saturated by c

Ω 4 2 is not needed, so long as we know that 12 2 shows the corresponding contours of h ). We will assume equal portions of TP and NTP axinos, which sa 10 (from Ω 5 ˜ TP a × /N . 2 R a . R . Axion and TP and NTP axino contributions to dark matter dens T f T error bars on the WMAP measured Ω = 1 From figure Figure σ The calculation of Ω 3 /N − a Figure 3 versus PQ breaking scale region and in the hyperbolic branch/focus point (HB/FP) reg too small even toaccommodate sustain the electroweak largest baryogenesis. values of The cen actually give the lowest values of with contours of log value of of high EWSB, while the left-sideLEP2 red limits region on yields the a chargino stau mass. NLSP. The g 100 (600) GeV in the stau (HB/FP) regions to values of precision in Ω calculate the sparticle mass spectrum, Ω then determine the necessary value of f than the stau and HB/FP regions, even these regions do not yie (we assume the factor of three downward fluctuation in Ω 1 also adopt mSUGRA parameters value of to sustain non-thermal leptogenesis. JHEP08(2009)080 0. 0. µ > µ > = 10 and = 10 and β β = 0, tan = 0, tan 0 0 A A ields a stau NLSP. The gray region is plane for plane for 2 2 / / 1 1 003. The lower right red region is excluded due 003. . . vs. m vs. m =0 0 0 =0 – 10 – m m ˜ NTP a ˜ a NTP =Ω in the in the =Ω 2 ˜ 2 a R h h T m ˜ TP a ˜ TP a 11, and Ω 11, and Ω . . =0 =0 2 2 h h a a . Contours of constant . Contours of constant Figure 5 Figure 4 We assume Ω We assume Ω to lack of appropriate EWSB,excluded while by the LEP2 left-side limits red on region the y chargino mass. JHEP08(2009)080 . . ˜ ˜ a a 4 0. 6 − m m with 10 µ > values will be 1 × ˜ a R T m = 6 respectively, are precisely 2 3%, since the 0 1 R h ˜ = 10 and χ T ¯ ∼ cally allowed. In f β 400 GeV allow for f ˜ NTP a − n this case we adopt by neutralino CDM! In and 200 0 1 = 0, tan an only sustain 0. In this region, squarks ˜ k point A in table χ ′ ∼ ino three-body decays into 0 ¯ f 2 . A / f 6 ) means the value of 1 µ > − 4 each occur at with the conjecture of thermally m d regions of high 10 − GeV regime: enough to sustain the × µ will be needed. We now see that the 7 500 GeV. LHC collider events should + plane for R µ case. To balance the lower value of =6 most disfavored ∼ 0 1 T 2 / ˜ 4 ˜ χ g = 10 and error bar), and take Ω 1 m β 2 ˜ NTP a 1 TeV and → h will decay into plane for the same parameters as in figure ∼ 0 2 vs. m 0 2 χ 0 2 χ 0 – 11 – / CDM 1 m m = 0, tan and ˜ 006 and Ω and ˜ . 0 − ± 1 A vs. m e (than that used in figure in the =0 χ + move well into the 10 0 2 2 e R h 6 h 0 1 m T GeV. This region of parameter space is usually neglected in ˜ χ 7 ˜ TP a higher, we would need to diminish even further the value of ˜ NTP a exchange. , a much higher value of → R 2 ).) which also diminishes the amount of NTP axino dark matter ∗ T 0 2 b h 2 Z χ = 200 GeV, ˜ TP a 2 / 11, and Ω . 1 m final states. The ˜ =0 plotted in figure 2 ± i h ˜ R χ a ′ T 006 (saturating the WMAP Ω ¯ q . , we again plot the GeV range. The regions with q 6 3 . Contours of constant denotes any SM states whose decay modes are kinemati = 0 f 2 and To push the value of h = 1500 GeV, 0 i values well in excess of 10 ˜ χ 0 ˜ TP a R ¯ q non-thermal leptogenesis mechanism. In fact, the preferre In figure those regions of mSUGRA parameter space that are Ω so that we saturate the CDM abundance with axions. However, i Figure 6 much smaller all over the plane than in the figure this case, the stau and HB/FP regions, preferred in mSUGRA, c m in the 10 and sleptons have mass in the TeV range, while The much smaller value of Ω T in the fixed value of Ω contours of simulation studies for the LHC,produced since it neutralino severely CDM. disagrees For this reason, we list a benchmar where particular, the decays ˜ We assume Ω q thus be dominated by gluino pair production, followed by glu (as suggested by figure decay is dominated by JHEP08(2009)080 0. = /N 0 a A f µ > 100%, . They 9 006 and ∼ . at = 0 = 1000 GeV, ark point A, Z 2 0 0 1 leads to larger plane for = 10 and h ˜ χ m 2 β β / would yield warm ˜ TP a 1 ]. → GeV, while regions ˜ a 0 2 5 . Here, we see much 36 f the PQ scale m 6 χ 10 11, Ω ]. This in turn leads to egion, to below 100 keV GeV, enough to sustain vs. m . = 0, tan onstituted by axions, the − 7 0 35 [ ng decreasingly low values 0 3 m = 0 . A A 6 10 is case, ˜ 2 − m h ∼ signatures [ a 10 . From the figure, it is seen that exchange diagrams, and somewhat R R in the × T T ∗ miss T R plane for A = 30 case are shown in figure T E =6 an mSUGRA benchmark point B with 2 β / in excess of 10 1 1 for the mSUGRA point ˜ NTP a R ˜ a plus T m Z vs. m -channel s 0 – 12 – m = 30. The larger value of tan for the tan 006 and Ω β ˜ a . for the case as shown in figure m ˜ a in the =0 may be generated. To illustrate this graphically, we plot ˜ 2 a m R h m T ˜ TP a required versus GeV. We list in table R 7 T 10 > 11, and Ω . R 2000 GeV can still lead to and calculate the requisite value of Yukawa couplings, and a lower value of T 6 =0 − τ − , we again plot contours of constant 2 shows contours of 8 h 10 0, but this time for tan the value of a 800 values below 100 keV are generated. These low values of 7 and × ˜ a b ∼ 10 . Contours of constant m 0 µ > = 6 = 30 and mainly axion CDM. In this case, as in the case of benchm m It should now be apparent that by conjecturing a large value o Figure In figure The corresponding contours of β ˜ NTP a gluino pair production occurs at a large rate. However, in th so LHC events will be rich in multi-jet plus values of 0 and Figure 7 smaller tan larger rates for neutralino annihilation via range from above 1 GeVin in the the regions stau of co-annihilation and HB/FP r We assume Ω in figure thermally produced axinos. However,temperature since of the the small bulk fraction of of DM axinos is is c not relevant. such that axion CDMof saturates axino the mass, relic large values density, of then by taki lower neutralino relic density values. We again asume Ω Ω the stau and HB/FP regions lead to lower values of with non-thermal leptogenesis. JHEP08(2009)080 0. 0. µ > µ > nce the 11, and that . = 30 and = 30 and β β = 0 2 h a = 0, tan = 0, tan 0 0 . . A A 6 6 DM from neutralino decay. As − − 10 10 × × plane for plane for =6 =6 2 2 0. We assume Ω / / 1 1 ˜ ˜ NTP a NTP a µ > vs. m vs. m 0 0 – 13 – m m 08 GeV, the axino portion of the relic density is . 006 and Ω 006 and Ω . . = 0 = 10 and in the in the =0 =0 ˜ a ˜ 2 a 2 R β m h h T m ˜ ˜ TP a TP a = 0, tan 006. For 0 . 11, and Ω 11, and Ω . . A from this value, the portion of NTP axino DM decreases, and si = 0 =0 =0 ˜ a 2 2 h h m a a ˜ NTP a . Contours of constant . Contours of constant +Ω = 300 GeV, 2 h 2 / 1 ˜ TP a Figure 9 Figure 8 comprised almost entirely of non-thermally produced axino we decrease Ω We assume Ω m We assume Ω JHEP08(2009)080 006 and . = 0 = 1000 GeV, 11, and that 0 . ˜ TP a m = 0 -1 hmark points with 10 2 h a -2 10 4 10 = 0.006 − 2 − h 10 10 -3 ~ a NTP GeV, along with Ω × × Ω 10 5 11 7 . . 2 9 10 -4 × 0. We assume Ω 4 10 10 for the mSUGRA point with − − ˜ a = 5 (GeV) 10 ~ a 10 m µ > 0 0 10 30 m 9.2 6.5 -5 200 300 × 80.0 122.4 /N × 1500 1000 148.7148.0 227.8 227.0 304.5 368.4 112.4 112.8 912.3 774.2 568.2 773.3 a 1500.6 1005.8 1541.1 1178.4 1510.6 912.2 1264.5 965.7 1 10 – 14 – 5 . f . 1 6 GeV. . -6 ) 3 10 = 10 and sγ = 172 needed versus β t → R 2 m -7 b T 11. We take 2 h β ( . ± 1 0 2 0 1 SUSY µ L / R 0 1 1 1 10 ˜ ˜ ˜ ˜ ˜ ˜ ˜ A h u 0 1 t g b χ χ χ e ˜ a ˜ 0 χ m m Ω BF ∆ tan µ m m m m m m m m parameterm m Pt. AA Pt. B = 0 2 -8 = 0, tan h 8 a 2 4 6 10 10 0

10 10 10 10

A 006. 10

R . (GeV) T . We also take 6 =0 − 10 ˜ a NTP . Plot of the value of × . Masses in GeV units and parameters for two mSUGRA model benc +Ω = 300 GeV, =6 2 h 2 / 1 ˜ ˜ NTP a TP a mainly axion CDM: Ω Ω Figure 10 Table 1 Ω m JHEP08(2009)080 , ˜ g ˜ a as q m R ]). → T chance q and es- 29 [ 0 ˜ disfavored a 2000 GeV, m m kawa unified − o problem) for 800 followed by gluino GeV. (In addition, ∼ quark masses which 6 0 values of is proportional to ction experiments will 10 m ctrum of scalars in the ). We find the highest with three components ns are of course model 2 r space most favored by s of thermally and non- h ion CDM allow for lower > R ∼ DM has been put forward axino DM. By combining duction rate, since ˜ T RA model if dark matter is ˜ TP a R e produced additionally via T Ω nos. We have considered this tino problem (which restricts , although it may also occur at R T Yukawa couplings. In this case, a lower GeV) and leptogenesis. While thermal 9 τ 10 < ∼ and b R – 15 – T Yukawa-unified SUSY models. These models — τ − b − GeV (in conflict with the gravitino problem), non-thermal t 9 GeV (far below the usual theory expectations for 10 8 − > ∼ 50. Thus, the mSUGRA model — in contrast to Yukawa-unified R is needed to keep pace. We see in the extreme limit, values of ], or other direct axion detection experiments, stand a good ∼ T R β 37 400 GeV. There are several consequences of this scenario: T − -quark jets is expected in LHC SUSY events. and hence smaller values of b values.) occur in the regions of mSUGRA space which are typically most as low as 10 ), we find mSUGRA with mainly axion CDM prefers 150 β R GeV can be generated (putting us in conflict with the gravitin 15 TeV: much higher than allowed in mSUGRA. Additionally, Yu 2 ˜ a / T R ] in the context of ∼ ] — allows for the possibility of first and second generation s 1 − 10 T m values with fine-tuning considerations (which prefer lower 2 38 m 39 / 5 TeV and re-heat temperatures 1 R of finding an axiondependent. signal. The ultimate axion rate predictio three body decays to charginos and neutralinos. Current and future WIMP direct andlikely indirect find dark null matter results. dete The ADMX [ LHC SUSY events will be dominated by gluino pair production, > T m A related scenario for sparticle spectra with mainly axion C We explored mSUGRA parameter space for regions of high 2 • • • / 3 leptogenesis requires inflaton decay — can allow for successful baryogenesis with in refs. [ leptogenesis — wherein heavy right-hand neutrino states ar Affleck-Dine leptogenesis may occur at these values of sum is constant, the TP portion increases. Since the value of even lower by neutralino CDM. 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