sign in sign up
<<
Home , Saxion

COSMOLOGY OF SUSY DFSZ MODEL

! Kyu Jung Bae, ! Department of Physics and Astronomy, University of Oklahoma ! based on KJB, Baer, Chun 1309.0515, 1309.5365 ! Phenoworkshop@KIAS Nov. 15, 2013 OUTLINE

• Introduction & Motivation

• & Axion DM

• Cosmology of SUSY DFSZ

• Summary SUSY & PQ Higgs discovery & Gauge hierarchy: m =125.8 0.5 (stat) 0.2 (syst) GeV (CMS) H ± ± 126.8 0.2 (stat) 0.7 (syst) GeV (ATLAS) ± ± At the quantum level, ⇤2 H 2 ⇠ cuto↵| | Introducing SUSY, it is removed, m2 log ⇤2 H 2 ⇠ soft | | Strong CP-problem:

2 gs a ˜aµ⌫ QCD θ-term, ✓ = ✓ Gµ⌫ G ✓(E B) L 32⇡2 ) · 11 From EDM, ✓ < 10 a g2 = + ✓ s Ga Gaµ⌫ With Peccei-Quinn symmetry, L f 32⇡2 µ⌫ ✓ a ◆ 2 2 e f⇡m⇡ 2 2 V = mu + md +2mumd cos(a/Fa + ✓) mu + md q a/F + ✓ =0 h a i μ-problem of MSSM:

WMSSM = µHuHd + Yukawas μ-term is supersymmetric; basically fundamental scale, Λ. For the natural EWSB, μ is required to be 100 GeV order. Howard Baer’s talk

SUSY DFSZ realization of μ-term: assigning PQ charges to Higgs multiplets (S, H H )=(1, 2) u d to forbid bare μ-term. Instead,

2 S A/vP Q WKN = HuHd with PQ breaking field, S = vPQe MP

2 10 2 vPQ 10 GeV µ 18 100 GeV Kim-Nilles mechanism! ⇠ MP ⇠ 10 GeV ⇠ NEUTRALINO & AXION 2 DM candidates: neutralino & axion 5

0.64 0.16 events from ER leakage are expected below are- obtainedneutralino for each WIMP DM mass fromin fullMSSM: simulations. admixture of bino, wino and the NR± mean, for the search dataset. The spatial distribution of the events matches that expected from the ER backgrounds in full detector simulations. We select constrains the size of mixing the upper bound of 30 phe (S1) for the signal estimation ) 2 analysis to avoid additional background from the 5 keVee Z1 B,W Hu,d Z1 x-ray from 127Xe. X X −44 10 1.3 keV 2.6 ee e e f e e 1.8 h 2.4 6 8 10 12

2.2 −40 10 cross section (cm − 2 3.5 −45 q q 4.6 10 −42 WIMP 10 1.8 5.9 7.1 /S1) x,y,z corrected b favors more mass gap between 1.6 −44 10 (S2 1 2 3 10 10 10 10 1.4 2 higgsinos and log m (GeV/c ) WIMP 1.2

3 6 9 12 15 18 21 24 27 30 keV FIG. 5. The LUX 90% confidence limit on the spin- 1 nr 0 10 20 30 40 50 independent- LHC elastic search WIMP-nucleon limit cross for section (blue), (m g˜ 1 . 4 TeV ) pushes up the S1 x,y,z corrected (phe) together with the 1 variation from repeated trials, where & trials fluctuating below± the expected number of events for FIG. 4. The LUX WIMP signal region. Events in the zeromasses BG are forced (under to 2.3 (blue shaded).assumption We also show of gaugino unification) 118 kg fiducial volume during the 85.3 live-day exposure are Edelweiss II [41] (dark yellow line), CDMS II [42] (green line), shown. Lines as shown in Fig. 3, with vertical dashed cyan ZEPLIN-III [43] (magenta line) and XENON100 100 live- lines showing the 2-30 phe range used for the signal estimation day- [44] prefers (orange line), andHiggsino-like 225 live-day [45] (red line) neutralino results. analysis. The inset (same axis units) also shows the regions measured from annual modulation in CoGeNT [46] (light red, shaded), along with exclusion limits from low threshold re-analysis of CDMS II data [47] (upper green line), 95% allowed Confidence intervals on the spin-independent WIMP- region from CDMS II silicon detectors [48] (green shaded) nucleon cross section are set using a profile likelihood and centroid (green x), 90% allowed region from CRESST ratio (PLR) test statistic [35], exploiting the separation II [49] (yellow shaded) and DAMA/LIBRA allowed region [50] of signal and background distributions in four physical interpreted by [51] (grey shaded). quantities: radius, depth, light (S1), and charge (S2). The fit is made over the parameter of interest plus three Gaussian-constrained nuisance parameters which encode The observed PLR for zero signal is entirely consistent uncertainty in the rates of 127Xe, -rays from internal with its simulated distribution, giving a p-value for the components and the combination of 214Pb and 85Kr. background-only hypothesis of 0.35. The 90% C. L. The distributions, in the observed quantities, of the four upper limit on the number of expected signal events model components are as described above and do not ranges, over WIMP masses, from 2.4 to 5.3. A variation vary in the fit: with the non-uniform spatial distributions of one standard deviation in detection eciency shifts of -ray backgrounds and x-ray lines from 127Xe obtained the limit by an average of only 5%. The systematic from energy-deposition simulations [31]. uncertainty in the position of the NR band was estimated The energy spectrum of WIMP-nucleus recoils is by averaging the di↵erence between the centroids of modeled using a standard isothermal Maxwellian velocity simulated and observed AmBe data in log(S2b/S1). This distribution [36], with v0 = 220 km/s; vesc = 544 km/s; yielded an uncertainty of 0.044 in the centroid, which 3 1 ⇢0 =0.3 GeV/c ; average Earth velocity of 245 km s , propagates to a maximum uncertainty of 25% in the high and Helm form factor [37, 38]. We conservatively model mass limit. no signal below 3.0 keVnr (the lowest energy for which The 90% upper C. L. cross sections for spin- direct NR yield measurements exist [30, 40]). We do independent WIMP models are thus shown in Fig. 5 46 2 not profile the uncertainties in NR yield, assuming a with a minimum cross section of 7.6 10 cm for a model which provides excellent agreement with LUX WIMP mass of 33 GeV/c2. This represents⇥ a significant data (Fig. 1 and [39]), in addition to being conservative improvement over the sensitivities of earlier searches [42, compared to past works [23]. We also do not account 43, 45, 46]. The low energy threshold of LUX permits for uncertainties in astrophysical parameters, which are direct testing of low mass WIMP hypotheses where beyond the scope of this work. Signal models in S1 and S2 there are potential hints of signal [42, 46, 49, 50]. DM: ⌦ h2 0.10 (µ/1 TeV)2 H ⇠ For µ = 150 GeV , Higgsinoe DM is less than 10% of the total DM.

1.19 Axion DM: 2 2 Fa ⇤QCD Turner; KJB, Huh, Kim; 13 ⌦ah =0.18 ✓1 12 10 Gev 400 MeV Visinelli, Gondolo ✓ ◆ ✓ ◆ ma !eV" 10!3 10!4 10!5 10!6 10!7 10!8 10!9 T = T1 1.0 R˙ 3 m R ⇠ a 0.8

0.6 ! "!

Π a CDM # i Θ 0.4 axion can be !a #!CDM sizable DM component 0.2 for proper θ1 and fa 0.0 109 1010 1011 1012 1013 1014 1015 1016 ! " fa GeV Visinelli and Gondolo

FIG. 2: The misalignment angle θi necessary for the axion to be 100% of the cold dark matter in

17 Scenario II (fa >HI/2π), as a function of fa.Abovethecurve,Ωa > ΩCDM.Forfa > 10 GeV, ∼ 17 3/4 19 one has θi 0.001(fa/10 GeV)− ;inparticular,forfa > 10 GeV, the initial misalignment ≃ ∼ 5 angle θi has to assume values θi < 10− . ∼ > 17 < 10 < For fa 10 GeV (ma 10− eV or θi 0.001), one has f(θi) 1andEq.(50) ∼ ∼ ∼ ≃ simplifies to 3/4 3 fa − 17 θ 0.84 10− , for f > 10 GeV, (51) i ≃ × 1017 GeV a ! " ∼ or 3/4 3 ma 10 − < − θi 1.2 10 10 , for ma 10 eV. (52) ≃ × 10− eV ∼ > 19 # $ In particular, for fa 10 GeV, the initial misalignment angle θi has to assume values ∼ 5 θi < 10− .Thiswasalsonotedin[17,28].Thesesmallvaluesofθi may be uncomfortable ∼ in a cosmological scenario. In the other limit of θ π,theformofthefunctionf(θ )assumedinEq.(40)gives i ≃ i eπ C/fa < 10 π θi e− , for fa 2 10 GeV, (53) − ≃ 2 ∼ × with C =7.48 1010 GeV. So, as θ approaches π from below, the corresponding f ap- × i a proaches 0. This gives rise to the linear dependence of fa on HI in the lower left corner of Keys for the DM cosmology: - 2 DM components: Higgsino-like neutralino and axion - not a simple composition; supersymmetrization the axion sector 1 2 a A = (s + ia)+p2✓a˜ + ✓ A ! p2 F long-lived saxion/ production & decay affect DM density

What we do: - Extensive study of saxion & axino decay: including all tree-level processes - Consider the DM re-annihilation from both saxion & axino decay - Dark Radiation and entropy are also considered - DM density is calculated depending on PQ parameters a" SUA 1000

100 " f !1010 GeV 10 a GeV ! ! 12 ã fa 10 GeV D

T 1 14 fa!10 GeV 0.1

0 2 4 6 8 10

mã !TeV" b" SOA 106

104 " 10 fa!10 GeV

GeV 100 ! ! 12

ã fa 10 GeV D

T ! 14 1 fa 10 GeV

0.01 0 2 4 6 8 10

mã !TeV"

12 Figure 6: Axino decay temperature for fa = 10 GeV and for a) SUA and b) SOA benchmark points. Previous studies for KSVZ model: - Effectiveanomaly interaction: interaction of dimension 1-loop 5: suppressed √2α = s d2θAW aW a +h.c. Lanomaly − 8πf a ! α [γµ, γν] = s sGa Gaµν ia˜¯ γ g˜aGa + . (5.2) 8πf µν − 2 5 µν ··· a " # - DueThis to higher the dimensionalderivative couplings coupling, lead to thermallyproduction produced of saxion saxion and axino & axino densities which are proportional to the reheat temperature TR. proportionalIn contrast, to T theR. axion supermultipletCovi, Kim, in Kim, the Roszkowski; SUSY DFSZ Brandenburg, model Steffen; has Yukawa-typeStrumia; Graf, Steffen (dimension 4) interactions as shown in Eq. (1.4). As a consequence, the most important - Saxioncontributions can have for the coherent saxion and axino oscillation. production arise near the kinematic thresholds of 12 2 2 TP scatteringTP processes6 10 leadingGeV to thermalTR production densitiesmin[ whichTR,T ares] independentfa of TR GeV Y Y 10 CO 5 s a˜ 8 Ys 10 ⇠ ⇠ fa 10 GeV ⇠ 108 GeV 1012 GeV m ✓ ◆ ✓ ◆ ✓ ◆✓ ◆ ✓ s ◆

- For very high TR, thermally produced saxion (also CO) & axino – 14 – can dominate the univ. - Late decays of saxion & axino produce DM, DR and entropy and constrained by DM density, DR and BBN. Choi, Kim, Lee, Seto; Baer, Lessa, Rajagopalan, Sreethawong; Baer, Lessa, Sreethawong; Moroi, Takimoto; Choi, Choi, Shin, KJB, Baer, Lessa; Graf, Steffen Brief History of the early Universe:

TR Tfreezeout T1 TBBN 106 GeV 10 GeV 1 GeV 1 MeV

inflation ends neutralino axion CO BBN decoupling starts s aa can contribute Ne↵ ! saxion decay dilutes ⇢ saxion/axino decays Z1 have no effect axino decay feeds saxion decaye dilutes axion CO

saxion/axino decays modify BBN KSVZ case: For higgsino-like neutralino DM

104 103 Xe100 Excluded 2 2 10 ~ (Z h > 0.026) 10 1 1 10-1 10-2 MSSM 2 -3 ~ h 2 10 Z1 -4 h

1 10 ~ Z 10-5 BBN Allowed 10-6 10-7 BBN Excluded 10-8 Neff > 1.6 10-9 10-10 10-11 10-12 109 1010 1011 1012 1013 1014 1015 1016 f a (GeV) KJB, Baer, Lessa SUSY DFSZ Interactions: - tree-level Yukawa-type interaction from superpotential; µ Hu Hu d2✓ eA/vPQH H a˜ s v u d Z PQ e e Hd Hd - At the 1-loop level; e Hu W Hu W a˜ s e × f e × H d W Hd W

2 2 e µ 2 µ 1PI amplitude is suppressed; 1PI ln A / E2 E2 KJB, Choi, Im ✓ ◆ - Tree-level processes are dominant for prod’n and decay. Production of saxion and axino: - Heavy decay, inverse decay and scattering processes are all comparable and dominant at T~TeV. 2 12 2 TP TP 7 µ 10 Gev Y Y 10 a˜ s Chun; KJB, Choi, Im; ⇠ ⇠ TeV fa ⇣ ⌘ ✓ ◆ KJB, Chun, Im - No TR dependence if TR>>μ. - No TP saxion/axino domination era. - Saxion CO can also exist (same as KSVZ); CO saxion domination is possible. Decay of saxion and axino: determines DM, DR, entropy s hh, V V, : contributes entropy prod’n. ! ··· s ZZ, W W, a˜a,˜ : contributes neutralino density. ! ··· s aa : contributes dark radiation. ! e e ff a˜ Zh, W ±H⌥, : contributes neutralino density. ! ··· e f Benchmark study: - MSSM benchmark point for RNS with Higgsino-like LSP.

SUA (RNS2) SOA (mSUGRA)

m0 7025 3500 m1/2 568.3 500 A0 -11426.6 -7000 tan β 8.55 10 µ 150 2598.1 mA 1000 4284.2 mh 125.0 125.0 mg˜ 1562 1312 mu˜ 7021 3612

mt˜1 1860 669 m 135.4 224.1 Z1 Ωstdh2 0.01 6.8 Z!1 SI 8 12 σ (Z1p)pb 1.7 10− 1.6 10− ! × × Table 1: Masses and parameters in GeV units for two benchmark points computed with Isajet 7.83 ! - Heavy enoughand using mgravitinot = 173.2 GeV. that is irrelavent for cosmology.

masses and direct detection cross sections are listed in Table 1. It has very low electroweak fa,ma˜,ms - implicationfinetuning. for varying PQ parameters, For the SOA case, we adopt the mSUGRA/CMSSM model with parameters

(m ,m ,A, tan β,sign(µ)) = (3500 GeV, 500 GeV, 7000 GeV, 10, +) (2.2) 0 1/2 0 − The SOA point has m =1.3 TeV and m 3.6 TeV, so it is just beyond current LHC g˜ q˜ ≃ sparticle search constraints. It is also consistent with the LHC Higgs discovery since mh = 125 GeV. The lightest neutralino is mainly bino-like with m = 224.1 GeV, and the Z1 standard neutralino thermal abundance is found to be ΩMSSMh2 =6.8, a factor of 60 Z1 ! ∼ above the measured value [29]. Due to its heavy 3rd generation squark masses and large µ parameter, this point has very high electroweak finetuning! [30].

3. Decay of saxion

In this section, we present simplified formulae for the partial decay widths of saxions. These widths play an essential role in determining the cosmic densities of mixed axion/neutralino cold dark matter. Since the saxion mixes with CP-even Higgs , h and H, it has similar decay channels via a tiny mixing coupling proportional to µ/f . The couplings ∼ a can be extracted by integrating Eq. (1.4). We list all the possible saxion decay channels in the following.

s hh / HH / hH / AA / H+H . • → − The saxion decays to pairs of Higgs states arise from the saxion trilinear interaction as well as its mixing in Eq. (1.4). For a very heavy saxion, the mixing effect can be safely neglected and the partial decay widths, neglecting phase space factors (these

–4– Decays of Saxion: 12 a SUA, fa#10 GeV, Ξ#1, mã#2 TeV higgses 0.01 gauge bosons "

" 10!5 X

" s ! 10!8 BR 10!11

10!14 axinos 0 2 4 6 8 10

ms TeV

SUA, mã!2 TeV 104 ! "

10 1000 fa!10 GeV, Ξ!1

12 " 100 fa!10 GeV, Ξ!1

14 GeV fa!10 GeV, Ξ!1

! 10 s D f !1010 GeV, Ξ!0 T 1 a 12 0.1 fa!10 GeV, Ξ!0 14 0.01 fa!10 GeV, Ξ!0 0 2 4 6 8 10

ms TeV

! " Decays of Axino: 12 a SUA, fa#10 GeV 1

0.01 " neutralino and neutral Higgs "

X and charged Higgs "

ã !4

! 10 neutralino and Z

BR chargino and W boson !6 10 and

0 2 4 6 8 10

mã TeV a SUA 1000 ! "

100 " " f !1010 GeV 10 a GeV ! 12

ã fa!10 GeV D

T 1 14 fa!10 GeV 0.1

0 2 4 6 8 10

mã TeV

! " Dark Matter:

a SUA, ms#mã#5 TeV 103

100 2 " "h neutalino; Ξ#1 10 "h2 axion; Ξ#1 2

h 1 "h2!neutalino; Ξ#0" " 2 0.1 "h !axion; Ξ#0" "h2#! 0.12 " 0.01 "h2#! 0.026 " 10!3 109 1010 1011 1012 1013 1014 1015 1016

fa GeV

! " Dark Radiation: from s aa !

SUA, Ξ"1, ms"5 TeV 1000

10

#Neff 0.1 r

#Neff"1.6 0.001

109 1010 1011 1012 1013 1014 1015 1016

fa GeV

! " Depending on fa: 10 12 - Low fa region: 10 GeV

12 13 - Intemediate fa region:10 GeV

13 16 - High fa region: 10 GeV

−41 10 50< <100 ∆EW <50 ∆EW Z B,W H Z −42 Xe−100 1 u,d 1 10 LUX300 X X SuperCDMS150kg Xe−1Ton

e e f e e −43 ) 10 h 2

−44 10 )(cm p

q q 1

˜ −45 Z 10 ( SI

−46 ξσ 10

−47 10

−48 10 100 150 200 250 300 350 m(higgsino) (GeV) Baer, Barger, Mickelson SI Figure 2: Plot of rescaled higgsino-like WIMP spin-independent direct detection rate ξσ (Z1p) ! versus m(higgsino) from a scan over NUHM2 parameter space with ∆EW < 50 (red crosses) and ∆EW < 100 (blue dots). Green points are excluded by current direct/indirect WIMP search experiments. We also show the current reach from Xe-100 experiment, and projected reaches of LUX, SuperCDMS 150 kg and Xe-1 ton.

6 Detection ofAxion axion: Haloscope Dark Matter Axions will convert to in a magnetic field.

The measurement is enhanced if the 's frequency corresponds to the cavity's resonant frequency.

See: Sikivie, Phys. Rev. Lett. 1983

Rybka’s Talk at Cosmic Frontier You2013 Want: You Don't Want: -Large Cavity Volume -High Thermal Noise -High Magnetic Field -High Amplifier Noise -High Cavity Q

Gray Rybka – Mar. 2013 3/53 SUMMARY

- SUSY DFSZ model is well-motivated: - gauge hierarchy prob./strong CP prob./mu prob. - Dark matter candidate: neutralino & axion - 2 DM candidates: - Higgsino-like neutralino: underabandant - coherent oscillation of axion - Long-live saxion & axino: 2 - thermal prod’n differs from KSVZ: Y (µ/fa) / - late decay produces neutralino, dark radiation & entropy - Mixed neutralino/axion DM: 10 13 - 10 GeV