COSMOLOGY OF SUSY AXION MODELS
Kyu Jung Bae,
Department of Physics and Astronomy, University of Oklahoma
Cosmic Frontier Workshop, SLAC National Accelerator Laboratory, March 6, 2013 OUTLINE
• Introduction
• Saxion cosmology
• Axino cosmology
• Summary and Implications FINE-TUNING IN SM
Gauge Hierarchy Problem: In the SM, m2 ⇤2 ( M 2 or M 2 ) h ⌧ ⇠ GUT Planck Quantum correction on Higgs mass is quadratically divergent, 3 2 m2 = m2 t ⇤2 + h 0 8⇡2 ··· Introducing SUSY,
3 2 ⇤2 m2 = m 1 t ln + h soft 8⇡2 m ··· ✓ soft ◆ Volume 88B, number 1, 2 PHYSICS LETTERS 3 December 1979
CHIRAL ESTIMATE OF THE ELECTRIC DIPOLE MOMENT OF THE NEUTRON IN QUANTUM CHROMODYNAMICS
R.J. CREWTHER, P. DI VECCHIA and G. VENEZIANO CERN, Geneva, Switzerland and E. WITTEN L yman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA
Received 7 September 1979
Current algebra for CP violating strong interactions is investigated. In particular, the neutron electric dipole moment Dn is shown to behave as Om~ In m~ for small pmn mass m n and CP violating parameter 0. This logarithm is exphcitly calculable: it contributes 5.2 × 10-160 cm to D n. This result is somewhat larger than a previous O(m2n) estimate based on the bag model.
In the last few years, it has been realized [1] that violating meson decays and pion-nucleon couplings, the usual lagrangian of quantum chromodynamics our most interesting current algebra theorem concerns (QCD) * 1 the electric dipole moment of the neutron, since it is here that a 0 dependent effect may be observable. ./2 = - ~ F 2 + ~ ~lk(iD - rag) qk, (I) When the up and down quark masses m u and m d are k very small (but not zero), the contribution of 0 to the can be generalized by including an additional P and CP neutron electric dipole moment D n can be calculated violating interaction: exphcitly, with no undetermined parameters. Instead of being proportional to m~ for small m u and m d , as -~ Z?QCo = Z?- O(g2/327r2)F.F*. (2) Strong CP problem: one might expect, D n actually behaves as m 2 In m 2. 2 Despite its being a total divergence, this additional inter- The coefficient of the logarithmically enhancedg sterm a ˜aµ⌫ action modifies the physics of strong interactions. is uniquelyQCD fixed θ by-term, current algebra, ✓as =in similar✓ 2 Gµ⌫ G The purpose of this paper is to investigate the cur- examples [3] of non-analytic deioendenceL on32 m 2.⇡ The rent-algebraic consequences of the CP violating param- logarithm comes from the p~r- intermediate states eter 0 being small but not zero. Using an effective showngenerating in fig. 1. CP-violating interaction, lagrangian originally derived by Baluni [2], we will Crewther et al. show that, to lowest order in chiral symmetry breaking, 16 (1979) Dn =5.2 10 ✓ ecm many O-dependent QCD amplitudes can be explicitly ⇥ calculated by means of current algebra. Although we will also consider processes such as CP Experiment:
26 11 Dn < 2.9 10 ecm ✓ . 10 ,1 Notation: gauge covariant derivative D. and field-strength , 1 r- ⇥ ) tensor F~uv, dual tensor F/~z, = ~et~vodF°t.a,with eo123 = +1 and Bjorken-Drell conventions for metric and ~/-matrices, Fig. 1. Mechamsm responsible for the 0 (m~r2 In mlt2 ) contribution topological charge [1] (g2/32,r2)fdaxF.F*, quark fields to theIntroducing electric dipole moment ofanomalous the neutron. The dark blobU(1) PQ symmetry, qk (or u, d, s,..) with flavour index k and mass parameters indicates a CP violating ~NN interaction reduced by the param- mk >O. eter 0. 2 gs a a ˜aµ⌫ 2 Gµ⌫ G 123 L 3 32⇡ fa Dynamical relaxation of θ, a + ✓ =0 f Peccei and Quinn ⌧ a Combining SUSY & PQ naturally solves GH & strong CP prob. SUSY AXION Axion supermultiplet contains
s + ia 2 A = + p2✓a˜ + ✓ A p2 F saxion, axion and axino.
p Interactions: vPQ = fa/ 2
⇠ 4 = d ✓A†AA +h.c. ; s aa, a˜a˜ L 2v ! PQ Z ↵s = d2✓AW aW a +h.c. ; s gg, g˜g,˜ a˜ gg˜ L 8⇡2v for KSVZ PQ Z ! ! µ 2 = d ✓AHuHd +h.c. for DFSZ ; s hh, a˜ ˜h L v ! ! PQ Z 9 12 Typical axion window: 10 GeV . vPQ . 10 GeV v 1016 GeV ✓ << 1 (But larger PQ ⇠ if i ) ⇒ tiny interactions, long life-time Negligible for LHC, but important for Cosmology SAXION COSMOLOGY Mass of Saxion: SUSY (holomorphicity) complexifies U(1): m m m TeV Saxion mass from SUSY breaking, s ⇠ 3/2 ⇠ soft ⇠
m m TeV For GMSB, saxion mass is generated by higher loops, s ⌧ soft ⇠ Production of Saxion: DFSZ µ by thermal scattering (KSVZ): / TP 12 2 ⇢s 5 6 1.01 10 GeV TR 1.33 10 g ln m s ' ⇥ s g f 108 GeV s ✓ s ◆✓ a ◆ ✓ ◆ Graf and Steffen by coherent oscillation:
TP 2 2 ⇢s 5 min [TR,Ts] fa s0 1.9 10 GeV s ' ⇥ 108 GeV 1012 GeV f ✓ ◆✓ ◆ ✓ a ◆ Decay of Saxion: Ichikawa, Kawasaki, Nakayama, Senami, Takahashi; Moroi, Takimoto; Choi, Choi, Shin; KJB, Baer, Lessa; Jeong, Takahashi; s aa Graf, Steffen If the dominant mode is ! ⇒ provides the dark radiation, constrained by CMB data.
N⌫ . 1.6
1016 1016
6 s0 = fa GeV) s0 = MP/100 1015 = 10 1015 > 1.6 (T R Neff 1014 10 GeV) 1014 = 10 R > 1.6 (T 1013 Neff 1013
(GeV) (GeV) 6 a 12 a 12 GeV)
10f 10f
= 10 10 GeV) R 11 11 10 10 = 10 > 1.6 (T R N eff 1010 = 1 1010 = 1 > 1.6 (T eff N
1 10 102 103 104 105 1 10 102 103 104 105 ms (GeV) ms (GeV) KJB, Baer, Lessa
f 1012 GeV 1013 GeV Similar to axion CDM, a . If the dominant mode is s gg( ) ! ⇒ produces large amount of entropy, dilutes existing relics
For, 1 MeV . T D . 1 GeV , CO axion is diluted. 15 ⇒ large PQ scale is allowed, f a . 10 GeV (for ✓ i 1 ) Lazarides, Schaefer, Seckel, ⇠ Shafi; Kawasaki, Moroi, For longer life-time, important constraints are Yanagida
dominant s aa no s aa ! ! Kawasaki, Nakayama, Senami If saxion is heavy enough to decay into sparticles, it also Figurecontributes 10: Cosmological neutralino constraints abundance. on the saxion abundance as a function of saxion 10 mass mσ for Fa =10 GeV in the KSVZ model ((a) and (b)) and DFSZ model ((c) and (d)). In (a) and (c), the saxion decay into axions is assumed to be unsuppressed. In (b) and (d), it is assumed to be suppressed. See [126] for more detail.
> 12 τσ 10 sec : Injected photons should not ionize the neutral hydrogen toomuch, • ∼ which would otherwise leads to too early epoch of reionization. Figure 10: Cosmological constraints on the saxion abundance as a function of saxion 10 mass m>σ for17Fa =10 GeV in the KSVZ model ((a) and (b)) and DFSZ model ((c) and τσ 10 sec : The saxion abundance itself should not exceed the observed DM (d)).• In∼ (a) and (c), the saxion decay into axions is assumed to be unsuppressed. In (b) and (d),abundance. it is assumed to be suppressed. See [126] for more detail. These set bound on the saxion abundance and reheating temperature for every mass > 12 τσ 10 sec : Injected photons should not ionize the neutral hydrogen toomuch, range• of∼ the saxion. Figure 10 shows cosmological constraints on the saxion abundance which would otherwise leads to too early epoch of reionization. for a wide range of the saxion mass. For more details on these constraints, see [126] and > 17 referencesτσ 10 therein.sec : The saxion abundance itself should not exceed the observed DM • ∼ Forabundance. Models B and C, the saxion is likely trapped at the origin φ =0duetothermal eTheseffects in set KSVZ-type bound on models. the saxion In this abundance case, thermal and reheating inflation temperat [131] takesure place for every because mass of therange potential of the saxion. energy V Figure( φ = 10 0). shows After cosmological thermal inflation, constraints the saxion on t oscillationhe saxion abundance dominates | | thefor a Universe wide range and of its the decay saxion causes mass. the For reheating. more details Cosmological on these const implicraints,ations see of [126] such and a references therein. For Models B and C, the saxion is likely32 trapped at the origin φ =0duetothermal effects in KSVZ-type models. In this case, thermal inflation [131] takes place because of the potential energy V ( φ = 0). After thermal inflation, the saxion oscillation dominates | | the Universe and its decay causes the reheating. Cosmological implications of such a
32 AXINO COSMOLOGY Production of Axino: by thermal scattering (KSVZ): by thermal scattering and decay (or inverse decay) (DFSZ): ⇢a˜ 5 6 3 0.9 10 gs ln s ' ⇥ gs 11 2 2 ✓ ◆ ⇢a˜ 5 10 GeV µ 12 2 10 ma˜ 10 GeV TR s ⇠ fa 1 TeV 8 ma˜ ✓ ◆ ⇣ ⌘ ⇥ fa 10 GeV Chun; KJB, Choi, Im; KJB, Chun, Im ✓ Covi,◆ Kim,✓ Kim, Roszkowski;◆ 103 105 107 109 1011 −2 Brandenburg, Steffen; Strumia 10 #scattering!Higgs"gauge# Μ!1 TeV
#scattering!Higgs"top# mHu !100 GeV #Higgsino decay mH !500 GeV 10#2 d 10#2 −4 mst!1.5 TeV 10 mã!100 GeV 11 vPQ!10 GeV 10#4 10#4
−6 ã
10 Y 10#6 10#6
−8 10 10#8 10#8
−10 10 4 6 8 10 12 10 10 10 10 10 103 105 107 109 1011 Brandenburg, Steffen TR in GeV
FIG. 4: The axino yield from the scattering diagrams in Fig. 2 (blue line), the scattering diagrams in Fig. 3 (red line), and the decay H˜ Ha˜ (green line). →
103 105 107 109 1011
#scattering!Higgs"gauge# Μ!1 TeV
#scattering!Higgs"top# mHu !100 GeV #Higgsino decay mH !500 GeV 10#2 d 10#2 mst!300 GeV mã!100 GeV 11 vPQ!10 GeV 10#4 10#4 ã Y 10#6 10#6
10#8 10#8
103 105 107 109 1011
TR in GeV
FIG. 5: Same as in Fig. 4 but with the parameter choice allowingaresonantaxinoproductionin the channel of Fig. 3(b)
8 Non-thermal production from out-of-equilibrium decay e.g. s a˜a,˜ ˜ a˜ ! ! Mass of Axino: mass generated by SUSY breaking, ma˜ m3/2 ⇠ It is highly model-dependent, and can be as light as keV or lighter. Chun, Kim, Nilles LSP Axino: non-LSP Axino: (hot/warm/cold) DM, decay after LSP freeze-out NLSP decay modifies feeds neutralino abundance: cosmological observables PQ augmented DM, (like saxion), possible entropy production
SuperWIMP scenario Choi, Kim, Lee, Seto; Baer, Lessa, Sreethawong; Rajagopal, Turner, Wilczek; Covi, Kim, Roszkowski; Chun; KJB, Chun, Im Feng, Rajaraman, Takayama; Kawasaki, Kohri, Moroi; Jedamzik, Lemoine, Moultaka; Baer, Box, Summy; Choi, Choi, Shin In any case, CO axion can be a (dominant) part of DM. Axino DM: Choi, Choi, Shin Produced by late decay of saxion Axino contributes to the warm dark matter,
FS =0.2 1.3MPc i.e. 4 ma˜ =0.25ms neglected in our discussion, because we assume that the 13.5 axion has a very small mass as that of the usual QCD 1.5 −6 12 6 4 axion, ma 6 10 eV(10 GeV/Fa). For the KSVZ 10 sec 10 sec type axion∼ model× [26], the above terms are enough, while for the DFSZ type axion model [27], saxion can have siz- 13.0 0.5 able couplings to the SM fermions which are charged un- Λ"0.1 der U(1)PQ.HerewetaketheKSVZtypemodelasour example, in which the SM fermions are not PQ charged, Fa GeV Λ"0.2 and so their couplings to saxion and axion can be ignored. 10 12.5 In the limit ms m, saxions decay dominantly to axion pairs with a decay# rate Log 0.001
3 CMB 1 ms Γ(s 2a) 2 , (20) → % 64π Fa 12.0 0.01 1.3 Mpc 0.2 Mpc BBN yielding the saxion lifetime
−3 2 #2.0 #1.5 #1.0 #0.5 0.0 0.5 1.0 5 ms Fa τ 1.3 10 sec . (21) mS s 12 Log % × 100 MeV 10 GeV 10! " ! " # $ GeV The saxion field is initially displaced from the present vacuum value, and starts oscillation at the moment when FIG. 2: Contour plots of ∆Neff and λFS in the (ms,Fa)plane the expansion rate H ms. If it happens before the with other cosmological constraints. Here we used TR =5× ∼ 5 reheating after inflation, the energy density to entropy 10 GeV, m/ms =0.25. Blue lines denote ∆Neff =0.5, 1.5. density ratio, which is constant during the radiation- Red lines show λFS =0.2, 1.3Mpc. Blacklinescorrespondto TP 2 dominated epoch, is given by thermal production of the axino Ωa˜ h =0.001, 0.01. Brown lines denote the lifetime of the saxion 104 sec, 106 sec. The 2 NTP 2 ρs −8 TR Fa horizontal magenta (dotted) lines represent Ωa˜ h =0.1 = msY =2.2 10 GeV, s s × 106 GeV 1012 GeV for λ =0.1, 0.2respectively.ThegreenlineshowstheBBN # $# $ (22) (solid) and CMB (dashed) constraint and the lower region is allowed. where we used the initial displacement of the saxion δs % Fa.WethenfindfromEq.(6)that∆Neff at the time of 0.2. Therefore in the overlapped region of blue and red saxion decay is given by bands, which corresponds to 100MeV ! ms ! 1GeVand 12 13 3/2 3 3 10 GeV ! Fa ! 10 GeV, both dark radiation and 100 MeV F TR × ∆N =0.056 a . small scale structure problems can be explained with cor- eff m 1012 GeV 106 GeV # s $ # $ # $ responding value of λ between 0.1and0.2 respectively. (23) In this region the relic density of the thermally produced axinos is less than about 10 % of dark matter (black solid The saxion also produces axinos with decay rate line), thus most of the axino dark matters are produced 3 2 from saxion decays. λ2m2m 4m2 / Γ(s a˜a˜)= s 1 , (24) The decay of saxions can produce electromagnetic and → 32πF 2 − m2 hadronic particles which can disrupt the light element a % # s $& abundances after BBN. The lifetime of saxion in the re- for which the branching ratio is given by gion of our interest is between 104 and 106 sec. In Fig. 2, we show the BBN and CMB bound with green lines [28] 2 2 2 3/2 2λ m 4m and the upper region is disallowed. In this region, the fm 1 . (25) % m2 − m2 constraints on the hadronic and electromagnetic injec- # s $# s $ tions lead to Such non-thermally produced axinos play the role of ρs −14 ρs −6 −13 warm dark matter and can solve the small scale struc- Bh ! 10 GeV,Bem ! 10 10 GeV, s s − ture problems as explained in the previous section. (26) In Fig. 2, we show the viable region in the plane of ms and Fa for m/ms =0.25 and the reheat temper- where Bh and Bem denote the branching ratios for the 5 ature TR =5 10 GeV of the primordial inflation. hadronic and electromagnetic injections. These con- × The blue lines denote ∆Neff =0.5 and 1.5, while the straints can be easily satisfied if the saxion mass is below red lines stand for λFS =0.2and1.3Mpc. On the the pion production threshold ms < 2mπ. dashed Magenta line, axinos produced by saxion decays For the axino mass much smaller than the value of constitute most of the dark matter for λ =0.1and (0.1)ms, the branching fraction (25) might be too small O Decaying Axino: Axino decay after neutralino freeze-out enhance DM abundance.
without axino decay with axino decay 1000 1000 1000 !8 10 mA"300 GeV mA!300 GeV mA!300 GeV M2"2 TeV M2!2 TeV M2!2 TeV tanΒ"10 Mã!500 GeV Mã!500 GeV !7 12 12 800 10 800 vPQ!10 GeV 800 vPQ!10 GeV tanΒ!10 tanΒ!10 0.01 0.1 1
1 600 0.1 1 600 1 600 !7 Axino LSP Axino LSP 10 10!8 M M M 10#7 0.01 # 400 400 400 10 5 10#6 1 10 10#6 1 100 #8 200 0.01 200 200 10 1 1 10 100 10#7 200 400 600 800 1000 200 400 600 800 1000 200 400 600 800 1000 Μ Μ Μ
KJB, Chun, Im 12 FIG. 9: Black lines stand for the standard freeze-out neutralino abundance. Blue lines stand for FIG. 12: Same as the previous figure with vPQ =10 GeV. spin-independent direct detection cross section with proton in unit of pb. The WMAP dark matter abundance is depicted by thick line. Higgsino mixing becomes negligible, and the axino decay is determined by the tree-level
axino-Higgino-Higgs5 coupling (3). This is why the contour is almost parallel to the vertical Figs. 10-12. To get an rough estimate, let us consider the largest axino lifetime 10− sec ∼ found in Fig. 12 for v =1012 GeV. This give T 0.1 GeV from Eq. (14). Thisaxis can in thebe large M1 region. Note that the phase space of the axino 2-body decay to the PQ D ∼ Higgsino-like LSP and the Higgs becomes very small for µ 400 GeV. For µ ! 400 GeV, the compared with the axino-radiation equality temperature Teq determined by Teq =4ma˜Ya˜/3 ≈ 4 7 phase space of the axino 2-body decay is closed, but the axino can decay to the Higgsino-like [15] which give T 10− GeV for m˜ 1TeVandY˜ 10− . Thus, it becomes clear to eq ∼ a ∼ a ∼ LSP through the processes like 3-body decays with almost massless quarks and leptons via have Teq
LSP and the direct detection rate in M1-µ plane, setting M2 = 2 TeV for simplicity.part Contours of the left panel is almost same as in Fig. 9 as the corresponding axino lifetime is short are numerically obtained by using SUSY-HIT [24] and micrOMEGAs 2.4 [23].enough Note that for the axino to decay before the Bino-like LSP freeze-out. 2 11 the WMAP consistent relic density Ω h 0.1 [25] is obtained in the Higgsino-likeFor LSPvPQ =10 GeV, the axino decays later as seen in the right panel of Fig. 11. As a DM ≈ region (M1 µ) and the resonant annihilation region with M1 m /2asexpected.Oneconsequence, the contour line for the right dark matter density changes slightly compared ≈ ≈ A 12 can also see that the direct detection experiment [26] excludes the Higgsino-like regionto the and previous case. More dramatic change can be found for vPQ =10 GeV as in Fig. 12. The Higgsino-like dark matter becomes significantly lighter (µ 250 GeV) and the Bino- ∼
14 16 SUMMARY & IMPLICATIONS
• SUSY axion solves both GH & strong CP prob. • Due to the suppressed interactions, saxion & axino are long- lived and affect cosmological observations (BBN, CMB, etc.). • Late decay of saxion can provide a source of DR as well as large amount of entropy (visible energy). It can also produce extra neutralinos. • Axino can be either DM or decaying particle. Stable axino can be a good WDM while Decaying axino feeds neutralino DM abundance. Implications for future research:
• SUSY models with standard underabundance can provide the right amount of DM (mostly neutralino or neutralino/axion admixture) • SUSY models with standard overabundance are possibly viable if neutralino decays into light axino (SWIMP) or it is diluted by saxion decay.
12 16 • Large PQ scale region, 10 GeV (e.g. molecular interferometry) Graham and Rajendran