Cosmological Constraint on the Minimal Universal Extra Dimension Model Mitsuru Kakizaki (Bonn University) September 7, 2007 @ KIAS In collaboration with Shigeki Matsumoto (Tohoku Univ.) Yoshio Sato (Saitama Univ.) Masato Senami (ICRR, Univ. of Tokyo) Refs: PRD 71 (2005) 123522 [hep-ph/0502059] NPB 735 (2006) 84 [hep-ph/0508283] PRD 74 (2006) 023504 [hep-ph/0605280]
1. Motivation Observations of cosmic microwave background structure of the universe etc. Non-baryonic dark matter [http://map.gsfc.nasa.gov] Weakly interacting massive particles (WIMPs) are good candidates The The predicted thermal relic relic abundance naturally explains the the observed dark dark matter matter abundance Neutralino (LSP) in supersymmetric (SUSY) models 1 st KK mode of the B boson (LKP) in universal extra dimension (UED) models etc. Today s topic September 7, 2007 Mitsuru Kakizaki 2
Outline Reevaluation of of the relic density of of LKPs including both coannihilation and resonance effects Cosmological constraint on on the minimal UED model 1. Motivation 2. Universal extra dimension (UED) models 3. Relic abundance of KK dark matter 4. Coannihilation processes 5. Resonance processes 6. Summary c.f.: SUSY 0 100 200 300 400 500 600 700 800 900 1000 September 7, 2007 Mitsuru Kakizaki 3 m 0 (GeV) 800 700 600 500 400 300 200 100 [From Ellis, Olive, Santoso, Spanos, PLB565 (2003) 176] m h = 114 GeV m χ ± = 104 GeV m 1/2 (GeV) tan β = 10, μ > 0
2. Universal extra dimension (UED) models Idea: All All SM particles propagate in in flat compact spatial extra dimensions [Appelquist, Cheng, Dobrescu, PRD64 (2001) 035002] Dispersion relation: Momentum along the extra dimension = Mass in four-dimensional viewpoint compactification with radius : quantized Macroscopic Microscopic KK tower Momentum conservation in the extra dimension Conservation of KK number at each vertex Magnify Mass spectrum for September 7, 2007 Mitsuru Kakizaki 4
Minimal UED (MUED) model In order to obtain chiral zero-mode fermions, the extra dimension is compactified on an orbifold [+ (--) for even (odd) ] Conservation of KK parity The lightest KK particle (LKP) is stable The The LKP LKP is is a good candidate for for dark dark matter c.f. R-parity and LSP Only two new parameters appear in the MUED model: : Size of extra dimension : Scale at which boundary terms vanish The Higgs mass remains a free parameter More fundamental theory Constraints coming from electroweak measurements are weak Precision tests for [Flacke, Hooper, March-Russell, PRD73 (2006); Erratum: PRD74 (2006); Gogoladze, Macesanu, PRD74 (2006)] [Haisch, Weiler, hep-ph/0703064 (2007)] September 7, 2007 Mitsuru Kakizaki 5
Mass spectra of KK states KK particles are degenerate in mass at tree level: Compactification 5D Lor. inv. Orbifolding Trans. Inv. in 5th dim. Radiative corrections relax the degeneracy Lightest KK Particle (LKP): (mixture of ) 1-loop corrected mass spectrum at the first KK level Degenerate in mass KK particles of leptons and Higgs bosons are highly degenerate with the LKP Coannihilation plays an important role in calculating the relic density [From Cheng, Matchev, Schmaltz, PRD66 (2002) 036005] September 7, 2007 Mitsuru Kakizaki 6
3. Relic abundance of KK dark matter 0-2 -4-6 Co-moving number density Decoupling Thermal equilibrium Increasing Standard thermal scenario Dark matter particles were in thermal equilibrium in the early universe After the annihilation rate dropped below the expansion rate, the number density per comoving volume is almost fixed Relic abundance of the LKP [From Servant, Tait, NPB 650 (2003) 391] Shortcomings: Coannihilation only with the NLKP No resonance process included 0 10 20 30 40 50 September 7, 2007 Mitsuru Kakizaki 7-8 Ωh 2 0.6 0.5 0.4 0.3 0.2 0.1 Overclosure Limit 3 flavors Including coannihilation Ωh 2 = 0.16 ± 0.04 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 m KK (TeV) Without coannihilation
4. Coannihilaition processes Previous calculation: Inclusion of coannihilation modes with all 1 st KK particles reduces the effective cross section Shortcomings: The Higgs mass is fixed to No resonance process included Our emphasis: [Burnell, Kribs, PRD73(2006); Kong, Matchev, JHEP0601(2006)] The The relic relic abundance depends on on the the SM SM Higgs mass Resonance effects also also shift shift the the allowed mass scale Relic abundance of the LKP: Disfavored by EWPT WMAP Without coannihilation [From Kong, Matchev, JHEP0601(2006)] September 7, 2007 Mitsuru Kakizaki 8
mh (GeV) Masses of the KK Higgs bosons 1 st KK Higgs boson masses: Contour plot of the mass splitting of 300 Charged LKP 250-0.5 % Larger Larger [Cheng, Matchev, Schmaltz, PRD66 (2002) 036005] ; smaller 500 1000 1500 (Enhancement of the annihilation cross sections for the KK Higgs bosons) Too large The 1 st KK charged Higgs boson is the LKP September 7, 2007 Mitsuru Kakizaki 9 200 150 100 1.5% 0.5 % 1% 1=R (GeV)
mh (GeV) Allowed region without resonance processes 280 240 200 160 Excluded (Charged LKP) KK Higgs coannihilation region Bulk region 120 400 600 800 1000 1200 1400 All coannihilation modes with 1 st KK particles included Bulk region (small ) Our result is consistent with previous works KK Higgs coannihilation region (large ) 1=R (GeV) The relic abundance decreases through the Higgs coannihilation Larger is allowed September 7, 2007 Mitsuru Kakizaki 10
5. Resonance processes KK particles were non-relativistic when they decoupled (Incident energy of two 1 st KK particles) (Masses of 2 nd KK particles) Annihilation cross sections are enhanced through s-channel 2 nd KK particle exchange at loop level e.g. Important processes: September 7, 2007 Mitsuru Kakizaki 11
mh (GeV) mh (GeV) Allowed region including coannihilation and resonance 280 240 200 160 Excluded (Charged LKP) Without resonances 120 400 600 800 1000 1200 1400 Cosmologically allowed region is shifted upward by 280 240 200 160 Excluded (Charged LKP) 1=R (GeV) Including resonances 120 400 600 800 1000 1200 1400 In the Bulk region: -resonances are effective In the KK Higgs coannihilation region: -resonance contributes as large as -resonances September 7, 2007 Mitsuru Kakizaki 12 1=R (GeV)
mh (GeV) Remark: KK graviton problem For, decays at late times Emitted photons would distort the CMB spectrum Attempts: [Feng, Rajaraman, Takayama PRL91 (2003)] Introduction of right-handed neutrinos of Dirac type is a DM candidate Radion stabilization? LKP in the MUED 120 400 600 800 1000 1200 1400 September 7, 2007 Mitsuru Kakizaki 13 280 240 200 160 KK graviton LKP region G (1) H ±(1) 1=R (GeV) fl (1) [From Matsumoto, Sato, Senami, Yamanaka, PLB647, 466 (2007)] WMAP data can be as low as [Matsumoto, Sato, Senami, Yamanaka, PRD76 (2007)]
mh (GeV) 1=R (GeV) 6. Summary UED models contain a candidate particle for CDM: The 1 st KK mode of the B boson (LKP) In UED models Coannihilation Resonance We calculated the LKP relic abundance in the MUED model including the resonance processes in all coannhilation modes Cosmologically allowed region 280 240 200 160 Excluded (Charged LKP) in the MUED model 120 400 600 800 1000 1200 1400 September 7, 2007 Mitsuru Kakizaki 14
Backup slides September 7, 2007 Mitsuru Kakizaki 15
Calculation of the LKP abundance The 1 st KK particle of the B boson is assumed to be the LKP The LKP relic abundance is dependent on the effective annihilation cross section Naïve calculation without coannihilation nor resonance WMAP data Coannihilation Coannihilation with KK right-handed leptons [Servant, Tait, NPB650 (2003) 391] Coannihilation with all 1 st KK particles ; [Burnell, Kribs, PRD73(2006); Kong, Matchev, JHEP0601(2006)] Coannihilation with KK Higgs bosons for large ; [Matsumoto, Senami, PLB633 (2006)] [Servant, Tait, NPB650 (2003) 391] Resonance [MK, Matsumoto, Sato, Senami, PRD71 (2005) 123522; NPB735 (2006) 84; PRD74 (2006) 023504] September 7, 2007 Mitsuru Kakizaki 16 ;
Constraint on in the MUED model Constraints coming from electroweak measurements are weak [Appelquist, Cheng, Dobrescu PRD64 (2001); Appelquist, Yee, PRD67 (2003); Flacke, Hooper, March-Russell, PRD73 (2006); Erratum: PRD74 (2006); Gogoladze, Macesanu, PRD74 (2006)] Requiring that LKPs account for for the CDM abundance in in Universe, the parameter space gets more constrained M (GeV) m H (GeV) September 7, 2007 Mitsuru Kakizaki 17 600 400 200 (Under the assumption of thermal production) Excluded Allowed 200 400 600 [From Gogoladze, Macesanu, PRD74 (2006)]
Relic abundance of the LKP (without coannihilation) The --resonance in annihilation effectively reduces the number density of dark matter 0.16 0.12 Dark Matter Abundance Ωh 2 WMAP Tree Tree + Res. 0.08 The resonance effect shifts upwards the LKP mass consistent with the WMAP data 0.8 0.9 1 m (TeV) September 7, 2007 Mitsuru Kakizaki 18
KK Higgs coannihilation region [Matsumoto, Senami, PLB633 (2006)] Larger Higgs mass (larger Higgs self-coupling) LKP relic abundance (ignoring resonance effects) 0.2 Mass degeneracy between 1 st KK Higgs bosons and the LKP in MUED Larger annihilation cross sections for the 1 st KK Higgs bosons Coannihilation effect with 1 st st KK KK Higgs bosons efficiently decrease the LKP abundance Ωh 2 0.15 0.1 0.05 0 120GeV 170GeV 200GeV 220GeV WMAP 230GeV 600 800 1000 1200 (GeV) 1=R of 1 TeV is compatible with the observation of the abundance September 7, 2007 Mitsuru Kakizaki 19
KK Higgs coannihilation region Freeze-out For larger (larger Higgs self-coupling) Degeneracy between the LKP and Free from a Boltzmann suppression Larger [Matsumoto, Senami, PLB633 (2006)] hff eff vi (GeV 2 ) 4 10 9 3 10 9 2 10 9 1 10 9 1 m h = 200 GeV m h = 120 GeV 30 100 300 1000 3000 x m h = 220 GeV The effective cross section can increase after freeze-out The LKP abundance can sizably decrease even after freeze-out Y=Y jm h =120GeV 0 September 7, 2007 Mitsuru Kakizaki 30 100 300 1000 20 3000 0.8 0.6 0.4 0.2 m h =120GeV m h =200GeV m h =220GeV x
mh (GeV) mh (GeV) Tree 280 240 200 160 280 240 200 160 Origin of the shift Excluded (Charged LKP) Without resonance 120 400 600 800 1000 1200 1400 Excluded (Charged LKP) 1=R (GeV) Including resonance 120 400 600 800 1000 1200 1400 Bulk region -res. are effective KK Higgs coannihilation region -res. contributes as large as -res. 0 400 500 600 700 800 900 1=R (GeV) 0 400 600 800 1000 1200 September 7, 2007 Mitsuru Kakizaki 21 Ωh 2 Ωh 2 0.2 0.15 0.1 0.05 res. 0.2 0.15 0.1 0.05 WMAP 2ff region 1=R (GeV) W (2) ;Z (2) ; H (2) resonance W (2) ;Z (2) resonance WMAP 2ff region Tree (2) ;Z (2) resonance W 1=R (GeV)
Positron experiments The HEAT experiment indicated an excess in the positron flux: Unnatural dark matter substructure is required to match the HEAT data in SUSY models [Hooper, Taylor, Silk, PRD69 (2004)] KK dark matter may explain the excess [Hooper, Kribs, PRD70 (2004)] Future experiments (PAMELA, AMS-02, ) will confirm or exclude the positron excess September 7, 2007 Mitsuru Kakizaki 22
Including coannihilation with 1 st KK singlet leptons The LKP is nearly degenerate with the 2 nd KK singlet leptons Coannihilation effect is important Annihilation cross sections The allowed LKP mass region is lowered due to the coannihilation effect c.f. SUSY models: coannihilation effect raises the allowed LSP mass September 7, 2007 Mitsuru Kakizaki 23
Coannihilaition processes KK particles of leptons and Higgs bosons are highly degenerate with the LKP Coannihilation plays an important role in calculating the relic density In generic: e.g.: coannihilation with KK leptons: e.g.: coannihilation with KK Higgs bosons: September 7, 2007 Mitsuru Kakizaki 24