Cosmological Constraint on the Minimal Universal Extra Dimension Model Mitsuru Kakizaki (Bonn Univ. & ICRR, Univ. of Tokyo) 20 September, 2006 @ SISSA In collaboration with Shigeki Matsumoto (KEK) 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 cold dark matter What is the constituent of dark matter? Weakly interacting massive particles are good candidates: Lightest supersymmetric particle (LSP) in supersymmetric (SUSY) models Lightest Kaluza-Klein particle (LKP) in universal extra dimension (UED) models etc. [http://map.gsfc.nasa.gov] Today s topic 20 September, 2006 Mitsuru Kakizaki 2
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 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] 20 September, 2006 Mitsuru Kakizaki 3 ;
Outline Reevaluation of of the relic density of of LKPs including coannihilation and resonance effects Constraint on on the parameter space of of 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 20 September, 2006 Mitsuru Kakizaki 4
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 Macroscopic Microscopic In case of compactification with radius, is quantized KK tower Momentum conservation in the extra dimension Conservation of KK number at each vertex Magnify Mass spectrum for 20 September, 2006 Mitsuru Kakizaki 5
Minimal UED (MUED) model In order to obtain chiral zero-mode fermions, the extra dimension is compactified on an orbifold Conservation of KK parity [+ (--) for even (odd) ] The lightest KK particle (LKP) is stable The LKP is is a good candidate for for 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 20 September, 2006 Mitsuru Kakizaki 6
Constraint on in the MUED model Constraints coming from electroweak measurements are weak [Appelquist, Cheng, Dobrescu PRD64 (2001); Appelquist, Yee, PRD67 (2003); Gogoladze, Macesanu, hep-ph/0605207] Requiring that LKPs account for for the CDM abundance in in Universe, the parameter space gets more constrained M (GeV) (Under the assumption of thermal production) m H (GeV) 20 September, 2006 Mitsuru Kakizaki 7 600 400 200 Excluded Allowed 200 400 600 [From Gogoladze, Macesanu, hep-ph/0605207]
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] 20 September, 2006 Mitsuru Kakizaki 8
3. Relic abundance of KK dark matter 0-2 -4-6 Co-moving number density Decoupling Thermal equilibrium Increasing Generic picture 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 [Servant, Tait, NPB 650 (2003) 391] Coannihilation only with the NLKP No resonance process 0 10 20 30 40 50 20 September, 2006 Mitsuru Kakizaki 9-8 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 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.: KK leptons: e.g.: KK Higgs bosons: 20 September, 2006 Mitsuru Kakizaki 10
Previous calculation Inclusion of coannihilation modes with all 1 st KK particles reduces the effective cross section [Burnell, Kribs, PRD73(2006); Kong, Matchev, JHEP0601(2006)] The Higgs mass is fixed to No resonance process is considered We emphasize: The relic abundance depends on on the SM Higgs mass Resonance effects also shift the allowed mass scale Disfavored by EWPT Relic abundance of the LKP WMAP Without coannihilation [From Kong, Matchev, JHEP0601(2006)] 20 September, 2006 Mitsuru Kakizaki 11
mh (GeV) Masses of the KK Higgs bosons 1 st KK Higgs boson masses: Contour plot of mass splitting 300 250 Charged LKP -0.5 % Larger Larger ; smaller 200 0.5 % 150 1% 1.5% 100 500 1000 1500 (GeV) 1=R (Enhancement of the annihilation cross sections for the KK Higgs bosons) Too large The 1 st KK charged Higgs boson is the LKP 20 September, 2006 Mitsuru Kakizaki 12
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 We investigate dependence of the LKP relic abundance on the Higgs mass, including all coannihilation modes with 1 st KK particles Bulk region (small ) The 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 20 September, 2006 Mitsuru Kakizaki 13
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 20 September, 2006 Mitsuru Kakizaki 30 100 300 1000 14 3000 0.8 0.6 0.4 0.2 m h =120GeV m h =200GeV m h =220GeV x
5. Resonance processes KK particles are non-relativistic when they decouple (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 Important processes: c.f. 20 September, 2006 Mitsuru Kakizaki 15
mh (GeV) mh (GeV) Inclusion of resonance processes Cosmologically allowed region is shifted upward by For the LKP may be the KK graviton KK graviton problem like the gravitino problem Some mechanism to make the KK graviton heavy is proposed [Dienes PLB633 (2006)] 280 240 200 160 120 400 600 800 1000 1200 1400 280 240 200 160 Excluded (Charged LKP) Without resonance Excluded (Charged LKP) 1=R (GeV) Including resonance 120 400 600 800 1000 1200 1400 20 September, 2006 Mitsuru Kakizaki 16 1=R (GeV)
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 20 September, 2006 Mitsuru Kakizaki 17 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)
mh (GeV) 6. Summary UED models provide a viable dark matter candidate: The lightest Kaluza-Klein particle (LKP) The LKP relic abundance is reduced by the coannihilation with the KK Higgs bosons and second KK 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 20 September, 2006 Mitsuru Kakizaki 18 1=R (GeV)
Backup slides 20 September, 2006 Mitsuru Kakizaki 19
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) 20 September, 2006 Mitsuru Kakizaki 20
KK Higgs coannihilation region [Matsumoto, Senami, PLB633 (2006)] Larger Higgs mass (larger Higgs self--coupling) Dependence of the LKP relic abundance on the Higgs mass (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 20 September, 2006 Mitsuru Kakizaki 21
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 20 September, 2006 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 20 September, 2006 Mitsuru Kakizaki 23