Brane vector dark matter T. E. Clark, S. T. Love, C. Xiong, --Purdue - PowerPoint PPT Presentation

Brane vector dark matter T. E. Clark, S. T. Love, C. Xiong, --Purdue University Muneto Nitta, -- Keio University Tonnis ter Veldhuis, -- Macalester College (conference speaker) Introduction We consider the effective theory describing the Standard Model on a brane in an embedding space. The effective theory generically contains additional scalar fields (global case) or massive vector fields (local case) associated with the spontaneous breaking of the translation symmetries. These degrees of freedom can be stable and they can have weak scale masses and interactions. Hence they are dark matter candidates. In this talk I consider the bounds on the parameters of the effective theory based on the observed dark matter relic abundance (WMAP) and the results of direct dark matter detection experiments (CDMSII, Xenon10), with a particular focus on extrinsic curvature interactions.

Other talks concerning the same model at this conference: “Higgs Decays and Brane Graviphotons,” Sherwin Love, 3.15 pm, this afternoon, Extra Dimensions session. “Brane Osciallation at the TeVatron and LHC,” Thomas Clark, 3.30 pm, this afternoon, Extra Dimensions session.

The Model Fields: brane vector field X Μ field strength for brane vector field F ΜΝ � field strength for hypercharge gauge field, and dual B ΜΝ , B ΜΝ 2 M X L SMX � L SM � 1 � F ΜΝ � F ΜΝ � 1 2 X Μ � X Ν � 1 SM � X Ν � M X 4 � X Μ � T ΜΝ 4 2 2 F X 2 � M X � ΜΝ � �� Μ X Ρ � Ρ X Ν 4 � � Κ 1 � B ΜΝ � Κ 2 B extrinsic curvature interaction F X Parameters: brane tension 4 F X brane vector mass M X dimensionless coupling constants Κ 1 , Κ 2

Additional comments The displayed action is the leading part of an underlying action that is invariant under all Standard Model symmetries and the non-linearly realized symmetries corresponding to extra dimensions. That underlying invariant action was constructed using the coset method An additional coupling of the brane vector to the Higgs bilinear invariant can also be included in the action but will not be consider it here. A flavor index for the brane vector has been suppressed. There is one flavor of brane vectors for each additional dimension. In this talk I will focus on the case of a single flavor. Generalization of the results is trivial. The link with the globally invariant action can be made with the identification 2 M X � Μ � 4 � X Μ Goldstone boson F X P. Creminelli, A. Strumia J. A. R. Cembranos, A. Dobado, A. L. Maroto Note that the extrinsic curvature interaction terms identically vanish in the global case.

Relic Density Calculation Brane vector annihilation cross-sections: (non-relativistic limits shown) X f MX 2 � mf 2 � MX 4 � mf 4 � � MX 2 1 8 � universal for all SM fermions 72 �Π F X s � 4 MX 2 � X f X A MX 2 � M H2 � 2 � MX 4 � M H4 � � MX 2 1 s � 4 MX 2 2 MX v 8 � 144 �Π F X s � 4 MX 2 X A X Z � MX 7 1 1 8 � 18 �Π F X s � 4 MX 2 X Z X H MX 2 � M Z2 � 10 � MX 4 � 8 � MX 2 � M Z2 � 3 � M Z4 � � MX 2 1 8 � 144 �Π F X s � 4 MX 2 X H

Relation between parameters so that WMAP result for the relic dark matter density is reproduced. 700 Energy momentum term only! 600 500 F X � GeV � 400 300 200 100 0 0 50 100 150 200 250 M X � GeV � Freeze � out temperature X Relic Abundance 25 1.0 20 0.8 0.6 15 x f � M X � T f � c h 2 0.4 10 0.2 5 0.0 0 0 50 100 150 200 250 0 50 100 150 200 250 M X � GeV � M X � GeV �

Additional contributions to the annihilation cross-sections f X � MX 2 s 1 s � 4 MX 2 � A 2 � 2 mf 2 � s � � B 2 � s � 4 mf 2 � � s � 4 mf 2 8 3456 Π F X , Z Γ � � s Κ 1 2 � Κ 2 2 � � s � 4 MX 2 �� X � f X W � � A 2 MX 2 s 2 1 s � 4 MX 2 � � 9 s 2 � 4 MW 2 s � 160 MW 4 � s � 4 MW 2 � � F 8 MW 4 27 648 Π , Z Γ � � s Κ 1 2 � Κ 2 2 � � s � 4 MX 2 �� W � X X Z A 2 MX 2 1 � 1 s � 4 MX 2 s � � MH � MZ � 2 � s � � MH � MZ � 2 8 � 13 824 �Π MZ 2 F X s Z � � MH 4 � MZ 4 � 26 MZ 2 s � s 2 � 2 MH 2 � MZ 2 � s �� � s Κ 1 2 � Κ 2 2 � � s � 4 MX 2 �� X H These contributions to the annihilation cross-sections are suppressed in the non-relativistic limit.

Relation between parameters so that WMAP result for the relic dark matter density is reproduced. 250 Extrinsic curvature terms only! 200 150 F X � GeV � Z-boson resonance 100 50 0 0 50 100 150 200 250 M X � GeV � Freeze � out temperature X Relic Abundance 25 1.0 20 0.8 15 0.6 x f � M X � T f � c h 2 10 0.4 0.2 5 0.0 0 0 50 100 150 200 250 0 50 100 150 200 250 M X � GeV � M X � GeV �

Direct Detection Elastic scattering cross-section f f Non-relativistic limit, M X �� m f 8 � � M X � m f � 4 4 7 2 M X � M X � m f � 6 � � v 0 4 � Σ el � �Κ 0 36 Π c F X X X 8 � � M X � m f � 4 4 � 5 2 �Α q 2 Cos 2 � � Θ W � M X � M X � m f � 6 � � v 0 4 � + �Κ 1 9 c F X 8 � � M X � m f � 2 4 2 �Α q 2 Cos 2 � � Θ W � M X � M X � m f � 2 � � v 0 2 � � Κ 2 f f c F X Suppression factor: X X v 0 � 0.001 c

-41 Estimate: 10 Cross-section [cm 2 ] (normalised to nucleon) http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini -42 10 M X � 100 GeV -43 10 F X � 250 GeV -44 10 Κ 2 � 1 -45 10 Σ el � 10 � 51 cm 2 -46 10 080428214401 1 2 3 10 10 10 WIMP Mass [GeV/c 2 ] DATA listed top to bottom on plot CDMS 2008 Ge CDMS: 2004+2005 (reanalysis) +2008 Ge XENON10 2007 (Net 136 kg-d) 080428214401 The parameter space of the model is not constrained by the direct detection data. Since the indirect detection signal from neutrinos due to annihilation of dark matter in the center of the Sun or the Earth is also determined by the same non-relativistic elastic scattering cross section, the neutrino data is not expected to constrain the model either.

Conclusions The brane vector model provides an effective description of some scenarios where our world is embedded in a higher dimensional space. The brane vector is a dark matter candidate as it can be stable. The WMAP observed relic dark matter can be correctly reproduced without straining the parameter space. The elastic scattering cross-section of the brane vector with fermions is suppressed in the non-relativistic limit. It seems therefore unlikely that the parameter space can be probed by using the data from the direct dark matter detection experiments. For the same reason it is expected that the indirect detection results which yield bounds on potential neutrinos produced in dark matter annihilations in the center of the Sun or the Earth do not put constraints on the parameter space. Additional constraints on the parameter space follow from collider experiments data See talk by Thomas Clark later this afternoon.