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Unparticle Dark Matter THE UNIVERSITY OF ALABAMA University Libraries Unparticle Dark Matter T. Kikuchi – KEK N. Okada – KEK Deposited 05/30/2019 Citation of published version: Kikuchi, T., Okada, N. (2008): Unparticle Dark Matter. Physics Letters B, 665(4). DOI: https://doi.org/10.1016/j.physletb.2008.06.021 © 2008 Elsevier Science B. V. All rights reserved. Physics Letters B 665 (2008) 186–189 Contents lists available at ScienceDirect Physics Letters B ELSEVIER www.elsevier.com/locate/physletb Unparticle dark matter ∗ Tatsuru Kikuchi a, , Nobuchika Okada a,b a Theory Division, KEK, 1-1 Oho, Tsukuba 305-0801, Japan b Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies, Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan article info abstract Article history: Once a parity is introduced in unparticle physics, under which unparticle provided in a hidden conformal Received 8 May 2008 sector is odd while all Standard Model particles are even, unparticle can be a suitable candidate for Received in revised form 4 June 2008 the cold dark matter (CDM) in the present universe through its coupling to the Standard Model Higgs Accepted 6 June 2008 doublet. We find that for Higgs boson mass in the range, 114.4GeV m 250 GeV, the relic abundance Availableonline18June2008 h of unparticle with mass 50 GeV mU 80 GeV can be consistent with the currently observed CDM Editor: T. Yanagida density. In this scenario, Higgs boson with mass mh 160 GeV dominantly decays into a pair of unparticles and such an invisible Higgs boson may be discovered in future collider experiments. © 2008 Elsevier B.V. Open access under CC BY license. Existence of the dark matter (DM) is now strongly supported In this Letter, we propose a new candidate for CDM in the by various observations of the present universe, in particular, the context of a new physics model recently proposed by Georgi [4], Wilkinson Microwave Anisotropy Probe (WMAP) satellite [1] have “unparticle”. We introduce a Z2 parity under which unparticle is determined the various cosmological parameters with greater ac- odd while all Standard Model particles are even. The unparticle, curacy. The relic abundance of cold dark matter (CDM) is estimated which is provided by a hidden conformal sector and is originally to be (in 2σ range) massless, obtains masses associated with the electroweak symme- try breaking through its coupling to the SM Higgs doublet. We find 2 0.096 ΩCDMh 0.122. (1) that the unparticle can be a suitable candidate for CDM through the coupling. In addition, in our scenario the SM Higgs boson can To clarify the identity of a particle as cold dark matter is still a invisibly decay into a pair of unparticles with a large branching prime open problem both in particle theory and cosmology. ratio. Absence of any suitable candidate of cold dark matter in the Unparticle provided in a hidden conformal sector could posses Standard Model (SM) suggests the existence of new physics be- strange properties, especially in its energy distributions. A concrete yond the SM in which a dark matter candidate is implemented. example which can proved unparticle was discussed by Banks– The most promising candidate of CDM is the so-called weakly in- Zaks [5] (BZ) many years ago, where introducing a suitable number teracting massive particle (WIMP). Once the stability of WIMP is of massless fermions, theory reaches a non-trivial infrared fixed ensured by some symmetry (parity), its relic abundance can nat- point and a conformal theory can be realized at low energy.1 Af- urally be consistent with the WMAP data for WIMP mass and its ter the Georgi’s proposal, it has been paid a lot of interests in the typical interaction scales around the electroweak scale. This scale is unparticle physics and various studies on the unparticle physics in accessible to future collider experiments such as the Large Hadron scope of the LHC, cosmology, etc., have been developed in the lit- Collider (LHC) at CERN which will be in store for its operation next erature. year. A large missing energy associated with WIMP DM production Now we begin with a very brief review of the basic structure of is one of the important keys to discover new physics at collider the unparticle physics. First, we introduce a coupling between the experiments. There have been proposed the WIMP DM candidates in several new physics models, such as neutralino as the light- est sparticle in supersymmetric model with R-parity, the neutral heavy vector boson in the littlest Higgs model with T-parity [2], the lightest Kaluza–Klein particle in the universal extra dimension 1 Our present analysis does not depend on the model behind unparticle. We sup- model [3] and so on. pose a more general theory than the BZ theory for the model behind the unparticle, where the unparticle provided as a composite state in low energy effective theory, like baryons in QCD. In such a theory, we may expect that a low energy effective theory includes a global symmetry like the baryon number in QCD and a compos- * Corresponding author. ite state has a non-trivial charge under it like the baryon number of proton and E-mail addresses: [email protected] (T. Kikuchi), [email protected] neutron. We assume such situation for the unparticle and introduce a Z2 symmetry (N. Okada). under which the unparticle is odd. 0370-2693 © 2008 Elsevier B.V. Open access under CC BY license. doi:10.1016/j.physletb.2008.06.021 T. Kikuchi, N. Okada / Physics Letters B 665 (2008) 186–189 187 new physics operator (OUV) with dimension dUV and the Standard Our scenario shares similar structures with some simple modes Model one (OSM) with dimension n, for dark matter [8], where the gauge singlet scalar is introduced into the SM and can be a suitable candidate for dark mater through L = cn O O + − UV SM, (2) couplings to Higgs boson. The crucial difference of unparticle from MdUV n 4 such a singlet scalar is that unparticle is originally massless be- where cn is a dimension-less constant, and M is the energy scale cause of the conformal invariance of a hidden sector. The absence characterizing the new physics. This new physics sector is assumed of mass term reduces the number of free parameters involved in to become conformal at a scale ΛU , and the operator OUV flows U dark matter physics and as a result, we can analyze the relic den- to the unparticle operator with dimension dU . In low energy ef- sity of unparticle dark matter as a function of only unparticle mass fective theory, we have the operator of the form (here we consider (mU ) and Higgs boson mass (mh), as we will see later. scalar unparticle, for simplicity), Now let us evaluate the relic density of unparticle dark mat- d −dU ∼ Λ UV ter. In our analysis, we consider the case dU 1, for simplicity, L = U UO ≡ 1 UO cn + − SM + − SM, (3) where unparticle is almost identical to a gauge singlet scalar. We MdUV n 4 ΛdU n 4 can expect that even for a general dU in the range, 1 dU < 2, where the scaling dimension of the unparticle (dU ) have been our results will remain almost the same in the following rea- matched by ΛU which is induced the dimensional transmutation, sons. First, the phase space factor AdU is a slowly varying function and Λ is the (effective) cutoff scale of low energy effective theory. of dU . Second, the unparticle dark matter decouples from thermal Interestingly, dU is not necessarily to be integer, but can be any bath in non-relativistic regime, where the most important factor − real number or even complex number. In this Letter we consider to fix the decoupling temperature is the Boltzmann factor e mU /T the scaling dimension in the range, 1 dU < 2, for simplicity. It independent of dU .2 Moreover, in non-relativistic regime, the un- was found in Ref. [4] that, by exploiting scale invariance of the un- dU −1 particle wave function behaves as mU and the interaction terms particle, the phase space for an unparticle operator with the scale in Eq. (8) becomes independent of dU in momentum space. dimension dU and momentum p is the same as the phase space The relic abundance of the dark matter is obtained by solving for dU invisible massless particles, the following Boltzmann equation [10], 4 0 2 2 dU −2 d p dY v dΦU (p) = A θ p θ p p , (4) σ 2 2 dU 4 =− s Y − Y , (9) (2π) dx Hx eq where where Y = n/s is the yield of the dark matter defined by the ra- 5 1 tio of the dark matter density (n) to the entropy density of the 16 2 Γ(dU + ) = π 2 = 3 3 = ≡ AdU . (5) universe (s 0.439g∗mU /x ), g∗ 86.25, and x mU /T (T is the 2dU − (2π) Γ(dU 1)Γ (2dU ) temperature of the universe). The Hubble parameter is given by 1/2 2 2 19 Also, based on the argument on the scale invariance, the (scalar) H = 1.66g∗ mU mPl/x , where mPl = 1.22 × 10 GeV is the Planck propagator for the unparticle was suggested to be [6,7] mass, and the yield in the equilibrium Yeq is written as Yeq = − (0.434/g∗)x3/2e x. After solving the Boltzmann equation with the AdU i −i(dU −2)π − e . (6) thermal averaged annihilation cross section σ v, we obtain the 2sin(πdU ) (p2)2 dU present abundance of dark matter (Y∞).
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