Dark matter in a Simplest Little Higgs with T-parity model Pat Kalyniak1 and Dmitriy Tseliakhovich2 1Ottawa Carleton Institute for Physics, Department of Physics, Carleton University, 1125 Colonel By Drive, Ottawa K1S5B6 Canada 2California Institute of Technology, Mail Code 249-17, Pasadena, CA 91125 (Dated: January 5, 2019) Little Higgs models may provide a viable alternative to supersymmetry as an extension of the Standard Model. After the introduction of a discrete Z2 symmetry, dubbed T-parity into Little Higgs models they also contain a promising dark matter candidate. We investigate a heavy neutrino as a dark matter candidate in the Simplest Little Higgs with T-parity (SLHT) model. First we calculate relic density constraints on the parameter space of the model and then discuss collider signatures for the SLHT dark matter. PACS numbers: 95.35.+d, 12.60.-i Keywords: Dark matter, LHC, Simplest Little Higgs I. INTRODUCTION extensions to the Standard Model that, in addition to remedying other Standard Model deficiencies, provide a The combined effort of theoretical and experimental candidate dark matter particle. For example, dark mat- research in physics and astronomy has resulted in the ter candidates naturally arise in Supersymmetry, Kaluza- formulation of two extremely successful models that de- Klein models of extra dimensions and Little Higgs models scribe most observed phenomena to date. The current (for a review see for example [5]). In this paper we con- knowledge in particle physics is summarized in what is sider dark matter candidates that arise in the Simplest known as the Standard Model [1] while the results of the Little Higgs with T-parity model (SLHT), as proposed astrophysical observations are described within the Cold by Martin [6]. Dark Matter with dark energy (ΛCDM) paradigm. There Various astronomical observations constrain properties is, however, broad acceptance that both models are in- of dark matter. The simplest constraint is on the amount complete. One particular problem inherent to both mod- of dark matter in the universe. Recent observations have els is the inability to coherently explain the phenomenon improved measurements of the total mass density and of dark matter. baryonic mass density to the point that we now know Dark matter dominates the mass budget of the uni- the total amount of dark matter to a precision of 10% [2]. verse [2], but the actual particle(s) that comprise dark The high precision of the current astrophysical searches matter are still unknown. Dark matter has yet to be allows to move beyond providing a general confirmation directly detected experimentally, despite attempts to in- of the CDM paradigm to specifically constraining particle tercept it passing through Earth and attempts to gen- physics models based on the dark matter properties they erate it via particle collisions. The broadest constraints predict. In the present study we focus on the relic density on the properties of dark matter result from astronomical constraints, which provide the most significant reduction observations, which, over the previous decades, have sup- of the allowed parameter space for any extensions of the ported what is known as the Cold Dark Matter (CDM) SM. paradigm [3]. CDM is a phenomenological model, speci- Imposing astrophysical constraints leads to a set of spe- arXiv:0903.4739v1 [hep-ph] 27 Mar 2009 fying a perfectly “cold” (i.e., without initial random mo- cific predictions for the observation and analysis of dark tions) particle that interacts only through gravity, and matter at the Large Hadron Collider at CERN. We ana- is consequently also dissipationless. There are no as- lyze collider signatures of the Simplest Little Higgs dark tronomical observations or particle physics experiments matter and discuss prospects and difficulties for dark that rule out a cold, non-interacting dark matter parti- matter detection at present day collider facilities. We cle, and many observations that support it. However, see this analysis as a great example of synergy between some theoretical predictions based on CDM models are particle physics and astronomy in solving one of the most mildly at odds with observations probing the kpc-scale outstanding problems in science. distribution of dark matter (e.g., [4]). More importantly The rest of the paper is organized as follows. In Sec- no particle physics model produces a dark matter can- tion 2 we review the foundations of the Simplest Little didate conforming to the ideal of the CDM paradigm. Higgs with T-parity (SLHT) model and discuss dark mat- Specifically, no particle can be perfectly cold or perfectly ter candidates that arise in it. In Section 3 we calculate non-interacting. the relic density constraints on the parameter space of While the Standard Model (SM) of particle physics the SLHT. Collider phenomenology of the SLHT dark does not provide a natural non-baryonic dark matter can- matter is discussed in Section 4. A summary of our re- didate, the near-universal acceptance of dark matter as sults follows in Section 5. Finally, in the Appendix, we a major constituent of the universe has inspired many provide Feynman rules for the Simplest Little Higgs with 2 T-parity model. Here η is a real scalar field and h = (h0,h−)T is an SU(2) doublet which can be identified as the SM Higgs. The remaining 5 degrees of freedom of the symme- II. SIMPLEST LITTLE HIGGS WITH T-PARITY try breaking are “eaten” by the additional heavy gauge bosons and therefore are omitted from Eq.(2). Scalar field interactions with the gauge boson sector Little Higgs models [7, 8, 9, 10, 11, 12] offer an inter- and the masses of gauge bosons are determined by the esting alternative to supersymmetry in solving various standard kinetic term for the Φ [18]: problems of the SM. For instance, the hierarchy prob- i lem is resolved by introducing new heavy particles at the 2 a a igx x TeV scale that cancel quadratic divergences of the Higgs Φ = ∂ + igA T B Φ , (3) L µ µ − 3 µ i boson mass arising in the SM from one-loop radiative corrections. This cancellation occurs between particles where the SU(3) gauge coupling g is equal to the SM with the same statistics in Little Higgs models, as op- SU(2) gauge coupling and the U(1) gauge coupling g posed to the case of supersymmetry where divergences L X x is fixed in terms of g and the weak mixing angle tW are canceled by opposite statistics partners of the SM tan θ by ≡ particles. The original little Higgs models [10, 13, 14], W however, suffered from stringent constraints from elec- gtW gx = . (4) troweak precision tests (EWPT) which required the in- 1 t2 /3 troduction of fine tuning. An elegant solution to this − W problem is to introduce a discrete symmetry (like the R- The gauge bosons correspondingp to the broken gener- parity in supersymmetry) called T-parity [15]. T-parity ators get masses of order f TeV and consist of a Zh not only remedies the problem of precision electroweak boson, which is a linear combination∼ of A8 and Bx constraints, but also leads to the appearance of promis- ing dark matter candidates. We must note that, recently, 1 2 8 x Zh = 3 t A + tW B , (5) it has been pointed out that T-parity in general may be √ − W 3 violated by anomalies [16], making the lightest T-odd q 0 − particle unstable. However, such violation strongly de- and a complex SU(2)L doublet (Y ,X ) pends on the UV completion of the Little Higgs model A6 iA7 A4 iA5 and may not be realized in nature [17]. Consequently, we X− = − , Y 0 = − . (6) consider models respecting T-parity here. √2 √2 The Simplest Little Higgs with T-parity model [6] is 0 The SM mass eigenstates W ±, Z , and A are also ex- constructed by enlarging the SM SU(2) U(1) gauge L ⊗ Y pressed in terms of the gauge fields: group to SU(3)W U(1)X in a minimal way. This en- tails enlarging the⊗ SU(2) doublets of the SM to SU(3) 1 2 ± A iA triplets, including additional SU(3) gauge bosons, and W = ∓ , (7) √2 writing SU(3) invariant interactions in a way that re- produces all the SM couplings when restricted to SM fields. The SU(3)W U(1)X gauge symmetry is broken 0 3 tW 8 x 2 ⊗ Z = A cW + (A sW B cW 3 tW ), (8) down to the SM electroweak gauge group by two com- √3 − − q plex scalar fields Φ1,2, which are triplets under the SU(3) with aligned vevs f1,2. When the scalar fields acquire 2 3 8 sW x cW 2 vevs, the initial global symmetry [SU(3)W U(1)X ] is A = A sW A + B 3 tW . (9) 2 √ √ spontaneously broken to [SU(2) U(1) ] .⊗ At the same − 3 3 − ⊗ X q time, the global symmetry is explicitly broken to its di- As in the SM, masses of the heavy gauge bosons are deter- agonal subgroup SU(3) U(1) by the gauge interactions. ⊗ mined by the symmetry breaking vev and can be written The scalar fields are conveniently parameterized by a as: 2 nonlinear sigma model of the [SU(3) U(1)X ] /[SU(2) U(1) ]2 symmetry breaking as ⊗ ⊗ √2gf gf X ± 0 MZh = , MX = MY = . (10) 3 t2 √2 − W f 0 f 0 iΘ 2 −iΘ 1 Φ1 = e f1 0 , Φ2 = e f2 0 (1) The symmetryp breaking SU(2) U(1)/U(1)em by the × f1 f2 vev of the SM Higgs introduces corrections to the masses of the gauge bosons.