First search for invisible decays of ortho-positronium confined in a vacuum cavity C. Vigo,1 L. Gerchow,1 L. Liszkay,2 A. Rubbia,1 and P. Crivelli1, ∗ 1Institute for Particle Physics and Astrophysics, ETH Zurich, 8093 Zurich, Switzerland 2IRFU, CEA, University Paris-Saclay F-91191 Gif-sur-Yvette Cedex, France (Dated: March 20, 2018) The experimental setup and results of the first search for invisible decays of ortho-positronium (o-Ps) confined in a vacuum cavity are reported. No evidence of invisible decays at a level Br (o-Ps ! invisible) < 5:9 × 10−4 (90 % C. L.) was found. This decay channel is predicted in Hidden Sector models such as the Mirror Matter (MM), which could be a candidate for Dark Mat- ter. Analyzed within the MM context, this result provides an upper limit on the kinetic mixing strength between ordinary and mirror photons of " < 3:1 × 10−7 (90 % C. L.). This limit was obtained for the first time in vacuum free of systematic effects due to collisions with matter. I. INTRODUCTION A. Mirror Matter The origin of Dark Matter is a question of great im- Mirror matter was originally discussed by Lee and portance for both cosmology and particle physics. The Yang [12] in 1956 as an attempt to preserve parity as existence of Dark Matter has very strong evidence from an unbroken symmetry of Nature after their discovery cosmological observations [1] at many different scales, of parity violation in the weak interaction. They sug- e.g. rotational curves of galaxies [2], gravitational lens- gested that the transformation in the particle space cor- ing [3] and the cosmic microwave background CMB spec- responding to the space inversion x! −x was not the trum. The latest Planck Mission results [4] provide an ac- usual transformation P but PR, where R corresponds to the transformation of a particle into a reflected state in curate estimate of the abundance of baryons Ωb = 0:048 the mirror particle space. and cold matter Ωc = 0:258, leading to an abundance of cold matter ∼ 5 times larger than ordinary matter. The The idea was further developed by A. Salam [13] explanation of such observations is one of the strongest and was clearly formulated in 1966 as a concept of hints of the existence of new physics. the mirror universe by Kobzarev, Okun and Pomer- anchuk [14]. They proposed a model in which mirror and Many Dark Matter candidates have been hypothesized ordinary matter communicate predominantly through so far, the most relevant being sterile neutrinos, axions gravity. This concept evolved further into two versions, and supersymmetric particles (see Ref. [5] for a detailed, the symmetric (developed by Foot, Lew and Volkas [15]), recent review). Supersymmetry is theoretically very at- and the asymmetric (proposed by Berezhiani and Moha- tractive since in addition of providing a good candidate patra [16]). For further historical details, see the review for DM (the Lightest Supersymmetric Particle, LSP), by Okun [17]. it could potentially solve the hierarchy problem [6] and The symmetric model provides a viable experimen- grant unification of gauge couplings at high energies [7], tal signature through positronium (Ps). The main idea necessary for Grand Unified Theories (GUT). However, is that each ordinary particle (i.e. photon or electron) all experimental searches have failed to provide any evi- has a mirror particle with the same properties (e.g. dence of supersymmetry so far [5, 8, 9]. mass and charge) but opposite chirality. These mir- Another interesting approach is the concept of a Hid- ror particles would be singlets under the standard G ≡ den Sector (HS) consisting of a SU (3)C⊗SU (2)L⊗U (1)Y SU (3)C ⊗ SU (2)L ⊗ U (1)Y gauge interactions [15]. In- singlet field [10]. These models extend the SM by intro- teractions within mirror particles are identical to their arXiv:1803.05744v2 [hep-ex] 19 Mar 2018 ducing a sector which transforms under the new gauge mirror partners: mirror electron and mirror photon will group. Among the many HS scenarios, the Mirror Sec- interact with each other in the same way ordinary elec- tor is a particularly interesting one, featuring a natural tron and ordinary photon do. Having opposite chirality, Dark Matter candidate (actually a whole set of candi- parity conservation is restored at a global level. dates) and feasible experimental signatures via oscilla- Being massive and stable, mirror particles are a very tions of ordinary matter into the HS, as well as a possi- good candidate for Dark Matter, because they interact ble explanation of the anomaly reported by the DAMA with ordinary matter primarily through gravitation [18{ Collaboration [11]. 22]. However, the model allows other interactions, lim- ited by charge conservation in each sector. Neutral par- ticles and composites can in principle mix with their re- spective mirror partner, e.g. neutrinos [23], photons [24], the neutral Higgs boson [25, 26], neutrons [27{30] or muo- nium [31]. The photon - mirror photon (γ - γ0) mix- ∗ [email protected] ing mechanism would then induce the Ps - Ps0oscillation 2 through the one-photon virtual annihilation channel of by the interaction Lagrangian density: ortho-positronium. L = "F µν F 0 (2) Mirror matter can also provide a natural explanation µν µν 0 for the similarity between Dark Matter and ordinary where F and Fµν are the field strength tensors for elec- baryonic fractions, ΩDM ' 5 Ωb. Although it is true that tromagnetism and mirror electromagnetism respectively. ordinary and mirror matter would have the same mi- Due to its one-photon virtual annihilation channel, crophysics, that does not necessarily imply they should ortho-positronium and mirror ortho-positronium are con- follow identical cosmological realizations. As pointed out nected and the degeneracy between the mass eigenstates by Berezhiani et al. [20], one can assume that the infla- is broken [34]. The vacuum eigenstates 0 tionary reheating temperature of the mirror sector T was o-Ps + o-Ps0 o-Ps − o-Ps0 lower than the ordinary one T . With this premise, and p p 2 2 since the two sectors can only interact very weakly, they would not reach thermal equilibrium with each other in are therefore split in energy by ∆E = 2h"f, where 4 early stages of the universe and hence would evolve in- f = 8:7 × 10 MHz is the contribution to the ortho { para dependently during the Universe expansion. Moreover, splitting from the one-photon virtual annihilation dia- since baryonic asymmetry (BA) depends on the depar- gram. This splitting leads to Rabi oscillations in which ture from thermal equilibrium, it is possible that the BA a state that is initially ordinary ortho-positronium will is larger in the mirror sector than in the ordinary one. oscillate into its mirror partner with a probability 0 A temperature ratio T =T < 0:2 could lead to mirror P (o-Ps ! o-Ps0) = sin2 Ωt (3) baryonic densities 1 ≤ ΩDM=Ωb ≤ 5 compatible with the latest Planck Mission results [4]. where Ω = 2πf" is the oscillation frequency. Mirror matter having the same micro-physics as ordinary mat- Finally, Mirror Matter is also an excellent candidate to 0 explain the annual modulation reported by the DAMA ter, o-Ps will decay into mirror photons, which are very Collaboration over 14 annual cycles with the former weakly coupled to ordinary matter and thus not de- DAMA/NaI experiment and with the second generation tected. Such oscillations will therefore result in an ap- DAMA/LIBRA phase1 (see [11] and references therein parent o-Ps ! invisible process with a branching ratio for latest reviews). The observed modulation has a pe- 2 riod T = 0:998(2) years and a phase t0 = 144(7) days, 2Ω Br (o-Ps ! invisible) = 2 2 (4) in good agreement with expectations for a Dark Mat- ΓSM + 4Ω ter annual modulation signal. These results give model- where Γ is the Standard Model decay rate of o-Ps [35, independent evidence for the presence of Dark Matter SM 36]. Assuming " = 4 × 10−9, the oscillation probability particles in the galactic halo, at a 9:3 σ C. L. is Cerulli et al. [32] recently showed how the mirror sec- −7 tor can successfully describe such modulation, providing Br (o-Ps ! invisible) = 2 × 10 (5) detailed characterizations of several chemical composi- Note that, within the SM, photonless (and thus invisible) tions of the mirror sector compatible with cosmological decays of both o-Ps and p-Ps into neutrinos are mediated bounds. In particular, for a reference DM density of by the weak interaction and are heavily suppressed with −3 ρDM = 0:3 GeV cm and many different halo tempera- a branching ratio below 10−17 due to the small mass of tures and compositions, they calculate coupling constants the positronium atom [37, 38]. −9 in the region " ∼ 10 , which has not been ruled out by The above calculations do not consider incoherent pro- any cosmological limits or direct experimental measure- cesses (e.g. collisions with matter) and the effect of en- ments. For comparison, the upper limit deduced by the ergy shifts induced by electromagnetic fields. Using the 4 successful prediction of the primordial He abundance by density matrix approach, the effect of electromagnetic the SM is [33]: fields on the branching ratio is shown to be negligible within the region of interest for this experimental search " ≤ 3 × 10−8 (1) (E ∼ 10 kV cm−1 and B ∼ 80 G) [39]. On the other hand, collisions of o-Ps with matter play a major role and can be source of large systematic effects and uncer- tainties [40]. B. Positronium as a Portal into the Mirror World In general, the number of collisions per lifetime will not be a well-defined value but rather a discrete distribution, Mirror and ordinary particles interact with each other i.e.