We suggest that the discrepant lifetime measurements of ortho-positronium can
be explained by ortho-positronium oscillations into mirror ortho-positronium.
This explanation can be tested in future vacuum experiments.Comment: about 6 pages, Latex, to appear in Phys.Lett.

Asai

Atojan

Carlson

Chang

Collie

De Rujula

Dobroliubov

Foot

Glashow

Gninenko

Holdom

Mitsui

Nico

Prinz

R Foot

S.N Gninenko

Skalsey

Westbrook

Physics Letters B

English

arXiv

We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments.We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments.We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments.We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments.We suggest that the discrepant lifetime measurements of ortho-positronium can be explained by ortho-positronium oscillations into mirror ortho-positronium. This explanation can be tested in future vacuum experiments

Foot, Robert

Gninenko, Sergei N.

CERN Document Server

arXiv:hep-ph/0003278v1  29 Mar 2000February 2000UM-P-012-2000To appear in Physics Letters BCan the mirror world explain the ortho-positronium lifetime puzzle?R. Foota∗ and S. N. Gninenkob†a Research Centre for High Energy PhysicsSchool of PhysicsUniversity of MelbourneParkville 3052 Australiab CERN, CH-1211 Geneva 23, SwitzerlandAbstractWe suggest that the discrepant lifetime measurements of ortho-positronium can be explainedby ortho-positronium oscillations into mirror ortho-positronium. This explanation can betested in future vacuum experiments.∗Foot@physics.unimelb.edu.au†Sergei.Gninenko@cern.chA “mirror universe” is predicted to exist if parity and/or time reversal are unbrokensymmetries of nature [1,2]. The idea is that for each ordinary particle, such as the photon,electron, proton and neutron, there is a corresponding mirror particle, of exactly the samemass as the ordinary particle. The parity symmetry interchanges the ordinary particleswith the mirror particles so that the properties of the mirror particles completely mirrorthose of the ordinary particles. For example the mirror proton and mirror electron arestable and interact with the mirror photon in the same way in which the ordinary protonand electron interacts with the ordinary photons. The mirror particles are not producedin Laboratory experiments just because they couple very weakly to the ordinary particles.In the modern language of gauge theories, the mirror particles are all singlets under thestandard G ≡ SU(3) ⊗ SU(2)L ⊗ U(1)Y gauge interactions. Instead the mirror particlesinteract with a set of mirror gauge particles, so that the gauge symmetry of the theory isdoubled, i.e. G ⊗ G (the ordinary particles are, of course, singlets under the mirror gaugesymmetry) [2]. Parity is conserved because the mirror particles experience V +A (i.e. right-handed) mirror weak interactions while the ordinary particles experience the usual V − A(i.e. left-handed) weak interactions. Ordinary and mirror particles interact with each otherpredominately by gravity only. At the present time there is some experimental evidencethat mirror matter exists coming from cosmology [3] as well as from the neutrino physicsanomalies [4].It was realized some time ago by Glashow [5] that the orthopositronium system pro-vides one sensitive way to search for the mirror universe. The idea is that small kineticmixing of the ordinary and mirror photons may exist which would mix ordinary and mirrororthopositronium, leading to maximal orthopositronium - mirror orthopositronium oscilla-tions.The ground state of orthopositronium (o-Ps) decays predominately into 3 photons witha theoretical decay rate computed to be (see e.g. [6] for a review)Γ =2(π2 − 9)α6me9π[1− 10.28661απ− α23ln1α+B0(απ)2− 3α32πln21α+O(α3lnα)]≃ (7.0382 + 3.9× 10−5B0)µs−1. (1)The B0 term parametrizes the non-logarithmic two-loop effects which have yet to be calcu-lated.On the experimental side, there have been a number of measurements of the lifetime oforthopositronium. The most accurate measurements are given in the table below:Reference ΓoPs(µs−1) Method ΓcollAnn Arbor [7] 7.0482± 0.0016 Vacuum Cavity ∼ (3− 10)ΓoPsAnn Arbor [8] 7.0514± 0.0014 Gas ∼ 103ΓoPsTokyo [9] 7.0398± 0.0029 Powder ∼ 104ΓoPsTable Caption: Some measurements of the orthopositronium lifetime. The last columnis an estimate of the mean scattering length of the orthopositronium in the experiment.1Comparison of the theoretical prediction with the experimental results suggests a sta-tistically significant discrepancy between the Theory/Tokyo results and the Ann Arbourresults. (Note that the B0 term would have to be anomalously large, ∼ 300, in order tomake the theory and the Ann Arbour result agree). Originally it was proposed that an ex-otic o-Ps decay mode would solve the Theory/Ann Arbor discrepancy. The puzzle seemed sointriguing that even the strongly forbidden decay o-Ps→ 2γ was searched for as a candidatefor solution. Now, it is believed that practically all possible contributions to the o-Ps decayrate from non-standard annihilation modes are excluded experimentally, for a review see [10]( and also [9]) and references therein. The purpose of this letter is to see if the oscillationsof orthopositronium with its mirror analogue can resolve this discrepancy.Photon - mirror photon kinetic mixing is described by the interaction Lagrangian densityL = ǫF µνF ′µν , (2)where F µν (F ′µν) is the field strength tensor for electromagnetism (mirror electromagnetism).This type of Lagrangian term is gauge invariant and renormalizable and can exist at treelevel [11,2] or maybe induced radiatively in models without U(1) gauge symmetries (suchas grand unified theories) [12,5,13]. The effect of ordinary photon - mirror photon kineticmixing is to give the mirror charged particles a small electric charge [12,5,2]. That is, theycouple to ordinary photons with charge 2ǫe‡.Orthopositronium is connected via a one-photon annihilation diagram to its mirror ver-sion (o-Ps’) [5]. This breaks the degeneracy between o-Ps and o-Ps’ so that the vacuumenergy eigenstates are (o-Ps + o-Ps’)/√2 and (o-Ps - o-Ps’)/√2, which are split in energyby ∆E = 2hǫf , where f = 8.7×104 MHz is the contribution to the ortho-para splitting fromthe one-photon annihilation diagram involving o-Ps [5]. Thus the interaction eigenstates aremaximal combinations of mass eigenstates which implies that o-Ps oscillates into o-Ps’ withprobability:P (o− Ps→ o− Ps′) = sin2 ωt, (3)where ω = 2πǫf . Note that the probability P (o− Ps → o− Ps′) can, in principle, alsobe affected by an additional splitting of o-Ps and o-Ps’ states by an external electric ormagnetic field [15].Let us first review the simplest case of o-Ps → o-Ps’ oscillations in vacuum [5]. In thiscase, because the mirror decays are not detected, this leads to an apparent increase in thedecay rate, since the number of o-Ps, N satisfiesN = cos2wte−Γsmt ≃ exp[−t(Γsm + w2t)], (4)where Γsm is the standard model decay rate of o-Ps (i.e. when the oscillation length goes toinfinity). Thus Γeff ≈ Γsm + w2/Γsm.‡Note that the direct experimental bound on ǫ from searches for ‘milli-charged’ particles is ǫ<∼ 10−5[14].2Actually the above computation is not applicable to any of the experiments listed inthe table because in each case the collision rate is larger than the decay rate and loss ofcoherence due to the collisions must be included [15].Observe that there is the interesting possibility that two different experiments could getdifferent values for the lifetime because of the different collision rates of the orthopositron-ium. It is well known that collisions damp the oscillations and in the limit where the collisionrate is much larger than the decay rate (or oscillation frequency; whichever is smaller) theeffect of the oscillations becomes negligible (Quantum Zeno effect). Let us assume for nowthat the theory computation is accurate (i.e. the unknown quantity B0 is not anomolouslylarge). The agreement with the Tokyo experiment can be explained because of the verylarge collision rate of the orthopositronium in the powder. However because of the twodifferent collision rates of the two Ann Arbour experiments, they cannot both be explained.Interestingly, some doubts about the Ann Arbour gas experiment have emerged due to thefact that the thermalization time of o-Ps (time of slowing of the orthopositronium atoms bycollisions in matter) needs to be taken into account for a precision measurement of the o-Psdecay rate, see e.g. [9], [16], [17]. If the o-Ps atoms are not completely thermalized, they aremoving faster and their decay rate is spuriously higher because of the higher pickoff annihi-lation rate. This could result in a systematic error in the determination of ΓoPs. A similarconclusion has been drawn in a recent paper of Skalsey et al. [18], where it is claimed thatat the lowest pressures used in the gas measurements [8] o-Ps were indeed not completelythermalized. This is crutial, since the Ann Arbor team used the asymptotic o-Ps decay rateextrapolated from low-pressure measurements. The size of the correction on the o-Ps decayrate due to incomplete thermalization still has to be determined.If we ignore this gas result then the discrepancy between the theory/Tokyo results andthe Ann Arbour vacuum cavity experiment can be explained by the orthopositronium-mirrororthopositronium oscillation mechanism. To see how this works in detail we need to considerthe case where Γcoll ≫ Γsm, then the evolution of the number of orthopositronium states,N , satisfies:dNdt≃ −ΓsmN − ΓcollNρ, (5)where the second term is the rate at which o-Ps oscillates into o-Ps’ (whose subsequentdecays are not detected). In this term, ρ denotes the average of oscillation probability overthe collision time. That is,ρ ≡ Γcoll∫ t0e−Γcollt′sin2wt′dt′ ≃ Γcoll∫ t0e−Γcollt′(wt′)2dt′, (6)where we have used the constraint that the oscillation probability is small, i.e. wt≪ 1 (whichmust be the case given that the discrepancy between say the vacuum cavity experiment andTokyo experiment is less than 1 percent). So long as t ≫ 1/Γcoll (which is an excellentapproximation for the gas and powder experiments and a reasonable one for the vacuumcavity experiment) thenρ ≃ 2w2Γ2coll. (7)3Thus substituting the above equation into Eq.(5) we haveΓeff ≃ Γsm + 2w2Γcoll= Γsm(1 +2w2ΓcollΓsm). (8)Thus the high decay rate measured in the vacuum cavity experiment relative to the theoryresult can be explained provied that2w2ΓcollΓsm≃ 0.0014± 0.0002. (9)The experiment involves a range of cavity sizes where the decay rate is obtained by extrap-olation to an infinite volume. From Ref. [7] we estimate that the largest cavity correspondsto Γcoll ∼ 3ΓoPs, which, neglecting the contribution from external fields (which are in factnegligible in this case [15]), implies thatw2 ∼ 2× 10−3Γ2oPs ⇒ ǫ ≃ (5± 1)× 10−7. (10)The much larger collision rates of the Tokyo (and gas) experiments means that the oscilla-tions can have no effect on these experiments. Thus the high value of the vacuum experimentrelative to the theory/Tokyo results can be explained. However the high value of the Michi-gan gas experiment cannot be explained by oscillations but is presumably due to larger thanexpected systematic errors (as discussed earlier).Interestingly the value of ǫ identified in Eq.(10) is consistent with all known experimentaland cosmological bounds (including SN1987) with the exception of the big bang nucleosyn-thesis bound (see figure 1 of Ref. [19] for a review and references). Big bang nucleosynthesissuggests the bound [20] ǫ<∼ 3 × 10−8. Thus, if it were experimentally proven that ǫ is aslarge as Eq.(10) then it would presumably mean that some of the assumptions of big bangnucleosynthesis would have to be modified.The experimental signature of the o-Ps → o-Ps’ oscillations is the ’disappearance’ ofan energy deposition of ∼ 1 MeV, which is expected from the ordinary o-Ps annihilationin a 4π calorimeter surrounding the o-Ps formation region, i.e. an invisible decay of o-Ps.The first experiment on such decays was performed a long time ago [21], and then repeatedwith higher sensitivity [22]. The results exclude contributions to the o-Ps decay rate frominvisible decay modes (such as o-Ps→ νν, millicharged particles, etc..) at the level ofBR(o-Ps→ invisible) < 3 · 10−6, but are not very sensitive to the o-Ps → o-Ps’ oscillationmechanism because of the high collision rate in these experiments. Indeed the limit on ǫextracted from the results of ref. [22], taking into account the suppression collision factor,is ǫ < 10−6 [15] and is not strong enough to exclude a possible mirror contribution givenby Eqs.(8,10) to the o-Ps decay rate. Thus, a vacuum experiment with significantly highersensitivity will be necessary to confirm or rule out the mirror world effect. The best approachwould be to combine the lifetime and invisible decay rate measurements in a single cavityexperiment. In this case one would have a good cross-check: the higher o-Ps decay rate thelarger peak at zero energy.If the photon - mirror photon mixing is as large as suggested here then there will bea number of interesting implications. For example, any mirror matter in the center of the4sun can become quite hot due to the absorption of ordinary photons. The subsequentradiation of mirror photons by the mirror matter would be absorbed by the surroundingordinary matter providing a new source of energy transport in the solar interior. Anotherimplication of the large photon - mirror photon kinetic mixing is that it may be large enough(depending on the chemical composition of the mirror planet) to make mirror planets opaqueto ordinary photons. Thus the recent observations [23] of a transit of the extrasolar planetHD 209458 does not exclude the hypothesis [24] that the close-in extrasolar planets aremirror planets. The remaining prediction of the mirror extrasolar planet hypothesis is thatthey cannot reflect the light from the star (i.e. their albedo is essentially zero). Thisprediction is currently being tested [25]. The photon - mirror photon kinetic mixing mayprovide a useful way of observing a mirror supernova explosion. This is because the rapidconversion of mirror matter into ordinary matter (via e′+e′− → e+e− → γ + γ) may providea burst of ordinary light. Indeed it may be possible that this is the mechanism which canrealize Blinnikov’s proposal [26] that gamma ray bursts are infact collapsing (or merging)mirror stars. Finally, it is interesting to note that composites of mirror matter with nonet mirror charge will exert small Van der Waals forces upon ordinary matter, possiblymaking terrestrial encounters with cosmic chunks of mirror matter also observable [5], [27].Indeed the collision of a mirror object (e.g. mirror asteroid) with the earth may well be ahealth hazard as the mirror object will not burn up in the atmosphere, but may neverthelessdeposit a large amount of energy when it hits the surface as the object losses energy due toelectromagnetic interactions induced by the kinetic mixing. Such an impact would not beexpected to leave any significant crater. §.While it is fun to speculate about the effects of large photon - mirror photon kineticmixing, real progress requires experiments. Given the already strong evidence for the mirrorworld coming from dark matter [3] and the neutrino physics anomalies [4] (as well as theintuitive expectation that nature should be left-right symmetric) it is obviously important toexperimentally determine whether the orthopositronium lifetime puzzle is one more windowon the mirror world. We hope that future experiments will shed light on this issue [28].Note AddedAfter completion of this paper the preprint [29] appeared which calculates the unknownB0 term in Eq.(1). They obtain the value B0 ≃ 44 which gives a theoretical orthopositroniumdecay rate of Γ = 7.0399 µs−1 [29]. Thus, the theoretical calculation agrees with the Tokyoexperiment which we in fact anticipated in this paper. 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Can the mirror world explain the ortho-positronium lifetime puzzle?

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Can the mirror world explain the ortho-positronium lifetime puzzle?

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