Muonium-antimuonium conversion in models with dilepton gauge bosons.

We examine the magnetic field dependence of the muonium(μe)antimuonium(μe) conversion in the models which accommodate the dilepton gauge bosons. The effective Hamiltonian for the conversion due to dileptons turns out to be in the (V −A)× (V +A) form and, in consequence, the conversion probability is rather insensitive to the strength of the magnetic field. The reduction is less than 20% for up to B ≈ 300 G and 33% even in the large B limit. PACS number(s): 11.30.Hv, 12.15.Cc, 12.15.Ji, 36.10.Dr YNU-HEPTh-107 March 1995 ∗e-mail address: [email protected] Muonium, which is a bound state of μ and e, can be transformed to antimuonium, a bound state of μ and e, if there exists a lepton-number-non-conserving interaction [1]. Feinberg and Weinberg [2] studied the M−M conversion with a postulated effective Hamiltonian of (V −A)×(V −A) form. Later, this process has been studied within the left-right symmetric models and the models with doubly-charged Higgs bosons [3]-[7]. In these models, the effective Hamiltonian for the conversion is expressed either in the (V −A)× (V −A) form or in the (V +A)× (V +A) form. Thus far no M −M conversion has been observed [8]. Recently, an interesting class of models which have new SU(2)L-doublet gauge bosons were proposed as extensions of the standard model [9]-[12]. In these models each family of leptons (l, νl, l )L transforms as a triplet under the gauge group SU(3) and the total lepton number defined as L = Le +Lμ +Lτ is conserved, while the separate lepton number for each family is not. The new gauge bosons (X, X) carry lepton number L = ±2. Hence, hereafter, we refer to these gauge bosons as dileptons. The gauge group SU(3) will be, for example, an SU(3)l in the SU(15) grand unification theory model [10] or an SU(3)L in the SU(3)C ×SU(3)L ×U(1)X model [12]. The phenomenology on dilepton gauge bosons has been extensively studied. When the doubly-charged dilepton exists, the mixing of muonium and antimuonium is possible through the diagram illustrated in Fig. 1 and thus M − M conversion takes place [13]-[15]. In particular, the effective Hamiltonian for the mixing turns out to be in the (V −A)×(V +A) form. One of the present authors (K.S.) and Fujii and Nakamura calculated the probability for the M −M conversion in the models with dileptons and examined the lower mass bound on the doubly-charged dilepton X in Ref.[14]. But the analysis was done in the case of absence of magnetic fields. In this paper we consider the M −M conversion in static external magnetic fields and study the field dependence of the conversion probability. The muonium or antimuonium system in the presence of static external magnetic field −→ B is described by the following Hamiltonian, Hint = A −→ Se · −→ Sμ + μBge −→ Se · −→ B + μB me mμ gμ −→ Sμ · −→ B , (1) where −→ Se, me, ge− = −ge+ and −→ Sμ, mμ, gμ+ = −gμ− are spin, mass, the gyromagnetic ratio of electron (or positron) and μ (or μ), respectively, and μB is Bohr magneton.