Modification of meson properties in the vicinty of nuclei

We suggest that modification of meson properties (lifetimes and branching ratios) can occur due to the interaction of constituent quark magnetic moments with strong magnetic fields present in the close vicinity of nuclei. A superposition of (J=0) and (J=1, mz=0) particle-antiparticle quantum states (as observed for ortho-Positronium) may occur also in the case of quarkonium states J/Ψ, ηc,Υ, ηb in heavy ion collisions. We speculate on possible modification of η(548) meson properties (related to C parity and CP violation) in strong magnetic fields which are present in the vicinity of nuclei.


Introduction
It has been pointed out already by Gell-Mann and Pais [1] that rigorous conservation of C parity should be expected only in the absence of external fields.Indeed, if Positronium (e + e − ) is created in magnetic field, admixture of para-Positronium J PC = 0 −+ wavefunction in ortho-Positronium (o−Ps) J PC = 0 −− substate (m z =0) allows for decay o−Ps → γγ (originally forbidden by C parity).This results in the "magnetic field quenching" of ortho-Positronium → 3γ decays [2], and the fraction of "forbidden" o−Ps → γγ decays depends on the external magnetic field strength.
We have suggested [3] that similar mechanism may apply to quarkonium mesons J/Ψ, η c and Υ, η b , when subject to extremal magnetic fields (B ≈ 10 14 T) created in heavy ion collisons [4].In this short note we point out that this phenomenon may take place also in the case of η(548) meson if bound to specific nuclei (for example 93 Nb) with large magnetic moments (e.g.μ Nb = 6.2μN ).
For this quantum "mixing" phenomenon to occur in the case of hadrons (mesons), it is necessary that constituent quarks have magnetic moments μ q .In this way, properties of QCD bound state (its C parity and decay channels) can be influenced by the external magnetic field, without direct involvement of gluonic (strong) interaction.In particular, 2-gluon decay J/Ψ → gg becomes possible in the magnetic field, because C parity of m z =0 (cc) meson substate Ψ + o is undefined -see Eq. ( 1).One may also suppose, that spurion-type γ * is involved in seemingly C-violating J/Ψ + o → gg decays (channel J/Ψ → ggγ is allowed [7]), and this "hidden" γ * is absorbed by the external magnetic field.
Measured magnetic moments of proton, neutron and hyperons [8] suggest that constituent quarks have their magnetic moments: The response of quarkonium states to extremal magnetic fields [4] created in collisions of nuclei at LHC and RHIC may be experimentally observable, for example, as anomalous suppression [9].
It is tempting to suggest [3], that behavior of quarkonium in strong magnetic field might apply also to (s s) meson ϕ(1019).However, the closest J = 0 +− mixing partner for ϕ(s s) state is η (958), and the mixing phenomenon may be non-trivial due to non-s s components in η wave function.In the next section we discuss η(548) meson behavior (neglecting its s s content) in the magnetic field.

Meson η(548) in external magnetic field
Conservation of C parity in η(548) decays has been experimentally measured [8] and it is the goal of intense experimental activity at JLAB.Therefore, a possibility of the modification of C parity properties of η(548) meson in the magnetic field is a relevant subject.
The closest √ 2 is present in the region of η(548) mass, with isospin structure of its wavefunction orthogonal to (u, d) part of η and ω mesons.We shall assume here that quantum mixing in the magnetic field happens preferably between states having the same u ↔ d isospin symmetry.
Because ω → π 0 π 0 decay is forbidden (by C parity) we have not suggested directly in Eq. ( 2) that decay channel η[B] → π 0 π 0 would become open in a sufficiently strong magnetic field.However, since mixed state η[B] ≈ (η + ε•ω) is neither C nor G-parity operator eigenstate, π 0 π 0 decays of η[B] state may possibly also become enhanced above the expected [12] rates in strong magnetic fields.

Conclusions
We have suggested that properties of η(548) mesons can be affected by magnetic fields in the vicinity of nuclei due to quantum superposition -mixing effect (observed to occur in Positronium).This may be relevant if conservation laws (CP or C parity) are tested in laboratory conditions at high precission.