Chiral Perturbation Theory for Tensor Mesons

Interactions of a2, K ∗ 2 , f2 and f ′ 2 tensor-mesons with low-energy π,K, η, η ′ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated as heavy non-relativistic matter fields. Using 1/Nc counting, we derive relations among unknown couplings of the chiral Lagrangian. Chiral perturbation theory is applied to the tensor-meson mass matrix. At one-loop there are large corrections to the individual tensor meson masses, but the singlet-octet mixing angle remains almost unchanged. We argue that all heavy mesons of spin ≥ 1 share common feature of chiral dynamics. Submitted to Physics Letters B 1 Work supported in part by NSF Grant, NSF-KOSEF Bilateral Grant, KOSEF Purpose-Oriented Research Grant 94-1400-04-01-3 and SRC-Program, Ministry of Education Grant BSRI 97-2410, the Monell Foundation and the Seoam Foundation Fellowships. An important application of chiral perturbation theory is to describe the interaction of matter fields (such as nucleons [1, 2] or hadrons containing a heavy quark [3, 4, 5, 6]) with lowmomentum pseudo-Goldstone bosons – the pions, kaons and eta. In Ref. [7] chiral perturbation theory was used to describe the interactions of the ρ, K∗, φ and ω vector mesons with lowmomentum pseudo-Goldstone bosons. In this article, we will extend the formalism to study the lowest-lying tensor meson nonet. This nonet is expected to have quantum numbers J = 2, and contains the isotriplet a2(1320) and the S = ±1 isodoublets K∗ 2(1430). The two isosinglet states are not as well established, but experimental evidences suggest that they are probably f2(1275) and f ′ 2(1525). The mass difference between these nine lowest-lying tensor mesons are small compared to the chiral symmetry breaking scale 4πfπ ≈ 1 GeV. Hence, chiral perturbation theory should be applicable as a systematic expansion procedure for a class of processes involving tensor mesons and soft Goldstone bosons. In the past, chiral perturbation theory has been used extensively to study processes which do not have a tensor meson in the final state. In such decays, the final state pions are not soft enough that the application of the chiral Lagrangian to such processes is not justified a priori. At the best, they serve as a phenomenological model. The pseudo-Goldstone boson fields can be written as a 3× 3 special unitary matrix Σ = exp 2iΠ f , (1) where Π = 