Charm meson radiative decays

Combining heavy quark effective theory and the chiral Lagrangian approach we investigate D meson radiative decays. First, we reanalyse D∗ → Dγ decays using heavy quark spin symmetry, chiral symmetry Lagrangian, but including also the light vector mesons. Then, we calculate branching ratios D → V γ. We make some comments on the Cabbibo suppressed decays D → ρ/ωγ and the branching ratios of D → PPγ decays. Experimentally radiative decays of D mesons have not been measured, while the known branching ratios of D∗ radiative decays [1, 2] can be described using the combination of heavy quark effective theory and chiral Lagrangians [3]-[15]. The strong interaction meson Lagrangian for the light pseudoscalar octet and heavy pseudoscalar and vector triplets in the chiral and heavy quark limits was first written down by Wise [16] (see also [4]). The electromagnetic interactions between these mesons was described in [1, 2, 6]. The octet of light vector mesons was included in the Wise Lagrangian [16] later by Casalbuoni, et al. [12] as the gauge particles associated with the hidden symmetry group SU(3)H [17]. The light pseudoscalar mesons are described by the 3×3 unitary matrix u = exp( iΠ f ), (f ≃ 132 MeV) with Π the usual pseudoscalar matrix as in ref. [14], while the octet of light vector mesons is described by the 3 × 3 matrix ρ̂μ = i gV 2ρμ where gV (≃ 5.8 √ 2/a with a = 2 in the case of exact vector dominance) is the coupling constant of the vector meson self– interaction [17] and ρμ the vector meson matrix. The heavy mesons are Qq̄ a ground states, where Q is a c quark and q = u, q = d and q = s. In the heavy quark limit they are described by 4× 4 matrix Ha (a = 1, 2, 3) [16] Ha = 1 2 (1+6v)(P ∗ aμγμ − Paγ5) (1) where P ∗ aμ and Pa annihilate, respectively, a spin-one and spin-zero meson Qq̄ of velocity vμ. Following the procedure of [14] we write down the even parity strong and electromagnetic Lagrangian for heavy and light pseudoscalar and vector mesons: