Abstract
We derive the scattering amplitude for Goldstone bosons of chiral symmetry off the pseudoscalar charmed mesons up to leading one-loop order in a covariant chiral effective field theory, using the so-called extended-on-mass-shell renormalization scheme. Then we use unitarized chiral perturbation theory to fit to the available lattice data of the S-wave scattering lengths. The lattice data are well described. However, most of the low-energy constants determined from the fit bear large uncertainties. Lattice simulations in more channels are necessary to pin down these values which can then be used to make predictions in other processes related by chiral and heavy quark symmetries.
Highlights
Introduction to the fitting procedureSince all the necessary preparations are completed, we proceed to the description of the lattice QCD data of the S-wave scattering lengths
Because the amplitudes derived here are based on SU(3) chiral perturbation theory (ChPT), we will only include in the fits the new result with Nf = 2 + 1, i.e. a(D1K,0)→DK = −1.33(20) fm obtained at Mπ = 156 MeV, and the unitarized amplitude used in the fits is obtained including the Dsη coupled channel
We show explicitly that the UV divergences and the power counting breaking (PCB) terms, both of which stem from the loops, can be absorbed into the low-energy constants (LECs)
Summary
We denote the D-φ interaction as D1(p1)φ1(p2) → D2(p3)φ2(p4). The scattering process is on-shell, p21 = MD2 1 , p22 = Mφ21 , p23 = MD2 2 and p24 = Mφ22 , with MD1 (Mφ1 ) and MD2 (Mφ2) being the masses of the incoming and outgoing D mesons (Goldstone bosons), respectively. In a more conventional notation, one denotes the small parameters by a unique symbol, say p, so that the power counting rules for the basic quantities read. Every physical observable has its own chiral dimension by using the above given power counting rules. Since the heavy charmed mesons are involved in some of one-loop graphs, there will be PCB terms if we use dimensional regularization with the MS scheme.
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