K-Meson Spectroscopy in the Static Limit of s-Quark

Abstract

The K-meson spectroscopy is studied in the static limit of the s-quark, which is motivated by the heavy quark symmetry. The spin-parity of the light degrees of freedom st is a good quantum number to classify the K mesons as well asthe D and B mesons. Then, K 1(1270) is assigned to be the st =(3/2)+ state and KI(1400) to be the st =(1/2)+ state. Our result will be tested in the mass differences between the spin one and two states of D and K mesons. The precise experimental decay widths of these mesons will also reveal the availability of the static limit of the s-quark system. In recent years, it has been shown that hadrons containing a single heavy quark exhibit a new flavor-spin symmetry of QCD.I)-5) The effective theory for heavy quarks has been appli~d in various areas of phenomenology,6)-lO) and successful results were obtained for the b-quark and c-quark systems. Since the s-quark is not sufficiently heavy compared with the QCD scale (AQCD) , one may consider that the heavy quark effective theory is invalid for the s-quark. However, previous challeng­ ing studies ll ),12) suggest that the heavy quark effective theory is still valid for the s-quark system if a constituent quark mass is employed for ms and the 11ms correc­ tions are properly taken into account. We have found that the predicted differential and total decay rates of 15--'> K* lfJ and 15--'> KlfJ were in agreement with the experi­ mental data very well in the heavy quark symmetry of the s-quark. 12 ) If those agreements are not accidental, the heavy quark theory of the s-quark works well in other phenomena such as the spectroscopy. Therefore, it is important to examine the availability of the heavy flavor symmetry with corrections in the s-quark system. In this work, the spectra of K mesons are investigated using the symmetry properties of the heavy quark effective theory. Analyses given by Aglietti 13 ) are compared with ours. The strong decay widths are also examined in the static limit of the s-quark. Let us begin with giving the hadron mass formula with properties of the heavy quark symmetry: