Study Of Doubly Charmed Baryons In Chiral Perturbation Theory

In the meson-doubly charmed baryon system,scattering length is an very important physical quantity,which is helpful for our understanding of the low-energy strong inter-actions between the pseudoscalar mesons and doubly charmed baryons.In this thesis,We present the calculation of S-and P-wave scattering lengths within the framework of chiral perturbation theory.Firstly,we introduce the generic procedure of the construction of the chiral effective meson-doubly charmed baryon Lagrangian.The minimal and complete set of chiral effec-tive Lagrangians up to_O(p~4)is constructed both in the relativistic and the non-relativistic cases.The numbers of linearly independent invariant monomials at_O(p~2),_O(p~3),and O(p~4)are 8,32 and 218,in order.Many unknown low-energy constants appear in these Lagrangians and their values can be determined by experimental or lattice QCD data.The obtained Lagrangians can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at one-loop level in future.Secondly,we use the Lagrangians we have constructed to calculate S-and P-wave scattering lengths at leading one-loop order.16 strangeness-isospin scattering amplitudes are calculated,based on the chiral effective Lagrangians up to_O(p~3)in the relativistic form.Utilizing the Extended-On-Mass-Shell(EOMS)subtraction scheme,these amplitudes are renormalized in the chiral limit,which possess the right analytic structure and respect the power counting rule.The S-and P-wave scattering lengths are calculated for the elas-tic scattering processes,using the theoretical formulas of scattering lengths that we have derived.We estimate some values of the low-energy constants at_O(p~2),according to the heavy quark-diquark symmetry,and calculate the scattering lengths up to_O(p~2)for the elas-tic scattering channels.These values will contribute to the study of meson-doubly charmed baryon scattering lengths in the future lattice QCD.Meanwhile,we hope more lattice QCD data will be available such that the unknown low-energy constants can be pinned down.In consequence,higher-order theoretical calculation of scattering lengths can be achieved,which in turn will serve the experimental high-precision measurements.In the framework of chiral perturbation theory,the obtained theoretical results is not only useful for us to explore the low-energy strong interactions between the pseudoscalar mesons and doubly charmed baryons,but also helpful for the study of doubly charmed baryon spectroscopy.Furthermore,it can be readily extended to the sector of doubly-bottomed baryons,which will be crucial for our understanding of some important properties of doubly-bottomed baryons.