Hadron Physics At The Low Energy With Chiral Perturbation Theory

The interaction between the low-energy hadrons is very essential for the studyof molecules and resonances. At the low energy, the coupling constant αsof quantumchromodynamics becomes very large, so the perturbative expansion by αsbreaksdown. However, one can express the results as a power series in the small momentumof external particles with chiral perturbation theory. In the thesis, the interactionbetween hadrons is studied at the one-loop level with chiral perturbation theory.The author has calculated the scattering lengths between the Goldstone particlesand charmed hadrons, and derived the interacting potentials between the heavypseudoscalar mesons. The scattering length and the interacting potential can refectthe interaction between low-energy hadrons.Heavy hadron efective feld theory is widely used to study the properties ofheavy hadrons. Its consistent power counting ensures that the results can be ex-panded order by order as a power series of small momentum. In the thesis, I havestudied the scattering length between the Goldstone particles and charmed hadronsto the third order, and discussed the convergence of chiral expansion in detail. The infrared regularization method is also frequently used to study the prop-erties of heavy hadrons as a variation of chiral perturbation theory. The relativisticLagrangian is used directly within this framework, which ensures the results to havegood analytic properties. I use heavy hadron efective feld theory and infrared reg-ularization method to study the scattering lengths between the Goldstone particlesand charmed vector mesons. I have compared the numerical results with the twomethods.The double poles in the two-heavy-hadron-reducible diagram will break thepower counting scheme when studying the scattering amplitude between two heavyhadrons etc. Weinberg noticed the problem at frst and proposed the solution,so-called “Weinberg scheme”. With the Weinberg scheme, I have calculated theinteracting potentials between the heavy psedoscalar mesons to the second order. Ihave considered not only the contribution from the two-boson exchange, but alsothe one-loop correction to the four-heavy-meson contact terms.In summary, the author has studied the interaction between low-energy hadronswith chiral perturbation theory. The techniques developed in the thesis can beextended to the other similar low-energy process. The results will be helpful to thestudy of hadron molecules etc. The nonanalytic parts of the expressions can beused in the chiral extrapolation in lattice quantum chromodynamics simulation.