Analyses Of Pion-nucleon Elastic Scattering Amplitudes Up To O(q~4) In Extended-on-mass-shell Subtraction Scheme

The present thesis is mainly devoted to studying π-N scatterings within covariantbaryon chiral perturbation theory (CBχPT). Since CBχPT is one of the effective fieldtheories of QCD at low energies, the basic ideas of effective field theories are firstlyintroduced. Then, the construction of chiral perturbation theory(χPT) and the powercounting breaking(PCB) problem encountered within CBχPT are shown. Also, the so-lutions to the PCB problem, eg. Heavy Baryon(HB) approach, Infrared Regularization(IR) prescription, Extended-On-Mass-Shell (EOMS) scheme, etc., are discussed in de-tail. Finally, the calculation of π-N scattering amplitude up to O(q~4) level in EOMSscheme is studied in great details, and some related phenomenology are also investigat-ed.The EOMS scheme provides a good solution to the PCB problem in the sense thatit faithfully respects the analytic structure of the original amplitudes, and being scaleindependent for merely making an additional subtraction of a polynomial of PCB termswith respect to the traditional substraction. The O(q~3) level calculation within EOMSshows that the size of the O(q~3) contribution can be very large and comparable to thosegiven by the lower-order terms even at very low energies above threshold. Thus, theapplicability of EOMS scheme to describe the partial wave phase shift at O(q~3) seemsto be questionable.In this thesis the analysis is extended up to O(q~4), and the convergence problemoccurred in the O(q~3)-level analysis is settled down, even when the (1232) resonanceis absent. Compared with the O(q~4)-IR results in the previous literature, the pion-nucleon scattering amplitude presented here is the first analytic and complete O(q~4)result. Especially, the substraction of PCB terms is paid great attention to, such thatthe “threshold divergence” problem never occurs. Fits to partial wave phase shift data are performed and all the LECs involved are determined. Besides, the leading ordercontribution from an explicit (1232) resonance and partially-included (1232) loopcontribution are included to describe phase shift data up to energies just below theresonance region.A phenomenological discussion is also made based on the pion-nucleon scatteringamplitude. The Goldberger-Treiman (GT) relation and the pion-nucleon sigma termσπNhave been mainly studied. The GT relation violation is a basic quantity to testthe applicability of EOMS-BχPT to the pion-nucleon system and it is calculated up toO(q~3). The prediction of the violation is in good agreement with other determinations,and its chiral series is found convergent rapidly. The analysis on σπNis important tounderstand the origin of the mass of the ordinary matter. Taking both pion-nucleonphase shift and the lattice QCD data into consideration, a reasonable prediction for thepion-nucleon sigma term is given: σπN=52±7MeV from the fit without (1232),and σπN=45±6MeV from the fit with an explicit (1232).