Abstract
We derive the complete set of crossing symmetric forward pion-pion amplitudes with non-negative absorptive parts obeying twice-subtracted dispersion relations. We give a method to eliminate subtraction constants for these amplitudes by making a simultaneous use of subtracted dispersion relations for the amplitude and its inverse, and unitarity. We thus deduce from axiomatic field theory (i) lower bounds on forward real parts in terms of physical forward amplitudes, (ii) lower bounds on S- and P-wave scattering lengths in terms of forward amplitudes in any part of the physical region, (iii) sum rules on scattering lengths in terms of physical forward amplitudes which provide a complete test of forward dispersion relations, (iv) upper bounds on scattering lengths in terms of total cross sections and (v) absolute sum rule inequalities on total and forward differential cross sections in terms of the pion mass alone which provide new tests of dispersion relations not involving scattering lengths.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
