Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnalytic properties of unitarization schemes
64
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The analytic properties of the elastic hadron scattering amplitude are examined in the impact parameter representation at high energies. Different unitarization procedures and the corresponding non-linear equations are presented. Several unitarisation schemes are presented. They lead to almost identical results at the LHC.
rate research
Read More
The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard asymptotic relations for the ratio of the elastic cross section to the total cross section. The relation between the phases of the unitarized amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.
We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarisation, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarisation is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.
Different forms of non-linear equations which mimic parton saturation in the non-perturbative regime are examined. These equations lead to corresponding unitarization schemes in the impact parameter representation of the hadron scattering amplitude. It is shown how specific properties of the non-linear equations reflect different features of the diffraction processes.
We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Pade approximants and the N/D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnes solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.
A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply $S$-matrix techniques, based on unitarity and analyticity, we first derive an $S$-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers ($J^{PC}=0^{++}$) that we call the textit{graviball}. Remarkably, this resonance is located below the Planck mass but deep in the complex $s$-plane (with $s$ the usual Mandelstam variable), so that its effects along the physical real $s$ axis peak for values significantly lower than this scale. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same $J=0$ partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
