DUBNA Baldin ISHEPP XXIII, September 19-24, 2016

GENERAL SPIN PARTICLE FORMALISM BASED ON SYMMETRY PROPERTIES AND MODEL-INDEPENDENT RESULTS M. P. Chavleishvili International University Dubna Dubna, RUSSIA

Symmetry means harmony, beauty, order.

A.M. Baldin suggested new approach in relativistic nuclear physics which is based on the application of the similarity laws, symmetry and other methods, not resting upon the Lagrange functions, to the construction of models starting from the first principles.

SYMMETRY AND SPIN In physics, symmetry has three levels: 1. Coordinate systems, frames (spherical system, inertial systems); 2. Variables. (For example, for binary processes we have two independent variables, energy and angle, or invariant variables -- s and t); 3. Functions. Amplitudes.

We consider the general spin particle formalism based on symmetry properties, including requirements of angular momentum conservation in the t-channel.

STRUCTUE OF HELICITY AMPLITUDES AND SOME RESULTS FOR BINARY PROCESSES

[6] M.P.Chavleishvili, High Energy Spin Physics, Proceedings of the 9th International Symposium, Eds. K.- H.Althoff W.Meyer, Bonn, vol1,p.489 (Springer-Verlag, Berlin, 1991) [7] M.P.Chavleishvili, Polarization Dynamics in Nuclear and Particle Physics, Proceedings of the International Symposium, Trieste,1992 [8] M.P.Chavleishvili, Ludwig-Maximilian University Preprint LMU-02-93, M\"unchen, 1993 [9] M.P.Chavleishvili, Ludwig-Maximilian University Preprint LMU-03-93, M"unchen, 1993 [10] M.P.Chavleishvili, JINR Preprint, E , Dubna, 1992 [11] M.P.Chavleishvili, High Energy Spin Physics, Proceedings of the 8th International Symposium, Ed.K.J.Heller, 1988,vol 1,p.123. New York, 1989

On the basis of general space-time and crossing symmetry general analitic structure for amplitudes describing spin-particle binary reactions are considered. Using knowledge about kinematic structure of helicity amplitudes in dynamic amplitude approach we can get:

For particles with nonzero spin, the process (1) can bedescribed by Jacob and Wick helicity amplitudes. The helicity amplitudes have clear physical meaning, the same dimensions, observables (polarization, cross sections, asymmetries, etc.) are simply expressed via them.

but helicity amplitudes contain kinematic singularities and the conservation laws are not guaranteed to fulfil (and these laws are not fulfilled automatically), thus kinematics and dynamics are not separated.

Kinematic singularities Helicity amplitudes have kinematic singularities. When one considers spin-zero particle scattering, by definition, one has no kinematic singularities connected with spin. There exist several different but in fact equivalent definitions of "kinematic singularities":

--- Kinematic singularities can be manifested by the fact that the generalization of the partial-wave decomposition in the Legandre polynomials of the scattering amplitude in the spin zero case to spin-particle scattering (based on the symmetry arguments) is the decomposition of the helicity amplitudes in the Wigner rotation functions. But these functions are not polynomials, they contain singularities, just the kinematic singularities of the helicity amplitudes. So, helicity amplitudes have the kinematic singularities and we face the problem to find and separate them.

For elastic scattering of equal mass spin- particles we can determine dynamic amplitudes by the following equation

Using knowledge about kinematic structure of helicity amplitudes in dynamic amplitude approach we can get: dispersion relations for each individual helicity amplitudes, describing any elastic processes; low-energy theorems (involving reactions with photon, graviton and gravitino); sum rules (including Drell-Hern-Gerasimov SR); -model-independent sum--rulle type inequalities for observable quantities -some asymptotic relations between polarization parameters.

-dispersion relations for each individual helicity amplitudes, describing any elastic processes; -low-energy theorems (involving reactions with photon, graviton and gravitino);

-sum rules (including Drell-Hern-Gerasimov SR); - model-independent sum--rulle type inequalities for observable quantities - asymptotic relations between polarization parameters.

a (s(1),m(1)) + b ( s(2),m(2)) c (s(3),m(3)) + d (s(4),m(4)). N=(2s(1) +1)(2s(2) +1)( s(3) +1)(2s(4) +1). p-p elastic we have 16 amplitudes, P, T and C 5 iamplitudes p-p elastic we have 165 amplitudes For forvard scattering 2 amplitudes

Quantum Chromodynamics: History and Prospects Oberwölz, Austria, 2012

PUZZLE OF HIGH ENERGY PP-SCATTERING. HELICITY CONSERVATION FROM PERTURBATIVE QCD OR KINEMATIC HIERARCHY?

We consider the general spin particle formalism based on symmetry properties, including requirements of angular momentum conservation in the t-channel. In such "a dynamic amplitude" approach obligatory kinematic factors arise in helicity amplitudes and consequently in expressions of all observable quantities.

The use of perturbative QCD for this reaction is based on the following assumptions: --- Factorization property. The quark subprocess is separable. --- A simple connection between quark and proton helicities. The proton helicity is just the sum of quark helicities.

The consequences of this rule are in contradiction with the experiment. It is difficult to expect for changing (and improving) the situation by calculating an enormous number of diagrams in higher order. (It seems That helicity conservation will remain in any finite order of aperturbative expansion.)

PERPURBATIVE QCD AND HARD PROTON-PROTON SCATTERING There exists contradiction between the perturbative QCD and experiment. This is connected with proton-proton scattering at high energies and large fixed angles. This is just the region where PQCD must work. But one can say that "the naive PQCD" has some difficulty here.

A.D.Krish Spin crisis A(3,56) = 0,26 A(4,79) = 0,52 A(5,56) = 0,59

PUZZLE OF HIGH ENERGY PP- SCATTERING. HELICITY CONSERVATION FROM PERTURBATIVE QCD OR KINEMATIC HIERARCHY? Brodski - Chavleishvili Austria

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