Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinite nuclei in the reggeon toy model
46
0
0.0
(
0
)
Authors
M.A. Braun
Ask ChatGPT about the research
No Arabic abstract
Hadron-nucleus amplitudes at high energies are studied in the toy Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.
rate research
Read More
The effective reggeon field theory in zero transverse dimension (the toy model) is studied. The transcendental equation for eigenvalues of the Hamiltonian of this theory is derived and solved numerically. The found eigenvalues are used for the calculation of the pomeron propagator.
We propose the one-dimensional reggeon theory describing local pomerons and odderons. It generalizes the well-known one-dimensional theory of pomerons (the Gribov model) and includes only triple interaction vertices. The proposed theory is studied by numerical methods: the one-particle pomeron and odderon propagators and the pA amplitude are found as functions of rapidity by integrating the evolution equation.
We discuss renormalization in a toy model with one fermion field and one real scalar field phi, featuring a spontaneously broken discrete symmetry which forbids a fermion mass term and a phi^3 term in the Lagrangian. We employ a renormalization scheme which uses the MSbar scheme for the Yukawa and quartic scalar couplings and renormalizes the vacuum expectation value of phi by requiring that the one-point function of the shifted field is zero. In this scheme, the tadpole contributions to the fermion and scalar selfenergies are canceled by choice of the renormalization parameter delta_v of the vacuum expectation value. However, delta_v and, therefore, the tadpole contributions reenter the scheme via the mass renormalization of the scalar, in which place they are indispensable for obtaining finiteness. We emphasize that the above renormalization scheme provides a clear formulation of the hierarchy problem and allows a straightforward generalization to an arbitrary number of fermion and scalar fields.
Fundamental inequalities for QCD sum-rules are applied to resolve a paradox recently encountered in a sum-rule calculation. This paradox was encountered in a toy model known to be free of resonances that yields an apparent resonance using a standard sum-rule stability analysis. Application of the inequalities does not support the existence of a well defined sum-rule calculation, and shows a strong distinction from typical behaviour in QCD.
In an attempt to regularize a previously known exactly solvable model [Yang and Zhang, Eur. J. Phys. textbf{40}, 035401 (2019)], we find yet another exactly solvable toy model. The interesting point is that while the Hamiltonian of the model is parameterized by a function $f(x)$ defined on $[0, infty )$, its spectrum depends only on the end values of $f$, i.e., $f(0)$ and $f(infty )$. This model can serve as a good exercise in quantum mechanics at the undergraduate level.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
