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M. A. Braun

Publications and source records attributed to M. A. Braun.

At least 19 recordsLinked to original sources
arXiv2026

Entropy from inclusive scattering

Introduction of probabilities from multiple inclusive cross-sections is studied in the unitary pomeron exchange models with no interaction between the pomerons themselves. Discrepancy is observed between the emerging inelasic cross-section and the one following from unitarity. It diminishes with energy and disappears in the high-energy limit. Probabilities and entropy are calculated numerically. Contrary to naive predictions as a function of energy the entropy first rises and after achievung its maximum at rapidity 12-17 slowly falls for higher energies

hep-ph↗
arXiv2026

The Regge-Gribov model with odderons

The Regge-Gribov model describing interacting pomerons and odderons is proposed with triple reggeon vertices taking into account the negative signature of the odderon. Its simplified version with zero transverse dimensions is first considered. No phase transition occurs in this case at the intercept crossing unity. This simplified model is studied without more approximations by numerical techniques. The physically relevant model in the two-dimensional transverse space is then studied by the renormalization group method in the single loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behaviour when the intercepts move from below to their critical values compatible with the Froissart limitation is studied. Five real fixed points are found with singularities in the form of non-trivial branch points indicating a phase transition as the intercepts cross unity. The new phases, however, are not physical, since they violate the projectile-target symmetry. In the vicinity of fixed points the asymptotical behaviour of Green functions and elastic scattering amplitude is found under Glauber approximation for couplings to participants.

hep-th↗
arXiv2025

On the reggeon model with the pomeron and odderon: singularities with non-zero masses

The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique in the single loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behaviour when the intercepts move from below to their critical values compatible with the Froissart limitation is studied. The singuarities in the form of non-trivial branch points indicating a phase transition are found in the vicinity of five fixed points found in the previous publication. Since new phases violate the projectile-target symmetry the model is found non-physical for the bare intercepts above their critical value.

hep-th↗
arXiv2025

Probabilities in Toy Regge models with odderons

The possibi;lity of a probabilistic interpretation is studied for the Regge-Gribov model in zero dimensional transverse world ("Toy") with interacting pomerons and odderons. It is found that the previously proposed recipe to introduce such interpretation in the model without odderons, does not work once odderons are included. Starting from the physically reasonable probabilites it leads to a pathological field theory violating $C$-parity invariance. Inversely, starting from an admissible field theory one comes to pathological probabilities, which not only violate $C$-nvariance but also allow particles to be created from or annihilated into the vacuum. A method is proposed to introduce reasonable probabilities besed directly on the Fock components of the wave function. Such probabilities manifest themselves in the multiplicity distributions of hadrons produced in high-energy collisions. The corresponding entropy grows with rapidity but saturates in the limit. It is found to be similar for processes of both parity exchanges.

hep-ph↗
arXiv2024

Entropy in Toy Regge models

The probabilistic interpretation of the standard Regge-Gribov model with triple pomeron interactions is discussed. It is stated that introduction of probabilities within this model is not unique and depends on what is meant under the relevant substructures, The traditional interpretation in terms of partons (quarks and gluons) is shown to be external to the model, imported from the QCD, and actually referring to the single pomeron exchange without interactions. So this interpretation actually forgets the model as such. Alternative probabilities based on the pomerons as basic quantities within the model are discussed. Two different approaches are considered, based either on the pomerons in Fock's expansion of the wave function or on pomeron propagators in Feynman diagrams. These pomeron probabilities and entropy turn out to be very different from the mentioned standard ones in the purelyp obabilistic treatment. The entropy, in particular, either rises with the rapidity and saturates at a certain fixed value or first rises, reaches some maximum and goes down to zero afterwards. Possible observable manifestations of these probabilities and entropy are to be seen in the distributions of the cross-section in powers of the coupling constants to the participants. 23

hep-ph↗
arXiv2024

The reggeon model with the pomeron and odderon: renormalization group approach

The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique. The single loop approximation is adopted. Five real fixed points are found and the high-energy behaviour of the propagators is correspondingly calculated. As without odderon, the asymptotic is modulated by logarithms of energy in certain rational powers. Movement of coupling constants away from the fixed points is investigated both analytically (close to the fixed points) and numerically (far away). In the former case attraction occurs only in restricted domains of initial coupling constants. More generally in one third of the cases the coupling constants instead grow large indicating the breakdown of the single loop approximation.

hep-th↗
arXiv2023

Production of cumulative pions and percolation of strings

Production of pions in high-energy collisions with nuclei in the kinematics prohibited for free nucleons ("cumulative pions") is studied in the fusing color string model.The model describes the so-called direct mechanism for cumulative production. The other, spectator mechanism dominates in production of cumulative protons but is suppressed for pions. In the model cumulative pions are generated by string fusion which raises the maximal energy of produced partons above the level of the free nucleon kinematics. Momentum and multiplicity sum rules are used to determine the spectra in the deep fragmentation region. Predicted spectra of cumulative pions exponentially fall with the scaling variable $x$ in the interval $1<x<3$ with a slope of the order 5$÷$5.6, which agrees well with the raw data obtained in the recent experiment at RHIC with Cu-Au collisioins. However the agreement is worse for the so-called unfolded data, presumably taking into account corrections due to the expermental set-up and having rather a power-like form.

hep-ph↗
arXiv2022

Local one-dimensional reggeon model of the interaction of several pomerons

We consider the one-dimensional local reggeon theory describing the leading pomeron with the conformal spin $l=0$ and two subdominant pomerons with $l=\pm 2$. The dependence of the propagators of pomerons and the $hA$ amplitude on rapidity are found numerically by integrating the evolution equation.

hep-ph↗
arXiv2021

3N potentials in the Faddeev coordinate space approach to Nd scattering

In the last decade, for studying 3$N$ bound states and $Nd$ scattering the Tucson-Melbourne (TM) and Urbana 3$N$ force derived from the chiral EFT have been applied. We plan to use the TM 3$N$ force for studying the $Nd$ scattering on the basis of the Faddeev equations in configuration space. In the given paper, we present our final formulas for components of the TM 3$N$ potential obtained in the coordinate space.

nucl-th↗
arXiv2021

Four-pomeron vertex

The four-pomeron vertex is studied in the perturbative QCD. Its dominating terms of the leading (zeroth and first) orders in the coupling constant and subdominant in the number of colors are constructed. The vertex consists of two terms, one with a derivative in rapidity $\pd_y$ and the other with the BFKL interaction between pomerons. The corresponding part of the action and equations of motion are found. The iterative solution of the latter is possible only for rapidities smaller than 2 and quite large coupling constant $α_s$, of the order or greater than unity, when the quadruple pomeron interaction is relatively small. Also iteration of the part with $\pd_y$ is unstable in the infrared region and compels to introduce an infrared cut. The variational approach with simple trying functions allows to find the minimum of the action at $α_s$ of the order 0.2 and rapidities up to 25. Numerical estimates for O-O collisions show that actually the influence of the quadruple pomeron interaction turns out to be rather small.

hep-ph↗
arXiv2021

Local one-dimensional reggeon model of the interaction of pomerons and odderons

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.

hep-ph↗
arXiv2021

On the Markov evolution of the $ρ$-matrix of a subsystem

Evolution of the reduced density matrix for a subsystem is studied to determine deviations from its Markov character for a system consisting of a closed chain of $N$ oscillators with one of them serving as a subsystem. The dependence on $N$ and on the coupling of the two subsystems is investigated numerically. The found deviations strongly depend on $N$ and the coupling. In the most beneficial case with $N-1=100$ and the coupling randomized in its structure the deviations fall with the evolution time up 3\%. In other cases they remain to be of the order 30\% or even more.

quant-ph↗
arXiv2020

The QCD odderon in elastic (anti)proton scattering

The C-odd amplitude for the elastic $pp$ and $p\bar{p}$ scattering due to the exchange of the QCD odderon proposed by J.Bartels, L.N.Lipatov and G.P. Vacca is calculated with the Fukugita-Kwiecinski proton impact factor. The found amplitude is very small and cannot be felt in the differential cross-sections at 2.76 and 1.96 Tev respectively.

hep-ph↗
arXiv2020

Triple-pomeron amplitude in the effective action approach

In the effective action approach the imaginary part of the triple pomeron amplitude is calculated. The found dependence on the longitudinal momentum transfer $\e$ is found to separate as a simple factor $1/|\e|$. This result is used to calculate the high-mass diffraction on a hadron and double scattering cross-section off a composite target}

hep-ph↗
arXiv2020

Evolution of pomeron and odderon at all angular momemnta

In the QCD the small~$x$ evolution of the interacting pomerons and odderons is studied with all angular momenta $l$ taken into account. The resulting system of coupled nonlinear evolution equations is formulated in the momentum space and solved numerically. Excellent convergence in $l$ is observed. Also it is found that states with $l>1$ play an important role and substantially reduce the basic pomeron state at large rapidities

hep-ph↗
arXiv2020

The odderon and BKP states in the Quantum Chromodynamics

We discuss the odderon in the QCD and analyze the effects of running coupling introduced in a particular way to preserve the reggeization of the gluon within the leading logarithmic description. This idea is also applied to a family of BKP states with arbitrarily number of gluons in the planar limit. The numerical analysis shows that contrary to the pomeron case where the leading states become discretized, the odderon states still remain a continuous family starting at intercept one. The following rapidity dependence of the amplitude is studied. For the pomeron-odderon system the relation between the descriptions in the reggeized gluon (BFKL) framework and the color dipole/CGC one is investigated.

hep-th↗
arXiv2019

Elliptic and triangular flows in dAu collisions at 200 GeV in the fusing color string model

In the color string picture with fusion and percolation the elliptic and triangular flows are studied for p-Au and d-Au collisions at 200 GeV. The ordering $v_n(d-Au)>v_n(p-Au)$ observed experimentally for central collisions is reproduced.The calculated elliptic flow $v_2$ at central collisions agrees satisfactorily with thedata. The triangular flow $v_3$ is found to be greater than the experimental values, similar to the resultsobtained in the approach based on the Color Glass Condensate initial conditions with subsequenthydrodynamical evolution.

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