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A<sc>bstract</sc> We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. We evolve theS-matrix of a single dressed gluon from the scaleQ_P, which is the inverse color correlation length in the projectile toQ≫Q_Pwhich corresponds to the hard resolution scale provided by the target. As expected,Sceases to be unitary if evolved to significant ln$$ {Q}^2/{Q}_P^2 $$ $Q^2/Q_P^2$. Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity. 

A<sc>bstract</sc> We reanalyze the origin of the large transverse logarithms associated with the QCD one loopβfunction coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders inα_sin the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrixS(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum. 

A bstract We explore possible extensions of the t -channel and s -channel unitary model of high energy evolution in zero transverse dimensions appropriate to very high energy/atomic number where the dipole density in a toy hadron is parametrically high. We suggest that the appropriate generalization is to allow emission of more than one dipole in a single step of energy evolution. We construct explicitly such a model that preserves the t -channel and s-channel unitarity and have the correct low density limit, and study the particle multiplicity distribution resulting from this evolution. We consider initial conditions of a single dipole and many dipoles at initial rapidity. We observe that the saturation regime in this model is preceded by a parametric range of rapidities $$ \frac{1}{\alpha_s}\ln \frac{1}{\alpha_s}<\frac{1}{\alpha_s}\ln \frac{1}{\alpha_s^2} $$ 1 α s ln 1 α s < Y < 1 α s ln 1 α s 2 , where the saturation effects are still unimportant, but multiple emissions determine the properties of the evolution. We also discuss the influence of the saturation on the parton cascade and, in particular, find that in the saturation regime the entropy of partons becomes S ≈ $$ \frac{1}{2} $$ 1 2 ln N where N is the mean multiplicity. 

Abstract Within the dense-dilute Color Glass Condensate approach, and using the Golec–Biernat–Wuesthoff model for the dipole scattering amplitude, we calculate$$v_2^2$$ $v_2^2$as well as the correlations between$$v_2^2$$ $v_2^2$and both the total multiplicity and the mean transverse momentum of produced particles. We find that the correlations are generally very small consistent with the observations. We note an interesting sharp change in the value of$$v^2_2$$ $v_2^2$as well as of its correlations as a function of the width of the transverse momentum bin. This crossover is associated with the change from Bose enhancement dominance of the correlation for narrow bin to HBT dominated correlations for larger bin width. 

A bstract Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians H RFT . We require that H RFT is self dual, reproduce all known limits (dilute-dense and dilute-dilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called “diamond action” discussed in [67, 68]. However we show by explicit calculation that the so called “diamond condition” is not satisfied beyond leading perturbative order. 

A bstract Further developing ideas set forth in [1], we discuss QCD Reggeon Field Theory (RFT) and formulate restrictions imposed on its Hamiltonian by the unitarity of underlying QCD. We identify explicitly the QCD RFT Hilbert space, provide algebra of the basic degrees of freedom (Wilson lines and their duals) and the algorithm for calculating the scattering amplitudes. We formulate conditions imposed on the “Fock states” of RFT by unitary nature of QCD, and explain how these constraints appear as unitarity constraints on possible RFT hamiltonians that generate energy evolution of scattering amplitudes. We study the realization of these constraints in the dense-dilute limit of RFT where the appropriate Hamiltonian is the JIMWLK Hamiltonian H JIMWLK . We find that the action H JIMWLK on the dilute projectile states is unitary, but acting on dense “target” states it violates unitarity and generates states with negative probabilities through energy evolution.