On the probability distribution of the stochastic saturation scale in QCD

It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations.Comment: 9 pages, 3 figures, misprints corrected, version to appear in PL

Interference Phenomena in Medium Induced Radiation

We consider the interference pattern for the medium-induced gluon radiation produced by a color singlet quark-antiquark antenna embedded in a QCD medium with size $L$ and `jet quenching' parameter $\hat q$. Within the BDMPS-Z regime, we demonstrate that, for a dipole opening angle $\theta_{q\bar q} \gg\theta_c\equiv {2}/{\sqrt{\hat q L^3}}$, the interference between the medium--induced gluon emissions by the quark and the antiquark is suppressed with respect to the direct emissions. This is so since direct emissions are delocalized throughout the medium and thus yield contributions proportional to $L$ while interference occurs only between emissions at early times, when both sources remain coherent. Thus, for \tqq \gg\theta_c, the medium-induced radiation is the sum of the two spectra individually produced by the quark and the antiquark, without coherence effects like angular ordering. For \tqq \ll\theta_c, the medium--induced radiation vanishes.Comment: 4 pages, 2 figures; Proceedings of the "Quark Matter 2011" conferenc

Forward gluon production in hadron-hadron scattering with Pomeron loops

We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomeron loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, `dilute-dense', collisions : a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the Pomeron loop effects become important in the evolution of the target wavefunction, gluon production is dominated by `black spots' (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy.Comment: 29 pages, 7 figure

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits

Small-x QCD effects in forward-jet and Mueller-Navelet jet production

We investigate small-x QCD effects in forward-jet production in deep inelastic scattering in the kinematic regime where the virtuality of the photon and the transverse momentum of the jet are two hard scales of about the same magnitude. We show that the data from HERA published by the H1 and ZEUS collaborations are well described by leading-logarithmic BFKL predictions. Parametrizations containing saturation effects expected to be relevant at higher energies also compare well to the present data. We extend our analysis to Mueller-Navelet jets at the LHC and discuss to what extent this observable could test these small-x effects and help distinguishing between the different descriptions.Comment: 18 pages, 9 figures, minor changes, published versio

Researches regarding structural modifications that appears in the material of tools used for rubber waste attrition

Tools commonly used for shredding rubber waste, currently produced, are made of neatly cast iron in the composite is to avoid the presence of sulfur and phosphorus. In this paper are presented the main structural material changes that occur in different areas, located at different distances from the active surface of tools. Structural changes occurred mainly refers to the transformation of white iron surface layer to gray cast iron and graphite separations appearance, which causes the crack primers and cracking corrosion phenomena in tools material

Researches on the chemical composition and hardness modifications that appear in the material of tools used for rubber waste attrition

This paper presents the results of the main changes in the chemical composition of the material, and changes in its hardness. The changes in terms of chemical composition refer primarily to changes in concentration of sulfur and carbon, and in terms of hardness material change there can be noticed a decrease in hardness of the material that is in direct contact with waste rubber

JIMWLK evolution in the Gaussian approximation

We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors Nc. This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite Nc. Any higher n-point function with n greater than or equal to 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to appear in JHE