We study effects of imposing various forms of the kinematical constraints on the full form of the CCFM equation and its non-linear extension. We find that imposing the constraint in its complete form modifies significantly way the shape of gluon density as compared to forms of the constraint used in the numerical calculations and phenomenological applications. In particular the resulting gluon density is suppressed for large values of hard scale related parameter and kT of gluon. This result might be important in description studies of jet correlations at Large Hadron Collider within CCFM approach.
One of the key ideas in describing the multiparticle production at high energies in the perturbative QCD is the angular ordering in successive soft-gluon emission. We analyse the angular distribution of particles in a jet, and investigate the corrections to the angular ordering. At a small angle from the jet direction, the angular ordering is exact at the next-to-leading order. At a large angle, the angular ordering overestimates the angular particle density by a factor $(1-γ\ln \cos^2(θ/2))$, where $γ$ is the anomalous dimension of the multiplicity. The $O(γ)$ correction restores the boost in…
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
We discuss the parton branching (PB) evolution equation for transverse momentum dependent (TMD) parton distribution functions (PDFs), especially we concentrate on the angular ordering constrain and its effect on the TMD distributions. We discuss application of the PB TMDs to precise prediction of Drell-Yan transverse momentum spectrum at LHC, stressing the role of angular ordering in the low transverse momentum region. We compare the PB implementation of the angular ordering condition with the Kimber-Martin-Ryskin-Watt (KMRW), both at the analytical and numerical level.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation, as well as some preliminary results on final-state properties.
We present new results of our studies of soft-gluon angular ordering effects on the evolution of both collinear and transverse momentum dependent (TMD) parton distribution functions, and discuss their implications for precision predictions of Drell-Yan transverse momentum spectra at the LHC. Our method is based on the parton branching (PB) approach. We compare this with the implementation of angular ordering in the Kimber-Martin-Ryskin-Watt (KMRW) approach and with the Collins-Soper-Sterman (CSS) approach. We illustrate numerically the effects of different ordering scenarios ($p_{\bot}$, angul…
We study the perturbative QCD description of the HERA measurements of $F_2 (x, Q^2)$ using a gluon distribution that is obtained from an evolution incorporating angular ordering of the gluon emissions, and which embodies both GLAP and BFKL dynamics. We compare the predictions with recent HERA data for $F_2$. We present estimates of the charm component $F_2^c (x, Q^2)$ and of $F_L (x, Q^2)$.
The assumption of angular ordering in gluon radiation is essential to obtain quantitative results concerning gluonic behaviors. In order to prove the validity of this assumption, we have applied our momentum space flux-tube formalism to check out the angular dependences of gluon radiation. We have calculated the probability amplitudes to get new gluon, and have found that the new gluon is generally expected to have the maximum amplitude when it is produced between the momentum directions of the last two partons.
Medium-induced gluon radiation gives rise to the strong energy-loss observed in single-hadron spectra in heavy-ion collisions. Its angular structure, leading e.g. to intra-jet correlations, is only known for the one-gluon inclusive case. In the vacuum, properties such as angular ordering appear when considering less inclusive distributions due to destructive interference effects. We present a calculation which takes into account interference effects in a medium for a setup in which we consider gluon radiation off a quark-antiquark pair with a given opening angle. Surprisingly, computing the sp…
We study the mismatch between a full calculation of non-global single-logarithms in the large-N_c limit and an approximation based on free azimuthal averaging, and the consequent angular-ordered pattern of soft gluon radiation in QCD. We compare the results obtained in either case to those obtained from the parton showers in the Monte Carlo event generators HERWIG and PYTHIA, with the aim of assessing the accuracy of the parton showers with regard to such observables where angular ordering is merely an approximation even at leading-logarithmic accuracy and which are commonly employed for the t…
We compute the gluon distribution in deep inelastic scattering at small x by solving numerically the angular ordering evolution equation. The leading order contribution, obtained by neglecting angular ordering, satisfies the BFKL equation. Our aim is the analysis of the subleading corrections. Although not complete - the exact next-to-leading contribution is not yet available - these corrections are important since they come from the physical property of coherence of QCD radiation. In particular we discuss the subleading correction to the BFKL characteristic function and the gluon distribution…
We consider the reaction dynamics of bosons with negative parity and spin $0$ or $1$ and fermions with positive parity and spin $\frac{1}{2}$ or $\frac{3}{2}$. Such systems are of central importance for the computation of the baryon resonance spectrum in the hadrogenesis conjecture. Based on a chiral Lagrangian the coupled-channel partial-wave scattering amplitudes have to be computed. We study the generic properties of such amplitudes. A decomposition of the various scattering amplitudes into suitable sets of invariant functions expected to satisfy Mandelstam's dispersion-integral representat…
We elaborate the frame dependence of the angular conditions for spin-1 form factors. An extra angular condition is found in addition to the usual angular condition relating the four helicity amplitudes. Investigating the frame-dependence of the angular conditions, we find that the extra angular condition is in general as complicated as the usual one, although it becomes very simple in the $q^+ = 0$ frame involving only two helicity amplitudes. It is confirmed that the angular conditions are identical in frames that are connected by kinematical transformations. The high $Q^2$ behaviors of the p…
To sum high energy leading logarithms in a consistent way, one has to impose the strong ordering in both projectile rapidity and dense target rapidity simultaneously, which results in a kinematically improved Balitsky-Kovchegov(BK) equation. We find that beyond this strong ordering region, the important sub-leading double logarithms arise at high order due to the incomplete cancellation between real corrections and virtual corrections in a t-channel calculation. Based on this observation, we further argue that these double logarithms are the Sudakov type ones, and thus can be resummed into an …
We study the differential cross section of the single inclusive $e^+e^-$ annihilation to the hadrons via $γ$-production, in the different ${k_{t}}$-factorization frameworks. In order to take into account the transverse momenta of the incoming partons, for the first time, we apply the Kimber et al (KMR) method to calculate the unintegrated parton fragmentation functions (UFFs) from the ordinary integrated one, i.e., the parton fragmentation functions (FFs), which satisfy the similar DGLAP evolution equations, such as those of parton distribution functions (PDFs). Also, by utilizing the differen…
We recall the origin of angular ordering of soft parton emission in the region of small $x$ and show that this coherent structure can be detected in associated distributions. For structure functions at small $x$ and at fixed transverse momentum the angular ordering is masked because of the complete inclusive cancellations of collinear singularities for \xt0. Therefore, in this case the dependence on the hard scale is lost and the angular ordered region becomes equivalent to multi-Regge region in which all transverse momenta are of the same order. In this limit one derives the BFKL equation. In…
In the present work, which is based on the k_-factorization framework, it is intended to make a detail study of the isolated prompt-photon pairs (IPPP) production in the high-energy inelastic hadron-hadron collisions differential cross section. The two scheme-dependent unintegrated parton distribution functions (UPDF) in which the angular ordering constraints (AOC) are imposed, namely the Kimber-Martin-Ryskin (KMR) and the Martin-Ryskin-Watt (MRW) approaches, in the leading and the next-to-leading orders (LO and NLO) are considered, respectively. These two prescriptions (KMR and MRW) utilize t…
We study the leading twist gluon generalized parton distributions (GPDs) and the gluon angular momentum inside the proton within a light-cone spectator model. Using the light-cone wave functions derived from the model, we provide the expressions of these distributions at the particular kinematical point $ξ=0$ in the overlap representation. The numerical results of the $H^g$, $E^g$, $\tilde{H}^g$, $H_T^g$ and $E_T^g$ as functions of $x$ at different $Δ_T$ are presented. Particularly, $H^g$, $\tilde{H}^g$ at non-zero $Δ_T$ are different from their forward counterparts, the unpolarized distributi…
We present a determination of parton densities at NLO obtained with the Parton Branching method using precision measurements of deep inelastic scattering cross sections at HERA. The two sets of parton densities shown in this work are obtained with the same angular angular ordering condition for the evolution scale and they differ in the chosen scale for the strong coupling evaluation, for which we consider two scenarios: the evolution scale, and the transverse momentum qT from the angular ordering prescription. The transverse momentum dependent densities obtained with the Parton Branching meth…
In the present work, it is intended to calculate and study the single and double differential cross-sections of the prompt single-photon production as a function of produced single-photon transverse momentum and rapidity, in the high-energy P-P(P) colliders, such as LHC and TEVATRON. The differential cross-sections of prompt single-photon production are calculated in the $k_t$-factorization frameworks using various angular ordering unintegrated parton distribution functions (UPDF), namely the Kimber et al. and Martin et al. procedures. These scheme-dependent UPDF are generated in the leading a…
In this work, the P-P(P) Drell-Yan lepton pair production (DY) differential cross sections at hadrons colliders, such as LHC and TEVATRON, are studied in the ${k_{t}}$-factorization framework. In order to take into account the transverse momenta of incoming partons, we use the unintegrated parton distribution functions (UPDF) of Kimber et al (KMR) and Martin et al (MRW) in the leading order (LO) and next-to-leading-order (NLO) levels with the input MMHT2014 PDF libraries. Based on the different off-shell partonic matrix elements, we analyze the behaviors of DY differential cross sections with …
We investigate angular and energy distributions of medium-induced gluon emission off a quark-antiquark antenna in the framework of perturbative QCD as an attempt toward understanding, from first principles, jet evolution inside the quark-gluon plasma. In-medium color coherence between emitters, neglected in all previous calculations, leads to a novel mechanism of soft-gluon radiation. The structure of the corresponding spectrum, in contrast with known medium-induced radiation, retains some properties of the vacuum case; in particular, it exhibits a soft divergency. However, as opposed to the v…
We study two-flavor collective neutrino oscillations in the dense-neutrino region above the neutrino sphere in a supernova (SN). The angular dependence of the neutrino-neutrino interaction potential causes "multi-angle" effects that can lead either to complete kinematical decoherence in flavor space or only to small differences between different trajectories. This nonlinear system switches abruptly between "self-maintained coherence" and "self-induced decoherence" among the angular modes, depending on the strength of the deleptonization flux. For a realistic SN the quasi single-angle behavior …
In these proceedings we present three possible interpretations of the ordering variable implemented in the Herwig7 angular-ordered parton shower. Each interpretation determines a different recoil-scheme prescription and we show how it can impact the logarithmic accuracy of the algorithm. We also present comparisons with LEP data.
We discuss the Drell-Yan dilepton production using the transverse momentum dependent parton distributions evolved with the Catani-Ciafaloni-Fiorani-Marchesini-Kwieciński (CCFM-K) equations in the single loop approximation. Such equations are obtained assuming angular ordering of emitted partons (coherence) for $x\sim 1$ and transverse momentum ordering for $x \ll 1$. This evolution scheme also contains the Collins-Soper-Sterman (CSS) soft gluon resummation. We make a comparison with a broad class of data on transverse momentum spectra of low mass Drell-Yan dileptons.
QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling $α_s$, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.
We perform a phenomenological analysis of the $\cos 2 ϕ$ azimuthal asymmetry in virtual photon plus jet production induced by the linear polarization of gluons in unpolarized $pA$ collisions. Although the linearly polarized gluon distribution becomes maximal at small $x$, TMD evolutionleads to a Sudakov suppression of the asymmetry with increasing invariant mass of the $γ^*$-jet pair. Employing a small-$x$ model input distribution, the asymmetry is found to be strongly suppressed under TMD evolution, but still remains sufficiently large to be measurable in the typical kinematical region access…
