arXiv subjects
Publications and source records attributed to Alessandro Cafarella.
The updated version of the Helac-Phegas event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations. Helac-Phegas generates parton-level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders.
We summarize the theoretical approach to the solution of the NNLO DGLAP equations using methods based on the logarithmic expansions in x-space and their implementation into the C program Candia 1.0. We present the various options implemented in the program and discuss the different solutions. The user can choose the order of the evolution, the type of the solution, which can be either exact or truncated, and the evolution either with a fixed or a varying flavor number, implemented in the varying-flavour-number scheme (VFNS). The renormalization and factorization scale dependences are treated separately. In the non-singlet sector the program implements an exact NNLO solution.
New methods of solutions of the DGLAP equation and their implementation through NNLO in QCD are briefly reviewed. We organize the perturbative expansion that describes in $x$-space the evolved parton distributions in terms of scale invariant functions, which are determined recursively, and logarithms of the ratio of the running couplings at the initial and final evolution scales. Resummed solutions are constructed within the same approach and involve logarithms of more complex functions, which are given in the non-singlet case. Differences in the evolution schemes are shown to be numerically sizeable and intrinsic to perturbation theory. We illustrate these points in the case of Drell-Yan lepton pair production near the Z resonance, analysis that can be extended to searches of extra $Z^{\prime}$. We show that the reduction of the NNLO cross section compared to the NLO prediction may be attributed to the NNLO evolution.
We present a comparative study of the invariant mass and rapidity distributions in Drell-Yan lepton pair production, with particular emphasis on the role played by the QCD evolution. We focus our study around the Z resonance ($50 <Q < 200$ GeV) and perform a general analysis of the factorization/renormalization scale dependence of the cross sections, with the two scales included both in the evolution and in the hard scatterings. We also present the variations of the cross sections due to the errors on the parton distributions (pdf's) and an analysis of the corresponding $K$-factors. Predictions from several sets of pdf's, evolved by MRST and Alekhin are compared with those generated using \textsc{Candia}, a NNLO evolution program that implements the theory of the logarithmic expansions, developed in a previous work. These expansions allow to select truncated solutions of varying accuracy using the method of the $x$-space iterates. The evolved parton distributions are in good agreement with other approaches. The study can be generalized for high precision searches of extra neutral gauge interactions at the LHC.
In the first part of my thesis I am concerned with the phenomenology of DGLAP equations, and in particular I propose an algorithm to solve them numerically and discuss its implementation in a computer program. I also illustrate some applications of these studies, including a prediction for the total cross section for Higgs detection at the LHC and for study of the Drell-Yan process for the PAX experiment. In the second part of my thesis I analyze some characteristic patterns of cosmic ray showers in the atmosphere through theoretical modeling and computer simulations, with the main idea of looking for some signatures to discriminate between exotic and standard events. In particular my attention has been focused on decay events of mini black holes, the formation of which is predicted by theories with extra dimensions.
We present next-to-leading order predictions for double transverse-spin asymmetries in Drell--Yan dilepton production initiated by proton--antiproton scattering. The kinematic region of the proposed PAX experiment at GSI: $30\lesssim{s}\lesssim200\GeV^2$ and $2\lesssim{M}\lesssim7\GeV$ is examined. The Drell--Yan asymmetries turn out to be large, in the range 20--40%. Measuring these asymmetries would provide the cleanest determination of the quark transversity distributions.
A NNLO analysis of certain logarithmic expansions, developed for precision studies of the evolution of the QCD parton distributions (pdf) at the Large Hadron Collider, is presented. We elaborate on their relations to all the solutions of the DGLAP equations that have been hitherto obtained from Mellin space, to which are equivalent. Exact expansions, equivalent to exact solutions of the equations, are constructed in the non-singlet sector. The algorithmic features of our approach are also emphasized, since this method allows to obtain numerical solutions of the evolution equations with the same accuracy of other methods, based on Mellin space, and of brute force methods, which solve the equations by finite differences. The implementation of our analysis allows to compare with existing benchmarks for the evolution of the pdf's, useful for applications at the LHC, and to extend them significantly in a systematic fashion, especially when solutions that retain logarithmic corrections only of a certain accuracy are searched for.
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using logarithmic expansions and overview their kinetic interpretation. We illustrate how a Fokker-Planck equation can be derived using the master formulation of the same equations and its construction in the case of the transverse spin distributions. A simple connection of the leading order DGLAP equation to fractional diffusion using fractional calculus is also briefly outlined.
We present a detailed study of the total $p p$ cross section for scalar Higgs production to next-to-next-to leading order in $α_s$ at LHC energies, and of the $p\bar p$ cross section at the Tevatron, combining an implementation of the solutions of the parton evolution equations at the 3-loop order with the corresponding hard scatterings, evaluated at the same perturbative order. Our solutions of the DGLAP equations are implemented directly in $x$-space and allow the study of the dependence of the results on the factorization ($μ_F$) and renormalization scales $(μ_R)$ typical of a given process, together with the stability of the perturbative expansion. The input sets for the parton evolutions are those given by Martin, Roberts, Stirling and Thorne and by Alekhin. Results for K-factors are also presented. The NNLO corrections can be quite sizeable at typical collider energies. The stability region of the perturbative expansion is found when $μ_R > m_H\simμ_F$.
We present a study of the decay of an intermediate mini black hole at the first impact of a cosmic ray particle with the atmosphere, in the context of D-brane world scenarios with TeV scale gravity and large extra dimensions. We model the decay of the black hole using the semiclassical approximation and include the corrections coming from energy loss into the bulk. Extensive simulations show that mini black hole events are characterized by essentially different multiplicities and wider lateral distributions of the air showers as a function of the energy of the incoming primary, as compared to standard events. Implications for their detection and some open issues on their possible discovery are also briefly addressed.
We present a study of the multiplicities, of the lateral distributions and of the ratio of the electromagnetic to the hadronic components in the air showers, generated by the collision in the atmosphere of an incoming high energy cosmic ray and mediated by the formation of a mini black hole, predicted in TeV scale gravity models with large extra dimensions. The analysis is performed via a large scale simulation of the resulting cascades over the entire range ($10^{15}-10^{19}$eV) of ultra high initial energies, for several values of the number of large extra dimensions, for a variety of altitudes of the initial interaction and with the energy losses in the bulk taken into account. The results are compared with a representative of the standard events, namely the shower due to the collision of a primary proton with a nucleon in the atmosphere. Both the multiplicities and the lateral distribution of the showers show important differences between the two cases and, consequently, may be useful for the observational characterization of the events. The electromagnetic/hadronic ratio is strongly fluctuating and, thus, less decisive for the altitudes considered.
We illustrate the implementation of a method based on the use of recursion relations in (Bjorken) $x-$space for the solution of the evolution equations of QCD for all the leading twist distributions. The algorithm has the advantage of being very fast. The implementation that we release is written in C and is performed to next-to-leading order in $α_s$.
The identification of string relics, or of other very massive states, at forthcoming ultra high energy cosmic rays experiments, requires a good reconstruction of the main properties of the extensive air showers produced by the collision of the primary protons with the atmosphere. In particular, the current hadronization models used in the simulations need to incorporate possible new interactions. We briefly discuss these aspects and then proceed by describing some of the observables which characterize the atmospheric shower. The linear growth of the multiplicities - as a function of the energy - for all the main particles in the shower can play an interesting role in an attempt to identify channels of missing energy due to a plausible dark matter component.
The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam - $β$ system is numerically investigated. No external perturbation is considered for the one-mode exact analytical solutions, the only perturbation being that introduced by computational errors in numerical integration of motion equations. The threshold energy for the excitation of the other normal modes and the dynamics of this excitation are studied as a function of the parameter $μ$ characterizing the nonlinearity, the energy density $ε$ and the number N of particles of the system. The achieved results confirm in part previous results, obtained with a linear analysis of the problem of the stability, and clarify the dynamics by which the one-mode exchanges energy with the other modes with increasing energy density. In a range of energy density near the threshold value and for various values of the number of particles N, the nonlinear one-mode exchanges energy with the other linear modes for a very short time, immediately recovering all its initial energy. This sort of recurrence is very similar to Fermi recurrences, even if in the Fermi recurrences the energy of the initially excited mode changes continuously and only periodically recovers its initial value. A tentative explanation of this intermittent behaviour, in terms of Floquet's theorem, is proposed.
Large scale airshower simulations around the GZK cutoff are performed. An extensive analysis of the behaviour of the various subcomponents of the cascade is presented. We focus our investigation both on the study of total and partial multiplicities along the entire atmosphere and on the geometrical structure of the various cascades, in particular on the lateral distributions. The possibility of detecting new physics in Ultra High Energy Cosmic Rays (UHECR) at AUGER is also investigated. We try to disentangle effects due to standard statistical fluctuations in the first proton impact in the shower formation from the underlying interaction and comment on these points. We argue that theoretical models predicting large missing energy may have a chance to be identified, once the calibration errors in the energy measurements are resolved by the experimental collaborations, in measurements of inclusive multiplicities.
Stable Superstring Relics (SSR) provide some of the candidates for the possible origin of the Ultra High Energy Cosmic Rays (UHECR). After a brief overview of the motivations for introducing such relics, we address the question whether statistical fluctuations in the formation of the air showers generated by the primary spectrum of protons can be separated from a possible signal of new physics hidden in the first impact with the atmosphere. Our results are generated by using minimal modifications in the cross section of the primaries, and using available simulation codes used by the experimental collaborations. The results indicate that substantial increases in the cross section of the first impact, possibly due to new interactions, are unlikely to be detected in geometrical and/or variations of multiplicities in the cascade.
We analize the use of algorithms based in x-space for the solution of renormalization group equations of DGLAP-type and test their consistency by studying bounds among partons distributions - in our specific case Soffer's inequality and the perturbative behaviour of the nucleon tensor charge - to next-to-leading order in QCD . A discussion of the perturbative resummation implicit in these expansions using Mellin moments is included. We also comment on the (kinetic) proof of positivity of the evolution of $h_1$, using a kinetic analogy and illustrate the extension of the algorithm to the evolution of generalized parton distributions. We prove positivity of the non-forward evolution in a special case and illustrate a Fokker-Planck approximation to it.
According to a rederivation - due to Collins and Qiu - the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound $|Δf(x,Q)| < f(x,Q)$ between polarized and unpolarized distributions, or positivity of the helicity distributions, for any $Q$. We reanalize this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in $α_s$, which we illustrate. We also elaborate on some of the formal properties of the Collins-Qiu form and comment on the underlying regularization, introduce a Kramers-Moyal expansion of the equation and briefly analize its Fokker-Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution $q_V$ and for the transverse spin distribution $h_1$.