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M. Ciafaloni

Publications and source records attributed to M. Ciafaloni.

At least 19 recordsLinked to original sources
arXiv2011

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.

hep-th↗
arXiv2011

Unitarity alternatives in the reduced-action model for gravitational collapse

Based on the ACV approach to transplanckian energies, the reduced-action model for the gravitational S-matrix predicts a critical impact parameter b_c ~ R = 2 G sqrt{s} such that S-matrix unitarity is satisfied in the perturbative region b > b_c, while it is exponentially suppressed with respect to s in the region b < b_c that we think corresponds to gravitational collapse. Here we definitely confirm this statement by a detailed analysis of both the critical region b ~ b_c and of further possible contributions due to quantum transitions for b < b_c. We point out, however, that the subcritical unitarity suppression is basically due to the boundary condition which insures that the solutions of the model be ultraviolet-safe. As an alternative, relaxing such condition leads to solutions which carry short-distance singularities presumably regularized by the string. We suggest that through such solutions - depending on the detailed dynamics at the string scale - the lost probability may be recovered.

hep-th↗
arXiv2009

Quantum Tunneling and Unitarity Features of an S-matrix for Gravitational Collapse

Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate the S-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < b_c, a critical value of the order of the gravitational radius R = 2 G sqrt(s), thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < b_c is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling G s / hbar itself. Some features of the resulting unitary model are discussed.

hep-th↗
arXiv2009

Parton Distributions

We provide an assessment of the state of the art in various issues related to experimental measurements, phenomenological methods and theoretical results relevant for the determination of parton distribution functions (PDFs) and their uncertainties, with the specific aim of providing benchmarks of different existing approaches and results in view of their application to physics at the LHC. We discuss higher order corrections, we review and compare different approaches to small x resummation, and we assess the possible relevance of parton saturation in the determination of PDFS at HERA and its possible study in LHC processes. We provide various benchmarks of PDF fits, with the specific aim of studying issues of error propagation, non-gaussian uncertainties, choice of functional forms of PDFs, and combination of data from different experiments and different processes. We study the impact of combined HERA (ZEUS-H1) structure function data, their impact on PDF uncertainties, and their implications for the computation of standard candle processes, and we review the recent F_L determination at HERA. Finally, we compare and assess methods for luminosity measurements at the LHC and the impact of PDFs on them.

hep-ph↗
arXiv2008

S-matrix and Quantum Tunneling in Gravitational Collapse

Using the recently introduced ACV reduced-action approach to transplanckian scattering of light particles, we show that the $S$-matrix in the region of classical gravitational collapse is related to a tunneling amplitude in an effective field space. We understand in this way the role of both real and complex field solutions, the choice of the physical ones, the absorption of the elastic channel associated to inelastic multigraviton production and the occurrence of extra absorption below the critical impact parameter. We are also able to compute a class of quantum corrections to the original semiclassical $S$-matrix that we argue to be qualitatively sensible and which, generally speaking, tend to smooth out the semiclassical results.

hep-th↗
arXiv2008

Electroweak double-logs at small x

We investigate enhanced EW corrections to inclusive hard processes in the TeV energy region with emphasis on the small-x situation, in which the hard scale Q is significantly smaller than the available energy \sqrt{s}= Q/x. We first propose and justify a general factorization formula in which the (double-log) EW form factor at scale Q^2 is factorized from EW parton distribution functions, which satisfy evolution equations of DGLAP type. We then investigate the small-x behavior of the EW parton distributions including the novel ones for non-vanishing t-channel weak isospin T and we compare it with a BFKL-type approach. In either approach we find that large small-x corrections of order α_w \log x \log Q^2/M^2 (M being the EW symmetry breaking scale) are present only for T=2 and not for T=1. This implies that only transverse WW interactions (coupled to T=2) are affected, while the T=1 components feel just the form factor at scale Q^2.

hep-ph↗
arXiv2007

Towards an S-matrix Description of Gravitational Collapse

Extending our previous results on trans-Planckian ($Gs \gg \hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \gg G\sqrt{s}>λ_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b \to 0$ region. We find that for $b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.

hep-th↗
arXiv2007

A matrix formulation for small-x singlet evolution

We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.

hep-ph↗
arXiv2007

HERA and the LHC - A workshop on the implications of HERA for LHC physics: Proceedings - Part B

The HERA electron--proton collider has collected 100 pb$^{-1}$ of data since its start-up in 1992, and recently moved into a high-luminosity operation mode, with upgraded detectors, aiming to increase the total integrated luminosity per experiment to more than 500 pb$^{-1}$. HERA has been a machine of excellence for the study of QCD and the structure of the proton. The Large Hadron Collider (LHC), which will collide protons with a centre-of-mass energy of 14 TeV, will be completed at CERN in 2007. The main mission of the LHC is to discover and study the mechanisms of electroweak symmetry breaking, possibly via the discovery of the Higgs particle, and search for new physics in the TeV energy scale, such as supersymmetry or extra dimensions. Besides these goals, the LHC will also make a substantial number of precision measurements and will offer a new regime to study the strong force via perturbative QCD processes and diffraction. For the full LHC physics programme a good understanding of QCD phenomena and the structure function of the proton is essential. Therefore, in March 2004, a one-year-long workshop started to study the implications of HERA on LHC physics. This included proposing new measurements to be made at HERA, extracting the maximum information from the available data, and developing/improving the theoretical and experimental tools. This report summarizes the results achieved during this workshop.

hep-ph↗
arXiv2006

HERA and the LHC - A workshop on the implications of HERA for LHC physics: Proceedings - Part A

The HERA electron--proton collider has collected 100 pb$^{-1}$ of data since its start-up in 1992, and recently moved into a high-luminosity operation mode, with upgraded detectors, aiming to increase the total integrated luminosity per experiment to more than 500 pb$^{-1}$. HERA has been a machine of excellence for the study of QCD and the structure of the proton. The Large Hadron Collider (LHC), which will collide protons with a centre-of-mass energy of 14 TeV, will be completed at CERN in 2007. The main mission of the LHC is to discover and study the mechanisms of electroweak symmetry breaking, possibly via the discovery of the Higgs particle, and search for new physics in the TeV energy scale, such as supersymmetry or extra dimensions. Besides these goals, the LHC will also make a substantial number of precision measurements and will offer a new regime to study the strong force via perturbative QCD processes and diffraction. For the full LHC physics programme a good understanding of QCD phenomena and the structure function of the proton is essential. Therefore, in March 2004, a one-year-long workshop started to study the implications of HERA on LHC physics. This included proposing new measurements to be made at HERA, extracting the maximum information from the available data, and developing/improving the theoretical and experimental tools. This report summarizes the results achieved during this workshop.

hep-ph↗
arXiv2006

Minimal Subtraction vs. Physical Factorisation Schemes in Small-x QCD

We investigate the relationship of ``physical'' parton densities defined by kt-factorisation, to those in the minimal subtraction scheme, by comparing their small-x behaviour. We first summarize recent results on the above scheme change derived from the BFKL equation at NLx level, and we then propose a simple extension to the renormalisation-group improved (RGI) equation. In this way we are able the examine the difference between resummed gluon distributions in the Q_0 and MSbar schemes and also to show MSbar scheme resummed results for P_gg and approximate ones for P_qg. We find that, due to the stability of the RGI approach, small-x resummation effects are not much affected by the scheme-change in the gluon channel, while they are relatively more sensitive for the quark-gluon mixing.

hep-ph↗
arXiv2005

Parton Distributions: Summary Report

We provide an assessment of the impact of parton distributions on the determination of LHC processes, and of the accuracy with which parton distributions (PDFs) can be extracted from data, in particular from current and forthcoming HERA experiments. We give an overview of reference LHC processes and their associated PDF uncertainties, and study in detail W and Z production at the LHC. We discuss the precision which may be obtained from the analysis of existing HERA data, tests of consistency of HERA data from different experiments, and the combination of these data. We determine further improvements on PDFs which may be obtained from future HERA data (including measurements of $F_L$), and from combining present and future HERA data with present and future hadron collider data. We review the current status of knowledge of higher (NNLO) QCD corrections to perturbative evolution and deep-inelastic scattering, and provide reference results for their impact on parton evolution, and we briefly examine non-perturbative models for parton distributions. We discuss the state-of-the art in global parton fits, we assess the impact on them of various kinds of data and of theoretical corrections, by providing benchmarks of Alekhin and MRST parton distributions and a CTEQ analysis of parton fit stability, and we briefly presents proposals for alternative approaches to parton fitting. We summarize the status of large and small x resummation, by providing estimates of the impact of large x resummation on parton fits, and a comparison of different approaches to small x resummation, for which we also discuss numerical techniques.

hep-ph↗
arXiv2005

Dimensional Regularisation and Factorisation Schemes in the BFKL Equation at Subleading Leve

We study the anomalous dimensions and coefficient functions generated by the BFKL equation in 4+2 epsilon dimensions, by investigating both running coupling effects, and the inclusion of the full next-to-leading kernel. After generalising the Fourier representation of the solutions to this case, we analyse the beta-dependent renormalisation-group factorisation of anomalous dimension and coefficient contributions to the gluon density. We derive on this basis the normalisation factor of the Q0-scheme with respect to the MSbar-scheme, including beta-dependent corrections to it, and we outline the derivation of the full next-to-leading contributions. We also provide an expression for the resummed gamma_qg in the MSbar-scheme which exhibits its universality and is explicit up to quadratures.

hep-ph↗
arXiv2003

Extending QCD perturbation theory to higher energies

On the basis of the results of a new renormalisation group improved small-x resummation scheme, we argue that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations. We thus provide predictions for the energy dependence of the gluon Green function in its perturbative domain and for the resummed splitting function. As in previous analyses, high-energy exponents are reduced to phenomenologically acceptable values. Additionally, interesting preasymptotic effects are observed. In particular, the splitting function shows a shallow dip in the moderate small-x region, followed by the expected power increase.

hep-ph↗
arXiv2003

Renormalisation group improved small-x Green's function

We investigate the basic features of the gluon density predicted by a renormalisation group improved small-x equation which incorporates both the gluon splitting function at leading collinear level and the exact BFKL kernel at next-to-leading level. We provide resummed results for the Green's function and its hard Pomeron exponent $ω_s(α_s)$, and for the splitting function and its critical exponent $ω_c(α_s)$. We find that non-linear resummation effects considerably extend the validity of the hard Pomeron regime by decreasing diffusion corrections to the Green's function exponent and by slowing down the drift towards the non-perturbative Pomeron regime. As in previous analyses, the resummed exponents are reduced to phenomenologically interesting values. Furthermore, significant preasymptotic effects are observed. In particular, the resummed splitting function departs from the DGLAP result in the moderate small-x region, showing a shallow dip followed by the expected power increase in the very small-x region. Finally, we outline the extension of the resummation procedure to include the photon impact factors.

hep-ph↗
arXiv2002

A Quantization of 2+1-Gravity Related to High-Energy Yang-Mills Theory

We point out that canonical quantization of the two-body problem in 2+1-Gravity is related to the high-energy equation in Yang-Mills theory by a proper ordering of the relevant operators. This feature arises from expanding the Hamiltonian around its conformal limit - or treating running coupling effects in the Yang-Mills case - and yields a peculiar short distance behaviour of the wave functions.

hep-ph↗
arXiv2002

Small x Phenomenology: Summary and Status

The aim of this paper is to summarize the general status of our understanding of small x physics. It is based on presentations and discussions at an informal meeting on this topic held in Lund, Sweden, in March 2001. This document also marks the founding of an informal collaboration between experimentalists and theoreticians with a special interest in small x physics. This paper is dedicated to the memory of Bo Andersson, who died unexpectedly from a heart attack on March 4th, 2002.

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