Knockout reactions on nuclei
Finally, in collaboration with S. Boffi, C. Giusti and F.D. Pacati from University of Pavia, by invitation of P.E. Hodgson, General Editor of Oxford University Press, I wrote a book on the electromagnetic response of the nucleus, published in the series Oxford Studies in Nuclear Physic (publ. c1). In particular, I took care of the chapters about the semi-inclusive and exclusive reactions with emission of one nucleon at low, medium and high energies, and the extension of the formalism and the phenomenology to the polarized reactions. At the time of its publication (1996), the book represented a turning point, summarizing the acquired knowledge in this field in a homogeneous formalism, but at the same time anticipating the topics and developments that should be achieved in the following years in higher-energy experiments (in particular, at the TJNAF laboratory, Virginia - USA). Because of the modern approach, the uniform formalism, and the wide variety of applications, the book has been adopted in Ph. D. courses in Physics in several american universities. Moreover, it is largely cited in research papers (see Google-Scholar), because, at present, it represents the only theoretical reference book for the experimental researchers in this field.
Quark models of the nucleon
When the QCD chiral symmetry is spontaneously broken, new dynamical degrees of freedom come into play: quarks get a dynamical mass related to the nontrivial structure of the ground state (constituent quarks), the Goldstone mechanism produces new bosons (usually identified with the pseudoscalar mesonic octet) that mediate the interactions among quarks. Traditional constituent quark models do not include the latter feature, since they describe the dynamics mainly by the hyperfine part of the one-gluon exchange interaction. There are "hybrid" versions that include also the one-pion exchange interaction, but the short-range behaviour and the corresponding spin-flavor symmetry do not seem adequate to reproduce the fine structure of the baryon spectrum, in particular the correct series of positive- and/or negative-parity energy levels.
In this context, I first studied the predictions of these models about the electromagnetic excitation of the most important nucleon resonances, namely the Delta(1232), the D13(1520) and the F15(1680), testing the limit of such framework when trying to coherently describe experimental data for the corresponding helicity amplitudes (publ. a16).
Next, in collaboration with the group of W. Plessas from the University of Graz, I implemented a new model where constituent quarks interact via the exchange of just the pseudoscalar meson octet, which is justified as the set of Goldstone bosons produced by the spontaneously broken QCD chiral symmetry. Wave functions have been constrained by reproducing the spectrum of light baryons including strangeness, and then they have been tested by calculating dynamical properties of the baryons themselves (form factors, magnetic moments,..) using first a semirelativistic description of the electromagnetic interaction (publ. a19, a20, a24). Later, in collaboration also with W. Klink from Iowa University (USA), a covariant hamiltonian description was introduced (using the point-form realization of relativistic quantum mechanics). This way, it was possible to simultaneously describe for the first time all the elastic form factors of the nucleon (electric, GE, magnetic, GM, axial, GA, pseudoscalar, GP, and, in particular, the last data collected at TJNAF - USA - about the ratio GE/GM for the proton), magnetic moments, root mean squared radii, without introducing new parameters with respect to the ones fixed in the Hamiltonian by reproducing the baryon spectrum (publ. a25-a27). Such a coherent picture strongly depends on the correct treatment of the relativistic aspects of the process. In the point-form realization of the relativistic quantum mechanics, the invariance under Poincaré transformations is trivial and, at variance with other approaches, it is possible to exactly calculate the transformations induced by the change of reference frame (boost).
The surprising behaviour of the GE/GM ratio for the proton, as measured at TJNAF-USA, stimulated a large theoretical activity, in particular about these form factors in the time-like region. In fact, while space-like form factors of stable hadrons are real because of the hermiticity of the electromagnetic Hamiltonian, time-like form factors, as they can be explored in electron-positron annihilations or hadronic collisions, are complex because of the (final/initial) residual interactions of the involved hadrons. The experimental knowledge of time-like form factors for the nucleon is poor. In principle, their absolute values can be extracted by combining the measurement of total cross sections and center-of-mass (c.m.) angular distributions of the final products; the phases can be deduced from specific spin asymmetries of the corresponding polarized reaction. In reality, the available unpolarized cross sections are integrated over a wide angular range because of low statistics with the net outcome that the absolute value of the proton electric form factor is basically unknown. Moreover, results from only one experiment are available for the neutron. Finally, no polarization data have ever been collected; therefore, also the phases of nucleon form factors are totally unknown, which could strongly discriminate the analytic continuation of models that successfully reproduce the ratio measured at JLab in the space-like region. Nevertheless, the few available results display puzzling properties. The recent BABAR measurement shows a proton electric-to-magnetic ratio larger than 1, which contradicts the space-like results of JLab and older time-like results of LEAR. The only neutron measurement from FENICE displays an absolute value of the magnetic form factor bigger than the proton one in the corresponding c.m. range. Similarly, the asymptotic behavior of the latter seems to contradict the requirements of dispersion relations, which would bind it to the corresponding trend in the space-like region. In collaboration with prof. A. Bianconi from University of Brescia, and with d.ssa B. Pasquini from University of Pavia, numerical simulations have been performed to explore the feasibility of the extraction of proton/neutron time-like form factors (publ. a42, a43) with the possible upgrade of the existing DAFNE facility to center-of-mass energies up to 2.5 GeV (see the Roadmap INFN 2006-2016, publ. a44, d6).
Partonic
(spin) structure of the nucleon and azimuthal asymmetries
The leading-order partonic structure of the nucleon is completely
determined by three distribution functions: the momentum distribution,
the helicity and the transverse spin distribution (transversity). Only
the first two ones are experimentally known because the third one is
odd under chiral transformations and it is not accessible in simple
processes like inclusive DIS. However, knowledge of the transversity is
crucial to determine the spin structure of the nucleon and to test QCD
predictions in the nonperturbative regime about the tensor charge and
its evolution properties with respect to the helicity ones. The strategy for extracting the transversity is simply defined: we need to identify a leading-order (-twist) process where the transversity is paired with a partner being itself also odd under chiral transformations.
The most natural process is the Drell-Yan with
two transversely polarized protons, where at
leading twist the cross section contains the product of the
transversities for the annihilating quark and antiquark. However, the
antiquark transversity is evidently suppressed since it is not a
valence distribution inside the parent proton. For these two
reasons, the suggestion to extract transversity from a fully polarized
Drell-Yan appeared early in the literature, but it has been quickly
discarded as well. Recently, new perspectives were offered in hadronic collisions by the developments of know-how about dealing with (un)polarized antiprotons inside the project FAIR (Facility with Antiproton and Ion Research) using the ring HESR (High Energy Storage Ring) at the GSI laboratory (Darmstadt - Germany). In collaboration with prof. A. Bianconi from University of Brescia, we wrote a Monte Carlo code for numerical simulations of the $p^\uparrow \bar{p}^\uparrow \to \mu^+\mu^- X$ process in the GSI kinematics to explore the feasibility for extracting transversity (pubbl. a39).
If the elementary annihilation is assumed to be non collinear, i.e. the partonic densities depend on an intrinsic transverse momentum of the partons with respect to the parent hadrons, the leading-twist Drell-Yan cross section shows a rich azimuthal dependence. In fact, the transversity appears convolved with a new parton spin density, the socalled Boer-Mulders function, which in turn produces an azimuthally asymmetric term in the unpolarized cross section. Recently, the latter raised much interest since it could give an explanation for a long lasting puzzle that perturbative QCD has not solved yet (the socalled violation of the Lam-Tung sum rule). In the polarized part of the cross section, another contribution shows up involving another interesting spin density, the Sivers function. It describes how the distribution of unpolarized partons is distorted by the transverse polarization of the parent hadron; hence, it gives information on the orbital angular momentum of partons and on its contribution to the proton spin sum rule. Moreover, the general properties of the defining operator imply an anomalous feature of the Sivers function with respect to universality: as it can be extracted in Drell-Yan processes, it would come out opposite from what can be extracted in semi-inclusive DIS processes (SIDIS). In this context, I made numerical simulations at GSI kinematics to study the feasibility for extracting the transversity and Boer-Mulders function in Drell-Yan processes with unpolarized or a single transversely polarized proton (pubbl. a37), in the first case analyzing also the azimuthal asymmetries produced by the crossing of the target nuclear medium (pubbl. a38). I extended the analysis to the kinematics foreseen for the upgrade RHIC-II at the Brookhaven National Laboratory, in order to verify the feasibility of extracting the Sivers function and to test its universality properties in high-energy proton collisions (pubbl. a40). I studied also the same physics case for a possible configuration of the COMPASS experiment with pion beams in the $\pi p^\uparrow \to \mu^+\mu^- X$ reaction (pubbl. a41). Finally, I explored also the role of unpolarized nonvalence partons in single-spin asymmetries, using Monte Carlo simulations as well (pubbl. a46).
An alternative way to extract the transversity is to search for a
semi-inclusive reaction in which the fragmentation function for the
observed hadron is also odd under chiral transformations and it
represents a partner for the transversity in the cross section at
leading twist. The new unknown function could be determined by
looking at the corresponding semi-inclusive e+e- annihilation provided that the related factorization theorem holds and
the fragmentation function is universal. All this has been realized for the first time only recently, by combining data from HERMES (DESY) for the $e p^\uparrow \to e' \pi X$ reaction and those from BELLE (KEK) for the $e^+e^- \to \pi^+ \pi^- X$ one. The unknown fragmentation function is called Collins function. However, the
azimuthal asymmetry necessary to isolate the "Collins effect" demands the cross section to depend
upon the transverse momentum of the observed pion, hence, at the
elementary level, upon the intrinsic transverse momentum of the
fragmenting parton. At present, this requirement prevents from getting
a complete proof of the factorization theorem. Moreover, it affects the final result since the
evolution of the transverse-momentum-dependent Collins function from the BELLE scale down to the HERMES one, is not known.
In this context, I studied an alternative SIDIS process where two hadrons are detected
inside the same jet, looking at the general properties of the socalled
interference fragmentation functions (or Dihadron Fragmentation Functions - DiFF) that show up at leading (publ. a22, a32)
and subleading twist (publ. a34).
Surprisingly, it is more useful to consider a more complicate final
state because it is possible to build a spin asymmetry that isolates
transversity at leading twist without keeping memory of the parton
transverse momenta (publ. a28).
The DiFF can be extracted
from the corresponding e+e- annihilation into two pion pairs, as their universality has been
directly checked at leading twist (publ. a33), and their evolution equations have been determined at leading log approximation such that the e+e- cross section can be expressed in factorized form at the same level of accuracy (pubbl. a47).
Coming back shortly to the case for hadron-hadron collisions, an interesting use of DiFF is possible in azimuthal asymmetries in processes like $H_1 H_2^\uparrow \to (\pi^+ \pi^-) X$ and $H_1 H_2\to (\pi^+ \pi^-)(\pi^+ \pi^-) X$. In fact, it is possible to determine all the unknowns, namely the transversity in $H_2$ and the corresponding DiFF partner, and the unpolarized DiFF paired to the partonic momentum distribution in $H_1$ as well, by performing one experiment only and measuring in turn one or two pion pairs (pubbl. a36) . This idea is being studied by the COMPASS collaboration for the case $H_1 = \pi$ (pubbl. a41).
The scarce amount of experimental data and, consequently, the lacking
of reliable parametrizations makes the use of phenomenological models
of fragmentation functions unavoidable, but also useful to determine
the experimental set-up. In the framework of the spectator model, I
co-worked an explorative calculation of interference fragmentation
functions for the production of a nucleon and a pion either directly or
through the Roper resonance (publ. a23),
and for the production of two pions either directly in relative s wave or through the $\rho$
resonance in p wave (publ. a28).
Recently, the model has been enlarged to include more resonances and, more importantly, by constraining the free parameters to the invariant-mass distribution of the pair, as it is output by the Monte Carlo PYTHIA code of the HERMES collaboration (pubbl. a45). In this way, it was possible to predict the single-spin asymmetry from which transversity can be extracted. The feasibility of azimuthal asymmetry measurements containing such
objects has been demonstrated by the collaborations HERMES (DESY) and COMPASS (CERN). Future upgrades of such a model require a more careful analysis of the statistics of the two pions in the final state, and the support to the analysis of the $e^+e^- \to (\pi^+\pi-)(\pi^+\pi^-) X$ reaction from the BELLE collaboration, in order to extract for the first time the chiral-odd DiFF that is the transversity partner.
The quest for understanding the spin structure of the nucleon has
benefit from the development of other sophisticated tools like the Generalized Parton Distributions (GPD), that are
partonic correlation functions based on nondiagonal hadronic matrix
elements. As such, they include as a specific limit the usual parton
distributions; but specific GPD moments are related to the
electromagnetic form factors in the exclusive limit. More generally,
GPD represent a unifying formalism for different classes of inclusive
and exclusive processes. Moreover, in the nucleon rest frame GPD
produce a 3dim map of the strong force, hence they contain information
on the 3dim (and transverse) localization of partons and on their
orbital angular momentum, giving for the first time the opportunity to
gain a complete and gauge invariant
information on the partonic spin structure of the nucleon.
GPD can be extracted from (spin or beam charge) asymmetry
measurements in reactions like the Deeply Virtual Compton Scattering (DVCS) or the exclusive
electroproduction of mesons. However, the complete determination of GPD
is still an open problem. Therefore, the use of phenomenological models
is still the only available tool, at present. In collaboration with the
group of K. Goeke from the University of Bochum , I checked that the chiral quark soliton model of the nucleon, based
on the instanton description of the QCD vacuum, meets some crucial
properties of GPD that are derived from general principles and,
therefore, must be satisfied by any model. In particular, the chiral
quark soliton model meets the consistency check of the socalled
polinomiality condition which derives from hermiticity and invariance
under Lorentz, parity and time-reversal transformations (publ. a31).
In this framework, from the collaboration of several active european
research groups the project Integrated Infrastructure Initiative in Hadronic Physics (I3HP) was elaborated, submitted
and funded by the European Community under the contract n.
RII3-CT-2004-506078 inside the programme FP6 . The I3HP project
contains several activities; I take part in three of them:
- Network N5 HadronTh: Structure and Dynamics of Hadrons, coordinator U.-G. Meissner (University of Bonn) made by 18 european institutes among which INFN with 2 local Sections.
- Network N7 Transversity: exploring the unknown transverse spin structure of the Nucleon, coordinator E. de Sanctis (for the collaboration HERMES) made by 11 european institutes among which INFN with 5 local Sections; in this network, I'm the local coordinator of the team Pavia and I co-organized the first workshop Transversity: New Developments in Nucleon Spin Structure at the ECT* (Trento), 14-18 June 2004; a review article has been published on the special number of the CERN COURIER in occasion of the 50o anniversary of CERN foundation (publ. d4).
- Joint Research Activity JRA5
GPD: Generalized Parton
Distributions, coordinator R.
Kaiser (University of
Glasgow) made by 21 european institutes among which INFN with 5 local Sections.