The problem of the U(1) axial symmetry and the chiral transition in QCD

We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. In particular, supported by recent lattice results, we analyse a scenario in which a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate on the slope of the topological susceptibility in the full theory with quarks are studied. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the light pseudoscalar mesons in two photons.Comment: Talk given at the ``10th High-Energy Physics International Conference in Quantum Chromo-Dynamics'' (QCD 03), Montpellier (France), 2-9 July 2003; 8 pages, LaTeX fil

Pseudoscalar Meson Decay Constants and Couplings, the Witten-Veneziano Formula beyond large N_c, and the Topological Susceptibility

The QCD formulae for the radiative decays \eta,\eta'\to\c\c, and the corresponding Dashen--Gell-Mann--Oakes--Renner relations, differ from conventional PCAC results due to the gluonic $U(1)_A$ axial anomaly. This introduces a critical dependence on the gluon topological susceptibility. In this paper, we revisit our earlier theoretical analysis of radiative pseudoscalar decays and the DGMOR relations and extract explicit experimental values for the decay constants. This is our main result. The flavour singlet DGMOR relation is the generalisation of the Witten-Veneziano formula beyond large $N_c$, so we are able to give a quantitative assessment of the realisation of the $1/N_c$ expansion in the $U(1)_A$ sector of QCD. Applications to other aspects of $\eta'$ physics, including the relation with the first moment sum rule for the polarised photon structure function g_1^\c, are highlighted. The $U(1)_A$ Goldberger-Treiman relation is extended to accommodate SU(3) flavour breaking and the implications of a more precise measurement of the $\eta$ and $\eta'$-nucleon couplings are discussed. A comparison with the existing literature on pseudoscalar meson decay constants using large-$N_c$ chiral Lagrangians is also made.Comment: 27 pages, 4 figure

Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD

We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be (effectively) restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, supported by recent lattice results, we analyse a scenario in which a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate on the slope of the topological susceptibility in the full theory with quarks are studied: we find that this quantity (in the chiral limit of zero quark masses) acts as an order parameter for the U(1) axial symmetry above the chiral transition. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the pseudoscalar mesons in two photons: a comparison of our results with the experimental data is performed.Comment: 27 pages, LaTeX file. Completely revised version including new references and new comments on the result

Radiative η′\eta' Decays, the Topological Susceptibility and the Witten-Veneziano Mass Formula

The formulae describing the radiative decays \eta'(\eta)\rta\c\c in QCD beyond the chiral limit are derived. The modifications of the conventional PCAC formulae due to the gluonic contribution to the axial anomaly in the flavour singlet channel are precisely described. The decay constants are found to satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. Combining these results, it is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of \eta'(\eta)\rta\c\c.Comment: TeX, 21 pages, no figures, uses harvma

The `Proton Spin' Effect - Theoretical Status '97

The theoretical status of the `proton spin' effect is reviewed. The conventional QCD parton model analysis of polarised DIS is compared with a complementary approach, the composite operator propagator-vertex (CPV) method, each of which provides its own insight into the origin of the observed suppression in the first moment of $g_1^p$. The current status of both experiment and non-perturbative calculations is summarised. The future role of semi-inclusive DIS experiments, in both the current and target fragmentation regions, is described.Comment: Review talk at QCD97 Montpellier, July 1997. 12 pages, LaTeX, incl. 13 figures. Typo corrected in eq(36

The effects of an extra U(1) axial condensate on the radiative decay eta' --> gamma gamma at finite temperature

Supported by recent lattice results, we consider a scenario in which a U(1)-breaking condensate survives across the chiral transition in QCD. This scenario has important consequences on the pseudoscalar-meson sector, which can be studied using an effective Lagrangian model. In particular, generalizing the results obtained in a previous paper (where the zero-temperature case was considered), we study the effects of this U(1) chiral condensate on the radiative decay eta' --> gamma gamma at finite temperature.Comment: 15 pages, LaTeX fil

Topological charge density renormalization in the presence of dynamical fermions

We study the renormalization group behaviour of the topological charge density in full QCD on the lattice. We propose a way of extracting the necessary renormalization functions from Monte Carlo simulations.Comment: 8 pages, Revte

The spin content of the proton in quenched QCD

We present preliminary results on the proton spin structure function at zero momentum, in the quenched approximation. Our calculation makes use of a nonperturbative means of determining the multiplicative renormalization of the topological charge density.Comment: REVTEX, 6 pages, 1 PS figure attached. Pisa preprint IFUP-TH-14/9

Target Independence of the Emc-SMC Effect

An approach to deep inelastic scattering is described in which the matrix elements arising from the operator product expansion are factorised into composite operator propagators and proper vertex functions. In the case of polarised \m p scattering, the composite operator propagator is identified with the square root of the QCD topological susceptibility $\sqrt{\chi^{\prime}(0)}$, while the corresponding proper vertex is a renormalisation group invariant. We estimate $\chi^{\prime}(0)$ using QCD spectral sum rules and find that it is significantly suppressed relative to the OZI expectation. Assuming OZI is a good approximation for the proper vertex, our predictions, \int_{0}^{1}dx g_1^p (x;Q^2=10\GV^2)= 0.143 \pm 0.005 and $G^{(0)}_A \equiv \Delta \Sigma = 0.353 \pm 0.052$, are in excellent agreement with the new SMC data. This result, together with one confirming the validity of the OZI rule in the \hp radiative decay, supports our earlier conjecture that the suppression in the flavour singlet component of the first moment of $g_1^p$ observed by the EMC-SMC collaboration is a target-independent feature of QCD related to the $U(1)$ anomaly and is not a property of the proton structure. As a corollary, we extract the magnitude of higher twist effects from the neutron and Bjorken sum rules.Comment: 22 pages, 8 figures available on request

The spin content of the proton in full QCD

We present preliminary results on the proton spin structure function in full QCD. The measurement has been done using 4 flavours of staggered fermions and an improved definition of the lattice topological charge density.Comment: 3 pages, 3 figures, contribution to Lattice-97. Latex file including espcrc2.sty. The colour of a line in the first figure has been changed to avoid problems on some printer