U_A(1) Problems and Gluon Topology - Anomalous Symmetry in QCD

Many of the distinctive and subtle features of the dynamics in the $U_A(1)$ channel in QCD can be related to gluon topology, more precisely to the topological susceptibility $\chi(k^2) = i\int d^4x~e^{ikx}$, where Q = {\a_s\over8\pi} {\rm tr} G_{\m\n} \tilde G^{\m\n} is the gluon topological charge density. The link is the $U_A(1)$ axial (ABJ) anomaly. In this lecture, we describe the anomalous $U_A(1)$ chiral Ward identities in a functional formalism and show how two apparently unrelated `$U_A(1)$ problems' -- the mass of the $\eta'$ and the violation of the Ellis-Jaffe sum rule in polarised deep-inelastic scattering -- can be explained in terms of the gluon topological susceptibility. They are related through a $U_A(1)$ extension of the Goldberger-Treiman formula, which is derived here for QCD with both massless and massive quarks.Comment: Lecture at 1998 Zuoz Summer School, `Hidden Symmetries and Higgs Phenomena'. 22 pages, plain TeX, 2 ps or eps figure

η′→γγ\eta'\to\gamma\gamma and the topological susceptibility

The radiative decays \eta'(\eta)\rta\gamma\gamma are discussed. The modifications of the conventional PCAC formulae due to the gluonic contribution to the flavour singlet axial anomaly are given. The decay constants satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. It is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of \eta'(\eta)\rta\gamma\gamma.Comment: 4 pages, LaTeX, uses espcrc2.sty. To appear in Proceedings, QCD99 Montpellie

The Proton-Spin Crisis: another ABJ anomaly?

Contents: 1. Introduction; 2. The First Moment Sum Rule for $g_1^p$; 3. The Parton Model and the `Proton Spin'; 4. The CPV Method and Topological Charge Screening; 5. Experiment; 6. Semi-Inclusive Polarised DIS.Comment: Lecture at the International School of Subnuclear Physics, `From the Planck Length to the Hubble Radius', Erice, 1998. 22 pages, plain TeX, 2ps or eps figure

Topological Charge Screening and the `Proton Spin' Beyond the Chiral Limit

The theory of the `proton spin' effect proposed in our earlier papers is extended to include the chiral SU(3) symmetry breaking and flavour mixing induced by non-vanishing quark masses in QCD. The theoretical basis is the derivation of exact, unified Goldberger-Treiman (GT) relations valid beyond the chiral limit. The observed suppression in the flavour singlet axial charge $a^0(Q^2)$ is explained by an anomalously small value for the slope of the singlet current correlation function <0|T~\pl^\m J_{\m 5}^0 ~ \pl^\n J_{\n 5}^0 |0>, a consequence of the screening of topological charge in the QCD vacuum. Numerical predictions are obtained by evaluating the current correlation functions using QCD spectral sum rules. The results, $a^0(Q^2) = 0.31 \pm 0.02$ and $\int dx ~g_1^p(x,Q^2) = 0.141 \pm 0.005$ (at Q^2=10 \~\GV^2), are in good agreement with current experimental data on the polarised proton structure function $g_1^p$.Comment: 44 pages, plain TeX, 2 ps figure

Graviton Propagation and Vacuum Polarization in Curved Space

The effects of vacuum polarization arising from loops of massive scalar particles on graviton propagation in curved space are considered. Physically, they are due to curvature induced tidal forces acting on the cloud of virtual scalar particles surrounding the graviton. The effects are tractable in a WKB and large mass limit and the results can be written as an effective refractive index for the graviton modes with both a real and imaginary part. The imaginary part of the refractive index is a curvature induced contribution to the wavefunction renormalization of the graviton in real affine time and can have the effect of dressing or un-dressing the graviton. The real part of the refractive index increases logarithmically at high frequency as long as the null energy condition is satisfied by the background.Comment: 21 pages, typos correcte

Master formula approach to broken chiral U(3)xU(3) symmetry

The master formula approach to chiral symmetry breaking proposed by Yamagishi and Zahed is extended to the U_R(3)xU_L(3) group, in which effects of the U_A(1) anomaly and the flavor symmetry breaking m_u \not= m_d \not= m_s are properly contained. New identities for the gluon topological susceptibility and pi^0, eta, eta' -> gamma^(*) gamma^(*) decays are derived, which exactly embody the consequence from broken chiral symmetry in QCD without relying on any unphysical limit.Comment: Version to appear in PRD, 25 page

The Polarised Photon g1γg_1^\gamma Sum Rule at the Linear Collider and High Luminosity B Factories

The sum rule for the first moment of the polarised (virtual) photon structure function $g_1^\gamma(x,Q^2;K^2)$ is revisited in the light of proposals for future $e^+ e^-$ colliders. The sum rule exhibits an array of phenomena characteristic of QCD: for real photons ($K^2=0$) electromagnetic gauge invariance constrains the first moment to vanish; the limit for asymptotic photon virtuality ($m_\rho^2 \ll K^2 \ll Q^2$) is governed by the electromagnetic $U_A(1)$ axial anomaly and the approach to asymptopia by the gluonic anomaly; for intermediate values of $K^2$, it reflects the realisation of chiral symmetry and is determined by the off-shell radiative couplings of the pseudoscalar mesons; finally, like many polarisation phenomena in QCD, the first moment of $g_1^\gamma$ involves the gluon topological susceptibility. In this paper, we review the original sum rule proposed by Narison, Shore and Veneziano and extend the relation with pseudoscalar mesons. The possibility of measuring the sum rule in future polarised $e^+ e^-$ colliders is then considered in detail, focusing on the International Linear Collider (ILC) and high luminosity $B$ factories. We conclude that all the above features of the sum rule should be accessible at a polarised collider with the characteristics of SuperKEKB.Comment: 17 pages, 5 figures, LaTe

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