The Polarised Photon $g_1^{\gamma }$ Sum Rule at the Linear Collider and High Luminosity B Factories

Abstract

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.

17 pages, 5 figures, LaTeX

References in corpus (10)

• Physics at Super B Factory
• The Spin Structure of the Proton
• Spin-Dependent Structure Functions of Real and Virtual Photons
• Spin-Dependent Structure Functions of the Photon
• Pseudoscalar Meson Decay Constants and Couplings, the Witten-Veneziano Formula beyond large N_c, and the Topological Susceptibility
• ${\eta }^{\prime }(\eta )\to \gamma \gamma$: A Tale of Two Anomalies
• Target Mass Effects in Polarized Virtual Photon Structure Functions
• Phenomenology of the <VVP> Green's function within the Resonance Chiral Theory
• Mass effects in the polarized virtual photon structure
• Virtual Photon Structure Functions

Cited by in corpus (7)

• X(1835) as the Lowest Mass Pseudoscalar Glueball and Proton Spin Problem
• Pseudoscalar Meson Decay Constants and Couplings, the Witten-Veneziano Formula beyond large N_c, and the Topological Susceptibility
• The $alphaalph{a}_s^2$ corrections to the first moment of the polarized virtual photon structure function $g_1^{g}amma(x,Q^2,P^2)$
• Transition from real to virtual polarized photon structures
• The U(1)_A Anomaly and QCD Phenomenology
• The polarized photon structure function $g_1^{\gamma }(x,Q^2)$ in massive parton model in NLO
• Polarized Structure Functions and Two-Photon Physics at Super-B