The polarised photong1γsum 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 γ 1 (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 2 ρ ≪ K 2 ≪ 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 γ 1 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.

Pseudoscalar meson decay constants and couplings, the Witten–Veneziano formula beyond large , and the topological susceptibility

“…9 So unlike g Gγγ in the flavour-singlet radiative decay formula, we would not be surprised if g GN N makes a sizeable numerical contribution to the U (1) A GT relation. 10 This is quantified in Fig.…”

“…1 Notice that compared to refs. [1,2,20,9] we have changed the normalisation of the flavour singlets by a factor 1/ √ 2n f = 1/ √ 6. The normalisations here are trT a T b = 1 2 δ ab for generators T a (a = 0, 1, .…”

“…The relation of our analysis of the low-energy decays η ′ (η) → γγ to high-energy physics in the form of the first moment sum rule for the polarised photon structure function g γ 1 [7,8] is also discussed. The dependence of this sum rule on the photon momentum encodes many aspects of non-perturbative QCD physics and its full measurement is now within the reach of planned high-luminosity e + e − colliders [9]. Our methods can also be readily extended to a variety of other reactions involving the pseudoscalar mesons, including η ′ (η) → V γ, where V is one of the flavour singlet vector mesons ρ, ω, φ, η ′ (η) → π + π − γ, a variety of electro and photoproduction reactions such as γp → pη ′ (η) and γp → pφ, and η and η ′ production in pp collisions, pp → ppη ′ (η).…”

Polarised structure functions and two-photon physics at Super-B

“…is defined in terms of the off-shell transition functions. 8 This is related to the inclusive cross-section (2.9) by the optical theorem, which for the specific meson final state P implies the substitution…”

“…With these cuts, we find [6,8] In Fig. 3, we plot σ (in pb) and ∆σ/σ for the Super-B √ s over the range of Q 2 min from 1 to 10 GeV 2 .…”