Pseudoscalar-pole Contribution Research Articles

Effects of longitudinal short-distance constraints on the hadronic light-by-light contribution to the muon mathbf {g-2}

We present a model-independent method to estimate the effects of short-distance constraints (SDCs) on the hadronic light-by-light contribution to the muon anomalous magnetic moment a_mu ^text {HLbL}. The relevant loop integral is evaluated using multi-parameter families of interpolation functions, which satisfy by construction all constraints derived from general principles and smoothly connect the low-energy region with those where either two or all three independent photon virtualities become large. In agreement with other recent model-based analyses, we find that the SDCs and thus the infinite towers of heavy intermediate states that are responsible for saturating them have a rather small effect on a_mu ^text {HLbL}. Taking as input the known ground-state pseudoscalar pole contributions, we obtain that the longitudinal SDCs increase a_mu ^text {HLbL} by (9.1pm 5.0) times 10^{-11}, where the isovector channel is responsible for (2.6pm 1.5) times 10^{-11}. More precise estimates can be obtained with our method as soon as further accurate, model-independent information about important low-energy contributions from hadronic states with masses up to 1–2 GeV become available.

Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon

A key ingredient in the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon $(g-2)_\mu$ concerns short-distance constraints (SDCs) that follow from QCD by means of the operator product expansion. Here we concentrate on the most important such constraint, in the longitudinal amplitudes, and show that it can be implemented efficiently in terms of a Regge sum over excited pseudoscalar states, constrained by phenomenological input on masses, two-photon couplings, as well as SDCs on HLbL scattering and the pseudoscalar transition form factors (TFFs). Our estimate of the effect of the longitudinal SDCs on the HLbL contribution is: $\Delta a_\mu^\text{LSDC}=13(6)\times 10^{-11}$. This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a $40\%$ increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant TFFs. We also comment on the status of the transversal SDCs and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.

Longitudinal short-distance constraints for the hadronic light-by-light contribution to (g \u2212 2)\u03bc with large-Nc Regge models

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon (g − 2)μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π0, η, η′. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by varDelta {a}_{mu}^{mathrm{LSDC}}=13(6) × 10-11. This number does not include the contribution from the charm quark, for which we find {a}_{mu}^{c- quark} = 3(1) × 10−11.

Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon

We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon's anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a systematic comparison with a strictly dispersive treatment and also with recent results from lattice QCD. Within error bars, we obtain excellent agreement for the pion electromagnetic and transition form factor and the resulting contributions to LBL. In addition, we present results for the η and η′ pole contributions and discuss the dynamical effects in the η−η′ mixing due to the strange quarks. Our result for the total pseudoscalar pole contributions is aμPS-pole=91.6(1.9)×10−11 and for the pion-box contribution we obtain aμπ−box=−16.3(2)(4)×10−11.

Dispersive analysis of light-meson transition form factors

We discuss status and prospects of a dispersive analysis of the π0, η, and η ′ transition form factors. Particular focus is put on the various pieces of experimental information that serve as input to such a calculation. These can help improve on the precision of an evaluation of the light pseudoscalar pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.**

Pseudoscalar pole light-by-light contributions to the muon (g \u2212 2) in resonance chiral theory

We have studied the P → γ⋆γ⋆ transition form-factors (P = π0, η, η′) within a chiral invariant framework that allows us to relate the three form-factors and evaluate the corresponding contributions to the muon anomalous magnetic moment aμ = (gμ−2)/2, through pseudoscalar pole contributions. We use a chiral invariant Lagrangian to describe the interactions between the pseudo-Goldstones from the spontaneous chiral symmetry breaking and the massive meson resonances. We will consider just the lightest vector and pseudoscalar resonance multiplets. Photon interactions and U(3) flavor breaking effects are accounted for in this covariant framework. This article studies the most general corrections of order mP2 within this setting. Requiring short-distance constraints fixes most of the parameters entering the form-factors, consistent with previous determinations. The remaining ones are obtained from a fit of these form-factors to experimental measurements in the space-like (q2 ≤ 0) region of photon momenta. No time-like observable is included in our fits. The combination of data, chiral symmetry relations between form-factors and high-energy constraints allows us to determine with improved precision the on-shell P -pole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain {a}_{mu}^{{}^{P, HLbL}}=left(8.47 pm 0.16right) cdotp {10}^{-10} for our best fit. This result was obtained excluding BaBar π0 data, which our analysis finds in conflict with the remaining experimental inputs. This study also allows us to determine the parameters describing the η−η′ system in the two-mixing angle scheme and their correlations. Finally, a preliminary rough estimate of the impact of loop corrections (1/NC ) and higher vector multiplets (asym) enlarges the uncertainty up to {a}_{mu}^{P, HLbL}=left(8.47pm {0.16}_{mathrm{sta}} pm {0.09}_{1/{mathrm{N}}_{mathrm{C}}}{{}_{-0}^{+0.5}}_{asym}right)cdotp {10}^{-10} .

Pseudoscalar pole contribution to the hadronic light-by-light piece of aμ

We have studied the P → γ⋆ γ⋆ form factor in Resonance Chiral Theory, with P = π0; η, η', to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading U(3) chiral symmetry breaking terms, obtaining the most general expression for the form factor of order O(m2P). The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike momentum region of the virtual photon. Chiral symmetry relations among the transition form factors for π0, η and η' allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar π0 data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of aP,HLbLη = (8:47 ± 0:16) · 10-10 for our best fit (neglecting the BaBar π0 data). Also, a preliminary rough estimate of the impact of NLO in 1=NC corrections and higher vector multiplets (asym) enlarges the uncertainty up to aP,HLbLη = (8:47 ± 0:16stat ± 0:09NC +0:5 -0:0asym).

Updated pseudoscalar contributions to the hadronic light-by-light of the muon (g − 2)

In this work, we present our recent results on a new and alternative data-driven determination for the hadronic light-by-light pseudoscalar pole contribution to the muon (g − 2). Our approach is based on Canterbury approximants, a rational approach to describe the required transition form factors, which provides a systematic and model-independent framework beyond traditional large-[Formula: see text] approaches. As a result, we obtain a competitive determination with errors according to future (g − 2) experiments including, for the first time, a well-defined systematic uncertainty.

Precision of a data-driven estimate of hadronic light-by-light scattering in the muong−2: Pseudoscalar-pole contribution

The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We show, in a largely model-independent way, that for pi^0 (eta, eta^\prime) the region of photon momenta below about 1 (1.5) GeV gives the main contribution to hadronic light-by-light scattering. We then discuss how the precision of current and future measurements of the single- and double-virtual transition form factor in different momentum regions impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering. Based on Monte Carlo simulations for a planned first measurement of the double-virtual form factor at BESIII, we find that for the pi^0, eta, eta^\prime-pole contributions a precision of 14\%, 23\%, 15\% seems feasible. Further improvements can be expected from other experimental data and also from the use of dispersion relations for the different form factors themselves.

On the precision of a data-driven estimate of the pseudoscalar-pole contribution to hadronic light-by-light scattering in the muong−2

The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime and, in general, two off-shell photons with spacelike momenta Q_{1,2}^2. We determine which regions of photon momenta give the main contribution for hadronic light-by-light scattering. Furthermore, we analyze how the precision of future measurements of the single- and double-virtual form factor impacts the precision of a data-driven estimate of this contribution to hadronic light-by-light scattering.

Erratum: Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muong−2[Phys. Rev. D57,465 (1998)

The pseudoscalar pole contribution is the dominant source of the $ {\cal O}(\alpha^3) $ hadronic light-by-light scattering effect in muon $g - 2$. We have examined this contribution taking account of the off-shell structure of the pseudoscalar-photon-photon anomaly vertex deduced from available experimental data. Our work leads to an improved estimate, $ -79.2 (15.4) \times 10^{-11}$, for the total hadronic light-by-light scattering contribution to the muon $g - 2$.

Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muong−2

The pseudoscalar pole contribution is the dominant source of the $\mathcal{O}({\ensuremath{\alpha}}^{3})$ hadronic light-by-light scattering effect in muon $g\ensuremath{-}2$. We have examined this contribution, taking account of the off-shell structure of the pseudoscalar-photon-photon anomaly vertex deduced from available experimental data. Our work leads to an improved estimate $\ensuremath{-}79.2 (15.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ for the total hadronic light-by-light scattering contribution to the muon $g\ensuremath{-}2$.