Abstract
We quantify the importance of dynamical spin effects in the holographic light-front wavefunctions of the pion, kaon, $\eta$ and $\eta^\prime$. Using a universal AdS/QCD scale and constituent quark masses, we find that such effects are maximal in the pion where they lead to an excellent simultaneous description of a wide range of data: the decay constant, charge radius, spacelike EM and transition form factors, as well as, after QCD evolution, both the parton distribution function and the parton distribution amplitude data from Fermilab. These dynamical spin effects lead up to a $30\%$ chance of finding the valence quark and antiquark with aligned spins in the pion. The situation is very different for the kaon, where a simultaneous description of the available data (decay constant, radius and spacelike EM form factor) prefer no dynamical spin effects at all. The situation is less clear for the $\eta$ and $\eta^\prime$: while their radiative decay widths data are consistent with dynamical spin effects only in $\eta^\prime$, the data on their spacelike transition form factors clearly favor maximal dynamical spin effects in both mesons.
Highlights
A remarkable equation in hadronic physics is the holographic Schrödinger equation for mesons [1,2,3,4], − d2 dζ2 − 4L2 4ζ2 þ Ueff ðζÞ φðζÞ 1⁄4M2φðζÞ; ð1Þ which is derived within a semiclassical approximation of light-front QCD, where quantum loops and quark masses are neglected
− 4L2 4ζ2 þ which is derived within a semiclassical approximation of light-front QCD, where quantum loops and quark masses are neglected
The second prediction is that the meson masses lie on universal Regge trajectories, as is experimentally observed, with slopes determined by the anti–de Sitter (AdS)/QCD scale κ
Summary
A remarkable equation in hadronic physics is the holographic Schrödinger equation for mesons [1,2,3,4],. The second prediction is that the meson masses lie on universal Regge trajectories, as is experimentally observed, with slopes determined by the AdS/QCD scale κ. This allows κ to be extracted from spectroscopic data. [22], dynamical spin effects are taken into account in the kaon holographic wavefunction in order to predict the decay B → Kμþμ−, the focus is not on whether such effects are required by the kaon data. One of our goals in this paper is to investigate whether the data show evidence for dynamical spin effects in pseudoscalar mesons heavier than the pion. We shall perform fits to the E615 data in order to determine the low hadronic scale (which was left unspecified in Ref. [16]) at which our predictions are valid
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