Holographic decays of large-spin mesons

TL;DR

This work uses gauge/string duality to study the decay of large-spin mesons by modeling them as macroscopic spinning open strings ending on flavour branes in confining backgrounds. A semi-classical analysis near the IR wall yields a decay width that factorizes into a string-splitting probability and a fluctuation-probability for the string to touch a flavour brane, reproducing key Lund-model features such as flavour conservation and the Zweig rule, and predicting linear scaling with the string length. Curvature corrections in the holographic background modify the exponential suppression and enhance stability for higher-spin states, with a corroborating discrete string-bit model supporting the continuum results. Overall, the holographic approach captures the main dynamical mechanisms behind meson decays, providing a first-principles rationale for the Lund model and making testable predictions about spin-dependent effects in high-spin regimes.

Abstract

We study the decay process of large-spin mesons in the context of the gauge/string duality, using generic properties of confining backgrounds and systems with flavour branes. In the string picture, meson decay corresponds to the quantum-mechanical process in which a string rotating on the IR "wall" fluctuates, touches a flavour brane and splits into two smaller strings. This process automatically encodes flavour conservation as well as the Zweig rule. We show that the decay width computed in the string picture is in remarkable agreement with the decay width obtained using the phenomenological Lund model.

Figures (15)

• Figure 1: A high-spin meson composed of heavy quarks, represented in the dual string picture as an open string ending on a flavour brane far away from the infrared "wall". To good approximation, the string consists of two vertical segments, called "region I" and one horizontal segment, called "region II".
• Figure 2: The basic idea behind the description of high-spin mesons in duals of confining gauge theories (left). The open string corresponding to the meson starts on a flavour brane, stretches to the infrared "wall", and then reaches up again to the (same or another) flavour brane. A decay process (right) requires that the string fluctuates, touches the flavour brane and then reconnects to it.
• Figure 3: Schematic overview of the embedding of the probe D6-brane, described by $r(\lambda)$, into the geometry of the stack of D4-branes (negative values of $\lambda$ correspond to points with $\phi\rightarrow \phi+\pi$ while negative values of $r$ correspond to $\theta\rightarrow \theta+\pi$). The dotted half-circles are equal-potential lines of the gravitational field, the solid half-circle is the IR "wall". Also depicted is a high-spin meson, represented by the thick vertical line. This is a side-on view of an open string stretching from the flavour D6-brane to the "wall", along the "wall", and then back up to the flavour D6-brane.
• Figure 4: The decay channels for a meson composed of one heavy and one intermediate-mass quark. When the newly produced quarks are massive, the computation of the decay width involves the computation of the probability that the string undergoes quantum fluctuations and touches a flavour brane. This is expected to lead to exponentially suppression (two figures on the left). Only when the new quarks are massless is the decay width given simply by the open string decay decay width.
• Figure 6: The approximation used to separate the $L$-dependent factor in the decay width from the dimensionless remainder. The integral over all configurations which touch the string at two points and have a maximum at $U = U_B$ is, after taking into account the dimensionful measure factor $K[\{{\cal N}_n\}]$, approximately equal to $L$ times the volume of this subspace of configuration space.