Short-range production of three bottom mesons

TL;DR

This work analyzes short-range production in three-bottom-mary meson systems within a pionless-like NREFT framework, confirming the absence of the Efimov effect and enabling parameter-free LO predictions based on two-body input. By formulating the dimer–particle and three-body production dynamics through the STM equations and partial-wave projections, it identifies unparticle-like power-law scaling in both two- and three-body production rates, governed by scaling dimensions $oldsymbol{ extDelta}=s+5/2$ and exponents $E^{s-1/2}$ (two-body) and $E^{s}$ (three-body). The study also incorporates finite-range corrections via the effective range $ ho$, finding notable low-energy shifts while preserving the universal high-energy behavior, and highlights the potential to extract two-body scattering lengths and test approximate conformal symmetry from upcoming experimental data on $Z_b$-related channels. Overall, the results provide a concrete pathway to probe $B^{(*)}$-$ar{B}^{(*)}$ interactions and the molecular interpretation of $Z_b$ states through short-range production observables at colliders.

Abstract

Previous investigations of the three-body dynamics of $B$ mesons have shown that no Efimov effect arises in systems composed of three $B$ and $B^*$ mesons. This implies that the properties of such three-body systems can be described reliably in nonrelativistic effective field theory (NREFT) with two-body input alone, as three-body forces are strongly suppressed. In this work, we present leading-order predictions for the three-body point production rates of systems consisting of three $B$ and $B^*$ mesons. These predictions provide a novel way to experimentally probe the $B^{(*)}$-$\bar{B}^{(*)}$ interactions, which play a crucial role in the hadronic-molecule interpretation of the $T_{b\bar{b}1}(10610)$ and $T_{b\bar{b}1}(10650)$ states. Moreover, they provide a way to test the approximate conformal symmetry predicted for such systems at low energies experimentally.

Figures (10)

• Figure 1: Diagrams illustrating the dressing of the dimer field. The solid and dashed lines represent the $Z$ and $B$ fields, respectively, while the double line on the left denotes the dressed dimer propagator. Here, $Z$ and $B$ serve as placeholders for the sets ${Z_b, Z'_b}$ and ${B, B^*}$, respectively.
• Figure 2: Kinematic definitions for the $ZB$ scattering. Energies and momenta assigned to the lines are given as (energy, momentum) with $E$ the center-of-mass energy. The associated momenta can be used in all $ZB$ scattering processes. The labels $a$, $b$, and $c$ denote $B$ or $B^*$ mesons.
• Figure 3: Diagrams for the short-range productions involved in this work for the three $B$ meson systems, which includes the channels {$B\bar{B}B^*$, $B\bar{B}^*B^*$, $B^*\bar{B}B^*$, $B^*\bar{B}^*B^*$}. The second column shows the short-range production of three $B$ mesons, while the third column presents the short-range production of $ZB$ dimer--particle channels. The $ZB$ amplitudes in the second and third rows are coupled. Dashed (solid) lines denote the $B$ and $\bar{B}$ ($B^*$ and $\bar{B}^*$) mesons, while double lines give the $Z$ and $Z'$ dimers.
• Figure 4: Kinematic definitions for the short-range production of three-body (left) and two-body (right) final states. The labels $a$, $b$, and $c$ denote $B$ or $B^*$ mesons.
• Figure 5: Short-range production rates for the $ZB$ and $Z^\prime B^*$ dimer--particle channels with $(I,S)=(3/2(1/2),1)$. The blue-dashed, red-dashed, orange-dashed and black--dash-dotted lines represent the $S$-, $P$-, $D$-wave and the total contributions, respectively. The green dotted lines shows the corresponding asymptotic behavior with the scaling dimensions derived from the asymptotic equations, that is, $E^{s_i-1/2}$ with $s_i$ given by Table. \ref{['Tab: scaling_1']}.