Instanton effects on the heavy-quark static potential**Supported by Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Korean government (Ministry of Education, Science and Technology, MEST), Grant Numbers 2016R1D1A1B03935053 (UY) and 2015R1D1A1A01060707 (HChK) and The work was also partly Supported by RIKEN iTHES Project

U T Yakhshiev,M M Musakhanov,Hyun-Chul Kim,B Turimov,Emiko Hiyama

doi:10.1088/1674-1137/41/8/083102

U T Yakhshiev, M M Musakhanov + Show 3 more

Open Access

https://doi.org/10.1088/1674-1137/41/8/083102

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Abstract

We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. Finally, we solve the nonrelativistic two-body problem, associated with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra.

Highlights

Heavy-quark physics has evolved into a new phase
3School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea 4Theoretical Physics Department, National University of Uzbekistan, Tashkent-174, Uzbekistan (Dated: June, 2016) We investigate the instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model
We aimed at investigating the instanton effects on the heavy-quark potential, based on the instanton liquid model

Summary

INTRODUCTION

Heavy-quark physics has evolved into a new phase. Charmonium-like states, which are known as XYZ states [1,2,3,4,5,6,7,8,9,10,11,12,13] and quite possibly exotic ones, conventional bottomonia including the lowest-lying state ηb [14,15,16,17,18,19,20], and heavy pentaquark states [21] have been newly reported by various experimental collaborations (see recent reviews [22,23,24,25]). We will examine the instanton effects on the heavy-quark potential from the instanton vacuum, including the spin-dependent parts in addition to the central one. In the present work, we want to obtain the instanton-induced spin-dependent parts of the heavy-quark potential, following closely Refs. As we will show in this work, the heavy-quark propagator is given as an integral equation Expanding it in powers of 1/m2Q, we are able to compute the spin-dependent part of the heavy-quark potential as was first shown in Ref.

Heavy-quark propagator

Heavy-quark potential from the instanton vacuum

Instanton potential

Gaussian Expansion Method

Quarkonium states

SUMMARY AND OUTLOOK