Towards reconciling the holographic and lattice descriptions of radially excited hadrons
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Regular Article - Theoretical Physics
Towards reconciling the holographic and lattice descriptions of radially excited hadrons S. S. Afonina Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
Received: 22 April 2020 / Accepted: 30 July 2020 © The Author(s) 2020
Abstract Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza–Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as ”excitations” of some ground state, but rather as independent states coupled to higher dimensional QCD operators – the larger is a basis of interpolating operators, the larger set of states can be resolved. A question arises whether is it possible to reconcile the holographic and lattice descriptions of radially excited hadrons? We propose a new phenomenological ”consistency test” for bottom-up holographic models: If the KK spectrum of massive 5D fields dual to higher dimensional operators in QCD coincides with the conventional radial KK spectrum, then the holographic KK states can be identified with real excited mesons in the large-Nc limit of QCD. We demonstrate that the Soft Wall holographic model passes this test while the Hard Wall model does not.
1 Introduction The confinement in QCD is known to lead to a rich spectrum of excited hadrons. A complete theoretical understanding of this spectrum is still missing despite of many fruitful ideas and models put forward in the last half of century. The problem becomes especially acute in the case of hadrons composed from light quarks where one observes plenty of higher spin and radial excitations. The corresponding hadron resonances usually have large decay widths and this causes many difficulties not only with experimental extraction of their characteristics but also with a clear theoretical identifia e-mail:
cation of the given objects. In this situation, it is very useful to consider a limit where many hadron resonances become well-defined particles while the underlying theory remains qualitatively similar. Quite remarkably, such a limit indeed exists in QCD – the large-Nc (called also planar) limit [1], in which the quark-antiquark states become stable particles: Both their strong decay width and corrections to masses are suppressed by 1/Nc . Baryons represent heavy objects in this limit [2] (their mass behaves as O(Nc ) while the mass of quark–antiquark mesons scales as O(1)) and will be of no interest for us. Matching the obtained meson theory to the . perturbative QCD at small ’t Hooft constant λ = g 2 Nc shows that the theory at small λ must contain an infinite number of states for each quantum number [2] – the ”radial” excitations in the language of non-relativistic pot
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