Partonic behavior of string scattering amplitudes from holographic QCD models

Abstract We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in partic...

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Main Authors: Massimo Bianchi, Maurizio Firrotta, Jacob Sonnenschein, Dorin Weissman
Format: Article
Language:English
Published: SpringerOpen 2022-05-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP05(2022)058
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author Massimo Bianchi
Maurizio Firrotta
Jacob Sonnenschein
Dorin Weissman
author_facet Massimo Bianchi
Maurizio Firrotta
Jacob Sonnenschein
Dorin Weissman
author_sort Massimo Bianchi
collection DOAJ
description Abstract We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that A $$ \mathcal{A} $$ ∼ s 2−∆/2 whereas in Witten’s model A $$ \mathcal{A} $$ ∼ s 3−∆/2 and A $$ \mathcal{A} $$ ∼ s 7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime A $$ \mathcal{A} $$ ∼ s 2 t −2+α (log s/t) −1+α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ A $$ \mathcal{A} $$ ] ∼ s −1, Im [ A $$ \mathcal{A} $$ ] ∼ s α . We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.
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spelling doaj.art-5212c5f924dc46428e74dc65938e4f6b2022-12-22T02:11:22ZengSpringerOpenJournal of High Energy Physics1029-84792022-05-012022514410.1007/JHEP05(2022)058Partonic behavior of string scattering amplitudes from holographic QCD modelsMassimo Bianchi0Maurizio Firrotta1Jacob Sonnenschein2Dorin Weissman3Dipartimento di Fisica, Università di Roma Tor VergataDipartimento di Fisica, Università di Roma Tor VergataThe Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv UniversityOkinawa Institute of Science and TechnologyAbstract We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that A $$ \mathcal{A} $$ ∼ s 2−∆/2 whereas in Witten’s model A $$ \mathcal{A} $$ ∼ s 3−∆/2 and A $$ \mathcal{A} $$ ∼ s 7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime A $$ \mathcal{A} $$ ∼ s 2 t −2+α (log s/t) −1+α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ A $$ \mathcal{A} $$ ] ∼ s −1, Im [ A $$ \mathcal{A} $$ ] ∼ s α . We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.https://doi.org/10.1007/JHEP05(2022)058Gauge-Gravity CorrespondenceScattering AmplitudesBosonic Strings
spellingShingle Massimo Bianchi
Maurizio Firrotta
Jacob Sonnenschein
Dorin Weissman
Partonic behavior of string scattering amplitudes from holographic QCD models
Journal of High Energy Physics
Gauge-Gravity Correspondence
Scattering Amplitudes
Bosonic Strings
title Partonic behavior of string scattering amplitudes from holographic QCD models
title_full Partonic behavior of string scattering amplitudes from holographic QCD models
title_fullStr Partonic behavior of string scattering amplitudes from holographic QCD models
title_full_unstemmed Partonic behavior of string scattering amplitudes from holographic QCD models
title_short Partonic behavior of string scattering amplitudes from holographic QCD models
title_sort partonic behavior of string scattering amplitudes from holographic qcd models
topic Gauge-Gravity Correspondence
Scattering Amplitudes
Bosonic Strings
url https://doi.org/10.1007/JHEP05(2022)058
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AT mauriziofirrotta partonicbehaviorofstringscatteringamplitudesfromholographicqcdmodels
AT jacobsonnenschein partonicbehaviorofstringscatteringamplitudesfromholographicqcdmodels
AT dorinweissman partonicbehaviorofstringscatteringamplitudesfromholographicqcdmodels