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Yukawa Bound States of a Large Number of Fermions

Wise, Mark B. and Zhang, Yue (2015) Yukawa Bound States of a Large Number of Fermions. Journal of High Energy Physics, 2015 (2). Art. No. 023. ISSN 1126-6708.

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We consider the bound state problem for a field theory that contains a Dirac fermion x that Yukawa couples to a (light) scalar field ø. We are interested in bound states with a large number N of x particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic x's are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic x particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and x mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. As an application to dark matter, our analysis offers the possibility of having a supermassive thermal DM candidate. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such x particles.

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Additional Information:© 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: November 26, 2014; Accepted: January 15, 2015; Published: February 3, 2015. This work started from discussions with Natalia Toro who pointed out the suppression at high energies of Yukawa couplings and the form of the effective classical particle theory in Eq.(3). We are grateful to her for these key insights. This work is supported by the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics, and by the DOE Grant DE-SC0011632, and also by a DOE Early Career Award under Grant No. DE-SC0010255. We are also grateful for the support provided by the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
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Gordon and Betty Moore Foundation776
Department of Energy (DOE)DE-SC0011632
Department of Energy (DOE)DE-SC0010255
Walter Burke Institute for Theoretical PhysicsUNSPECIFIED
Subject Keywords:High Energy Physics - Phenomenology (hep-ph); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE)
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Issue or Number:2
Record Number:CaltechAUTHORS:20141116-071612082
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51812
Deposited By: Joy Painter
Deposited On:17 Nov 2014 19:03
Last Modified:03 Oct 2019 07:36

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