Simple eigenvalue formula for the Coulomb-plus-linear potential

Hall, Richard L.

doi:10.1103/physrevd.30.433

Cited by 31 publications

(35 citation statements)

References 4 publications

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“…In the opposite limit where the linear force dominates and the Coulomb-like force can be neglected, all energy levels are positive and states with higher have higher energy [12] Eñ ≈…”

Section: Eigenvalues In a Linear Plus Coulombian Potentialmentioning

confidence: 99%

“…such that thermalisation lowers . The dependence on σ, µ and the ground state energy can also be computed variationally, assuming a trial wave-function ψ(r) = e −r/rc /r 3/2 c , such that 3 We thank C. Gross for having pointed out a typo in [12].…”

Section: Eigenvalues In a Linear Plus Coulombian Potentialmentioning

confidence: 99%

“…11 Similar considerations apply to formation of B QQ from free Q at T > ∼ Λ QCD , but this phase is not relevant for the final DM abundance. 12 In the numerical computation such entropy factor was accounted in section 2.5 by imposing a small time allowed to radiate enough energy down to an unbreakable state. To keep the argument simple we here ignore the Boltzmann suppression in the π abundance at T < ∼ m π (in the full numerical computation this is taken into account and increases the σ fall computed in section 2.5, consequently suppressing the hybrid abundances).…”

Section: B Toy Redecouplingmentioning

confidence: 99%

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Colored dark matter

et al. 2018

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We explore the possibility that dark matter (DM) is the lightest hadron made of two stable color octet Dirac fermions Q. The cosmological DM abundance is reproduced for M Q ≈ 12.5 TeV, compatibly with direct searches (the Rayleigh cross section, suppressed by 1=M 6 Q , is close to present bounds), indirect searches (enhanced by QQ þQQ → QQ þ QQ recombination), and with collider searches (where Q manifests as tracks, pair produced via QCD). Hybrid hadrons, made of Q and of standard model quarks and gluons, have large QCD cross sections, and do not reach underground detectors. Their cosmological abundance is 10 5 times smaller than DM, such that their unusual signals seem compatible with bounds. Those in the Earth and stars sank to their centers; the Earth crust and meteorites later accumulate a secondary abundance, although their present abundance depends on nuclear and geological properties that we cannot compute from first principles.

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“…In the opposite limit where the linear force dominates and the Coulomb-like force can be neglected, all energy levels are positive and states with higher have higher energy [12] Eñ ≈…”

Section: Eigenvalues In a Linear Plus Coulombian Potentialmentioning

confidence: 99%

Section: Eigenvalues In a Linear Plus Coulombian Potentialmentioning

confidence: 99%

Section: B Toy Redecouplingmentioning

confidence: 99%

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Colored dark matter

et al. 2018

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“…We checked that the above approximation well reproduces a quantum statistical partition function with approximate energy eigenvalues in Ref. [35]. For ease of the computation, we rely on the approximation in Eq.…”

Section: B Bound State Formationmentioning

confidence: 96%

Thermal relic dark matter beyond the unitarity limit

Harigaya

Ibe

Kaneta

et al. 2016

J. High Energ. Phys.

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We discuss a simple model of thermal relic dark matter whose mass can be much larger than the so-called unitarity limit on the mass of point-like particle dark matter. The model consists of new strong dynamics with one flavor of fermions in the fundamental representation which is much heavier than the dynamical scale of the new strong dynamics. Dark matter is identified with the lightest baryonic hadron of the new dynamics. The baryonic hadrons annihilate into the mesonic hadrons of the new strong dynamics when they have large radii. Resultantly, thermal relic dark matter with a mass in the PeV range is possible. *

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“…This class of potentials has been well studied and much work has been done to approximate the eigenvalues, with or without the Coulomb term necessitated by QCD [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Our goal in this paper is to provide simple formulas for upper and lower energy bounds for this class of potentials.…”

Section: Introductionmentioning

confidence: 99%

Coulomb plus power-law potentials in quantum mechanics

Ciftci

Hall

Katatbeh

2003

J. Phys. A: Math. Gen.

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We study the discrete spectrum of the Hamiltonian H = −∆ + V (r) for the Coulomb plus power-law potential V (r) = −1/r + β sgn(q)r q , where β > 0, q > −2 and q = 0 . We show by envelope theory that the discrete eigenvalues E nℓ of H may be approximated by the semiclassical expression E nℓ (q) ≈ min r>0 {1/r 2 − 1/(µr) + sgn(q)β(νr) q }. Values of µ and ν are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, ψ(r) = r ℓ+1 e −(xr) q . We give detailed results for V (r) = −1/r + βr q , q = 0.5, 1, 2 for n = 1, ℓ = 0, 1, 2, along with comparison eigenvalues found by direct numerical methods.

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Simple eigenvalue formula for the Coulomb-plus-linear potential

Cited by 31 publications

References 4 publications

Colored dark matter

Colored dark matter

Thermal relic dark matter beyond the unitarity limit

Coulomb plus power-law potentials in quantum mechanics

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