Modifying the Skyrme model: Pion mass and higher derivatives

Marleau, Luc

doi:10.1103/physrevd.43.885

Cited by 45 publications

(56 citation statements)

References 8 publications

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“…Unfortunately, it turns out that simply substituting the solution (35) in the expression for energy associated with the full Lagrangian leads to divergences. So, however small the parameters α and β are, these BPS solutions cannot be considered as appropriate approximations of the solutions for (4).…”

Section: Bps-type Solutionsmentioning

confidence: 99%

“…Using these heavier elements as input parameters changes slightly the overall predicting accuracy. Whereas the best overall accuracy is achieved using 16 O parametrization in Set Ib, the lightest isotopes are best described by choosing 4 He as input (Set Ia). Note that the lightest nuclei have lower moments of inertia and get relatively large rotational contribution to their mass.…”

Section: Bps-type Solutionsmentioning

confidence: 99%

“…Now comes the time to choose a specific potential. The choice for mass term of the Skyrme is not unique and indeed has been the object of several discussions [4,6,13]. The usual mass term V = 1 − cos F was considered in [12].…”

Section: Bps-type Solutionsmentioning

confidence: 99%

“…For this purpose, we propose to write the potential in the form of the generalized mass term introduced by [4] …”

Section: Bps-type Solutionsmentioning

confidence: 99%

“…Several modifications to the model have been considered to improve these predictions, from the generalization of the mass term [4][5][6] to the explicit addition of vector mesons [7,8], aside form higher order terms in derivatives of the pion field [4]. Unfortunately, the analysis of these models has been hampered by their nonlinear nature and the absence of analytical solutions.…”

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confidence: 99%

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Nuclei as near BPS Skyrmions

Bonenfant

Marleau

2010

Phys. Rev. D

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We study a generalization of the Skyrme model with the inclusion of a sixth-order term and a generalized mass term. We first analyze the model in a regime where the nonlinear σ and Skyrme terms are switched to zero which leads to well-behaved analytical BPS-type solutions. Adding contributions from the rotational energy, we reproduce the mass of the most abundant isotopes to rather good accuracy. These BPS-type solutions are then used to compute the contributions from the nonlinear sigma and Skyrme terms when these are switched on. We then adjust the four parameters of the model using two different procedures and find that the additional terms only represent small perturbations to the system. We finally calculate the binding energy per nucleon and compare our results with the experimental values.

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Section: Bps-type Solutionsmentioning

confidence: 99%

Section: Bps-type Solutionsmentioning

confidence: 99%

Section: Bps-type Solutionsmentioning

confidence: 99%

“…For this purpose, we propose to write the potential in the form of the generalized mass term introduced by [4] …”

Section: Bps-type Solutionsmentioning

confidence: 99%

mentioning

confidence: 99%

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Nuclei as near BPS Skyrmions

Bonenfant

Marleau

2010

Phys. Rev. D

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Higher-order Skyrme hair of black holes

Gudnason¹,

Nitta²

2018

J. High Energ. Phys.

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Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.

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A higher-order Skyrme model

Gudnason

Nitta

2017

J. High Energ. Phys.

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We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However, we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally, we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.

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Modifying the Skyrme model: Pion mass and higher derivatives

Cited by 45 publications

References 8 publications

Nuclei as near BPS Skyrmions

Nuclei as near BPS Skyrmions

Higher-order Skyrme hair of black holes

A higher-order Skyrme model

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