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Entanglement Suppression and Emergent Symmetries of Strong Interactions
Silas R. Beane, David B. Kaplan, Natalie Klco, Martin J. Savage
TL;DR
The paper examines how NN contact interactions and low-energy constants determine S-matrix entanglement in pionless EFT. It relates spin-channel phase shifts and interaction coefficients to entanglement power, using scattering data to evaluate the physical interaction.
Problem
The paper addresses how low-energy NN interaction coefficients and channel phase shifts determine the entanglement power of the scattering S-matrix.
Source: Supplemental Material for… · p. 8, A , (15) · p. 8Method
The analysis uses pionless EFT in the PDS scheme, decomposes the contact vertex into CS and CT, and relates these coefficients to the 1S0 and 3S1 channels.
Source: Supplemental Material for… · p. 8, A , (15) · p. 8Results
The entanglement power is evaluated as a function of CT using CS = −1.2 × 10−4 MeV−2 and physical scattering parameters.
Source: A , (15) · p. 8Takeaways & Limitations
The supplement provides an EFT-based connection between fitted low-energy constants, channel phase shifts, and the unitary S-matrix used in the entanglement analysis.
Source: Supplemental Material for… · pp. 7–8, A , (15) · p. 8
Abstract
from arXiv · showhide
Entanglement suppression in the strong interaction $S$-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter.
Supplemental Material for “Entanglement Suppression and Emergent Symmetries of Strong Interactions”
The supplement documents how low-energy constants are constrained by fitted NN and πN scattering data and relates pionless-EFT amplitudes to a unitary S-matrix.
Supplemental Material for “Entanglement Suppression and Emergent Symmetries of Strong Interactions”
- The stability of the potential coefficients indicates that low-energy data well below pion threshold constrain the LECs.Source: Supplemental Material for… · p. 7
- The low-energy constants are compiled from spectroscopic fits to NN and πN scattering data, with correlated uncertainties and regulator cutoffs Λ = 450, 475, 550, 600 MeV.Numerical values are tabulated in Table I.Source: Supplemental Material for… · p. 7, Table I · p. 8
- In pionless EFT, the NN scattering amplitude in the PDS scheme is expressed through the contact-interaction coefficient C(p^2, µ).The resulting expression furnishes a unitary S-matrix.Source: Supplemental Material for… · p. 8
A , (15)
This section decomposes the NN contact interaction into spin-independent and spin-dependent coefficients, relates them to channel phase shifts, and evaluates the resulting S-matrix entanglement power.
A , (15)
- The contact vertex is decomposed as C(p^2, µ)σ = CS 1 + CT σ·σ to analyze entanglement production in the spin sector.Here M, µ, p, and C(p^2, µ) denote the nucleon mass, renormalization scale, center-of-mass momentum, and tree-level s-wave vertex.Source: A , (15) · p. 8
- The appendix also provides the relation between the renormalization-scale-dependent coefficients and the channel phase shifts used to obtain the S-matrix entanglement power.Source: A , (15) · p. 8
- The coefficients C0 = (CS − 3CT) and C1 = (CS + CT) connect the Lagrangian interaction to the 1S0 and 3S1 channels.Source: A , (15) · p. 8
- The entanglement power is evaluated as a function of CT at fixed CS = −1.2 × 10−4 MeV−2, µ = 140 MeV, M = 939 MeV, and p = 19.4 MeV.The physical CT value is obtained from the stated scattering lengths and effective ranges.Source: A , (15) · p. 8, Figure 4 · p. 9