What question did this study set out to answer?

To analytically derive the string tension from the geometric and mechanical properties of nonlinear elastic media.

July 12, 20260 citationsOpen Access

Analytic Derivation of the String Tension From Nonlinear Elastic Media to Quark Confinement

Key Points

To analytically derive the string tension from the geometric and mechanical properties of nonlinear elastic media.
Developed a formula using Gluon Elastic Lattice Theory (GELT) to calculate string tension.
Used parameters such as strain hardening coefficient, background stiffness, and lattice spacing in the formula.
Substituted determined GELT parameters for precise calculations of the string tension.
Derived string tension formula yielding σ ∼ 1 GeV/fm, aligning with numerical results from lattice QCD.
Established that string tension arises from the nonlinear elastic medium's response to stretching.
Showed quark confinement can be computed mechanically rather than accepted as a QCD postulate.

Abstract

Lattice QCD numerically gives the string tension σ ≈ 0. 9 GeV/fm, but cannot derive this value analytically from first principles. This paper provides a rigorous analytical formula for the string tension within the Gluon Elastic Lattice Theory (GELT): σ = ζσ η K₀ d₀², where ζσ is a dimensionless constant emerging from the cross-sectional integral of the tube geometry, η is the strain hardening coefficient of the medium, K₀ is the background stiffness, and d₀ is the lattice spacing. Substituting the precisely determined GELT parameters yields σ ∼ 1 GeV/fm in order of magnitude. The string tension — the slope of the linear confining potential — is an inevitable consequence of the hardening response of a nonlinear elastic medium to stretching. Quark confinement is not a QCD postulate to be accepted, but a directly computable mechanical quantity determined by basic medium parameters.

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