Determine the dipole-suppression constant C in the IFS-induced DP-like model

Determine the magnitude of the dimensionless constant C in the relation τ_dip = C ℓ_s / g_s that sets the lifetime τ_dip of the growing energy dipole produced by the splitting of an instant folded string in the instant-folded-string (IFS) cosmological setup, thereby fixing the effective Diòsi–Penrose parameters G_eff and R_0,eff for this string-theoretic realization.

Background

In the proposed string-theoretic realization of a Diòsi–Penrose-like collapse mechanism, instant folded strings (IFSs) nucleate and split, producing an energy-EPR state that behaves as a growing gravitational dipole. The growth persists for a characteristic time τ_dip before being suppressed by further splittings and interactions.

The authors argue that τ_dip scales as τ_dip = C ℓ_s / g_s with C ≫ 1, where ℓ_s is the string length and g_s the string coupling, and that C directly controls the effective collapse parameters (G_eff and R_0,eff). Although “in principle calculable,” the constant C has not been estimated due to the complexity of the exact CFT and uncertainties about which interaction channels dominate the suppression of dipole growth.

Fixing C is phenomenologically important because it determines the temporal color (cutoff) of the noise and the strength of induced diffusion/heating relative to collapse rates, thereby affecting the model’s consistency with experimental bounds.