The Stefan–Boltzmann constant (σ) isn’t directly related to the Planck mass, though both involve the same fundamental constants: h, c, and k_B​. σ comes from blackbody radiation theory and depends on how photons behave thermally. The Planck mass, on the other hand, comes from gravity, it's the mass scale where quantum and gravitational effects become comparable. σ can be expressed in Planck units, but linking it to the Planck mass doesn’t reveal deeper physics unless we're working in contexts like quantum gravity or black hole thermodynamics.

Full agreement with Amrit Roy . There is no good reason for introducing the mass of a hypothetical particle when you can use measurable fundamental constants instead.

Fair point, I agree that measurable constants are the standard and practical choice. I was just curious whether the Planck mass, as a derived scale from those same constants, might offer any conceptual insight in more theoretical settings. But yes, for physical predictions, sticking to measurable quantities definitely makes sense.