# About the fine structure constant value

In the PARTICLE PHYSICS BOOKLET, Extracted from the Review of Particle Physics, we read that the fine structure constant has a value $$\alpha \approx 1/137$$ at $$Q^2=0$$ and $$\alpha\approx 1/128$$ at $$Q^2\approx m^2(W)$$. What are those $$Q^2$$ and $$m(W)$$ and what does it means such difference?

• Where in that 256 page document are we supposed to be looking ? – StephenG Feb 25 at 23:04
• Near duplicate. "Constant" is a historical misnomer. It is actually a "running coupling" dependent on the energy scale of the process in question, as dictated by the Renormalization Group of QFT. – Cosmas Zachos Feb 25 at 23:21
• @StephenG. It is at pg. 6: the table1.1 of Physical constants. – Emilio Novati Feb 26 at 21:27

Even though they are called coupling "constants", the strong, weak and electromagnetic coupling constants all vary depending on the energy scale of the involved particles. In this case, the second value of approximately $$1/128$$ can be measured at the energy scale of the W boson (so around $$80$$ GeV).
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