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In Flavour physics, amplitude of decay processes is generally expressed in terms of effective operators (reference). In the framework of effective field theory amplitude $\propto C_iO_i$, where $O_i$ are the operators (currents) and $C_i$ are the wilson coefficients (numbers).

Now, effective field theory and full theory are matched at a particular scale to find values of Wilson coefficients. In this particular paper, where they are studying a $b\rightarrow s~ l^+l^-$ transition, they choose the matching scale to be $m_W$ (Mass of W boson).Why is that? Whay are they not choosing matching scale to be 246 GeV which is the electroweak scale?

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Because W boson is the lightest particle which is being integrated out. Below this scale Standard Model picture and effective picture vary but the physics remain same. So, the two pictures should match at the boundary.

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