Raising each beam energy to 250 MeV makes MeV. The kaon denominator is now dominated by
(1)
rather than by . Substituting into a gives
(2)
The enormous change is a tiny-width effect, not a comparably abrupt change in the broad rho contribution. The center-of-momentum energy has moved about kaon widths from the peak. A width of MeV is only eV, requiring an energy-selection scale of order relative to the several-hundred-MeV beam energy.
Real beams have vastly broader energy distributions. Averaging over such a distribution suppresses the useful narrow-resonance contribution: the finite peak value does not imply a large energy-integrated formation rate, whose resonant area shrinks with the width at fixed branching fractions. The weak inverse-decay entrance coupling and the broad strong-interaction rho background therefore make this a poor way to study kaon resonant formation. The supplied broad-resonance formula is used algebraically as requested; a practical calculation would convolve an appropriate narrow line shape with the actual beam distribution.
Figure 1.
A broad rho background and an extremely narrow kaon resonance
. Original evaluation of the stipulated line shapes. The kaon inset uses its own width-scale horizontal axis; drawing it visibly broad on a MeV axis would misrepresent the given width. Details.

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