Controlling $rho$ width effects for a precise value of $alpha$ in $B to rho rho$

It has been pointed out that the currently most precise determination of the weak phase $phi_2 = alpha$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix achieved in $B to rhorho$ decays is susceptible to a small correction at a level of $(Gamma_rho/m_rho)^2$ due to an $I=1$ amplitude caused by the $rho$ width. Using Breit-Wigner distributions for the two pairs of pions forming $rho$ mesons, we study the $I=1$ contribution to $Bto rhorho$ decay rates as function of the width and location of the $rho$ band. We find that in the absence of a particular enhancement of the $I=1$ amplitude reducing a single band to a width $Gamma_rho$ at SuperKEKB leads to results which are completely insensitive to the $rho$ width. If the $I=1$ amplitude is dynamically enhanced relative to the $I=0,2$ amplitude one could subject its contribution to a magnifying glass measurement using two separated $rho$ bands of width $Gamma_rho$. Subtraction of the $I=1$ contribution from the measured decay rate would lead to a very precise determination of the $I=0,2$ amplitude needed for performing the isospin analysis.