Comment on extracting alpha from B -> rho rho

Abstract

Recent experimental results on $B\to \rho \rho$ decays indicate that the CP asymmetry $S_{{\rho }^{+}{\rho }^{-}}$ will give an interesting determination of $\alpha =\arg [-(V_{td}{V}_{tb}^{\ast })/(V_{ud}{V}_{ub}^{\ast })]$. In the limit when the $\rho$ width is neglected, the $B\to \pi \pi$ isospin analysis can also be applied to $B\to \rho \rho$, once an angular analysis is used to separate transversity modes. The present bound on the shift of $S_{{\rho }^{+}{\rho }^{-}}$ from the true $\sin 2\alpha$ is already stronger than it is for $S_{{\pi }^{+}{\pi }^{-}}$. We point out a subtle violation of the isospin relations when the two $\rho$ mesons are observed with different invariant masses, and how to constrain this effect experimentally.

12 pages, minor changes

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• A Study of B0 to rho+rho- Decays and Constraints on the CKM Angle alpha
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• Measurement of the branching fraction, polarization, and CP asymmetry for B0->rho+rho- decays, and determination of the CKM phase phi_2
• CP violation and the CKM matrix
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• Improved Measurement of the CKM Angle alpha Using B0->rho+rho- Decays
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• The CKM matrix and CP Violation
• Limit on the B0->rho0rho0 Branching Fraction and Implications for the CKM Angle alpha
• B Meson Decays
• Reducing the Error on alpha in B-> pi pi, rho rho, rho pi
• Study of ${\mathbf{B}}^0\to {\rho }^{+}{\rho }^{-}$ decays and implications for the CKM angle ${\varphi }_2$
• Time-dependent CP asymmetries in D and B decays
• Measurement of $B^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ Decays and Search for $B^0\to {\rho }^0{\rho }^0$
• Testing the dynamics of B -> ππand constraints on α
• Evidence for B0->rho0rho0 Decay and Implications for the CKM Angle alpha
• CP violation in beauty decays
• Measurement of the CKM angle alpha with the B-factories
• Penguin pollution estimates relevant for phi_2/alpha extraction
• Bounding hadronic uncertainties in $c\to u$ decays
• CP violation in B meson decays
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B^0\to a_1^{\pm }{\pi }^{\mp }$
• Weak Phases and CP Violation
• Impact of systematic and amplitude model correlations within and between systems of combined input: A case study with ${\varphi }_2$ ($\alpha$)
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B\to \rho \rho$
• Constraining electroweak penguin graph contributions in measurements of the CKM phase alpha using $B\to \pi \pi$ and $B\to \rho \rho$ decays
• Precision Tests of Flavor and CP violation in B Decays
• Rescaling the isospin triangle argument for constraining ${\varphi }_2$ ($\alpha$): consolidating Belle II and a potential path forward for LHCb
• Constraints on the CKM angle alpha in the B --> rho rho decays
• Constraints upon the CKM angle phi_2 (alpha) from Belle and BaBar
• CP Violation Results from B Decays at BaBar