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Register a new userStrong Phases in the Decays B to pi pi
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Two sources of strong phases in the decays $B$ to $pipi$ are identified: (1) quasi-elastic scattering corresponding to intermediate states like $pipi$ and $rhorho$, (2) ``$cbar{c}$ corresponding to intermediate states like $Dbar{D}$ and $D^{*}bar{D}^{*}$. Possibilities of using data to identify these two sources are discussed and illustrated. Present data suggests both sources may be significant.
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The observed strong phase difference of 30^{o} between I=(3/2) and I=(1/2) final states for the decay B to D Pi is analyzed in terms of rescattering like D^{∗}Pi to D Pi, etc. It is concluded that for the decay B^{o}to D^{+} Pi^{-} the strong phase is only about 10^{o}. Implications for the determination of sin(2 Beta + gamma) are discussed.
The scattering amplitude of D Pi at the energy of the B mass can be calculated using Regge theory. Recent papers have used this to calculate the final state strong phases in the decays B to D Pi. It is argued that while the Regge amplitude can yield an absorption correction to the decay rate, it is not useful for determining the strong phase.
We summarize a recent strategy for a global analysis of the B -> pi pi, pi K systems and rare decays. We find that the present B -> pi pi and B -> pi K data cannot be simultaneously described in the Standard Model. In a simple extension in which new physics enters dominantly through Z^0 penguins with a CP-violating phase, only certain B -> pi K modes are affected by new physics. The B -> pi pi data can then be described entirely within the Standard Model but with values of hadronic parameters that reflect large non-factorizable contributions. Using the SU(3) flavour symmetry and plausible dynamical assumptions, we can then use the B -> pi pi decays to fix the hadronic part of the B -> pi K system and make predictions for various observables in the B_d -> pi^-+ K^+- and B^+- -> pi^+- K decays that are practically unaffected by electroweak penguins. The data on the B^+- -> pi^0 K^+- and B_d -> pi^0 K modes allow us then to determine the electroweak penguin component which differs from the Standard Model one, in particular through a large additional CP-violating phase. The implications for rare K and B decays are spectacular. In particular, the rate for K_L -> pi^0 nu bar nu is enhanced by one order of magnitude, the branching ratios for B_{d,s} -> mu^+ mu^- by a factor of five, and BR(K_L -> pi^0 e^+ e^-, pi^0 mu^+ mu^-) by factors of three.
If new physics (NP) is present in B -> pi pi decays, it can affect the isospin I=2 or I=0 channels. In this paper, we discuss various methods for detecting and measuring this NP. The techniques have increasing amounts of theoretical hadronic input. If NP is eventually detected in B -> pi pi -- there is no evidence for it at present -- one will be able to distinguish I=2 and I=0, and measure its parameters, using these methods.
The Dalitz plot analysis technique is used to study the resonant substructures of $B^{-} to D^{+} pi^{-} pi^{-}$ decays in a data sample corresponding to 3.0 ${rm fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. A model-independent analysis of the angular moments demonstrates the presence of resonances with spins 1, 2 and 3 at high $D^{+}pi^{-}$ mass. The data are fitted with an amplitude model composed of a quasi-model-independent function to describe the $D^{+}pi^{-}$ S-wave together with virtual contributions from the $D^{*}(2007)^{0}$ and $B^{*0}$ states, and components corresponding to the $D^{*}_{2}(2460)^{0}$, $D^{*}_{1}(2680)^{0}$, $D^{*}_{3}(2760)^{0}$ and $D^{*}_{2}(3000)^{0}$ resonances. The masses and widths of these resonances are determined together with the branching fractions for their production in $B^{-} to D^{+} pi^{-} pi^{-}$ decays. The $D^{+}pi^{-}$ S-wave has phase motion consistent with that expected due to the presence of the $D^{*}_{0}(2400)^{0}$ state. These results constitute the first observations of the $D^{*}_{3}(2760)^{0}$ and $D^{*}_{2}(3000)^{0}$ resonances.
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