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Measurement of alpha / phi_2 from B to pi pi decays

The current results on B to pipi decays and SU2 constraints on the Unitarity Triangle angle alpha or phi_2 from the B-factories are summarised. Based on these measurements, predictions of the isospin analysis constraints at the end of the lifetime of both B-factories are given.


I. INTRODUCTION
These proceedings are a summary of the experimental constraints on the Unitarity Triangle angle α (or φ 2 )obtained from B-meson decays to ππ final states. Measurements of α have recently been performed at the B-factories, the BABAR experiment [1] at SLAC and the Belle experiment [2] at KEK using ππ, ρπ and ρρ decays which proceed via b → u transitions as discussed in Ref. [3]. Details of the constraints on α from ρπ and ρρ decays can be found in Refs. [4,5,6,7,8,9,10,11].
The decays B → ππ proceed mainly through a b → uud tree diagram as shown in Fig. 1. Interference between the direct decay and decay after BB mixing in B 0 → π + π − results in a time-dependent decay rate asymmetry that is sensitive to the angle α. The presence of gluonic loop (penguin) contributions with a different weak phase to the tree contribution shifts the measured angle from the Unitarity Triangle angle α to an effective parameter α ππ ef f , where the shift is defined as δα ππ = α − α ππ ef f . The time-dependent CP asymmetry measured in B 0 → π + π − has the form 1 where ∆m d is the BB mixing frequency, ∆t is the proper time difference between the decay of the two B mesons in an event, and where λ = (q/p)(A/A). The ratio q/p is related to CP violation in mixing of neutral B mesons, and A/A is the ratio of decay amplitudes of B 0 → π + π − to B 0 → π − π + decays. If penguin amplitudes contribute to the decay, S = √ 1 − C 2 sin(2α ππ ef f ), and C can be non-zero. Gronau and London proposed a method using SU (2) isospin symmetry to cleanly disentangle the penguin contribution and extract α from measurements of S and C [12]. This method relates the isospin amplitudes of B 0 → π − π + , B 0 → π 0 π 0 and B + → π + π 0 processes and their complex conjugates as two triangles in a complex plane. As shown in Fig. 2, where A ij (A ij ) are the amplitudes of B (B) decays to the final state with charge ij, andÃ ij denotes a rotated amplitude A ij . After aligning the amplitudes for π + π 0 and π − π 0 decays, the phase difference between the A +− andÃ +− is a measure of 2δα ππ . The theoretical uncertainties in this method are at a level of a few degrees and are discussed at length in Ref. [13].

A. Signal Extraction
Continuum e + e − → qq (q = u, d, s, c) events are the dominant background to B → ππ decays. Sig-nal candidates are identified using two kinematic variables: the difference ∆E between the energy of the B candidate and the beam energy √ s/2 in the center of mass frame; and the beam-energy substituted mass The B momentum p B and four-momentum of the initial state (E i , p i ) are defined in the laboratory frame. Event shape variables are used to further discriminate between signal and continuum background. The selection of B 0 → π + π − decays also depends on particle identification information to discriminate between the signal π + π − and background K ± π ∓ decays.

B. Recent improvements in analysis techniques
The Belle analysis of B 0 → π + π − has recently been improved by using particle identification information from the aerogel cherenkov counters and dE/dx from the drift chamber to discriminate between charged π and K mesons. The BABAR analysis of B 0 → π 0 π 0 and B ± → π ± π 0 has recently benefited from an improved π 0 meson selection. The original selection technique used in these analyses reconstructed π 0 → γγ decays where the final state photons deposit all of their energy in distinct regions of the BABAR electromagnetic calorimeter. There is a class of high energy π 0 mesons where the two photons deposit all of their energy in indistinguishable regions of the calorimeter. The lateral shower profile in the calorimeter is used to select such π 0 mesons [14]. In addition to this, it is possible to reconstruct π 0 mesons where photons undergo γ → e + e − conversion in detector material. Inclusion of both of these classes of events results in an increased selection efficiency of approximately 10% for B 0 → π 0 π 0 .  When calculating the branching fraction, both collaborations have accounted for possible final state radiation in this decay.   uncertainty from EWP contributions to B + → π + π 0 on α are at the level of a few degrees [13,18,19].

III. EXPERIMENTAL RESULTS
Table III summarises the experimental measurements of B 0 → π 0 π 0 decays reported in Refs. [14,20]. The measurement of C in this mode is an important contribution to the isospin analysis as the measured B → ππ branching fractions, with C from π + π − and π 0 π 0 give as many constraints as observables required to fully constrain the isospin analysis. Experimental knowledge of this decay is the limiting factor in improving the constraint on α in B → ππ decays using an isospin analysis.

D. Results of the Isospin Analysis
Fig. 5 shows the one minus confidence level (1-CL) distribution for |δα ππ | obtained from an isospin analysis of B → ππ decays. The upper limit from penguin pollution in the measurement of α from B → ππ is 41 • (90%) CL from BABAR. The constraint from Belle is tighter as the π 0 π 0 branching fraction from Belle is smaller than the one from BABAR. There is a dip on the 1-CL distribution between |δα| ∼ 10 • and |δα| ∼ 35 • (See Fig. 5) which is the result of including the measurement of C from B 0 → π 0 π 0 decays in the isospin analysis. The 1-CL distribution for α obtained from an isospin analysis of B → ππ decays is shown in Fig. 6. Values of α between 11 • and 79 • are excluded at 95.4% CL by Belle, and weaker constraints are obtained by BABAR. The main reason for the difference between the constraints reported by the B-factories is that the BABAR paper uses only BABAR results, whereas the Belle paper uses the average of the BABAR and Belle results. In the latter case the isospin triangles are flatter than in the former case. The effect this has on the 8-fold ambiguity on α from an isospin analysis is to overlap adjacent solutions.

IV. SENSITIVITY PROJECTIONS
Using the current experimental knowledge of B → ππ decays, it is possible to make predictions of the constraint on α from a B-factory with 1ab −1 of data, and by com- bining the results of Belle and BABAR for a total data sample of 2ab −1 . These predictions use the central values given by BABAR, and scale the statistical and the subset of reducible systematic uncertainties to higher luminosity, and have been made using the statistical technique described in [7]. The results of the isospin analysis predictions for 1ab −1 and 2ab −1 are shown in Fig. 7. The precision of a single SM solution from 1ab −1 (2ab −1 ) of data is expected to be ±6 • (±4.2 • ) at 68% CL, which remains larger than current theoretical uncertainties from the isospin analysis. If one performs an isospin analysis projection using the world average of the inputs (also shown), then the precision of each distinct solution is degraded by a few degrees. As a result the eight-fold ambiguity in the solution for alpha is manifest as four distinct solutions for α between zero and 180 • .
It is not possible to select between the different ambiguities of the isospin analysis with B → ππ decays, and one will ultimately have to combine the constraints obtained from ππ, ρπ [8,9] and ρρ [10,11,21,22,23] for the final B-factory measurement of α.
As the π 0 π 0 final state is difficult to isolate in a hadronic environment, it is expected that a Super Flavor Factory operating at an e + e − collider will be required to significantly improve upon the B-factory isospin analysis constraint on α from ππ decays. It might become feasible to perform a time-dependent analysis of B 0 → π 0 π 0 at a future Super Flavor Factory. This would require reconstruction of the decay vertex of the π 0 π 0 final state where the π 0 mesons undergo conversion in detector material, or Dalitz decay. If this was achievable, the measurement of S in B 0 → π 0 π 0 could be used to overconstrain the ππ isospin analysis.

V. SUMMARY
The B-factories have seen compelling evidence for CP violation in B → π + π − decays. The Belle data are compatible with observations of both direct and mixinginduced CP violation signals. The BABAR data provides weaker evidence for such effects. There is still a small discrepancy between the two experiments in the measurement of C in this channel, however it is expected that the two experiments will continue to move toward a common value with more data. The α constraint obtained from an isospin analysis of ππ decays at 68% CL is becoming increasingly precise. A single solution could be measured to 4.2 • at 68% CL, with a data sample of 2ab −1 , at the end of the lifetime of the B-factories. This would provide a non-trivial constraint on α after combination with the available information from ρρ and ρπ decays.