CKM Angle Gamma Research Articles

Toward extracting gamma from Brightarrow DK without binning

B^pm rightarrow DK^pm transitions are known to provide theoretically clean information about the CKM angle gamma , with the most precise available methods exploiting the cascade decay of the neutral D into CP self-conjugate states. Such analyses currently require binning in the D decay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of gamma , with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to gamma , its conceptually novel approach opens the door to new strategies for gamma extraction. More studies are required to see if these can be competitive with the existing methods.

Dalitz plot studies ofD0→KS0π+π−decays in a factorization approach

The presently available high-statistics data of the D0 --> K0S pi+ pi- processes measured by the Belle and BABAR Collaborations are analyzed within a quasi two-body QCD factorization framework. Starting from the weak effective Hamiltonian, tree and annihilation amplitudes build up the D0 --> K0S pi+ pi- decay amplitude. Two of the three final-state mesons are assumed to form a single scalar, vector or tensor state originating from a quark-antiquark pair so that the factorization hypothesis can be applied. The meson-meson final state interactions are described by K pi and pi pi scalar and vector form factors for the S and P waves and by relativistic Breit-Wigner formulae for the D waves. A combined chi^2 fit to a Belle Dalitz plot density distribution, to the total experimental branching fraction and to the tau^- --> K0S pi- nu_tau decay data is carried out to fix the 33 free parameters. These are mainly related to the strengths of the scalar form factors and to unknown meson to meson transition form factors at a large momentum transfer squared equal to the D0 mass squared. A good overall agreement to the Belle Dalitz plot density distribution is achieved. Another set of parameters fits equally well the BABAR Collaboration Dalitz plot model. The branching fractions of the dominant channels compare well with those of the isobar Belle or BABAR models.The lower-limit values of the branching fractions of the annihilation amplitudes are significant. Built upon experimental data from other processes, the unitary K pi and pi pi scalar form factors, entering our decay amplitude and satisfying analyticity and chiral symmetry constraints, are furthermore constrained by the present Dalitz plot analysis. Our decay amplitude could be a useful input for determinations of D0-D0bar mixing parameters and of the CKM angle gamma (or phi3).

Measurements of the CKM angleγin tree-dominated decays at LHCb

We review the first measurements of the CKM angle gamma from LHCb. These measurements have been performed with b-hadron decays dominated by b -> u and b -> c tree-level amplitudes, from which gamma can be determined without theoretical uncertainties. Precision is achieved by averaging results from B- -> Dh- (h= K,pi) decays with D -> h+h-, D -> K+pi-, and D -> K+pi-pi+pi-, and D -> K_S^0h+h-. Prospects for these and future measurements of gamma using neutral b-hadron decays are briefly discussed.

Determining weak phases fromB→J/ψPdecays

The decay B -> J/Psi K_S remains the most important source of information for the B_d mixing phase, determined by the CKM angle beta in the standard model. When aiming at a precision appropriate for present and coming high luminosity colliders, the corresponding hadronic matrix elements are a major obstacle, as their precise calculation is still not feasible with existing methods. Flavour symmetries offer a possibility to extract them from data, however again with limited precision. In this article, we propose a framework to take subleading contributions in B_{u,d,s} -> J/Psi P decays into account, P=(pi,K,(eta_8)), using an SU(3) analysis, together with the leading corrections to the symmetry limit. This allows for a model-independent extraction of the B_d mixing phase adequate for coming high precision data, and additionally yields information on possible New Physics contributions in these modes. We find the penguin-induced correction to be small, |Delta S|<~0.01, a limit which can be improved with coming data on CP asymmetries and branching ratios. Finally, the sensitivity on the CKM angle gamma from these modes is critically examined, yielding a less optimistic picture than previously envisaged.

Measurements of branching fraction ratios andCPasymmetries inB±→DCPK±decays in hadron collisions

We reconstruct B+/- -> D K+/- decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1 fb-1 of integrated luminosity. We select decay modes where the D meson decays to either K- pi+ (flavor eigenstate) or K- K+, pi- pi+ (CP-even eigenstates), and measure the direct CP asymmetry A_CP+ = 0.39 +/- 0.17(stat) +/- 0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions R_CP+ = 1.30 +/- 0.24(stat) +/- 0.12(syst). These measurements will improve the determination of the CKM angle gamma. They are performed here for the first time using data from hadron collisions.

LHCb Upgrade Plans

The LHCb experiment will operate for about five years at a luminosity of 2x10^32 cm^-2 s^-1 and plans are to accumulate a data sample of ~10 fb^-1. Here we present the physics programme and detector design for a future high luminosity phase of the LHCb experiment. An upgraded LHCb experiment would operate at ten times the design luminosity, i.e. at ~2x10^33 cm^-2 s^-1 and aims to collect a data sample of ~100 fb^-1 over five years. This programme would allow the probe of new physics at an unprecedented level. Key measurements include the B^0_s mixing phase phi_s in B^0_s -> J/\psi phi and B^0_s -> phi phi decays with a significant sensitivity to the small Standard Model prediction and a very precise measurement of the CKM angle gamma in tree diagram decays. Initial studies of the modified LHCb trigger and detectors are presented. The upgraded LHCb experiment can run with or without an LHC luminosity upgrade.

Study ofb→cinterference in the decayB−→[K+π−]DK*−

Using a sample of 232 x 10^6 Upsilon(4S)--> B B-bar events collected with the BABAR detector at the PEP-II B-factory we study the decay B- --> [K+ pi-]_D K*- where the K+ pi- is either from a Cabibbo-favored D0-bar decay or doubly-suppressed D0 decay. We measure two observables that are sensitive to the CKM angle gamma; the ratio R of the charge-averaged branching fractions for the suppressed and favored decays; and the charge asymmetry A of the suppressed decays: R=0.046 +/- 0.031(stat.) +/- 0.008(syst.) A=-0.22 +/- 0.61(stat.) +/- 0.17(syst.).

ExploringCPviolation through correlations inB→πK,Bd→π+π−,Bs→K+K−observable space

We investigate allowed regions in observable space of B --> pi K, B_d --> pi^+pi^- and B_s --> K^+K^- decays, characterizing these modes in the Standard Model. After a discussion of a new kind of contour plots for the $B\to\pi K$ system, we focus on the mixing- induced and direct CP asymmetries of the decays B_d --> pi^+pi^- and B_s--> K^+K^-. Using experimental information on the CP-averaged B_d --> pi^{+/-}K^{+/-} and B_d --> pi^+pi^- branching ratios, the relevant hadronic penguin parameters can be constrained,implying certain allowed regions in observable space. In the case of B_d --> pi^+pi^-, an interesting situation arises now in view of the recent B-factory measurements of CP violation in this channel, allowing us to obtain new constraints on the CKM angle gamma as a function of the B^0_d--\bar{B^0_d} mixing phase phi_d=2beta, which is fixed through A_{CP}^{mix}(B_d --> J/psi K_S) up to a twofold ambiguity. If we assume that A_{CP}^{mix}(B_d --> pi^+pi^-) is positive, as indicated by recent Belle data, and that phi_d is in agreement with the ``indirect'' fits of the unitarity triangle, also the corresponding values for gamma around 60 degrees can be accommodated. On the other hand, for the second solution of phi_d, we obtain a gap around gamma ~ 60 degrees. The allowed region in the space of A_{CP}^{mix}(B_s --> K^+K^-) and A_{CP}^{dir}(B_s --> K^+K^-) is very constrained in the Standard Model, thereby providing a narrow target range for run II of the Tevatron and the experiments of the LHC era.

Improved methods for observingCPviolation inB±→KDand measuring the CKM phaseγ

Various methods are discussed for obtaining the CKM angle gamma through the interference of the charged B-meson decay channels B- -> K- D0 and B- -> K- D0-bar where the D0 and D0-bar decay to common final states. It is found that choosing final states which are not CP eigenstates can lead to large direct CP violation which can give significant bounds on gamma without any theoretical assumptions. If two or more modes are studied, gamma may be extracted with a precision on the order of +/-15 degrees given about 10^8 B-mesons. We also discuss the case of three body decays of the D0 where additional information may be obtained from the distribution of the D0 decay products and consider the impact of D-D-bar oscillations.