Sin 2β Research Articles

Neutral B-meson Mixing and CP Violation at LHCb

The LHCb detector is a single-arm forward spectrometer that collects data at the LHC, designed for studies of flavour physics with high precision. We present a selection of recent measurements of mixing and CP-violating parameters, including sin 2β and weak phase ϕ s, using several decays. A good understanding of the pollution from sub-leading penguin to pologies in these measurements can be achieved by measuring CP violation and polarization in the decay Bs0→Jψ⁄K0* and B0→Jψ⁄ ρ0. All results here presented are obtained using the full Run I dataset.

Re-examining [formula omitted] and [formula omitted] from evolution of [formula omitted] mesons with decoherence

In the time evolution of neutral meson systems, a perfect quantum coherence is usually assumed. The important quantities of the Bd0 system, such as sin⁡2β and Δmd, are determined under this assumption. However, the meson system interacts with its environment. This interaction can lead to decoherence in the mesons even before they decay. In our formalism this decoherence is modelled by a single parameter λ. It is desirable to re-examine the procedures of determination of sin⁡2β and Δmd in meson systems with decoherence. We find that the present values of these two quantities are modulated by λ. Re-analysis of Bd0 data from B-factories and LHCb can lead to a clean determination of λ, sin⁡2β and Δmd.

Measurement ofCPViolation inB0→J/ψKS0Decays

Measurements are presented of the CP violation observables S and C in the decays of B(0) and Bover ¯]0 mesons to the J/ψK(S)(0) final state. The data sample corresponds to an integrated luminosity of 3.0 fb(-1) collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, and contains a total of 41 560 selected B^{0} and B[over ¯]^{0} decays. The analysis of the time evolution of these decays yields S=0.731±0.035(stat)±0.020(syst) and C=-0.038±0.032(stat)±0.005(syst). In the standard model, S equals sin(2β) to a good level of precision. The values are consistent with the current world averages and with the standard model expectations.

REVISITING THE POSSIBILITY OF NEW PHYSICS IN THE $K\hbox{--}\bar{K}$ AND $B_d\hbox{--}\bar{B}_d$ SYSTEMS

Recently several developments have taken place in the lattice QCD calculations of hadronic factors in the case of [Formula: see text] and the [Formula: see text] mixings along with contribution of the long distance effects in the [Formula: see text] system. These have led some authors (Refs. 12 and 13) to point towards the possibility of New Physics (NP) in these systems to the tune of 20% or so. However, the present analysis, based on essentially NP free inputs and incorporating constraints of unitarity, shows that in case the NP effects are there in the parameters associated with these systems, e.g. sin 2β, Vtd, ϵK, etc., these seem to be only at a few percent level.

A precise isospin analysis of [formula omitted] decays

We present a precise isospin analysis of the B→D¯(⁎)D(⁎)K decays using new recent experimental measurements on these final states. The decays B→D¯(⁎)D(⁎)K, originating from b→cc¯s transitions, are linked by a rich set of isospin properties. The isospin relations that connect the decay modes are presented and a fit is performed to obtain the isospin amplitudes and phases. We discuss the results of the fit and present a new measurement of the ratio of branching fractions B(ϒ(4S)→B+B−) and B(ϒ(4S)→B0B¯0). We finally discuss the implications of our findings for the measurement of the unitarity matrix parameters sin(2β) and cos(2β) using these decays.

Possible evidence for the breakdown of the CKM-paradigm of CP-violation

Using primarily experimental inputs for S(Bd→ψKs), ΔMBs, ΔMBd, BR(B→τν) and ϵK along with necessary inputs from the lattice, we find that the measured value of sin(2β) is smaller than expectations of the Standard Model by as much as 3.3σ, and also that the measured value of the BR(B→τν) seems to be less than the predicted value by about 2.8σ. However, through a critical study we show that most likely the dominant source of these deviations is in Bd(s) mixings and in sin(2β) and less so in B→τν, and also that the bulk of the problem persists even if input from ϵK is not used. The fact that kaon mixing and ϵK are not the dominant source of the deviation from the Standard Model has the very important consequence that model independent considerations imply that the scale of the relevant new CP-violating physics is below O(2TeV), and possibly even a few hundred GeVs, thus suggesting that direct signals of the new particle(s) may well be accessible in collider experiments at the LHC and perhaps even at the Tevatron.

IMPLICATIONS OF PRECISION MEASUREMENTS ON TEXTURE SPECIFIC FERMION MASS MATRICES

Implications of texture specific mass matrices have been investigated for both quarks and neutrinos. Interestingly, for the case of quarks Fritzsch-like texture 4 zero mass matrices have been found to be compatible with the present precisely known sin 2β as well as other precise CKM matrix elements. In the case of leptonic mass matrices, for both Majorana and Dirac neutrinos we find that for texture 4, 5, 6 zero mass matrices the inverted hierarchy and degenerate scenarios of neutrino masses are ruled out by the present data.

Precocious signs of new physics: Are we eight now?

Although the CKM-paradigm seems to work to an accuracy of about 15–20%, we emphasize that there are by now several indications that suggest the need for a beyond the Standard Model CP-odd phase. The value of sin 2β measured via the goldplated (tree) mode, B → ψKs is smaller than the value deduced by using improved lattice matrix elements. The value of sin 2β measured via ‘penguin-dominated’ (loop) decays tends to be even smaller still. There is also a rather large difference between the direct CP asymmetries in \( \bar B^0 \) → K−π+ and B− → K−π0 that is rather difficult to understand. More recently, CDF and D0 are finding about a 2σ signal in CP asymmetry in the corresponding gold-plated mode Bs → ψϕ. If true, this would be consistent with the indications of new CP-phase in penguin b → s transitions seen at B-factories. After describing these possible signs of trouble for the SM-CKM paradigm, we give a brief discussion of some of the BSM scenarios that could be the underlying cause of these deviations. In particular, we find that the data are quite suggestive of a fourth family with m′t in the range of 400–600 GeV as perhaps the simplest BSM candidate which ‘naturally’ explains the data.

A method of measuring cos(2β) using a time-dependent dalitz plot analysis of B0 → DCPπ+π−

We present a feasibility study of a previously outlined method for measuring both the sine and the cosine of twice the Cabibbo–Kobayashi—Maskawa (CKM) Unitarity Triangle angle β using a time-dependent Dalitz plot analysis of B0 → Dπ+π− decays, where the neutral D meson is reconstructed in decays to CP eigenstates. We show that this method can be used at the B factories to make a measurement of cos(2β) that is competitive with, or more precise than, other techniques using different quark-level transitions, while sin(2β) can be measured to a better precision than any existing measurement using transitions. Furthermore, this technique has great potential to be employed at LHCb.

Benchmarks for the new-physics search throughCPviolation inB0→π0KS

Using isospin relations, we predict the standard model correlation between Sπ0KS≡(sin⁡2β)π0KS and Aπ0KS, the mixing-induced and direct CP asymmetries of B0→π0KS. The calculation uses flavor SU(3) only to fix the isospin-3/2 amplitude through the B±→π±π0 branching ratio, and thus has a small irreducible theoretical error. It can reach percent level precision thanks to expected future lattice-QCD progress for the calculation of the relevant SU(3)-breaking form-factor ratio, and serves as a benchmark for new-physics searches. We obtain an interesting picture in the Aπ0KS–Sπ0KS plane, where the current experimental data show a discrepancy with the standard model, and comment on the direct CP asymmetries of B0→π-K+ and B+→π0K+. A modified electroweak penguin with a large new CP-violating phase can explain the discrepancy and allows us to accommodate also the corresponding data for other b→s penguin-dominated decays.

CHARMLESS 3-BODY B DECAYS: RESONANT AND NONRESONANT CONTRIBUTIONS

Charmless 3-body decays of B mesons are studied using a simple model based on the framework of the factorization approach. We have identified a large source of the nonresonant signal in the matrix elements of scalar densities, e.g. [Formula: see text]. This explains the dominance of the nonresonant background in B → KKK decays, the sizable nonresonant fraction of order (35 ~ 40)% in K−π+π− and [Formula: see text] modes and the smallness of nonresonant rates in B → πππ decays. We have computed the resonant and nonresonant contributions to charmless 3-body decays and determined the rates for the quasi-two-body decays B → VP and B → SP. Time-dependent CP asymmetries sin 2β eff and ACP in K+K−KS, KSKSKS, KSπ+π− and KSπ0π0 modes are estimated.

Possible indications of new physics in [formula omitted]-mixing and in [formula omitted] determinations

Using the hadronic matrix elements from the lattice, BK and ξs, involving only the 4-quark operators for Δflavor=2 Hamiltonian relevant for K–K¯, Bd–B¯d and Bs–B¯s mixing, along with Vcb, we deduce a non-trivial constraint on the SM, sin(2β)=0.87±0.09. This deviates from direct experimental measurements via the tree process, b→cc¯s as well as the one via the penguin-loop b→s decays by around 2.1 and 2.7σ respectively. If these deviations are confirmed they would imply the presence of new physics rather pervasively in both Bd–B¯d (i.e. very likely in b→d) as well as in b→s transitions requiring a beyond the SM CP-odd phase. Consequently, improvements in the relevant lattice calculations should be given a high priority.

Flavor mixing and rare B and K decays in the minimal 331 model

We analyze the implications of the minimal 331 model with respect to flavor physics. These new contributions stem from the tree level exchange of a flavor changing additional Z' gauge boson. The observables under investigation are the mixing related observables ϵK δMK, δMK, δMd/s and sin 2β, which we use to constrain the parameter space, as well as the rare decays K →, KL → and Bd/s → μ+μ-1. We find that significant effects are still possible in the K physics sector, while the B physics sector is already rather strongly constrained. The exception is the Bs - B̄s mixing phase βs, which can be large.

B-physics prospects with the LHCb experiment

This paper summarizes the B-physics prospects of the LHCb experiment. Firstly, a brief introduction to the CKM matrix and the mechanism of CP violation in the Standard Model is given. The advantages of the LHCb experiment for B-physics exploitation will then be described, together with a short description of the detector components. Finally, the LHCb physics aims and prospects will be summarized, focusing on the measurements of sin(2β) in tree and gluonic penguin diagrams, sin(2α) in Bd0 → π+π− and π+π−π0, neutral B-meson oscillations and the Bs0 mixing phase, and the measurement of γ using a variety of complementary methods.

Non-leptonic B-decays, CP violation & the UT

We study the implication of the time-dependent CP asymmetry in B → π + π − decays on the extraction of weak phases taking into account the precise measurement of sin 2β, obtained from the “gold-plated” mode B → J/ ψK s . Predictions and uncertainties for the hadronic parameters are investigated in QCD factorization. Fürthermore, independent theoretical and experimental tests of the factorization framework are briefly discussed. Finally, a model-independent bound on the unitarity triangle from CP violation in B → π + π − and B → J/ ψK S is derived.

THE CKM MATRIX AND CP VIOLATION

The status of CP violation and the CKM matrix is reviewed. Direct CP violation in B decay has been established and the measurement of sin 2β in ψK modes reached 5% accuracy. I discuss the implications of these, and of the possible deviations of the CP asymmetries in b → s modes from that in ψK. The first meaningful measurements of α and γ are explained, together with their significance for constraining both the SM and new physics in [Formula: see text] mixing. I also discuss implications of recent developments in the theory of nonleptonic decays for B → πK rates and CP asymmetries, and for the polarization in charmless B decays to two vector mesons.

Corrections to [formula omitted] from CP asymmetries in [formula omitted] decays

Neglecting smaller amplitudes the time-dependent CP asymmetry in penguin-dominated b→sqq¯ transitions (such as B→ϕKS) is expected to equal ±sin(2β), an expectation not borne out by the present average experimental data. I compute and discuss the correction due to the smaller amplitudes in the framework of QCD factorization.

Is the β phase maximal?

The current experimental determination of the absolute values of the CKM elements indicates that 2|Vub/VcbVus|=(1−z), with z given by z=0.19±0.14. This fact implies that irrespective of the form of the quark Yukawa matrices, the measured value of the SM CP phase β is approximately the maximum allowed by the measured absolute values of the CKM elements. This is β=(π/6−z/3) for γ=(π/3+z/3), which implies α=π/2. Alternatively, assuming that β is exactly maximal and using the experimental measurement sin(2β)=0.726±0.037, the phase γ is predicted to be γ=(π/2−β)=66.3°±1.7°. The maximality of β, if confirmed by near-future experiments, may give us some clues as to the origin of CP violation.

Improved measurement of CP-violation in $B \to (c{\bar c})K^{(\ast)0}$ decays

We present results on time-dependent CP asymmetries in neutral B decays. The amplitude of the CP asymmetry, sin 2β in the Standard Model, is derived from decay-time distributions from events in which one neutral B meson is fully reconstructed in a final state containing a charmonium meson and the other B meson is determined to be either a B0or [Formula: see text] from its decay products. Using data collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC, we measure sin 2β = 0.722 ± 0.040( stat ) ± 0.023( syst ) and [Formula: see text], determining the sign of cos 2β to be positive at 86% CL.

Semileptonic decays of D, B, K mesons and the full CKM matrix from unquenched lattice QCD

We use lattice QCD to fully determine the CKM matrix. |Vcd|, |Vcs|, |Vub|, |Vcb| and |Vus| are, respectively, directly determined with our lattice results for form factors of semileptonic D → πlν, D → Klν, B → πlν, B → Dlν and K → πlν decays. The accuracy is comparable to that of the Particle Data Group averages. In addition, |Vud|, |Vtb|, |Vts| and |Vtd| are determined by using unitarity of the CKM matrix and the experimental result for sin (2β). In this way, we obtain all 9 CKM matrix elements, where the only theoretical input is lattice QCD.