Elsevier

Physics Letters B

Volume 452, Issues 3–4, 22 April 1999, Pages 318-326
Physics Letters B

The B→Xd+ decay in general two Higgs doublet model

https://doi.org/10.1016/S0370-2693(99)00282-8Get rights and content

Abstract

The branching ratio, forward–backward asymmetry and CP violating asymmetry for B→Xd+ decay, in framework of the general two Higgs doublet model, with extra phase angle in the charged-Higgs-fermion coupling, are calculated. It is shown that studying the CP violating asymmetry is an efficient tool for establishing new physics.

Introduction

Rare B meson decays, induced by the flavor-changing neutral current (FCNC) b→s(d) transitions is one of the most promising research area in particle physics. Theoretical interest to the rare B decays lies in their role as a potential precision testing ground for the Standard Model (SM) at loop level. Experimentally, these decays will provide a more precise determination of the elements of the Cabibbo–Kobayashi–Maskawa matrix (CKM), such as Vtq,(q=d,s,b) and Vub and CP violation.

The impressive experimental search for the study of the B meson decay will be carried out in future, when new experimental facilities, especially the B-factories at Belle [1] and BaBar [2], are upgraded, and after which the large number (108–1012) of B hadrons that is expected to be produced in these factories, will allow measuring the FCNC decays of B mesons.

In the first hand, the most reliable quantitative test of FCNC in B meson decays is expected to be measured in the BXs(d)+ decay. The matrix elements of the bs+ transition contains terms describing the virtual effects by tt̄, cc̄ and uū loops which are proportional to combination of the CKM elements VtbVts, VcbVcs and VubVus respectively. Using the unitarity condition of the CKM matrix and neglecting VubVus in comparison to VtbVts and VcbVcs, it is obvious that the matrix element for the bs+ decay involves only one independent CKM matrix factor, VtbVts, so that CP-violation in this channel is strongly suppressed in the SM.

The situation is totally different for the bd+ decay, since all three CKM factors are of the same order in SM, and therefore can induce considerable CP violation in the decay rate difference of the bd+ and b̄d̄+ processes (for the current status of BXs(d)+ decay in SM, see [3] and the references therein). So, the bd+ is a promising decay for establishing CP violation in B mesons.

The rare B meson decays are also very sensitive to the 'new physics' beyond SM, such as the two Higgs doublet model (2HDM), minimal supersymmetric extension of the SM (MSSM) [4], etc.

One of the most popular extension of the SM is the 2HDM [5], which contains two complex Higgs doublets rather than one, as is the case in the SM. In the 2HDM, the FCNC that appear at the tree level, are avoided by imposing an ad hoc discrete symmetry [6]. One possible way to avoid these unwanted FCNC at tree level, is to couple all fermions to only one of the two Higgs doublets (Model I). The other possibility is the coupling of the up and down quarks to the first and second doublets, respectively (Model II).

Models I and II have been extensively investigated theoretically and tested experimentally (see [5] and references therein). The 2HDM without the ad hoc discrete symmetry was analyzed in 7, 8, 9. It is clear that the tree level FCNC appears in this model, however their couplings involving first and second generations must be strongly suppressed. This conclusion is the result of the analysis of low energy experiments. Therefore, Model III should be parametrized in a way that suppresses the tree level FCNC couplings of the first generation, while the tree level FCNC couplings involving the third generation can be made non-zero as long as they do not violate the existing experimental data, i.e., BB̄0 mixing.

In this work, following [7], we assume that all tree level FCNC couplings are negligible. However, even under this assumption, the couplings of fermions with Higgs bosons may have a complex phase e (see [7] and [10]). The constraints on the phase angle θ in the product λttλbb (see below) of Higgs-fermion couplings imposed by the neutron electric dipole moment, B-B̄0 mixing, ρ0 parameter and b decay are discussed in [7].

The aim of the present work is the quantitative investigation of the CP violation in the inclusive B→Xd+ decay in context of the general 2HDM, in which a new phase parameter is present (see below). In other words, this model contains a new source of CP violation whose interference with the SM phase can induce considerable difference in the CP violation predicted by the SM. To find an answer to the question of, “to what extend the new physics effects the results of the SM”, is the main goal of the present work.

The paper is organized as follows. In Section 2, we present the necessary theoretical background for the general 2HDM and calculate the branching ratio, CP violation and forward–backward asymmetry in the bd+ decay. Finally, Section 3 is devoted to the numerical analysis and concluding remarks.

Section snippets

The formalism

Before presenting the necessary theoretical expressions for studying bd+ decay, let us briefly remind the main essential points of the Model III. In this model, without loss of generality, we can choose a basis such that the first Higgs doublet creates all fermion and gauge boson masses, whose vacuum expectation values areH1=0v2,H2=0.In this basis the first doublet H1 is the same as in the SM, and all new Higgs bosons result from the second doublet H2, which can be written asH1=122G+v+χ10+iG

Numerical analysis

The values of the main input parameters we have used in the numerical analysis are as follows: sin2θW=0.2255, mt=173.8GeV, α=1/129, BSL=0.104. Further, the Wolfenstein parametrization of the CKM matrix [18] with A=0.819 and λ=0.2196 [19] has been used. In this parametrization Vcb=2, VtdVtb=Aλ3(1−ρ̄+iη̄), VubVud=Aλ3(ρ̄−iη̄), where ρ̄=ρ(1−λ2/2) and η̄=η(1−λ2/2). Fits of the CKM matrix elements were performed in [20]. In further analysis ρ=0.3, η=0.34 have been used. For the values of the

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