^{1}

^{1}

^{3}.

We investigate the direct

The measurement of

The hadronic matrix elements of the nonleptonic weak decay are known to be associated with the strong phase. We can estimate the power contribution by the factorization method in the limit of

Isospin symmetry plays an important part in the weak decay process of B meson. We can infer sum rule associated with the isospin symmetry to form a triangular shape on a complex plane for the decay amplitude. One can eliminate uncertainty from the penguin diagram by the isospin analysis in B decays [

The remainder of this paper is organized as follows. In Section

With the operator product expansion, the effective weak Hamiltonian can be written as [

We can obtain numerical values of

One can obtain numerical values of

It is convenient to introduce isospin vector triplet

The relevant decay constants can be written as [

One can understand that isospin symmetry breaking comes from the electroweak interaction and

The mixing is generated by the strong interaction from

Generally, the mesons

For the

The wave functions of

The wave function of the meson is applied to describe the formation of hadron from the positive and negative quarks, which provides distribution of the momentum carried by the parton. It is non-perturbative and process independent from partons to hadrons. The wave function of the meson is transverse-momentum-dependent wave fucnction in PQCD. The results show that there is large contribution from transverse-momentum for the heavy meson function. However, the wave function of light meson is less reliant on transverse-momentum. Currently, it is reasonable that the results form Light-cone QCD sum rule and Lattice QCD. The wave function of light pseudoscalar meson is usually obtained by Light-cone QCD sum rule. The branching ratios and CP violations are calculated in the framework of PQCD. The theoretical prediction is in good agreement with the experimental results for the most decay processes of

The transverse momentum cannot be neglected for eliminating the divergence in the endpoints. The double logarithms will be obtained when collinear divergent is overlapping with soft divergen considering radiative corrections for the form factor. For the effective perturbative expansion, we need to sum the double logarithmic terms by the resummation technique [

Recently, an evolution for the B meson wave fucntions are constructed in the

In the framework of PQCD, we can calculate the

We take the decay process of

Based on the CKM matrix elements of

The amplitudes T and P from the decay process of

One can see that the Eq.(

The relevant weak phase

The

Due to the interference between

Taking into account of

In the same way, we can present the decay amplitudes

Hence, depending on the CKM matrix elements

The CKM matrix, the elements of which are determined from experiments, can be expressed in terms of the Wolfenstein parameters

The CP violation depends on the weak phase differences from the CKM matrix elements and the strong phase differences associated with QCD. The CKM matrix elements are determined by the parameters of

The CP violation of

decay mode | isospin symmetry | | the increasing rate |
---|---|---|---|

| | | |

| | | |

| | | |

| | | |

| | | |

From Table

The direct

It can be seen from the Eq.(

(a) The direct

(a) The value of

(a) The value of

In this paper, we study the

In order to achieve the required energy and luminosity requirements, the Large Hadron Collider (LHC), which has currently started at CERN, has been upgraded many times. The LHC Run I data started in 2010. The peak instantaneous luminosity documentary during Run I was

The functions related with the tree and penguin contributions are presented for the factorization and non-factorization amplitudes with PQCD approach [

The hard scales

The function

The

The evolution factors

The

where the color factor

The functions are related with the annihilation type process, whose contributions are:

No data were used to support this study.

The authors declare that they have no conflicts of interest.

This work was supported by National Natural Science Foundation of China (Project Numbers 11605041), and the Research Foundation of the young core teacher from Henan province.

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