^{3}

We have investigated

With the discovery of the Higgs boson, the standard model (SM) could be considered as the most successful theory for particle physics. It is well established experimentally, but due to some basic shortcomings like the absence of gravity, the hierarchy problem of the CKM matrix, the existence of massive neutrinos, etc. the SM could not be regarded as the fundamental theory yet. To overcome these deficiencies one needs to go beyond the SM in search of new physics (NP). In this context, rare B meson decays have been central in recent times. The rare decay modes of the B meson provide a stringent way to test the SM [

Recently, among all rare decays the semileptonic channel

Thus, there is 2.6

The rare semileptonic decay modes of B meson having

Experimentally observed discrepancies for the exclusive decay channels of the B meson have motivated many researchers to investigate whether the deviations are coming from unknown factorizable power corrections or from NP. After taking into account both the arguments, global analyses [

At tree level there are very few candidates that can be utilized in probing the NP responsible for B anomalies. These are basically the leptoquark [

From previous studies of

In this paper, we intend to study the effect of the non-universal

The paper is organized as follows. In

In the SM neglecting the doubly Cabibbo-supressed contributions, the effective Hamiltonian describing the

Values of Wilson coefficients

1.009 | 0.00 | 0.001 | 4.211 |

The four quark operators

The short-distance contributions mainly lie in the perturbative part which is due to the oneloop correction in the matrix elements of four-quark operators. Besides that

After replacing the coefficient successfully, the above Hamiltonian leads to the following free quark matrix element [

Several studies have been done considering universal

In the presence of non-universal

Here,

The numerical values of the

The numerical values of the

1.09 |
||||

2.20 |
1.2 |
|||

4.0 |
150 |
0.8 |

The right-handed couplings of

It is clear from the above relations that we can use the same values of the coupling parameters as for

In

Some previous works on the

The long-distance contribution to the

Here, we consider the transition of an initial meson

In the dispersion quark model, only two particle

To obtain form factors that are more reliable at large

Parameters for GI-OGE model fit [

0.33 | –0.27 | 0.057 | 0.063 | 2.01 | –0.0454 | 0.053 | 0.0056 | –0.354 | 0.313 | |

0.0519 | 0.0524 | 0.0517 | 0.0523 | 0.0212 | 0.039 | 0.044 | 0.0657 | 0.0523 | 0.053 | |

0.00065 | 0.00066 | 0.00064 | 0.00066 | 0.00009 | 0.00004 | 0.00023 | 0.0010 | 0.0007 | 0.00067 |

In this section we present formulas for differential decay rates, forward–backward asymmetries and lepton polarization asymmetries. The expressions for differential decay rates and forward–backward asymmetry agree with the formulation of Ref. [

Introducing the dimensionless kinematical variables

After that, we integrate

For the decay channel

After integrating over the variable

The expression for the differential decay rates for

For

Within the SM,

In order to find the longitudinal lepton polarization asymmetry, we can define it in the following way:

For the

The parameters

The impact of the non-universal

We have predicted the branching ratio for

(a) Differential branching ratio for

Branching ratios of

Decay modes | SM prediction | Expt. result [ |
||||
---|---|---|---|---|---|---|

3.50 |
3.39 |
4.83 |
4.15 |
1.69 |
||

1.01 |
— | 1.59 |
1.27 |
0.42 |
||

1.16 |
0.94 |
1.42 |
1.16 |
0.49 |
||

0.18 |
— | 0.26 |
0.21 |
0.008 |
||

2.43 |
2.98 |
2.77 |
2.69 |
|||

6.57 |
8.05 |
7.49 |
7.29 |

Those channels which include neutrinos (e.g.

Corresponding to

We have observed another important fact from our prediction that the bands for the third scenario of each case (except neutrino channels) go down from the SM curve whereas the other two scenarios make the branching ratio higher than the SM. The reason behind such fascinating behavior might come from the coupling of quarks with

The forward–backward asymmetries for the

Forward–backward asymmetry for

Besides these estimations we have adopted another sign-flipping relation i.e.

To understand the behavior of lepton polarization asymmetry

Lepton polarization asymmetry for

For the

The best way to consider a non-universal

Values of

Parameter | Bin size | Expt. results | |||
---|---|---|---|---|---|

1–6 GeV |
0.468 |
0.702 |
0.778 |
||

0.045–1.1 GeV |
0.75 |
0.81 |
0.89 |
||

1.1–6 GeV |
0.50 |
0.71 |
0.89 |

In

a.

b.

c.

The figures included in

Correlation between

In this paper we have presented our analysis of the

From

The predictions for

From our study of

The longitudinal lepton polarization asymmetry for both

In our non-universal

P. Maji acknowledges the DST, Govt. of India for providing an INSPIRE Fellowship through IF160115 for her research work. S. Sahoo and P. Nayek would like to thank SERB, DST, Govt. of India for financial support through grant no. EMR/2015/000817. S. Sahoo also acknowledges the financial support of NIT Durgapur through “Research Initiation Grant” office order No. NITD/Regis/OR/25 dated 31st March, 2014 and NITD/Regis/OR/2014 dated 12th August, 2014. We thank the reviewer for suggesting valuable improvements to our manuscript.

Open Access funding: SCOAP

The contributing basis operators for the semileptonic decays consisting of

The amplitudes for meson decays could be written as

Where

The spectral representation of the form factors at

The triangle function is defined as

The parameters used for calculating the branching ratio and other observables of

Here,