The black curve corresponds to the central values of SM, while the red and blue correspond to C8′ = −2.0 and 4.0, respectively. The black curve corresponds to the central SM values, while the red and blue correspond to C9′ = −3.0 and 1.0, respectively.
Parametrizations of CKM matrix
Now we want to find out the number of independent parameters needed to parametrize the CKM matrix. However, there are N2 limits arising from the unity condition of the CKM matrix, such as V†V =V†V = 1, and the (2N−1) number of phases can be absorbed by redefinitions of the quark field.
The Unitarity Triangle (UT) of the CKM Matrix
It provides us with the unitarity triangle which has a very transparent geometric representation of the structure of the CKM matrix and also enables us to find some analytical results. We denote the three angles of the triangle of unity as α, β and γ. All six parameters of the triangle of unity, three angles and three sides, are very significant from the point of view of the physics of taste.
The significance of discrete symmetries
The third source of CP violations is in the lepton sector and is described by the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix. It is expected that new sources of CP violation will be found in the future that can resolve the whole matter-antimatter asymmetry.
Flavour Changing Neutral Currents
The first of these is the complex phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix [4] in the quark sector. There may also be a CP violation in the strong interaction, but the inability to observe the neutron's electric dipole moment in experiments suggests that any CP violation in the strong sector is also very small to provide the necessary CP violation in the explain the early universe.
Motivation for studying B Decays
Theory is used to convert experimental data to contours in the ρ−η plane, where semileptonicb→ulνl,clνldecays andBd,s-Bd,smixing allow us to determine the UT sidesRu≡VVudcdVVubcb. The two groups CKM-fitter [16] and UT-fit [17] worked on global analysis to convert the experimental data into contours in the ¯ρ−η¯plane.
Basic Formalism of the CP Phenomenology in the B meson decays
Neutral Meson Mixing
The sides and angles of the unit triangle can be determined from the study of B decay. Under the Wigner Weisskopf formalism [19, 20], the time evolution of the state vector can be expressed as, .
CP violating observables
CP Violation in B meson system
CP violation in mixing the decay with or without mixing, which is due to decay in flavor-blind final states common to both states, i.e.
Effective Hamiltonian of B decays
In the last few years, semileptonic B →D(∗)l ν decays have been extensively studied after BaBar measurement of RDs and RD∗s rather than Bs → D(∗)s l ν semileptonic decays. The latest measurements suggest the possibility of having new physics only in third generation leptons.
Effective Lagrangian and decay amplitude
B to π Form Factors
For the B →π transition shape factors, there are two non-perturbative methods for calculating the B →π shape factors: light cone sum rules (LCSR) and lattice QCD (LQCD). QCD light-cone sum rules with pion distribution amplitudes allow the calculation of the B → π form factors at small and moderate momentum transfers 0 ≤ q2 ≤qmax2 , where qmax2 ranges from 12 to 16 GeV2 [65-69]. The latest lattice QCD calculations with three dynamic flavors predict these shape factors at q2 ≥ 16 GeV2, in the upper part of the semileptonic region 0 ≤ q2 ≤ (mB−mπ)2, with an accuracy of 10%.
58], the author uses the results of the sum rule for form factors as input to the parameterization of the series z, which gives the form q2 in the entire semileptonic range B →π l ν.
The ω-dependence of the form factors in the heavy quark limit can be written as [35, 61]. In the next section, we give the details of the kinematics and helicity method to calculate the different helicity amplitudes for B→P l ν and B→V l ν semileptonic decays.
Kinematics and Helicity Amplitudes
The leptonic tensorL(m, n) is evaluated in the l−νl center-of-mass frame, i.e. in the q2 rest frame. Our formulas for the differential branching ratio in the presence of NP couplings in Eq. 2.36) differ slightly from those given in Ref. Correspondingly, the differential decay distribution for B → V l ν is in the form of the helicity amplitudes A0,Ak,A⊥,AP andAtis. 2.39).
We see that in SM for light leptonels, µ the forward-backward asymmetry is vanishingly small due to them2l/q2term for the decay modes B →P l ν. Theoretical uncertainties in the calculation of decay branch fractions arise from different input parameters.
Results and discussion
- Scenario A
- Scenario B
- Scenario C
- Scenario D
The corresponding ranges in B(B →πτ ν) and the ratioRπ in the presence of these NP links are shown in the right panel. The darker (blue) inner region corresponds to the SM prediction, while the lighter (red), larger region corresponds to the allowed (VL, VR) NP links of figure. The darker (blue) inner region corresponds to the SM prediction, while the lighter (red), larger region corresponds to the allowed (SL, SR) NP links of Fig.
The resulting region in (B→πτ ν) and Rπ is shown in the right panel with these NP couplings. The allowed ranges of all the different observed with these NP couplings are shown in Fig.
Conclusion
The 3σ allowed ranges of the branching ratio B →πτ ν and the ratio Rπ are shown in the right panel of figure. Although we see a zero crossing in the q2 distribution, it may or may not be there depending on the NP links. Although in the standard model there is no zero crossing in the forward-backward asymmetry parameter for the decay modes B → πτ ν and B → Dτ ν, depending on the value of SL and SR, one can see a zero crossing for both. the decay modes.
Three body decays are more preferable due to the increased threshold in dibaryon in-. Several theoretical approaches have been proposed to explain the threshold enhancement in the invariant dibaryon mass distribution [111–124] .
Theory
With Lorentz invariance, the most general form of the B → BB¯′ transition matrix elements is due to the scalar, pseudoscalar, vector and axial vector currents [122, 152]. The momentum dependence of the shape factors has been studied within the polar model framework, with the dominant contributions coming from the baryon and meson intermediate. The dependence of the form factors arises due to the intermediate meson state, while the dependence of the form factors on the invariant mass of one of the baryons and the emitted meson arises from the low-lying intermediate baryon state.
The dependence of the shape factors on other variables, such as the invariant mass of one of the baryons and the invariant mass of the lepton pair, is contained in the Dfi coefficients. The azimuthal angle φ between the dibaryon and dilepton decay planes is also sensitive to CP-violating coupling.
Results and discussion
We show the effect on different observables for two different values of the NP coupling. The black curve corresponds to the central values of the SM, while the red and blue curves correspond to C7NP = 0.03 and −0.15, respectively. The black curve corresponds to the central values of the SM, while the red and blue correspond to C8NP = −1.1 and 1.6, respectively.
The black curve corresponds to the central SM values, while the red and blue ones correspond to C9NP= 1.6 and −1.2, respectively. The black curve corresponds to the central values of SM, while the red and blue correspond to C7′ = −0.4 and 0.3, respectively.
Conclusion
We see a significant deviation from the SM in the angular distribution, leaving all other observables approximately SM. Thus, in the presence of such NP, the peak of the distribution is no longer at the threshold. Similarly, we see no asymmetry in the azimuthal angular distribution and triple product correlation.
However, if we turn on NP in CS,CP,CS′ and CP′ simultaneously, we see a significant deviation from the SM prediction in the invariant mass spectrum as a function of the invariant massmµ+µ−. In the last few years, semileptonic B →D(∗)l ν decay has been extensively studied following BaBar measurement rather than Bs→D(∗)s l νsemileptonic decay.
Effective Lagrangian and decay amplitude
Moreover, the significant deviations between the SM prediction and the BaBar measurement [34] for measuring the ratios such as RD and RD∗ also motivated us to study for Bs → Ds(∗)l νl decay modes to estimate the numerical values branching ratio and ratio of branching ratios that could be measured in the upcoming Super-B experiments where the SM predictions could be verified. Furthermore, we study physical observables such as differential branching ratio (DBR) and forward-backward asymmetry and their implications. The numerical prediction of the branching ratios and the relationship between the branching ratio for the different decay states is presented in section 4.3.
We define some physical observables, such as the differential branching ratio DBR(q2), the ratios of branching fractionsR(q2),Rτ,l(q2) and the forward-backward asymmetryAF B(q2) as follows. We present an analysis of physical observables such as differential branching ratio, differential branching ratio ratio, and forward-backward asymmetry.
Results and discussion
In the Bs→Dsl ν decay, the peak is noticeable in the region of low q2, since the threshold energy of this decay is relatively lower, and the peak of the DBR distribution reaches at q2 ≈2.6 Gev2 with a value of the differential branching ratio of 6.0×10−4 GeV−2 . For Bs →Dsl ν, we can see that the value of RDs(q2) slowly increases up to a certain value of q2(≈ 9.5GeV2), and then suddenly the rate of increase is very fast, due to the low value of the differential branching ratio Bs → Dsl ν in highq2 area. Here again we can see that the value of RD*s(q2) increases with q2 according to the differential branching ratio for the corresponding decay modes.
In the plot of Rτ we can see the dependence of the uncertainties, while the dependence of Rl is comparatively smaller, which can be explained from the equation. The SM prediction of the forward–backward asymmetries (AFB) for Bs→Dsτ(l)ν and Bs→ Ds∗τ(l)ν is shown in Figure 4.3.
Conclusion
Abeet al. [Belle Collaboration], “Observation of large CP violation in the neutral B meson system,” Phys. Ghosh, “Diagnosing new physics inb→c τ ντ decays in light of the latest BaBar result,” Phys. Cheeky al. [Belle Collaboration], “Investigation of baryon-antibaryon low-mass enhancements in charmless three-body baryonic B decays,” Phys.
Aubertet al.[BaBar Collaboration], “Measurement of the B+→p¯pK+ branching fraction and study of the decay dynamics,” Phys. Chatrchyanet al.[CMS Collaboration], “Measurement of the branching fraction Bs→µ+µ− and the search for B0 →µ+µ− with the CMS Experiment”, Phys.
