Despite most experiments in agreement with the standard model (SM) predictions, it is believed that SM is an effective theory at electroweak scale. For understanding the neutrino oscillations, matter-antimatter asymmetry, dark matter, etc., new physics beyond the SM should be included. A direct way to explore the exotic events is through high energy collisions, such as Large Hadron Collider (LHC) and International Linear Collider (ILC). However, by precision measurement and small theoretical uncertainties, low energy system could also provide a good environment to detect the new physics effects indirectly. Recently, since the experimental data have been reached a new precise level and some inconsistent results between theory and experiment are revealed, the potential of testing the SM in P → ℓ ¯ ν has been studied broadly and seriously [1–6], where P denotes the charged K , D and B mesons. The current relevant measurements and SM predictions for the leptonic decays are summarized as follows: the world average (WA) of f$_{D}$$_{s}$ extracted by D$_{s}$ → ℓ $^{+}$ν is [7] where the new measurement on D$_{s}$ → τ $^{+}$ν by BaBar Collaboration [8] has been taken into account; however, the theoretical average of HPQCD (241 ± 3 MeV) [9] and Fermilab/MILC (260 ± 10 MeV) [10] is given by f Latt D$_{s}$ = 242 . 6 ± 2 . 9 MeV [11]. Other theoretical prediction could be referred to Ref. [12]. The 2 . 4 σ deviation from the measurement is the so-called f$_{D}$$_{s}$ puzzle. The WA of BR for B → τν now is [13] With | V$_{ub}$ | = (0 . 393 ± 0 . 036)% [14] and average of f$_{B}$ in calculations of HPQCD (190 ± 13 MeV) [15] and Fermilab/MILC (195 ± 11 MeV) [16], the SM prediction can be read by B $^{SM}$( B + → τ $^{+}$ν ) = (1 . 01 ± 0 . 19 ± 0 . 13) × 10 − $^{4}$. The theoretical prediction is somewhat smaller than experimental value. As to K + → ℓ $^{+}$ν decays, the WA with the measurements of KLOE [17] and NA62 [18] is whereas the SM predicts R SM K = (2 . 477 ± 0 . 001) × 10 − 5 [19]. By the accurate measurement of 0 . 4% on R$_{K}$ [18], the violation of lepton universality may have the chance to be explored in mesonic decays. f$_{D}$$_{s}$ = 257 . 5 ± 6 . 1 MeV , (1) B ( B + → τ $^{+}$ν ) = (1 . 73 ± 0 . 37) × 10 − $^{4}$. (2) R$_{K}$ = Γ$_{K}$$_{e}$$_{2}$ Γ$_{K}$$_{µ}$$_{2}$ = Γ( K + → e $^{+}$ν ) Γ( K + µ $^{+}$ν ) , = (2 . 498 ± 0 . 014) × 10 − $^{5}$, (3) 2