# Semilptonic decay of B mesons

1. Feb 24, 2015

### Safinaz

Hi there,

Since some time I started to study the semilptonic decay of B meson : $B \to D \tau \nu$ that there is an excess in the value R (D) = $\frac{ Br ( B \to D \tau \nu) } {Br (B \to D l \nu) }$ in BABAR experiment than the SM expectations- See for example arXiv:1302.7031v5- Now I have two questions about the numirecal results of such decay, if any one has an experience about ..

* Since Br = the partial decay width/ the total decay width, won't R(D) = $\frac{d \Gamma ( B \to D \tau \nu) }{ d q^2 d \cos \theta_l } ÷ \frac{d \Gamma ( B \to D l \nu) }{ d q^2 d \cos \theta_l}$ ?

According to [1302.7031v5] notation. Where q^2 is the centre of mass energy squared and $\cos \theta_l$ is the angle of the lepton relative to the B rest frame.

* If we used $d q^2 = 2 q dq$, are the integration limits for $\cos \theta$ : 0 < $\cos\theta$ < $\pi$ and for q: 0 < q < $\sqrt{10}$ .. I think if we set all NP couplings to zero in Equ. 2.2 [1302.7031v5] we should have the SM value of R(D) ..

Thanx.

Last edited: Feb 24, 2015
2. Feb 24, 2015

### Staff: Mentor

Oh, an interesting deviation.

2012 they studied it without considering the angular distributions, 2013 they took that into account.
You can always consider the partial decay width for the decay channel (integrated over its own phase-space), then the ratio is given by the ratios of branching fractions.
What is an angle relative to a rest frame?

Theory paper link. If you set all NP contributions to zero you get the SM, sure.

3. Feb 25, 2015

### Safinaz

Hi, the attached papers are so useful .. but I think the angle $\theta_l$ is just the angle of the emitted $\tau$ or lepton regarding to B meson .. it can be $d_0$ in Equ. 8 [ 1303.0571], so in all cases we should integrate over , whether it set in a formula tells about the angular distribution or not.

Also notice that the NP 2HDM contribution to $\Gamma$ (B-> D tau nu) in [ 1303.0571] is considered by multiplying the SM amplitude by a factor ~ tan theta/ mH+ , While in other references as 1302.7031v5, the NP considered starting by adding new couplings to the SM effective Lagrangian.