- #1
Safinaz
- 260
- 8
Hi there,
In the decay of ## B \to D^* l \nu ##, I found that the polarization vectors are described as following:
In the B rest frame the helicity basis
## \bar{\epsilon}(0)= \frac{1}{\sqrt{q^2}} (p_{D^*},0,0,-q_0), \\
\bar{\epsilon}(\pm)=\pm \frac{1}{\sqrt{2}} (0,\pm 1,- i,0), \\
\bar{\epsilon}(t)= \frac{1}{\sqrt{q^2}} (q_0,0,0,-p_{D^*}). ##
and the polarization vectors for ## D^*##
## \epsilon(0)= \frac{1}{m_{D^*}} (p_{D^*},0,0,E_{D^*}),\\
\epsilon(\pm)= \mp \frac{1}{\sqrt{2}} (0,1,\pm i,0). ##
While for leptons the polarization vectors of W boson into its rest frame:
## \bar{\epsilon}(0)= (0,0,0,-1), \\
\bar{\epsilon}(\pm)= \frac{1}{\sqrt{q^2}} (0,\pm 1,- i,0), \\
\bar{\epsilon}(t)= \frac{1}{\sqrt{q^2}} (1,0 0,0). ##
Have anyone an explanation for this convention ?
I know from Ryder's book for example that the polarization vectors of a massive spin-1 particle are described by 3 components.
Also what is meant by the helicity basis ## \bar{\epsilon} ##, are they different than the polarization vectors of D, B mesons or W ?
Bests.
In the decay of ## B \to D^* l \nu ##, I found that the polarization vectors are described as following:
In the B rest frame the helicity basis
## \bar{\epsilon}(0)= \frac{1}{\sqrt{q^2}} (p_{D^*},0,0,-q_0), \\
\bar{\epsilon}(\pm)=\pm \frac{1}{\sqrt{2}} (0,\pm 1,- i,0), \\
\bar{\epsilon}(t)= \frac{1}{\sqrt{q^2}} (q_0,0,0,-p_{D^*}). ##
and the polarization vectors for ## D^*##
## \epsilon(0)= \frac{1}{m_{D^*}} (p_{D^*},0,0,E_{D^*}),\\
\epsilon(\pm)= \mp \frac{1}{\sqrt{2}} (0,1,\pm i,0). ##
While for leptons the polarization vectors of W boson into its rest frame:
## \bar{\epsilon}(0)= (0,0,0,-1), \\
\bar{\epsilon}(\pm)= \frac{1}{\sqrt{q^2}} (0,\pm 1,- i,0), \\
\bar{\epsilon}(t)= \frac{1}{\sqrt{q^2}} (1,0 0,0). ##
Have anyone an explanation for this convention ?
I know from Ryder's book for example that the polarization vectors of a massive spin-1 particle are described by 3 components.
Also what is meant by the helicity basis ## \bar{\epsilon} ##, are they different than the polarization vectors of D, B mesons or W ?
Bests.