A polarization amplitude A$_{{{\mathit D}_{{1}}}}$ is a parameter that depends on the initial polarization of the ${{\mathit D}_{{1}}}$ and is sensitive to a possible ${\mathit S}{\mathrm -wave}$ contribution to its decay. For ${{\mathit D}_{{1}}}$ decays the helicity angle, $\theta _{h}$, distribution varies like 1 + A$_{{{\mathit D}_{{1}}}}$cos $^2\theta _{h}$, where $\theta _{h}$ is the angle in the ${{\mathit D}^{*}}$ rest frame between the two pions emitted by the ${{\mathit D}_{{1}}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \pi}}$ and the ${{\mathit D}^{*}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}}$ .

Unpolarized ${{\mathit D}_{{1}}}$ decaying purely via ${\mathit D}{\mathrm -wave}$ is predicted to give A$_{{{\mathit D}_{{1}}}}$ = 3.

VALUE DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • $3.8$ $\pm0.6$ $\pm0.8$ 1 AUBERT 2009 Y BABR ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}_{{1}}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ 1  Assuming $\Gamma $( ${{\mathit \Upsilon}{(4S)}}$ $\rightarrow$ ${{\mathit B}^{+}}{{\mathit B}^{-}}$ ) $/$ $\Gamma $( ${{\mathit \Upsilon}{(4S)}}$ $\rightarrow$ ${{\mathit B}^{0}}{{\overline{\mathit B}}^{0}}$ ) = $1.065$ $\pm0.026$ and equal partial widths and helicity angle distributions for charged and neutral ${{\mathit D}_{{1}}}$ mesons.

References:

AUBERT 2009Y PRL 103 051803 Measurement of Semileptonic ${{\mathit B}}$ Decays into Orbitally-Excited Charmed Mesons