#### ${{\mathit D}_{{1}}{(2420)}}$ POLARIZATION AMPLITUDE A$_{{{\mathit D}_{{1}}}}$

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 EVTS DOCUMENT ID TECN CHG  COMMENT
 $\bf{ 5.73 \pm0.25}$ OUR AVERAGE
$7.8$ ${}^{+6.7}_{-2.7}$ ${}^{+4.6}_{-1.8}$ 2.7k 1
 2013
ZEUS 0 ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit D}^{(*)+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$5.72$ $\pm0.25$ 103k
 2010 P
BABR 0 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$5.9$ ${}^{+3.0}_{-1.7}$ ${}^{+2.4}_{-1.0}$
 2009
ZEUS 0 ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}{{\mathit X}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$3.30$ $\pm0.48$ 210k 2
 2013 CC
LHCB 0 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$3.8$ $\pm0.6$ $\pm0.8$ 3
 2009 Y
BABR 0 ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}_{{1}}^{0}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$
$3.8$ $\pm0.6$ $\pm0.8$ 3
 2009 Y
BABR + ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}_{{1}}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$
$2.74$ ${}^{+1.40}_{-0.93}$ 4
 1994 C
CLE2 0 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}{{\mathit X}}$
 1 From the combined fit of the ${{\mathit M}}$( ${{\mathit D}^{+}}{{\mathit \pi}^{-}}$ ) and ${{\mathit M}}$( ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}$ ) distributions. and A$_{{{\mathit D}_{{2}}}}$ fixed to the theoretical prediction of $-1$. A pure ${\mathit D}{\mathrm -wave}$ not excluded although some ${\mathit S}{\mathrm -wave}$ mixing possible.
 2 Systematic uncertainty not estimated. Resonance parameters fixed.
 3 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.
 4 Systematic uncertainties not estimated.
References:
 AAIJ 2013CC
JHEP 1309 145 Study of ${{\mathit D}_{{J}}}$ Meson Decays to ${{\mathit D}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ and ${{\mathit D}^{*+}}{{\mathit \pi}^{-}}$ Final States in ${{\mathit p}}{{\mathit p}}$ Collisions
 ABRAMOWICZ 2013
NP B866 229 Production of the Excited Charm Mesons ${{\mathit D}_{{1}}}$ and ${{\mathit D}_{{2}}^{*}}$ at HERA
 DEL-AMO-SANCHEZ 2010P
PR D82 111101 Observation of New Resonances Decaying to ${{\mathit D}}{{\mathit \pi}}$ and ${{\mathit D}^{*}}{{\mathit \pi}}$ in Inclusive ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions near $\sqrt {s }$ = 10.58 GeV
 AUBERT 2009Y
PRL 103 051803 Measurement of Semileptonic ${{\mathit B}}$ Decays into Orbitally-Excited Charmed Mesons
 CHEKANOV 2009
EPJ C60 25 Production of Excited Charm and Charm-Strange Mesons at HERA
 AVERY 1994C
PL B331 236 Production and Decay of ${{\mathit D}_{{1}}{(2420)}^{0}}$ and ${{\mathit D}_{{2}}^{*}{(2460)}^{0}}$