${{\mathit \Delta}}$ BARYONS
($\mathit S$ = 0, $\mathit I$ = 3/2)
${{\mathit \Delta}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit u}}$ , ${{\mathit \Delta}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$
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${{\boldsymbol \Delta}{(1900)}}$

$I(J^P)$ = $3/2(1/2^{-})$ 
Older and obsolete values are listed and referenced in the 2014 edition, Chinese Physics C38 070001 (2014).
${{\boldsymbol \Delta}{(1900)}}$ POLE POSITION
REAL PART   $1830\text{ to }1900\text{ }(\approx1865) $ MeV 
 
$-2{\times }$IMAGINARY PART   $180\text{ to }300\text{ }(\approx240) $ MeV 
 
${{\boldsymbol \Delta}{(1900)}}$ ELASTIC POLE RESIDUE
MODULUS $\vert \mathit r\vert $   $8\text{ to }14\text{ }(\approx11) $ MeV 
 
PHASE $\theta $
 
${{\boldsymbol \Delta}{(1900)}}$ INELASTIC POLE RESIDUE
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit K}}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit N}{(1440)}}{{\mathit \pi}}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit N}{(1520)}}{{\mathit \pi}}$
 
${{\mathit \Delta}{(1900)}}$ BREIT-WIGNER MASS   $1840\text{ to }1920\text{ }(\approx1860) $ MeV 
 
${{\mathit \Delta}{(1900)}}$ BREIT-WIGNER WIDTH   $180\text{ to }320\text{ }(\approx250) $ MeV 
 
${{\boldsymbol \Delta}{(1900)}}$ PHOTON DECAY AMPLITUDES AT THE POLE
${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$
 
${{\boldsymbol \Delta}{(1900)}}$ BREIT-WIGNER PHOTON DECAY AMPLITUDES
${{\mathit \Delta}{(1900)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$
 
The following branching fractions are our estimates, not fits or averages.
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$  $4 - 12\%$ 685
 
$\Gamma_{2}$ ${{\mathit \Sigma}}{{\mathit K}}$  seen 367
 
$\Gamma_{3}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$  $45 - 85\%$ 660
 
$\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$  509
 
$\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$  $30 - 70\%$ 509
 
$\Gamma_{6}$ ${{\mathit N}}{{\mathit \rho}}$  360
 
$\Gamma_{7}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=1/2, ${\mathit S}{\mathrm -wave}$  $8 - 16\%$ 360
 
$\Gamma_{8}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2, ${\mathit D}{\mathrm -wave}$  $18 - 28\%$ 360
 
$\Gamma_{9}$ ${{\mathit N}{(1440)}}{{\mathit \pi}}$  $8 - 32\%$ 353
 
$\Gamma_{10}$ ${{\mathit N}{(1520)}}{{\mathit \pi}}$  $2 - 10\%$ 288
 
$\Gamma_{11}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$  $0 - 2\%$ 251
 
$\Gamma_{12}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2  $0.06 - 0.43\%$ 693
 
FOOTNOTES