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

${{\boldsymbol \Delta}{(1905)}}$

$I(J^P)$ = $3/2(5/2^{+})$ 
Older and obsolete values are listed and referenced in the 2014 edition, Chinese Physics C38 070001 (2014).
${{\boldsymbol \Delta}{(1905)}}$ POLE POSITION
REAL PART   $1770\text{ to }1830\text{ }(\approx1800) $ MeV 
 
$-2{\times }$IMAGINARY PART   $260\text{ to }340\text{ }(\approx300) $ MeV 
 
${{\boldsymbol \Delta}{(1905)}}$ ELASTIC POLE RESIDUE
MODULUS $\vert \mathit r\vert $   $15\text{ to }25\text{ }(\approx20) $ MeV 
 
PHASE $\theta $   $-120\text{ to }-30\text{ }(\approx-50) $ $^\circ{}$ 
 
${{\boldsymbol \Delta}{(1905)}}$ INELASTIC POLE RESIDUE
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit K}}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$
 
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$
 
${{\mathit \Delta}{(1905)}}$ BREIT-WIGNER MASS   $1855\text{ to }1910\text{ }(\approx1880) $ MeV 
 
${{\mathit \Delta}{(1905)}}$ BREIT-WIGNER WIDTH   $270\text{ to }400\text{ }(\approx330) $ MeV 
 
${{\boldsymbol \Delta}{(1905)}}$ PHOTON DECAY AMPLITUDES AT THE POLE
${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$
 
${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$
 
${{\boldsymbol \Delta}{(1905)}}$ BREIT-WIGNER PHOTON DECAY AMPLITUDES
${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$   $0.017\text{ to }0.027\text{ }(\approx0.022) $ GeV${}^{−1/2}$ 
 
${{\mathit \Delta}{(1905)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$   $-0.055\text{ to }-0.035\text{ }(\approx-0.045) $ GeV${}^{−1/2}$ 
 
The following branching fractions are our estimates, not fits or averages.
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$  $9 - 15\%$ 698
 
$\Gamma_{2}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$  673
 
$\Gamma_{3}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$  $80 - 100\%$ 524
 
$\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$  $23 - 43\%$ 524
 
$\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$  $56 - 72\%$ 524
 
$\Gamma_{6}$ ${{\mathit N}}{{\mathit \rho}}$  385
 
$\Gamma_{7}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2, ${\mathit P}{\mathrm -wave}$  seen 385
 
$\Gamma_{8}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$  $<$ 1$\%$ 293
 
$\Gamma_{9}$ ${{\mathit N}{(1680)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$  $5 - 15\%$ 133
 
$\Gamma_{10}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$  $2 - 6\%$ 282
 
$\Gamma_{11}$ ${{\mathit N}}{{\mathit \gamma}}$  $0.012 - 0.036\%$ 706
 
$\Gamma_{12}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2  $0.002 - 0.006\%$ 706
 
$\Gamma_{13}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=3/2  $0.01 - 0.03\%$ 706
 
FOOTNOTES