${{\boldsymbol \Delta}}$ BARYONS
($\boldsymbol S$ = 0, $\boldsymbol I$ = 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{ }(\approx 0.022) $ 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, ${\mathit P}{\mathrm -wave}$ seen385
$\Gamma_{8}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$ $<$ 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