${{\boldsymbol \Delta}}$ 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

${{\boldsymbol \Delta}{(1940)}}$ $I(J^P)$ = $3/2(3/2^{-})$

${{\boldsymbol \Delta}{(1940)}}$ POLE POSITION
REAL PART   $1850\text{ to }2050\text{ }(\approx1950) $ MeV 
$-2{\times }$IMAGINARY PART   $200\text{ to }500\text{ }(\approx350) $ MeV 
${{\boldsymbol \Delta}{(1940)}}$ ELASTIC POLE RESIDUE
MODULUS $\vert \mathit r\vert $   $4\text{ to }10\text{ }(\approx7) $ MeV 
PHASE $\theta $   $150\text{ to }250\text{ }(\approx200) $ $^\circ{}$ 
${{\boldsymbol \Delta}{(1940)}}$ INELASTIC POLE RESIDUE
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit S}{\mathrm -wave}$
Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$
${{\mathit \Delta}{(1940)}}$ BREIT-WIGNER MASS   $1940\text{ to }2060\text{ }(\approx2000) $ MeV 
${{\mathit \Delta}{(1940)}}$ BREIT-WIGNER WIDTH   $300\text{ to }500\text{ }(\approx400) $ MeV 
${{\boldsymbol \Delta}{(1940)}}$ PHOTON DECAY AMPLITUDES AT THE POLE
${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$
${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$
${{\boldsymbol \Delta}{(1940)}}$ BREIT-WIGNER PHOTON DECAY AMPLITUDES
${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$
${{\mathit \Delta}{(1940)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$ $1 - 7\%$773
$\Gamma_{2}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$ 751
$\Gamma_{3}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ $30 - 85\%$610
$\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit S}{\mathrm -wave}$ $25 - 65\%$610
$\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$ $5 - 20\%$610
$\Gamma_{6}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$ $2 - 14\%$397
$\Gamma_{7}$ ${{\mathit N}}{{\mathit a}_{{0}}{(980)}}$ seen283
$\Gamma_{8}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$ $4 - 16\%$429
$\Gamma_{9}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2 seen780
$\Gamma_{10}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=3/2 seen780