${{\mathit \Delta}}$ 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

${{\mathit \Delta}{(1940)}}$

$I(J^P)$ = $3/2(3/2^{-})$ 
${{\mathit \Delta}{(1940)}}$ POLE POSITION
REAL PART   $1850\text{ to }2050\text{ }(\approx1950) $ MeV 
 
$-2{\times }$IMAGINARY PART   $200\text{ to }500\text{ }(\approx350) $ MeV 
 
${{\mathit \Delta}{(1940)}}$ ELASTIC POLE RESIDUE
MODULUS $\vert \mathit r\vert $   $4\text{ to }10\text{ }(\approx7) $ MeV 
 
PHASE $\theta $   $150\text{ to }250\text{ }(\approx200) $ $^\circ{}$ 
 
${{\mathit \Delta}{(1940)}}$ 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 
 
${{\mathit \Delta}{(1940)}}$ 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$_{3/2}$
 
${{\mathit \Delta}{(1940)}}$ 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$_{3/2}$
 
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$  $1 - 20$ $\%$ 773
 
$\Gamma_{2}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$  $>$81 $\%$ 751
 
$\Gamma_{3}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$  $6 - 85$ $\%$ 610
 
$\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit S}{\mathrm -wave}$  $1 - 65$ $\%$ 610
 
$\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$  $5 - 20\%$ 610
 
$\Gamma_{6}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit S}{\mathrm -wave}$  $75 - 85$ $\%$ 514
 
$\Gamma_{7}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$  $2 - 14\%$ 397
 
$\Gamma_{8}$ ${{\mathit N}}{{\mathit a}_{{0}}{(980)}}$  seen 283
 
$\Gamma_{9}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$  $4 - 16$ $\%$ 429
 
$\Gamma_{10}$ ${{\mathit N}}{{\mathit \gamma}}$  $0.06 - 2.53$ $\%$ 780
 
$\Gamma_{11}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2  $0.06 - 1.51$ $\%$ 780
 
$\Gamma_{12}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=3/2  $0 - 1.02$ $\%$ 780
 
FOOTNOTES