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${{\mathit \Delta}}$ 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

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

${{\mathit \Delta}{(1940)}}$ 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$_{3/2}$

${{\mathit \Delta}{(1940)}}$ Decay Modes
Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c)   $\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$   $1 - 20$ $\%$ 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
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