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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

${{\mathit \Delta}{(1920)}}$ $I(J^P)$ = $3/2(3/2^{+})$

Older and obsolete values are listed and referenced in the 2014 edition, Chinese Physics C38 070001 (2014).

${{\mathit \Delta}{(1920)}}$ POLE POSITION

REAL PART   $1850\text{ to }1950\text{ }(\approx1900) $ MeV

$-2{\times }$IMAGINARY PART   $200\text{ to }400\text{ }(\approx300) $ MeV

${{\mathit \Delta}{(1920)}}$ ELASTIC POLE RESIDUE

MODULUS $\vert \mathit r\vert $   $8\text{ to }24\text{ }(\approx16) $ MeV

PHASE $\theta $   $-150\text{ to }-50\text{ }(\approx-100) $ $^\circ{}$

${{\mathit \Delta}{(1920)}}$ INELASTIC POLE RESIDUE

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \eta}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit K}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit a}_{{0}}{(980)}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}{(1440)}}{{\mathit \pi}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}{(1520)}}{{\mathit \pi}}$ , ${\mathit S}{\mathrm -wave}$

${{\mathit \Delta}{(1920)}}$ BREIT-WIGNER MASS   $1870\text{ to }1970\text{ }(\approx1920) $ MeV

${{\mathit \Delta}{(1920)}}$ BREIT-WIGNER WIDTH   $240\text{ to }360\text{ }(\approx300) $ MeV

${{\mathit \Delta}{(1920)}}$ PHOTON DECAY AMPLITUDES AT THE POLE

${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$

${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$

${{\mathit \Delta}{(1920)}}$ BREIT-WIGNER PHOTON DECAY AMPLITUDES

${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$

${{\mathit \Delta}{(1920)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$

${{\mathit \Delta}{(1920)}}$ Decay Modes
The following branching fractions are our estimates, not fits or averages.
Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c)   $\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$   $5 - 20$ $\%$ 723   $\Gamma_{2}$ ${{\mathit \Sigma}}{{\mathit K}}$   $2 - 6$ $\%$ 431   $\Gamma_{3}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$   $>$46 $\%$ 699   $\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$   $>$46 $\%$ 553   $\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $2 - 28$ $\%$ 553   $\Gamma_{6}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$   $44 - 72$ $\%$ 553   $\Gamma_{7}$ ${{\mathit N}{(1440)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $4 - 86$ $\%$ 403   $\Gamma_{8}$ ${{\mathit N}{(1520)}}{{\mathit \pi}}$ , ${\mathit S}{\mathrm -wave}$   $<5\%$ 341   $\Gamma_{9}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$   $<2\%$ 328   $\Gamma_{10}$ ${{\mathit N}}{{\mathit a}_{{0}}{(980)}}$   seen 41   $\Gamma_{11}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$   $5 - 17$ $\%$ 336   $\Gamma_{12}$ ${{\mathit N}}{{\mathit \gamma}}$   $0.01 - 0.84$ $\%$ 731   $\Gamma_{13}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2   $0.0 - 0.42$ $\%$ 731   $\Gamma_{14}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=3/2   $0.01 - 0.42$ $\%$ 731
FOOTNOTES