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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   JSON  (beta) PDGID: B011

${{\mathit \Delta}{(1905)}}$ $I(J^P)$ = $3/2(5/2^{+})$

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

${{\mathit \Delta}{(1905)}}$ POLE POSITION

REAL PART   $1750\text{ to }1800\text{ }(\approx1770) $ MeV

$-2{\times }$IMAGINARY PART   $260\text{ to }340\text{ }(\approx300) $ MeV

${{\mathit \Delta}{(1905)}}$ ELASTIC POLE RESIDUE

MODULUS $\vert \mathit r\vert $   $15\text{ to }25\text{ }(\approx20) $ MeV

PHASE $\theta $   $-120\text{ to }-30\text{ }(\approx-45) $ $^\circ{}$

${{\mathit \Delta}{(1905)}}$ 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

${{\mathit \Delta}{(1905)}}$ 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$_{3/2}$

${{\mathit \Delta}{(1905)}}$ 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{ }(\approx0.022) $ 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${}^{−1/2}$

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)   $\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$   $9 - 15\%$ 698   $\Gamma_{2}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$   $>65\%$ 673   $\Gamma_{3}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$   $>48\%$ 524   $\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $8 - 43\%$ 524   $\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$   $40 - 58\%$ 524   $\Gamma_{6}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2, ${\mathit P}{\mathrm -wave}$   $17 - 35\%$ 385   $\Gamma_{7}$ ${{\mathit N}{(1535)}}{{\mathit \pi}}$   $<$ 1$\%$ 293   $\Gamma_{8}$ ${{\mathit N}{(1680)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $5 - 15\%$ 133   $\Gamma_{9}$ ${{\mathit \Delta}{(1232)}}{{\mathit \eta}}$   $2 - 6\%$ 282   $\Gamma_{10}$ ${{\mathit N}}{{\mathit \gamma}}$   $0.012 - 0.036\%$ 706   $\Gamma_{11}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=1/2   $0.002 - 0.006\%$ 706   $\Gamma_{12}$ ${{\mathit N}}{{\mathit \gamma}}$ , helicity=3/2   $0.01 - 0.03\%$ 706
FOOTNOTES