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${{\boldsymbol N}}$ BARYONS
($\boldsymbol S$ = 0, $\boldsymbol I$ = 1/2)
${{\mathit p}}$, ${{\mathit N}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$; ${{\mathit n}}$, ${{\mathit N}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$

${{\boldsymbol N}{(1680)}}$ $I(J^P)$ = $1/2(5/2^{+})$

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

${{\boldsymbol N}{(1680)}}$ POLE POSITION

$1665\text{ to }1680\text{ }(\approx1675) $ MeV

$-2{\times }$IMAGINARY PART

$110\text{ to }135\text{ }(\approx120) $ MeV

${{\boldsymbol N}{(1680)}}$ ELASTIC POLE RESIDUE

MODULUS $\vert \mathit r\vert $

$35\text{ to }45\text{ }(\approx40) $ MeV

PHASE $\theta $

$-20\text{ to }10\text{ }(\approx-5) $ $^\circ{}$

${{\boldsymbol N}{(1680)}}$ INELASTIC POLE RESIDUE

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit N}}{{\mathit \eta}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit K}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit K}}$

Normalized residue in ${{\mathit N}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit N}}$ (${{\mathit \pi}{\mathit \pi}}){}^{\mathit I = 0}_{{\mathit S}{\mathrm -wave}}$

${{\mathit N}{(1680)}}$ BREIT-WIGNER MASS

$1680\text{ to }1690\text{ }(\approx1685) $ MeV

${{\mathit N}{(1680)}}$ BREIT-WIGNER WIDTH

$115\text{ to }130\text{ }(\approx120) $ MeV

${{\boldsymbol N}{(1680)}}$ PHOTON DECAY AMPLITUDES AT THE POLE

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$

${{\boldsymbol N}{(1680)}}$ BREIT-WIGNER PHOTON DECAY AMPLITUDES

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$

$-0.018\text{ to }-0.005\text{ }(\approx-0.010) $ GeV${}^{−1/2}$

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$

$0.130\text{ to }0.140\text{ }(\approx0.135) $ GeV${}^{−1/2}$

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity-1/2 amplitude A$_{1/2}$

$0.020\text{ to }0.040\text{ }(\approx0.030) $ GeV${}^{−1/2}$

${{\mathit N}{(1680)}}$ $\rightarrow$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity-3/2 amplitude A$_{3/2}$

$-0.050\text{ to }-0.025\text{ }(\approx-0.035) $ GeV${}^{−1/2}$

Decay Modes

The following branching fractions are our estimates, not fits or averages.

${{\mathit N}}{{\mathit \pi}}$

${{\mathit N}}{{\mathit \eta}}$

${{\mathit \Lambda}}{{\mathit K}}$

${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$

${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$

${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$

${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$

${{\mathit N}}{{\mathit \rho}}$

${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit P}{\mathrm -wave}$

${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit F}{\mathrm -wave}$

${{\mathit N}}{{\mathit \sigma}}$

${{\mathit p}}{{\mathit \gamma}}$

$0.21 - 0.32\%$

${{\mathit p}}{{\mathit \gamma}}$ , helicity=1/2

$0.001 - 0.011\%$

${{\mathit p}}{{\mathit \gamma}}$ , helicity=3/2

$0.20 - 0.32\%$

${{\mathit n}}{{\mathit \gamma}}$

$0.021 - 0.046\%$

${{\mathit n}}{{\mathit \gamma}}$ , helicity=1/2

$0.004 - 0.029\%$

${{\mathit n}}{{\mathit \gamma}}$ , helicity=3/2

$0.01 - 0.024\%$