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

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

$I(J^P)$ = $1/2(5/2^{+})$ 
Older and obsolete values are listed and referenced in the 2014 edition, Chinese Physics C38 070001 (2014).
${{\boldsymbol N}{(1680)}}$ POLE POSITION
REAL PART   $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${}^{−1/2}$ 
 
The following branching fractions are our estimates, not fits or averages.
$\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$  $60 - 70\%$ 571
 
$\Gamma_{2}$ ${{\mathit N}}{{\mathit \eta}}$  $<1\%$ 386
 
$\Gamma_{3}$ ${{\mathit \Lambda}}{{\mathit K}}$  232
 
$\Gamma_{4}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$  $20 - 40\%$ 539
 
$\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$  $11 - 23\%$ 374
 
$\Gamma_{6}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$  $4 - 10\%$ 374
 
$\Gamma_{7}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$  $1 - 13\%$ 374
 
$\Gamma_{8}$ ${{\mathit N}}{{\mathit \rho}}$  -1
 
$\Gamma_{9}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit P}{\mathrm -wave}$  -1
 
$\Gamma_{10}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit F}{\mathrm -wave}$  -1
 
$\Gamma_{11}$ ${{\mathit N}}{{\mathit \sigma}}$  $9 - 19\%$  
 
$\Gamma_{12}$ ${{\mathit p}}{{\mathit \gamma}}$  $0.21 - 0.32\%$ 581
 
$\Gamma_{13}$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity=1/2  $0.001 - 0.011\%$ 581
 
$\Gamma_{14}$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity=3/2  $0.20 - 0.32\%$ 581
 
$\Gamma_{15}$ ${{\mathit n}}{{\mathit \gamma}}$  $0.021 - 0.046\%$ 581
 
$\Gamma_{16}$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity=1/2  $0.004 - 0.029\%$ 581
 
$\Gamma_{17}$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity=3/2  $0.01 - 0.024\%$ 581
 
FOOTNOTES