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${{\mathit N}}$ 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   JSON  (beta) PDGID: B065

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

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

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

REAL PART   $1660\text{ to }1680\text{ }(\approx1670) $ MeV

$-2{\times }$IMAGINARY PART   $110\text{ to }135\text{ }(\approx120) $ MeV

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

MODULUS $\vert \mathit r\vert $   $35\text{ to }45\text{ }(\approx40) $ MeV

PHASE $\theta $   $-30\text{ to }-10\text{ }(\approx-20) $ $^\circ{}$

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

${{\mathit N}{(1680)}}$ 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$_{3/2}$

${{\mathit N}{(1680)}}$ 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.
Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c)   $\Gamma_{1}$ ${{\mathit N}}{{\mathit \pi}}$   $60 - 70\%$ 571   $\Gamma_{2}$ ${{\mathit N}}{{\mathit \eta}}$   $<1\%$ 386   $\Gamma_{3}$ ${{\mathit N}}{{\mathit \pi}}{{\mathit \pi}}$   $28 - 53$ $\%$ 539   $\Gamma_{4}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$   $11 - 23\%$ 374   $\Gamma_{5}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $4 - 10\%$ 374   $\Gamma_{6}$ ${{\mathit \Delta}{(1232)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$   $1 - 13\%$ 374   $\Gamma_{7}$ ${{\mathit N}}{{\mathit \rho}}$   $8 - 11$ $\%$ -1   $\Gamma_{8}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit P}{\mathrm -wave}$   $6 - 8$ $\%$ -1   $\Gamma_{9}$ ${{\mathit N}}{{\mathit \rho}}$ , $\mathit S$=3/2 , ${\mathit F}{\mathrm -wave}$   $2 - 3$ $\%$ -1   $\Gamma_{10}$ ${{\mathit N}}{{\mathit \sigma}}$   $9 - 19\%$     $\Gamma_{11}$ ${{\mathit p}}{{\mathit \gamma}}$   $0.21 - 0.32\%$ 581   $\Gamma_{12}$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity=1/2   $0.001 - 0.011\%$ 581   $\Gamma_{13}$ ${{\mathit p}}{{\mathit \gamma}}$ , helicity=3/2   $0.20 - 0.32\%$ 581   $\Gamma_{14}$ ${{\mathit n}}{{\mathit \gamma}}$   $0.021 - 0.046\%$ 581   $\Gamma_{15}$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity=1/2   $0.004 - 0.029\%$ 581   $\Gamma_{16}$ ${{\mathit n}}{{\mathit \gamma}}$ , helicity=3/2   $0.01 - 0.024\%$ 581
FOOTNOTES