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${{\mathit \Sigma}}$ BARYONS ($\mathit S$ = $-1$, $\mathit I$ = 1) ${{\mathit \Sigma}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$

INSPIRE search

${{\boldsymbol \Sigma}{(1775)}}$ $I(J^P)$ = $1(5/2^{-})$

Discovered by GALTIERI 1963 , this resonance plays the same role as cornerstone for isospin-1 analyses in this region as the ${{\mathit \Lambda}{(1820)}}{\mathit F}_{\mathrm 05}$ does in the isospin-0 channel. For most results published before 1974 (they are now obsolete), see our 1982 edition Physics Letters 111B 1 (1982).

${{\boldsymbol \Sigma}{(1775)}}$ POLE POSITION

REAL PART   $1760\text{ to }1780\text{ }(\approx1770) $ MeV

$-2{\times }$IMAGINARY PART   $45\text{ to }65\text{ }(\approx55) $ MeV

${{\boldsymbol \Sigma}{(1775)}}$ POLE RESIDUES

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit \pi}}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$ , ${\mathit G}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=1/2, ${\mathit D}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=3/2, ${\mathit D}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=3/2, ${\mathit G}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Xi}}{{\mathit K}}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}}$ , ${\mathit F}{\mathrm -wave}$

Normalized residue in ${{\mathit N}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \Sigma}{(1775)}}$ $\rightarrow$ ${{\mathit \Delta}}{{\overline{\mathit K}}}$ , ${\mathit D}{\mathrm -wave}$

${{\mathit \Sigma}{(1775)}}$ MASS   $1770\text{ to }1780\text{ }(\approx1775) $ MeV

${{\mathit \Sigma}{(1775)}}$ WIDTH   $105\text{ to }135\text{ }(\approx120) $ MeV

${{\boldsymbol \Sigma}{(1775)}}$ Decay Modes
Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c) $\Gamma_{1}$ ${{\mathit N}}{{\overline{\mathit K}}}$   $37-43\%$ 508   $\Gamma_{2}$ ${{\mathit \Lambda}}{{\mathit \pi}}$   $14-20\%$ 525   $\Gamma_{3}$ ${{\mathit \Sigma}}{{\mathit \pi}}$   $2-5\%$ 475   $\Gamma_{4}$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$   $8-12\%$ 327   $\Gamma_{5}$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$   327   $\Gamma_{6}$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$ , ${\mathit D}{\mathrm -wave}$   327   $\Gamma_{7}$ ${{\mathit \Sigma}{(1385)}}{{\mathit \pi}}$ , ${\mathit G}{\mathrm -wave}$   327   $\Gamma_{8}$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}}$ , ${\mathit P}{\mathrm -wave}$   $17-23\%$ 202   $\Gamma_{9}$ ${{\mathit \Sigma}}{{\mathit \pi}}{{\mathit \pi}}$   432   $\Gamma_{10}$ ${{\mathit \Delta}{(1232)}}{{\overline{\mathit K}}}$ , ${\mathit D}{\mathrm -wave}$   189   $\Gamma_{11}$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=1/2   -1   $\Gamma_{12}$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=1/2, ${\mathit D}{\mathrm -wave}$   -1   $\Gamma_{13}$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=3/2, ${\mathit D}{\mathrm -wave}$   -1   $\Gamma_{14}$ ${{\mathit N}}{{\overline{\mathit K}}^{*}{(892)}}$ , $\mathit S$=3/2, ${\mathit G}{\mathrm -wave}$   -1
FOOTNOTES