${{\mathit \Sigma}}$ 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 
 
$\Gamma_{1}$ ${{\mathit N}}{{\overline{\mathit K}}}$  $37-43\%$ 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