We introduce new color indices cn ^ { \prime } _ { JWL } ( = Ca _ { CTIO } - Ca _ { JWL } ) and ch _ { JWL } [ = ( JWL 43 - b ) - ( b - y ) ] , accurate photometric measures of the CN band at \lambda 3883 and the CH G band , respectively , in the study of the multiple populations ( MPs ) in globular clusters ( GCs ) .
Our photometric CN–CH relation for a large number of red-giant branch ( RGB ) in M5 shows that the evolutions of the CN and CH between the CN-w and CN-s populations are not continuous .
Armed with our new color indices , we investigate the MPs of NGC 6723 , finding the RGB populational number ratio of n ( CN-w ) : n ( CN-s ) \approx 35.5:64.5 ( \pm 2.8 ) with no radial gradient .
Similar to other normal GCs with MPs , the helium abundance of the CN-s population inferred from the RGB bump magnitude is slightly enhanced by \Delta Y = 0.012 \pm 0.012 .
Our cn _ { JWL } and cn ^ { \prime } _ { JWL } color-magnitude diagrams clearly show the discrete double AGB populations in NGC 6723 , whose bright AGB populational number ratio is in marginally agreement with that of the RGB stars within the statistical errors .
Finally , our synthetic cn _ { JWL } index is in good agreement with observations , except for the CN-w asymptotic giant branch ( AGB ) .
To mitigate the discrepancy in the CN-w AGB may require a mild nitrogen enhancement and/or a large decrement in the ^ { 12 } C/ ^ { 13 } C ratio with respect to the bright RGB .