1. Making sense of staggered light-quark baryons: Insights from the quark model
Jon A. Bailey
August 23, 2007

2. Challenge of staggered baryon spectroscopy
Extract the masses of the lightest octet and decuplet baryons using rooted staggered QCD
Success would provide valuable evidence for
rooted staggered QCD
rooted SχPT
Taste quantum numbers complicate analysis
Deducing the lightest staggered baryon multiplets involved but straightforward

3. Taste quantum numbers M = @ ^ m I 1 A S U ( 3 ) ! 1 2
Four tastes for each physical quark flavor M = @ ^ m I 4 s 1 A
Larger flavor symmetry group S U ( 3 ) F ! 1 2 f

4. Consider the quark modelL i g h t e s o c a n d u p l m b y r f S U ( 6 ) S U ( 6 ) 2 3 F 5 ! 1 ; 8 M S u c e s o f n - r l a t i v q k m d y g I f r o t e d s a g Q C D i c , h n q u k m l d e s c r i b l g h t a y o n m u p

5. Staggered quark model W h e r a t p y s i c l o n d u ? ² L i g h t eb a r y o n m u l p d c f S U ( 2 4 ) S U ( 2 4 ) 1 f 6 ! ; 5 7 M 3 W h e r a t p y s i c l o n d u ? N e d t o k n w f r p a s l c i h x

6. Identifying physical baryons: Single-taste baryonsI f r o t e d s a g Q C D i c , h n S U ( 4 ) T i n t h e c o u m l T a s t e r j u l i k x v o ; q n C o n s i d e r b a y c t g l f q u k ; t o h a v e c r S U ( 2 ) 1 f s y m , S U ( 3 ) F s y m e t r u b a 1 2 f S U ( 2 4 ) 1 f 6 ! ; 5 7 M 3

7. Flavor-taste basis ² D i s e n t a g l ° v o r S U ( 3 ) d 4 q u m b :1 2 ) f 3 F 4 T 5 7 M ! ; 8 A 6 I n t h e c o i u m l , a b r s f g v p a r e d g n t A l 2 S b a r y o n s c e p d t h i

8. Continuum symmetry ) S U ( 8 £ 4 ¾ M = @ ^ m I 1 A µ ¶ ^ T m
Continuum symmetry is larger than taste alone M = @ ^ m I 4 s 1 A 8 ) S U ( 8 ^ m 4 s T
Baryons transforming within a given irrep of continuum symmetry
are degenerate

9. Continuum irreps S U ( 1 2 ) ¾ 8 £ 4 3 6 4 ! ( 1 2 ; ) © 8 5 7 :f 8 ^ m 4 s 3 6 4 S ! ( 1 2 ; ) 8 5 7 M A :
Deduce correspondence between continuum irreps and physical states by locating single-taste baryons in each continuum irrep

10. Correspondence with physical baryonsU ( 1 2 ) f 8 ^ m 4 s 3 6 4 S ! ( 1 2 ; ) 8 5 7 M A : N s N ( 1 4 ) ( 1 6 )
All irreps but two correspond to physical states
Exceptions are partially quenched baryons

11. Wait a minute! ) K e y : I s t a S U ( 4 r o d i n h c u m l ? ² D o ep r n c f t a w i h u y l m v d r o t e d s a g Q C D ? ) N o . C n s e r v a t i f S U ( 8 ^ m 4 q u b f o r b i d s m x n g t h e a w p y c l . T s i t u a o n w h e c r p l y q d . ) K e y : I s t a S U ( 4 T r o d i n h c u m l ?

12. Summary
If rooted staggered QCD is correct, then lightest multiplets of staggered baryons are straightforwardly, accurately described by quark model
Testing resulting picture means testing rooted staggered QCD
Analysis can immediately be extended to excited states, heavy-light-light baryons, . . .
hep-lat/

13. N o . f l a t i c e r p s n u m S U ( 1 2 ) ¾ 8 £ 4 ¢ § ¥ ­ 1 3 2 7 Nx = y ^ a n d z s S U ( 1 2 ) f 8 x ; y 4 z 3 6 4 S ! ( 1 2 ; ) 8 5 7 M A : 1 3 2 7 N 1 2 s N 5 7 4

14. Mixing § ¤ § ( ; 6 4 ) ! 1 8 © 7 : 5 ) F o r e a c h m b f t ( ; 1 6 i
States with the same conserved quantum numbers—i.e., corresponding members of the same type of irrep—mix ( 3 2 ; 6 S 4 ) ! 1 8 7 : 5 A ) F o r e a c h m b f t ( ; 1 6 i s 9 - d x n g

15. Swapping degeneracies with physical statesm x = y ^ ; z s ^ m à ! s m x = y s ; z ^ S U ( 8 ) x ; y 1 z 4 S U ( 2 ) I 1 z G T N à ! s