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

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

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

Consider the quark model ² L 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 ) ¾ 2 £ 3 F 5 ! 1 ; 8 M © ² S u c e s o f n - r l a t i v q k m d y g ² 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

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 e b a r y o n m u l p d c f S U ( 2 4 ) S U ( 2 4 ) ¾ £ 1 f 6 ! ; 5 7 M © 3 W h e r a t p y s i c l o n d u ? ² N e d t o k n w f r p a s l c i h x

Identifying physical baryons: Single-taste baryons ² I 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 ² T a s t e r j u l i k x ° v o ; q n ² 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 ) ¾ £ 1 f 6 ! ; 5 7 M © 3

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 ¾ 3 F £ 4 T 5 7 M ! ; © 8 ¹ A 6 ² 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 ² A l 2 S b a r y o n s c e p d t h i

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 µ 8 ¶ ) S U ( 8 ^ m £ 4 s ¾ T Baryons transforming within a given irrep of continuum symmetry are degenerate

Continuum irreps S U ( 1 2 ) ¾ 8 £ 4 3 6 4 ! ( 1 2 ; ) © 8 5 7 : f ¾ 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

Correspondence with physical baryons U ( 1 2 ) f ¾ 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

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 e p 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 ?

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/0611023

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 N x = y ^ a n d z s S U ( 1 2 ) f ¾ 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

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

Swapping degeneracies with physical states m 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 ¤ § ¥ ¢ ­ ¡