C o l o r G l a s s C o n d e n s a t e a n d p a r t o n s a t u r a t i o n : o v e r v i e w o f r e c e n t d e v e l o p m e n t s A d r i a n D u m i t r u R I K E N B N L a n d B a r u c h C o l l e g e , C U N Y Q u a r k M a t t e r 2 0 1 2 , A u g u s t 1 3 – 1 8 , Wa s h i n g t o n D . C .
O u t l i n e O u t l i n e ● I n t r o d u c t i o n & M o t i v a t i o n ● M u l t i p l i c i t y f l u c t u a t i o n s a n d K N O s c a l i n g ● t o n o n - l i n e a r c o l o r f i e l d s i n n u c l e i : F r o m P r o t o n s t e s t i n g q u a n t u m e v o l u t i o n a n d i n i t i a l c o n d i t i o n s d N / d y , d N / d p , R i n p + P b a t L H C T p A ● F r o m d i p o l e s t o q u a d r u p o l e s : h - h a n g u l a r c o r r e l a t i o n s ● γ - h a n g u l a r c o r r e l a t i o n s ● S u m m a r y & O u t l o o k
(p)QCD very successful for successful for short-distance short-distance (p)QCD very phenomena involving few few particles / quanta particles / quanta phenomena involving ● Q Q q u a r k o n i u m s p e c t r u m , M / Λ ≫ 1 Q Q C D + - ● H i g h - E j e t s i n h a d r o n i c c o l l i s i o n s a n d e e → q q g T E / Λ ≫ 1 T Q C D 2 ● D I S w i t h h i g h l y v i r t u a l p h o t o n √ Q / Λ ≫ 1 Q C D ● . . .
Because: Because: 2 ● α ( Q ) ≪ 1 s ● E x p a n d a b o u t f r e e q u a n t a , a d d i n i n t e r a c t i o n s o n e b y o n e
But fails for: But fails for: ● D i s t a n c e s ~ 1 f m ; o k , l e t ' s l e a v e c o n f i n e m e n t f o r a n o t h e r d a y . . . ● H o t Q C D , e v e n w h e n T / Λ ≫ 1 Q C D ( P i s a r s k i : n e c e s s a r y t o e x p a n d a b o u t D e b y e s c r e e n e d E f i e l d ! ) ● H i g h - e n e r g y p r o c e s s e s a t f i x e d v i r t u a l i t y : 2 2 e f f e c t i v e c h a r g e α ( Q ) ≪ 1 b u t t h e r e a r e m a n y O ( 1 / α ) s s p a r t n e r s t o i n t e r a c t w i t h : g l u o n s i n t e r a c t a l o t ! → ( s e m i - h a r d ) Q C D b e c o m e s n o n - l i n e a r
G l u o n d e n s i t y p e r u n i t t r a n s v e r s e a r e a a t s m a l l x : i n t r i n s i c s e m i - h a r d s c a l e ! l a r g e p h a s e - s p a c e d e n s i t y , o c c u p a t i o n n u m b e r O ( 1 / α ) s M c L e r r a n & V e n u g o p a l a n ( 1 9 9 4 + ) :
N o n - l i n e a r f i e l d s a r e a g r e a t i n t e l l e c t u a l c h a l l e n g e i n m o d e r n p h y s i c s : ● G r a v i t y : f o r m a t i o n o f b l a c k h o l e s , . . . ● Q E D p a i r c r e a t i o n i n e x t r e m e l a s e r f i e l d s ● Q C D : n o n - l i n e a r c o l o r f i e l d s i n h a d r o n s / n u c l e i b o o s t e d t o r a p i d i t y y ≫ 1
● M V : t r y c l i m b i n g t h e c a m e l f r o m b a c k ! ● I f o c c u p a t i o n n u m b e r i s h i g h , e x p a n d a b o u t c l a s s i c a l s o l u t i o n r a t h e r t h a n a b o u t “ n o t h i n g ” c l a s s i c a l f i e l d b e h i n d “ p a n c a k e ” o f v a l e n c e c h a r g e s q u a n t u m f l u c t u a t i o n s ( s m a l l - x e v o l u t i o n )
e&m fields of boosted charge (v→1): J.D. Jackson: classical E&M 2d Coulomb potential valence charge density “shock wave” shock wave” “
In a hadron / nucleus the local valence color charge density is random + s o f t Y M f i e l d s + ↔ hard c o u p l i n g o f s o f t μ 2 ~ g 2 A 1/3 ; κ 3 ~ g 3 A 2/3 ; κ 4 ~ g 4 A Averages:
M u l t i p l i c i t y d i s t r i b u t i o n : N e g a t i v e B i n o m i a l f r o m M V m o d e l Gelis, Lappi, McLerran: NPA (2009) Schenke, Tribedy, Venugopalan: 2012 N B D t w o p a r a m e t e r d i s t r i b u t i o n : m e a n n , w i d t h
Multiplicity distributions in pp pp collisions T r i b e d y & V e n u g o p a l a n : P L B 2 0 1 2 P ( n ) : n e g a t i v e b i n o m i a l d i s t r i b u t i o n
K N O s c a l i n g ( e v e n p + P b a p p r o x . ) K N O s c a l i n g ( e v e n p + P b a p p r o x . ) f o r A + B : p A @ L H C , m b d + A u @ R H I C = = ) ) D u m i t r u & N a r a : z z ( ( P R C 2 0 1 2 Ψ Ψ z = z =
KNO from Neg. Binomial Distribution ? KNO from Neg. Binomial Distribution ? i s u n i v e r s a l ( i n d e p e n d e n t o f e n e r g y ) n P ( n ) ≡ ψ ( z ) u n i v e r s a l K o b a , N i e l s e n , O l e s e n , N P B ( 1 9 7 2 ) In the limit 1 1 « « n n / k / k, NBD can be written as which is independent of n n ! !
4 F o r a c t i o n w i t h ~ ρ o p e r a t o r : Poster by Elena Petreska ! Poster by Elena Petreska ! 4 G a u s s / M V ρ KNO in terms of small-x gluons (p T ~Q s ): KNO in terms of small-x gluons (p T ~Q s ): i ) a p p r o x . G a u s s i a n a c t i o n i i ) h i g h o c c u p a t i o n n u m b e r
S u b n u c l e o n s c a l e f o r K N O f l u c t u a t i o n s ? - 1 Q s s e e L a p p i & M c L e r r a n , M ü l l e r & S c h ä f e r , S c h e n k e , T r i b e d y , V e n u g o p a l a n , . . . ● → “ s p i k i e r ” i n i t i a l d e n s i t y d i s t r i b u t i o n f o r h y d r o ? ( s e e w o r k b y G a v i n & M o s c h e l l i , H . P e t e r s e n , T . K o d a m a e t a l , . . . ) Talk by S. Moreland at QM12 ! Talk by S. Moreland at QM12 !
R i d g e i n v e r y h i g h - m u l t i p l i c i t y p p @ 7 T e V R i d g e i n v e r y h i g h - m u l t i p l i c i t y p p @ 7 T e V ( We i L i f o r C M S , Q u a r k M a t t e r 2 0 1 1 , A n n e c y ) p e a k s a t ~ 3 . 5 G e V ! p e a k s a t ~ 3 . 5 G e V ! D u s l i n g & V e n u g o p a l a n : a r X i v : 1 2 0 1 . 2 6 5 8
Eccentricity ε ε 3 in Au+Au Eccentricity 3 in Au+Au D u m i t r u & N a r a : P R C 2 0 1 2 G l a u b e r + N B D G l a u b e r f l u c o n l y k ~ m i n ( T , T ) A B
Evolution with energy: quantum fluctuations Evolution with energy: quantum fluctuations ● A t r a p i d i t y f a r f r o m v a l e n c e c h a r g e s , r e s u m m a t i o n t o a l l n o r d e r s i n ( α Y ) r e q u i r e d s
r c B K ( g e n e r a l i z e d ) u n i n t e g r . g l u o n d e n s i t y r c B K ( g e n e r a l i z e d ) u n i n t e g r . g l u o n d e n s i t y center of A~200 nucleus proton J . A l b a c e t e 2 0 1 0 + J . A l b a c e t e 2 0 1 0 + f o r w . R H I C L H C γ 2 γ ~1/k 2 ~1/k 2 ~1/k 2 ~1/k
Energy and centrality dependence of multiplicities i ) K h a r z e e v , L e v i n , N a r d i m o d e l i ) K h a r z e e v , L e v i n , N a r d i m o d e l ( u p d a t e d p r e d i c t i o n s f r o m a r X i v : 1 1 1 1 . 3 0 3 1 ) w i t h
d + A u @ R H I C d + A u @ R H I C A A @ R H I C & L H C A A @ R H I C & L H C
p + p @ 9 0 0 p + p @ 9 0 0 p + p @ 2 3 6 0 p + p @ 2 3 6 0 p + p @ 7 0 0 0 p + p @ 7 0 0 0 p + P b @ 4 4 0 0 p + P b @ 4 4 0 0 p r e d i c t i o n p r e d i c t i o n
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