Multi-particle production in small systems from CGC Prithwish - PowerPoint PPT Presentation

Multi-particle production in small systems from CGC Prithwish Tribedy 7th International Workshop on Multiple Partonic Interactions at the LHC The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy 1

outline • Introduction • Framework of color glass condensate • Phenomenology of high multiplicity events • Combining CGC with PYTHIA Based on the work done in collaboration with : K. Dusling, L. McLerran, B. Schenke, S. Schlichting & R. Venugopalan 2

Multi-particle production at high energies Goal : Study correlated production of particles * + * + ⌧ � d N d N d N ( ) d y 1 d 2 p ⊥ 1 . . . d y q d 2 p ⊥ q d y 1 d 2 p ⊥ 1 d y q d 2 p ⊥ q . . . Focus : Collisions of small systems p+p and p+Pb are interesting as final state effects are minimal We need : • An ab-initio framework of particle production • Full treatment of different sources of fluctuations • State-of-the art treatment of fragmentation 3

Phenomena we want to describe arXiv: 1011.5531 Origin of high multiplicity events 4

Phenomena we want to describe arXiv: 1509.04776, 1210.5482 arXiv: 1011.5531 p+p p+A Systematics of Δη - Δφ correlations Origin of high multiplicity events Similar underlying dynamics must drive these phenomenon Energy dependence of ridge in p+p 5

Particle production at high energies Multi-particle production at high energies in Regge Gribov limit (x → 0) Colliding hadrons/nuclei : • Saturation : Non-linear process strops growth of gluons, semi- hard saturation scale Q s (x) > Λ QCD -Y ) • Gluon dominated wave function, peaked at Q s (x~x 0 e arXiv: 1212.1701 6

Particle production at high energies Multi-particle production at high energies in Regge Gribov limit (x → 0) Colliding hadrons/nuclei : • Saturation : Non-linear process strops growth of gluons, semi-hard saturation scale Q s (x) > Λ QCD -Y ) • Gluon dominated wave function , peaked at Q s (x~x 0 e arXiv: 1212.1701 Dusling, Li, Schenke 1509.07939 un-integrated gluon distribution 1.2 Y=0 2 =0.168 GeV 2 Q 0 Y=4 1 Y=8 Y=12 N o n linear 0.8 Q s r e g i m e of QCD 0.6 0.4 0.2 0 0.1 1 10 parton transverse momentum (k T ) GeV 7

Particle production at high energies Multi-particle production at high energies in Regge Gribov limit (x → 0) Initial configuration Particle production : • t-channel exchange of ladder JIMWLK evolution like emissions of gluons, • Strong color fields, weak 3 dN/d p coupling, high occupation of gluonic states f(k) ~ A 2 ~1/g 2 8

Particle production at high energies Multi-particle production at high energies in Regge Gribov limit (x → 0) Initial configuration Particle production : • t-channel exchange of ladder JIMWLK evolution like emissions of gluons, • Strong color fields, weak Single gluon emission coupling, high occupancy of gluonic states ~1/g 2 A (classical field) (classical approximation) McLerran, Venugopalan hep-ph/9309289 Color Glass condensate effective field theory → ab-inito framework to this problem 9

Details of CGC the framework h i h ρρ i B • Fundamental objects are Color h ρρ i A Charge density matrices ρ a(x ⊥ , Y) Local Gaussian distribution W[ ρ ] (MV-Model) classical color charge = δ ab δ 2 ( x ⊥ − y ⊥ ) g 2 µ 2 ( x ⊥ ) ρ a ( x ⊥ ) ρ b ( y ⊥ ) ⌦ ↵ h V † V i B • Color field before collisions : solving h V † V i A Yang Mills equations [D μ ,F μν ] = J ν for each configuration of source ρ (x ⊥ ) classical color field D F = 0 D F = J A after collisions ( τ >0) before collisions ( τ <0) Glasma flux tubes —> Domains of free streaming gluons chromo-electric field hep-ph/9809433, hep-ph/0303076, D F = J D F = J B arXiv: 1206.6805 arXiv: 1202.6646 10

Details of the CGC framework Input is constrained by dipole-cross sections in e+p/A collisions Perturbative approach • Employ k T -factorization (p T >Q s ), dilute-dilute/dense systems Non-perturbative approach • Full solutions of CYM on 2+1D lattice : IP-Glasma Monte-Carlo model of initial conditions 11

Multi-particle productions Single-Inclusive M ⇠ ρ 1 ( k ⊥ ) ρ 2 ( p ⊥ � k ⊥ ) ( p ⊥ � k ⊥ ) 2 L γ ( p , k ⊥ ) k ⊥ 2 D E dN |M| 2 ↵ ⌦ ⇠ h ρ ∗ 1 ρ 1 ρ ∗ on ⇠ 2 ρ 2 i Color Averaging dy p d 2 p ⊥ Double-Inclusive ⌧ � ⌧ � ⌧ � dN 2 dN dN C 2 ( p , q ) ≡ − q dy p d 2 p ⊥ dy q d 2 q ⊥ dy p d 2 p ⊥ dy q d 2 q ⊥ ↓ ↓ p connected disconnected ⊥ � ⊥ ⊥ ⊥ q |M| 2 ↵ p ⌦ ! h ρ ∗ 2 ρ 2 ρ 2 i ) 1 ρ ∗ 1 ρ 1 ρ 1 ρ ∗ 2 ρ ∗ ⌦ ↵ 8 topologies 1 topology Dumitru, Gelis, McLerran, It can be shown Venugopalan 0804.3858 12

n-particle correlations CGC framework is extendable to n-particle correlations 1 ... q ... 2 ... q ... p p p p p p p p p p q q 1 1 2 1 2 n (n-1)! topologies Naturally generates Negative Binomial distribution probability distribution n n k k Γ ( k + n ) ¯ 2 − 1) Q s 2 S ⊥ k = κ ( N c NB = P n n + k ) n + k Γ ( k ) Γ ( n + 1) (¯ 2 π High-multiplicity events —> originate from correlated production of n-particles —> Highly non-perturbative Gelis, Lappi, McLerran 0905.3234 13

Description of Multiplicity distribution/ high multiplicity events IP-Glasma model : combines CGC framework & different sources of initial state fluctuations 1. Collision geometry and impact parameter 2. Color charge 3. Rare Fock-Space configurations 14

(I) Fluctuation of collision geometry • Collision geometry is not calculable from first principle • Eikonal model with thickness profile from HERA data Proton profile Schenke, Tribedy, Venugopalan 1311.3636 ✓ � s ⊥ 2 1 ◆ T p ( s ⊥ ) = exp Impact parameter distribution 2 π B G 2 B G Z 1 � e − σ gg N 2 g T pp ( b ) Overlap function dP d 2 b ( b ) = g T pp ( b ) ⌘ , ⇣ Z 1 � e − σ gg N 2 R d 2 b d 2 s ⊥ T A p ( s ⊥ ) T B T pp ( b ) = p ( s ⊥ � b ⊥ ) . Making Nucleus out of proton scattering A p S i Y S p S A dip ( r ⊥ , x , b ⊥ ) = dip ( r ⊥ , x , b ⊥ ) i =0 ) Nuclear saturation scale : Q 2 sA ⇠ A 1 / 3 Q 2 sp color charge distribution in nucleus 15

(II) Fluctuation of color charge For a given geometry fluctuations of color charge —> Negative Binomial distribution at each impact parameter 10 1 IP-Glasma CMS p+p 7 TeV 0<b<0.5 fm 10 0 0.5<b<1.0 fm p+p 7 TeV, = 0.48 fm IP-Glasma τ 3 P(N ch / 〈 N ch 〉 ) 10 1.0<b<1.5 fm 1.5<b<2.0 fm 10 -1 Entries Entries Entries 0 0 2 10 10 -2 10 -3 10 10 -4 0 2 4 6 8 10 N ch / 〈 N ch 〉 0 5 10 15 20 dN /dy g Convolution of many NBDs However the distribution is not wide enough to describe data Some sources of fluctuation missing 16

(III) Intrinsic fluctuations of saturation scale Input to CGC framework —> dipole cross section e+p/A Color dipole picture : distribution of partons —> dist. of color dipoles Iancu, Mueller, Munier z * γ (hep-ph/0410018) T T T T T T T T r r r r q i i i i 1 1 1 1 r 2 2 2 2 Golec-Biernat, Wustho ff α α α α q hep-ph/9807513 s 1-z dipole-probe r r r r 2 2 2 2 2 2 2 2 log(r /r ) log(r /r ) log(r /r ) log(r /r ) i i i i 0 0 0 0 target saturation saturation saturation saturation 2 2 2 2 α α α α 2 2 2 2 2 2 2 2 log(r /r ) log(r /r ) log(r /r ) log(r /r ) 0 0 0 0 dipoles dipoles dipoles dipoles With evolution of rapidity each dipole split with probability ~ α s dY —> dipole splitting is however stochastic Stochastic dipole splitting —> not present in BK/JIMWLK —>beyond CGC 17

Intrinsic fluctuations of saturation momentum of a proton/nuclei Dipole amplitude Saturation scale 10 1 1 σ =0.4 Y=8 10 0 σ =0.5 Y=0 0.8 P(Q S / 〈 Q S 〉 ) 10 -1 0.6 T(r,Y) 10 -2 0.4 10 -3 0.2 10 -4 0 0 0.5 1 1.5 2 2.5 3 0.1 1 10 2 /r 2 ) Q S / 〈 Q S 〉 log(r 0 Marquet, Soyez, Xiao hep-ph/0606233 Stochastic splitting of dipole leads to a distribution of Qs � ln 2 ( Q 2 S ( s ⊥ ) / h Q 2 ✓ S ( s ⊥ ) i ) ◆ 1 P (ln( Q 2 S / h Q 2 σ 2 ( Y ) = σ 2 0 ( Y 0 ) + σ 2 S i )) = p exp 1 ( Y � Y 0 ) , 2 σ 2 2 πσ 18

Distribution of multiplicity McLerran, Tribedy 1508.03292 pp@LHC pp@RHIC 10 1 10 1 UA5 p+p 200 GeV CMS p+p 7 TeV 10 0 10 0 IP-Glasma σ =0.4 IP-Glasma σ =0 P(N ch / 〈 N ch 〉 ) P(N ch / 〈 N ch 〉 ) IP-Glasma σ =0.5 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 0 2 4 6 8 10 0 2 4 6 8 10 N ch / 〈 N ch 〉 N ch / 〈 N ch 〉 Origin of High multiplicity events (Tail of distributions) High multiplicity events —> rare configuration of high color charge density (1/g 2 ) 19

Azimuthal Correlations in CGC • Intrinsic momentum space correlation from initial state ~ E • Originate probe scattering ∼ Q − 1 s off a color domain • Suppressed by number of Dumitru, Dusling, Gelis, Jalilian-Marian, color sources/domains . Lappi, Venugopalan 1009.5295 Kovner, Lublinsky 1012.3398 Dusling, Venugopalan 1201.2658 Kovchegov, Wertepny 1212.1195 Dumitru, Giannini 1406.5781 Lappi, Schenke, Schlichting, Venugopalan 1509.03499 Very distinct from Hydrodynamic flow (driven by geometry ) 20