PROBING GLUON SATURATION THROUGH DI-HADRON AND TRI-HADRON - PowerPoint PPT Presentation

PROBING GLUON SATURATION THROUGH DI-HADRON AND TRI-HADRON CORRELATIONS AT A FUTURE ELECTRON ION COLLIDER MARTIN HENTSCHINSKI martin.hentschinski@gmail.com IN COLLABORATION WITH A. AYALA, J. JALILIAN-MARIAN, M.E. TEJEDA YEOMANS, XV MEXICAN WORKSHOP ON PARTICLES AND FIELDS (02.-06. NOV. 2015)


 
 
 
 DIS AT HERA: PARTON DISTRIBUTION FUNCTIONS k' HERA collider (92-07): Deep Inelastic Scattering (DIS) of 
 k of electrons on protons q Photon virtuality Q 2 = − q 2 p X H1 and ZEUS 1 xf 2 2 = 10 GeV µ f observation: gluon g(x) and sea-quark s(x) • HERAPDF2.0 NLO 0.8 uncertainties: parton distribution functions grow like experimental model xu v powers for x → 0 with x=Q 2 /2p ･ q ∈ [0,1] parameterisation HERAPDF2.0AG NLO 0.6 parton distribution functions f(x): probability • xg ( 0.05) xd 0.4 × v to find a quark, gluon with proton momentum fraction x in proton 0.2 xS ( 0.05) × power like growth 
 • → integral over x does not convergent at x=0 
 -4 -3 -2 -1 10 10 10 10 1 → invalidates probability interpretation 
 x at some x, new QCD dynamics must set in

Open Questions The proton at high energies: saturation theory considerations: I e ff ective finite size 1 /Q of Q 2 s (Y) s a t u r a t i o n Geometric partons at finite Q 2 r e g i o n Scaling I at some x ⌧ 1 , partons non-perturbative region ‘overlap’ = recominbation Y = ln 1/x BK/JIMWLK e ff ects I turning it around: system is characterized by saturation BFKL scale Q s DGLAP I grows with energy Q s ⇠ x − ∆ , ∆ > 0 & can reach in Λ 2 ln Q 2 principle perturbative values QCD α s ~ 1 α s < < 1 Q s > 1 GeV

THEORY PREDICTIONS FOR HIGH & SATURATED GLUON DENSITIES k' x =Q 2 /2p ･ q → 0 limit corresponds to perturbative 
 k high energy limit 2p ･ q → ∞ for fixed resolution Q 2 q make use of factorisation of cross-sections in the 
 p X • high energy limit allows to resum interaction of quarks & gluons with strong gluon field to all • orders in the strong coupling → resummation of finite density effects DIS X-sec. as convolution of “photon wave function” (process-dependent) and • “color dipole factor” 
 1 (universal, resums ln1/x) 2 Z Z � � � ψ ( f ) σ γ ∗ A L,T ( x, Q 2 ) = 2 X d 2 b d 2 r L,T ( r, z ; Q 2 ) N ( x, r , b ) dz � � � f gluon densities multiple scatterings 0 in Hentschinski (ICN-UNAM) The glue that binds us all November 3, 2015 physical picture: virtual photon 
 • γ ∗ splits into color dipole (quark- 
 γ ∗ → antiquark pair) which 
 interacts with Lorentz contracted 
 ≡ ≡ target field 
 x → 0 : a single interaction with a strong & Lorentz A + ,a ( z − , z ) = ↵ a ( z ) � ( z − ) contracted gluon field 4 φ φ Δ Δ Δ φ Δ φ

PROPAGATORS IN THE PRESENCE OF A STRONG BACKGROUND FIELD use light-cone gauge, with k - =n - ･ k, (n - ) 2 =0, n - ~ target momentum ip � + m µ ν ( p ) = id µ ν ( p ) S (0) ˜ ˜ G (0) F ( p ) = p 2 − m 2 + i 0 p 2 + i 0 S (0) S (0) p q S (0) p q = (2 π ) d δ ( d ) ( p − q ) ˜ F ( p ) + ˜ ˜ F ( p ) F ( q ) d µ ν ( p ) = − g µ ν + n − µ p ν + p µ n − ν n − · p p q p, µ q, ν = (2 π ) d δ ( d ) ( p − q ) ˜ G (0) µ ν ( p ) + ˜ G (0) G (0) ˜ µ α ( p ) αν ( q ) [Balitsky, Belitsky; NPB 629 (2002) 290], [Ayala, Jalilian-Marian, McLerran, Venugopalan, PRD 52 (1995) 2935-2943], … interaction with the background field: Z ∞ dx − A + ,c ( x − , z ) t c V ( z ) ≡ V ij ( z ) ≡ P exp ig −∞ Z Z ∞ p q d d − 2 z e − i z · ( p − q ) = 2 ⇡� ( p − − q − ) n � − dx − A + ,c ( x − , z ) T c U ( z ) ≡ U ab ( z ) ≡ P exp ig −∞ n o ✓ ( p − )[ V ( z ) − 1] − ✓ ( − p − )[ V † ( z ) − 1] · strong background field resummed into path ordered exponentials p q Z d d − 2 z e − i z · ( p − q ) = − 2 ⇡� ( p − − q − )2 p − (Wilson lines) n o ✓ ( p − )[ U ( z ) − 1] − ✓ ( − p − )[ U † ( z ) − 1] ·


 PHENOMENOLOGY: DIS AT HERA 1 2 Z Z γ ∗ � � � ψ ( f ) σ γ ∗ A L,T ( x, Q 2 ) = 2 X d 2 b d 2 r L,T ( r, z ; Q 2 ) N ( x, r , b ) dz � � � f 0 in Hentschinski (ICN-UNAM) The glue that binds us all November 3, 2015 DIS cross-section as convolution of • 2 2 2 2 Q =0.85 GeV Data Q =2.0 GeV 1.5 Theory photon wave function and dipole 1 ! r 0.5 density 5 3 5 3 2 2 2 2 Q =4.5 GeV Q =8.5 GeV 1.5 color dipole follows non-linear • 1 ! JIMWLK or BK evolution equation in r 0.5 ln(1/x) 
 2 2 2 2 Q =12.0 GeV Q =10.0 GeV 1.5 splitting recombination 1 ! r 0.5 2 2 2 2 Q =15.0 GeV Q =28.0 GeV 1.5 fixing initial conditions through fit • 1 allows description of combined ! r 0.5 HERA data, but also (dilute!) DGLAP 5 3 5 3 2 2 2 2 Q =35 GeV Q =45 GeV 1.5 describes data 1 ! r 0.5 saturation at the edge Q s ~1-2GeV 2 • − 5 − 4 − 3 − 2 − 4 − 3 − 2 10 10 10 10 10 10 10 x x [Albacete, Armesto, Milhano,Quiroga, Salgado,EPJ C71 (2011) 1705] 6

PHENOMENOLOGY IN COLLISIONS WITH HEAVY NUCLEI instead of going to higher energies (expensive), COLOR GLASS CONDENSATE (CGC)= possible to study large nuclei …. BUZZWORD WHICH REFERS TO THE PHYSICS Saturation: high densities in the fast nucleus OF SATURATION AND IN PARTICULAR THE DEVELOPED THEORY Expect those e ff ects to Boost be even more enhanced in boosted nuclei: s ∼ # gluons/unit transverse area ∼ A 1 / 3 Q 2 d-Au collisions at RHIC: depletion of away side peak in central collisions described by CGC many more studies at RHIC, LHC in pp, pA, AA collisions plethora of interesting phenomena, but also subject to large theory uncertainties due to uncontrolled re- scatterings → no ultimate proof 7

A COLLIDER TO SEARCH FOR A DEFINITE ANSWER: THE ELECTRON ION COLLIDER PROJECT the world’s first eA collider: will allow to probe heavy nuclei at small x (using 16GeV electrons on 100GeV/u ions) Brookhaven National Laboratory: Jefferson Lab: supplement CEBAF supplement RHIC with Electron with hadron accelerator (MEIC) Recovery Linac (eRHIC) 2015: ENDORSED BY NUCLEAR SCIENCE ADVISORY COMMITTEE (NSAC) AS HIGHEST PRIORITY FOR NEW FACILITY CONSTRUCTION IN US NUCLEAR SCIENCE LONG RANGE PLAN


 AN EIC OBSERVABLE TO SEARCH FOR SATURATION EFFECTS: 
 DI-HADRON DE-CORRELATION IN DIS measure azimuthal angle of di- γ ∗ ~ 1/k T hadron final state 2 ) k T φ (x, k T max. density collinear factorization (dilute pQCD): gluon kT peaked at kT=0 - expect dihadrons back-to-back 
 know how to ? do physics here Q s α s ∼ 1 Λ QCD α s < < 1 Saturation (CGC): gluon kT peaked at saturation k T scale - expect de-correlated di-hadrons 0.25 20 GeV on 100 GeV 20 GeV on 100 GeV trig > 2 GeV/c p T 0.4 assoc < p T trig 1 GeV/c < p T 2 2 0.2 Q =1 GeV , y=0.7 trig , z h assoc < 0.4 0.2 < z h 1 < Q 2 < 2 GeV 2 ep e+Au - no-sat 0.6 < y < 0.8 0.3 0.15 eAu - sat ) ) φ φ eCa Δ Δ C( C( 0.2 0.1 eAu 0.1 0.05 0 0 2 2.5 3 3.5 4 4.5 2 2.5 3 3.5 4 4.5 (rad) (rad) Δ φ Δ φ


 
 
 
 PRECISION EXPERIMENTS REQUIRE THEORY PRECISION • current studies: LO accuracy + Sudakov resummation of soft logarithms 
 0.45 expect also (large?) collinear logs 
 10 GeV x 100 GeV 0.4 ep, No Sudakov + scale setting uncertainties 2 2 Q = 1 GeV eAu, No Sudakov 0.35 ep, With Sudakov 0.3 eAu, With Sudakov ) 0.25 φ → higher order correction can 
 ∆ C( 0.2 lead to large effects 
 0.15 0.1 0.05 0 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 [rad] ∆ φ [Zheng,Aschenauer, Lee, Xiao, PRD89 (2014)7, 074037] evolution of dipole etc. densities & higher [Balitsky, Chirilli; PRD 88 (2013) 111501, PRD 77 (2008) 014019]; [Kovner,Lublinsky, Mulian; PRD 89 (2014) 6, 061704] correlators know up to NLO [Iancu, Madrigal, Mueller, Soyez, Triantafyllopoulos; PLB 744 (2015) 293] instabilities get addressed photon wave function: only inclusive 
 [Balitsky, Chirilli; PRD 87 (2013) 1, 014013], [Beuf; PRD 85 (2012) 034039] (on the level of correlation functions)


 
 
 
 PRECISION EXPERIMENTS REQUIRE THEORY PRECISION • current studies: LO accuracy + Sudakov resummation of soft logarithms 
 0.45 expect also (large?) collinear logs 
 10 GeV x 100 GeV 0.4 ep, No Sudakov + scale setting uncertainties 2 2 Q = 1 GeV eAu, No Sudakov 0.35 ep, With Sudakov 0.3 eAu, With Sudakov ) 0.25 φ → higher order correction can 
 ∆ C( 0.2 lead to large effects 
 0.15 0.1 0.05 0 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 [rad] ∆ φ [Zheng,Aschenauer, Lee, Xiao, PRD89 (2014)7, 074037] our project: calculate (NEW: NLO from momentum space) A. tri-hadron production at LO (new observable!) 
 expect more stringent tests of CGC through more complex final state B. di-hadron production at NLO (3 partons a subset!) 
 reduce uncertainties + possibly identify overlap region between collinear factorisation and saturation physics