Towards 3 particle correlations in the Color Glass Condensate - PowerPoint PPT Presentation

Towards 3 particle correlations in the Color Glass Condensate framework Martin Hentschinski martin.hentschinski@gmail.com IN COLLABORATION WITH A. Ayala, J. Jalilian-Marian, M.E. Tejeda Yeomans, QCD Challenges at the LHC: from pp to AA (Taxco, 18.-22. Jan. 2016)


 
 DIS at HERA: parton Distribution functions HERA collider (92-07): Deep Inelastic Scattering (DIS) of 
 k' of electrons on protons H1 and ZEUS k 1 xf Photon virtuality q 2 2 = 10 GeV µ Q 2 = − q 2 f HERAPDF2.0 NLO p X Q 2 0.8 uncertainties: Bjorken x = experimental 2 p · q model xu v parameterisation HERAPDF2.0AG NLO 0.6 gluon g(x) and sea-quark S(x) distribution like powers ~ x - λ for xg ( 0.05) xd x → 0 0.4 × v → invalidates probability 0.2 xS ( 0.05) × interpretation if continued forever (integral over x diverges) 
 -3 -4 -2 -1 10 10 10 10 1 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

High gluon densities & heavy ions Saturation: high densities in the fast nucleus Expect those e ff ects to Boost be even more enhanced in boosted nuclei: pocket formula: 
 x eff (A)= x Bjorken /A s ∼ # gluons/unit transverse area ∼ A 1 / 3 Q 2 Believed: heavy ion collisions at RHIC, LHC • = collisions of two Color Glass Condensate but what are the correct initial conditions? •

CGC and long-range rapidity correlations in high multiplicity events d 2 N d 2 N 1 1 Jet Graph N Trig d ∆ φ N Trig d ∆ η d ∆ φ pp s = 7 TeV, N 110 CMS Preliminary ≥ trig 2<p <3 GeV/c p T assoc 1<p <2 GeV/c T q Glasma Graph φ 1.40 1.40 pair ∆ d N η 1.35 1.35 p 2 ∆ d d 1.30 1.30 trg q 1 N 4 4 4 2 2 2 ∆ ∆ 0 φ φ η 0 0 ∆ -2 -2 -4 -4 ∆ φ π • high multiplicities → screening of color charges introduces → saturation scale • high & saturated gluon densities (HERA fit with modified initial saturation scale, higher correlators from “Gaussian/dilute approximation”) • take limit p T /Q S ≪ 1, 2 contributions: “glasma” and “jet” graph 
 AA: glasma dominates, pp, pA also jet graph ( 𝞫 S suppressed)

CGC & Ridges [Dusling, Venugopalan, Phys.Rev. D87 (2013) 9, 094034; 5, 051502] 0.08 0.90 jet+glasma ALICE Data ATLAS Central offline < 110 0.07 90 < N trk Pb = 12-14 Q 2 0, proton =0.336 GeV 2 ; N Part CMS Data ATLAS Peripheral 0.88 1.0 < p T < 2.0 GeV 0.06 trig < 4 GeV; 1 < p T asc < 2 GeV 0.86 2 < p T trig < 2.0 GeV; 1.0 < p T asc < 2.0 GeV pPb - data 1.0 < p T 0.05 0.04 0.84 0.03 0.82 0.02 0.80 0.01 0 0.78 -0.01 π − π π π 0 0 0 0 0.5 1 1.5 2 2.5 3 -1 0 1 2 3 4 0 0.5 1 1.5 2 2.5 3 ∆ φ ∆ φ ∆φ ∆ φ ∆φ 0.09 0.12 BFKL + glasma Q 2 s0 = 1.008 GeV 2 BFKL Q 2 s0 = 1.008 GeV 2 0.08 BFKL + glasma Q 2 s0 = 0.840 GeV 2 BFKL Q 2 s0 = 0.840 GeV 2 0.1 0.07 BFKL + glasma Q 2 s0 = 0.672 GeV 2 glasma graphs Q 2 s0 = 1.008 GeV 2 CMS: N trk >110, 1 GeV < p T a,b < 2 GeV glasma graphs Q 2 s0 = 0.840 GeV 2 0.08 0.06 pp - data p+p s 1/2 = 7 TeV 0.05 d 2 N/d ∆φ d 2 N/d ∆φ 0.06 0.04 0.04 0.03 0.02 0.02 0.01 0 0 -0.01 -0.02 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 ∆φ ∆φ Fig. 33. Long range (2 ≤ ∆ η ≤ 4) per-trigger yield of charged hadrons as a function of ∆ φ for p-p collisions at √ s = 7 TeV. Data points are from the CMS collaboration. The curves show the 0 ( x = 10 − 2 ) = 0 . 840 GeV 2 and Q 2 results for Q 2 0 ( x = 10 − 2 ) = 1 . 008 GeV 2 . works rather good, some say too good …

What do we know really about saturated gluons? — DIS on a proton at HERA factorisation into photon wave function 𝜔 ] ⟩ ( ɣ * → qqbar) & color dipole 𝓞 (~dense gluon field) 2 2 2 2 Data Q =0.85 GeV Q =2.0 GeV 1.5 Theory 1 ! r 1 0.5 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 � � 5 3 5 3 2 2 2 2 Q =4.5 GeV Q =8.5 GeV 1.5 � f 0 1 in Hentschinski (ICN-UNAM) The glue that binds us all November 3, 2015 ! r 0.5 color dipole 𝓞 : all information about 2 2 2 2 Q =12.0 GeV Q =10.0 GeV 1.5 1 gluon distribution + follows non-linear ! r 0.5 evolution in ln(1/x) [JIMWLK or BK] 2 2 2 2 Q =15.0 GeV Q =28.0 GeV 1.5 1 splitting recombination ! r 0.5 5 3 5 3 2 2 2 2 Q =35 GeV Q =45 GeV 1.5 1 ! r 0.5 − 5 − 3 − 3 − 4 − 2 − 4 − 2 achieve a good description of 10 10 10 10 10 10 10 x x combined (= high precision!) [Albacete, Armesto, Milhano,Quiroga, Salgado, EPJ C71 (2011) 1705] HERA data through rcBK fit

But … data also described by pdf-fits (=DGLAP) — intrinsically Q 2 s (x) dilute (virtual photon interacts with single α s < < 1 geometric scaling quark, gluon) 
 DGLAP ln Q 2 JIMWLK 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 BK BFKL Q ² = 1.2 GeV ² Q ² = 1.5 GeV ² Q ² = 2.0 GeV ² Q ² = 2.7 GeV ² 1.4 1.4 F 2 H x,Q ² L 1.0 1.0 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 0.6 Ê 0.6 Ê Ê Ê Ê Ê ÊÊ Ê Ê Ê Ê Ê Ê Ê saturation Ê Ê Ê Ê 0.2 0.2 Q ² = 3.5 GeV ² Q ² = 4.5 GeV ² Q ² = 6.5 GeV ² Q ² = 8.5 GeV ² α s ~ 1 non-perturbative region 1.4 1.4 Ê Ê Ê Ê F 2 H x,Q ² L Ê Ê Ê 1.0 Ê Ê Ê 1.0 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê ln x Ê Ê Ê Ê Ê Ê Ê Ê 0.6 0.6 Ê Ê Ê Ê Ê 0.2 0.2 Q ² = 10 GeV ² Q ² = 12 GeV ² Q ² = 15 GeV ² Q ² = 18 GeV ² 1.4 Ê 1.4 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê F 2 H x,Q ² L Ê Ê Ê Ê 1.0 1.0 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 0.6 Ê Ê 0.6 0.2 0.2 Q ² = 22 GeV ² Q ² = 27 GeV ² Q ² = 35 GeV ² Q ² = 45 GeV ² Ê Ê Ê Ê Ê 1.4 1.4 Ê Ê Ê Ê Ê Ê … and also (collinear Ê Ê Ê F 2 H x,Q ² L Ê Ê Ê 1.0 Ê Ê 1.0 Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê improved) NLO BFKL evolution 0.6 0.6 0.2 0.2 can fit data 
 Q ² = 70 GeV ² Q ² = 90 GeV ² Q ² = 120 GeV ² Q ² = 60 GeV ² Ê Ê Ê Ê 1.4 1.4 Ê Ê Ê Ê Ê Ê Ê [MH, Salas, Sabio Vera; PRD 87 (2013) 7, 076005] F 2 H x,Q ² L Ê Ê Ê Ê 1.0 1.0 Ê Ê Ê Ê Ê Ê 0.6 0.6 0.2 0.2 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 10 - 4 10 - 3 10 - 2 x x x x

What we know and what we don’t know • extracted saturation scales at HERA not so large (0.75-2 GeV 2 ) + DGLAP fits initial conditions at small Q 2 • description of HERA data by saturation AND DGLAP not really a contradiction, but also not yet definite proof for saturation, cannot claim complete control • can use HERA fits ( e.g. rcBK) in pA , AA , high multiplicity events through scaling of (initial) saturation scale 
 Q s (A) = Q sHERA ・ A 1/3 , but rely on assumptions/arguments • in general: initial conditions not controlled on the level of accuracy as e.g. in pp through conventional pdfs

A collider to search for a definite Answer: the world’s first eA collider: will allow to probe heavy nuclei at small x (using 16GeV electrons on 100GeV/u ions) Jefferson Lab: supplement CEBAF Brookhaven National Laboratory: supplement RHIC with Electron Recovery Linac (eRHIC) with hadron accelerator (MEIC) 2015: endorsed by Nuclear Science Advisory Committee (NSAC) As highest priority for new Facility construction in US Nuclear Science Long Range plan + plans for LHeC etc.


 Tasks for theory… so far: still rely often on models (even though an sophisticated level) such • as IPsat, bCGC → x-dependence = assumption + fit fits with evolution (rcBK): LO BK + running coupling corrections, • coefficients at LO, with a few NLO exceptions ( inclusive DIS, single inclusive jet in pA ) 
 recent progress: • NLO corrections for evolution [Balitsky, Chirilli; PRD 88 (2013) 111501, PRD 77 (2008) 014019]; [Kovner,Lublinsky, Mulian; PRD 89 (2014) 6, 061704] known & studied + resummed & used for first HERA fit [Iancu, Madrigal, Mueller, Soyez, Triantafyllopoulos, PLB750 (2015) 643] missing: 
 → NLO corrections for coefficients of exclusive observables — provide strongest constraints on saturation