QCD Factorization Approach to Cold Nuclear Matter Effect

Physics Division Seminar April 25, 2016 Mini-symposium on Cold Nuclear Matter from Fixed-Target Energies to the LHC SCGP: Small Auditorium Rm 102, October 9-10, 2016 QCD Factorization Approach to Cold Nuclear Matter Effect Jianwei Qiu Theory Center, Jefferson Lab Based on work done in collaboration with E.L. Berger, K.J. Eskola, X. Guo, Z.-B. Kang, M. Luo, A.H. Mueller, G. Sterman, I. Vitev, X.-N. Wang, H. Xing, X. Zhang,

A long history, Cronin effect - 1975 Process: h + A E d ha d 3 p particle(p)+x E d hn d 3 p A (p) Cronin et al., Phys. Rev. D11, 3105

A long history, Cronin effect - 1975 Nuclear Shadowing -1981 Process: h + A E d ha d 3 p particle(p)+x E d hn d 3 p A (p) Cronin et al., Phys. Rev. D11, 3105 Process: (q)+a X Goodman et al., Phys. Rev. D47, 293

Cronin effect - 1975 A long history, Nuclear Shadowing -1981 EMC Effect 1983 Process: h + A E d ha d 3 p particle(p)+x E d hn d 3 p A (p) Cronin et al., Phys. Rev. D11, 3105 Process: (q)+a X Goodman et al., Phys. Rev. D47, 293 Process: (l)+a(p A ) (l )+X Aubert et al., Phys. Lett. B123, 275

A long history, PT Broadening, Process: Johnson et al, PRC 2007

A long history, PT Broadening, Energy loss, Process: Johnson et al, PRC 2007 Process: ` + A! `0 + h + X R h A h A/(A h N ) z = p h / W. Brooks, EICAC,

PT Broadening, A long history, Energy loss, J/ψ suppression, X 2 scaling? Process: Johnson et al, PRC 2007 Process: ` + A! `0 + h + X R h A h A/(A h N ) z = p h / W. Brooks, EICAC, Process: p + A! J/ + X J/ pa J/ pn A + LHC data, R. Vogt, QWG2016,

The rest of my talk, q Cold nuclear matter: nucleons and nuclei q Why we need QCD factorization approach? q How QCD factorization quantify cold nuclear effect? q Progresses in last many years examples q NLO calculation is necessary, q Summary and outlook

Nucleon, nuclei, cold nuclear matter, q QCD landscape of nucleon and nuclei? Color Confinement Asymptotic freedom 200 MeV (1 fm) 2 GeV (1/10 fm) Q (GeV) Probing momentum q In a gas target: ² Nucleons have a large empty space between them ² Effectively, they are quantum mechanically incoherent for the short-range strong interaction, and are free nucleons q In a nuclear target: ² Nucleons are very close to each other rescattering ² Nature of nuclear force, if we only see quarks and gluons? ² Hard probe is not necessarily local coherence at small-x q Magic of heavy ion beams not to be discussed here

How to see quarks and gluons inside hadrons? q High energy probes see the boosted partonic structure: Hard probe (t ~ 1/Q < fm): ² Longitudinal momentum fraction x : ² Transverse momentum confined motion: Boost = time dilation Catches the quantum fluctuation! xp Q 1/R QCD Q q Challenge: No modern detector can see quarks and gluons in isolation! q Question: How to quantify the partonic structure if we cannot see quarks and gluons? We need the probe! q Answer: QCD factorization! Not exact, but, controllable approximation! P, P, A,...

QCD Factorization: connecting parton to hadron q One hadron: e p σ DIS tot 1 + O QR Hard-part Probe Parton-distribution Structure Power corrections Approximation q Two hadrons: σ DY tot s 1 + O QR q Predictive power: Universal Parton Distributions Controlable corrections,

Nuclear effect within leading power factorization q QCD factorization at Leading Power: σ DIS tot + O QR DIS ea (x B,Q; A) X A 1/3 ˆef (x B /x, Q/µ) f/a (x, µ)+o (QR) 2 f DY ea (y, Q; A) X A ˆff 0(y, 1/3,B 1/3 Q; x 1,x 2,µ) f/a (x 1,µ) f 0 /B(x 2,µ)+O (QR) 2 f,f 0 ² Partonic hard parts - ˆ0s are independent of the hadron type! ² At LP, only cold nuclear effect are in npdfs, including EMC effect, anti- and shadowing, ² QCD global analyses of nuclear data to extract npdfs, or model calculations catch some features and helpful, 1

Gluon distribution at small-x q Run away gluon density at small x? q QCD vs. QED: QCD gluon in a proton: Q 2 QED photon in a positronium: Q 2 d dq 2 xg(x, Q2 ) sn c d dq 2 x + Z 1 x (x, Q2 ) em Z 1 apple 2 3 x (x, Q2 ) dx 0 x 0 x0 [ e +(x0,q 2 )+ e (x 0,Q 2 )] x What causes the low-x rise? gluon radiation non-linear gluon interaction What tames the low-x rise? gluon recombination non-linear gluon interaction power suppressed by (Q s /Q) n dx 0 x 0 x0 G(x 0,Q 2 ) ² At very small-x, proton is black, positronium is still transparent! ² Recombination of large numbers of glue could lead to saturation phenomena In the dipole model: @N(x, k 2 ) @ ln(1/x) = s K BFKL N(x, k 2 ) s N(x, k 2 ) 2 BK Equ.

Gluon distribution at small-x q Run away gluon density at small x? What causes the low-x rise? gluon radiation non-linear gluon interaction What tames the low-x rise? gluon recombination non-linear gluon interaction power suppressed by (Q s /Q) n q Particle vs. wave feature: Gluon saturation Color Glass Condensate Radiation = Recombination & '! ()* 21"& ' 9 pqcd evolution equation! "##""$ = at Q s Leading to a collective gluonic system?!+,-.+,/01 with a universal property of QCD? 101345.,-.6+,/75".58/01 21")! "%"$ new effective theory QCD CGC?

Multiple scattering and power corrections q Coherent multiple scattering ( dσ dσ S ) D + dσ ( ) +... ² Naïve power counting: ( dσ D ) ( ) dσ S α s 1 Q 2 R 2 F +α + F α A 1/3 ² Medium parton density: ² For a hard probe: ² Nuclear size enhancement: ² Small x enhancement: F +α F α + α s Q 2 R 2 1 A 1/3 6 x ϕ ( x )

QCD factorization for power corrections q Inclusive DIS single hadron state: As the consequence of the OPE, QCD factorization is valid to all powers: h σ phys = ˆσ 2 i [1+C (1,2) α s +C (2,2) α s 2 +...] T 2 i/h (x) + ˆσ i 4 Q [1+C (1,4) α 2 s +C (2,4) α 2 s +...] T i/h 4 (x) + +... ˆσ 6 i q Predictive power: Q [1+C (1,6) α 4 s +C (2,6) α 2 s +...] T i/h 6 (x) Power corrections Leading twist ² Coefficient functions are UV&IR safe, independent of the nuclei ² High twist correlations/matrix elements are defined to remove all perturbative collinear divergences of the partonic cross sections ² High twist corrections are fundamental, nonperturbative, and universal extracted from date or from model calculations

Tree-level power corrections to DIS on nuclei q Hard probe - Large momentum transfer: q µ with Q q 2 Λ QCD q It could see multiple Lorentz contracted nucleons : 1 Q 1 xp 2R! m $ # & or equivalently x x " p c 1 % 2mR 0.1 + + The probe could interact with partons from multiple nucleon coherently q To take care of the coherence, we need to sum over all cuts for a given forward scattering amplitude Scatterings Cuts Collinear factorized correlation functions are independent of the cut!!!

Tree-level power corrections to DIS on nuclei q Collinear factorization approximation: Scatterings Cuts q Model approximation: Cuts i A i i ( yi ) + ixi p yi + dy e P F P ² No net color exchange between the bound nucleons inside nuclei ² Nuclear state is a direct product of nucleon states: P A i/ p 1 i p 2 i... p A i ² Only diagonal matrix elements contribute to nuclear matrix element: N N P A Ô 0 Ô i P A A p Ô0 p p Ôi p P A p with p = P A i=1 i=1 i=1 A Z ² Integration of partonic momenta, dx i, fixed by unpinched poles of the scattering diagrams A A

Tree-level power corrections to DIS on nuclei q LO contribution to DIS cross section: q NLO contribution: q Nth order contribution: Infrared safe!

Tree-level power corrections to DIS on nuclei q Transverse structure function: +Δx Single parameter for the power correction, and is proportional to the same characteristic scale Suppression of cross section if small-x coherent interaction if relevant! q Similar result for longitudinal structure function

Neglect LT shadowing upper limit of ξ 2 2 2 ξ : 0.09-0.12 GeV Message: One number for all x B, Q, and A dependence!

QCD factorization for hadron-hadron collisions q Soft-gluon interactions take place all the time: q Soft-gluon interactions are powerly suppressed q NO factorization beyond 1/Q 2 term! Good for double scattering Drell-Yan Doria, et al (1980) Basu et al. (1984) Brandt, et al (1989)

Nuclear size enhanced power corrections q A-enhanced power corrections, A 1/3 /Q 2, may be factorizable: No A 1/3 -enhancement + + + + ² Collinear power expansion single hard scale cases: Multi-parton matrix elements independent of the cut! ² TMD factorization two scale observables: Matrix elements of multi-partons with kt sensitive to the cut

Transverse momentum broadening Vector boson: γ*, W, Z, J/ψ, Only Initial-state effect for DY Both initial- and final-effects for J/ψ Cronin effect Use heavy quarkonium as an example

Quarkonium pt distribution q Quarkonium production is dominated by low p T region q Low p T distribution at collider energies: determined mainly by gluon shower of incoming partons initial-state effect Qiu, Zhang, PRL, 2001 q Final-state interactions suppress the formation of J/ψ: Also modify the p T spectrum move low pt to high pt broadening Final-state effect q Broadening: ² Sensitive to the medium properties ² Perturbatively calculable q R pa at low q T : 1+ Guo, Qiu, Zhang, PRL, PRD 2002 hq 2 T i A 1/3 hq 2 T i hn apple 1+ q2 T hq 2 T i hn

A-dependence in P T in p(d)+a q Ratio of x-sections: Guo, Qiu, Zhang, PRL, PRD 2002 Similar formula for J/ψ q Spectrum and ratio: E772 data

Quarkonium P T -broadening in p(d)+a q Initial-state only: Kang, Qiu, PRD77(2008) q Experimental data from d+a: Clear A 1/3 dependence But, wrong normalization! Final-state effect octet channel dominated! Only depend on observed quarkonia J.C.Peng, hep-ph/9912371 Johnson,et al, 2007

Final-state multiple scattering q Heavy quarkonium is unlikely to be formed when the heavy quark pair was produced Kang, Qiu, PRD77(2008) ² If the formation length: no A-enhancement from final-state interaction ² If the formation length: additional A 1/3 -type enhancement from the final-state interaction q Final-state effect depends on how quarkonium is formed NRQCD model, color evaporation model,

q Broadening: Quarkonium P T -broadening in p(d)+a hqt 2 i (I) 8 2 s J/ = C A Nc 2 1 (A1/3 1) 2 hq 2 T i (F ) J/ Kang, Qiu, PRD77(2008) Calculated in both NRQCD and CEM 2 = apple ln(q) x / ˆq, apple =3.51 10 3 1/GeV 2, =1.71 10 1 J.C.Peng, hep-ph/9912371

Quarkonium P T -distribution in p(d)+a q Nuclear modification low pt region: d AB dyd 2 p T d AB dy apple 1 (hp 2 T i NN + hp 2 T i AB) e p 2 T /(hp2 T i NN+ hp 2 T i AB) E772 data ALICE data

NLO contribution to the broadening q Drell-Yan broadening: Z.B. Kang, J.W. Qiu, X.N. Wang, H. Xing, 2016 PRD q LO calculation: q NLO contribution: X. Guo, 1998 R.J. Fries, 2013 IR safe & Well-behaved

Summary q QCD factorization provides the necessary connection between QCD partonic dynamics and the measured hadronic cross sections q In terms of QCD factorization approach, cold nuclear effects are organized into two types: ² A-dependence of npdfs, and ² A-dependence of multiple scattering in nuclei q QCD multiple scattering is closely connected to the power corrections in QCD factorization approach q QCD factorization could, in general, be valid ONLY for the FIRST power corrections in hadronic collisions q However, nuclear sized enhanced power corrections in p+a collisions could be valid beyond the FIRST power corrections q QCD factorization for power corrections is verified at NLO for DY! Thank you!

Backup slides

Color evaporation model q Double scattering A 1/3 dependence: q Multiparton correlation: q Broadening twice of initial-state effect: if gluon-gluon dominates, and if r F > R A

NRQCD model q Cross section: q Broadening: Hard parts: Only color octet channel contributes q Leading features:

Big questions to be answered, q Emergence of a hadron? = Q2 2mx Control of ν and medium length! D 0 q Heavy quark energy loss: - Mass dependence of fragmentation π pion D 0 Need the collider energy of EIC and its control on parton kinematics