Spin physics at Electron-Ion Collider

Transcription

1 Spin physics at Electron-Ion Collider Jianwei Qiu Brookhaven National Laboratory Workshop on The Science Case for an EIC November 16-19, 2010; INT, University of Washington, Seattle, WA

2 Outline of my talk Why we believe QCD? Why we need EIC to study QCD? Spin as a hadron property probe hadron structure Generalized momentum/spatial parton distribution functions Spin as a tool probe direct QCD quantum interference Summary

3 QCD asymptotic freedom: PQCD cannot calculate cross section with identified hadron: Dynamics at hadronic scale cannot be calculated perturbatively! The question: QCD at work QCD is a gauge theory of quarks and gluons: But, we do not see free quarks and gluons confinement QCD is much more richer in dynamics than QED Perturbative QCD works for short-distance infrared safe quantities! Connect the quarks and gluons to the hadrons: PQCD factorization approximation! p, s ψ(0)γψ(y) p, s p, s F +α (0)F α + (y) p, s Why should we believe QCD if we do not see the quarks and gluons?

4 Jets in e + e - : See the trace of quarks and gluons

5 See quarks and gluons inside a hadron Rutherford experiment: Long-lived parton state k 2 << Q 2, k ~ xp Past Now Unitarity summing over all hard jets: Matrix element Future k 2 +O Q 2 d 4 k δ(x k + /P + ) Interaction between the past and now are suppressed! PQCD factorization approximation neglect power corrections!

6 Gauge invariance and universality of PDFs Gauge link QCD phase: + + = Summation of leading power gluon field contribution produces the gauge link: Gauge invariant PDFs: Collinear PDFs: Localized operator with size ~ 1/xp ~ 1/Q localized color flow Universality of PDFs predictive power of pqcd: Gauge link should be process independent!

7 DIS cross section: From HERA single hadron Q 2 2 GeV 2

8 Jet cross section: To Tevatron multiple hadrons With one set universal PDFs QCD is successful in last 30 years we now believe it

9 Are there anything left to do in QCD? QCD is right but, no longer interesting or challenging: became the background for the search of new physics beyond SM no more discovery or Nobel prize level work left? Question: How many Nobel Prizes have been awarded to CMP after QED? QCD is only tested in the most trivial regime of its dynamics! the asymptotic regime: < 1/10 fm (~ 2 GeV) Leading power dynamics from single parton-parton scattering New measurements and new questions: Hints in disagreement when extrapolating to Q < 1 GeV, Multi-parton dynamics when s >> Q 2 the unitarity limit?, Novel and puzzling phenomena with spin, nuclei, Thermodynamics, hydrodynamics, and CMP of color forces,

10 Challenges for QCD in next 30 years Hadron properties the origin of the visible matter: in terms of the properties of quarks and gluons, and its dynamics Mass: the role of glue m q << m N << Q energy exchange, Spin: could be the first example for QCD to describe,... QCD bound states color confinement? QED: nucleons is so much heavier than electron localized charge QCD: heavy quarkonium localized color source but, unstable proton and neutron no localized color source but, stable Probe the spatial distribution of parton/color inside a hadron GPDs? QCD in extreme conditions: Diehl s talk Multi-particle dynamics, saturation (s >> Q 2 ), sqgp, phase transition, Kovchegov s talk An EIC with polarization could meet some of these challenges

11 Spin as a hadron property Like the mass, spin decomposition could be studied on the Lattice! Understand the spin decomposition in high energy collisions at various distance scales help us to learn QCD dynamics and explore the parton structure of a hadron

12 Spin of an elementary particle: An intrinsic quantum property of the particle Spin of a composite particle: Spin Angular momentum when the particle is at rest Spin in QCD: S(µ) = P, S Ĵ f z (µ) P, S = 1 2 J q(µ)+j g (µ) f Quark angular momentum operator: J q (µ) 1 2 q(µ)+l q(µ) Gluon angular momentum operator: The decomposition is not unique! J g (µ) G(µ)+L g (µ) Jaffe-Manohar, Ji, Chen et al, Wakamatsu, Only the total sum is physical! link individual pieces to other observables?

13 Proton spin Complexity of the proton state: S(µ) = f P, S Ĵ z f (µ) P, S = 1 2 J q(µ)+j g (µ) = 1 2 Σ(µ)+L q(µ)+j g (µ) S(µ) = 1 2 µ Qaurk Model: Asymptotic limit: J q (µ ) 1 2 3N f N f 1 4 Proton spin structure: Intrinsic parton s spin: vs. dynamical parton motion: J g (µ ) 1 2 Σ(Q 2 )= q L q (Q 2 ), L g (Q 2 ) q(q 2 )+ q(q 2 ), N f 1 4 G(Q 2 ) If they could be measured separately Ji, 2005

14 Twenty years since the crisis The Plot is improved: The puzzle stays: Σ(Q 2 )= q q(q 2 )+ q(q 2 ) 1

15 RHIC Measurements on ΔG Small asymmetry leads to small gluon helicity distribution

16 Contribution from intrinsic parton s spin DSSV 2008: Hirai-Kumano 2008:

17 Uncertainty on ΔG NLO QCD global fit - DSSV: PRL101,072001(2008) Node NLO QCD global fit - HK: Without a node! With current data accuracy, large bias on the fitting form

18 Status and improvement on ΔG ΔG is likely to be small: Σ(Q 2 )=Σ(Q 2 α s (Q 2 ) ) true N f G(Q) 2π Nonlocal nature of ΔG very interesting small-x behavior: = 1 0 dx xp + dy 2π eixp Collinear factorization does not work when No anomalous gluon contribution + y p, s F +µ (0)F +ν (y ) p, s( i µν ) Cannot be calculated on Lattice at small x Role of power correction? Could be proportional to Not positive definite! i µν γ α d σ(p, s ν µ ν µ )= i µν d µν γ α γ 5 q G,

19 Future RHIC measurement on ΔG STAR multiple channels inclusive jet: PHENIX multiple channels γ:

20 EIC coverage Bruell, Ent If intrinsic spin of quarks and gluons do not contribute much to proton s spin, Need to exam parton s transverse motion inside a proton!

21 Contribution from parton orbital motion Generalized parton distributions (GPDs) - quark: Muller, 94 Ji, 96, P P with Like PDFs, GPDs are not physical observables, scheme dependent! Net parton s orbital motion: Ji, PRL78, 1997 Lattice QCD could calculate contribution to J q

22 Lattice calculation on parton orbital motion Moments of GPDs on lattice: Negele et al Ji s relation: Both L u and L d large: But, L u + L d ~ 0 Role of disconnected diagram cloud? Haegler, BNL-spin

23 From cross sections to GPDs Inclusive DIS cross section LO factorization: q q Necessary conditions for CO fact. k xp k xp k 2 Q 2 s Q 2 xp + Q k T k 2 DVCS LO factorization: Caution: q =(x + ξ)p + q (x ξ)p,... 2 =0 ξ = x B /2 Leading pole: x = x B /2 The necessary CO factorization condition Heavy quarkonium production helps, since k + k T k m 2 J/ψ k2 is not satisfied! EIC is an ideal place to measure GPDs: No pqcd factorization for diffractive scattering of a proton on a proton!

24 Generalized TMDs and Wigner function Toward the full mapping/imaging of single parton distribution inside a hadron

25 Single parton distribution Fully unintegrated distribution: Meissner, Metz, Schiegel, 2009 gauge invariant but, not necessarily measurable! Generalized TMDs: H(x, k T, ) Γ = dk 2 W (P, k, ) Γ Assume: k 2 Q 2 on-shell parton for partonic collision Could be studied on the Lattice pqcd factorization needs k + k T k Only EIC could have a chance to probe this via diffractive observables! Wigner function: W (x, k T,b) d 3 e ib H(x, k T, ) Γ=γ + Belitsky, Ji, Yuan

26 Connection to all other known distributions Anselmino, INT

27 QED charge distribution: P µ q Challenges to 3D imaging P Photon carries no charge Form factor Fourier transform of charge distribution QCD color charge distribution clues on confinement? q P µ P Gluon carries color Color singlet multi-parton interaction Spatial parton distribution Fourier transform: Only EIC could have a chance to probe this! Vacuum quantum number Real and imaginary amplitude Factorization breaks when (P-P ) 2 increases

28 Spin/polarization as a powerful tool Observables constructed from cross sections with different spin orientations could probe QCD dynamics and hadron structure that could not be accessed by unpolarized cross sections

29 Single transverse spin asymmetry Left-right asymmetry: A(p A,s )+B(p B ) π(p)+x Vanish without parton s transverse motion: A direct probe for parton s transverse motion A direct probe of QCD quantum interference

30 Single transverse spin asymmetry SSA corresponds to a naively T-odd triple product: A N i s p (p ) i µναβ p µ s ν α p β Novanish A N requires a phase, enough vectors to fix a scattering plan, and a spin flip at the partonic scattering Leading power in QCD: Kane, Pumplin, Repko, PRL, 1978 σ AB (p T, s) = α s m q p T A N connects to parton s transverse motion! +...

31 Quark TMD distributions: TMD PDFs ˆk µ = xp µ + k2 T 2xp + nµ + k µ T dk 2 dk + δ(x k + /P + ) Total 8 TMD quark distributions Gluon TMD distributions, Production of quarkonium, two-photon,

32 Process dependence of TMDs The form of gauge link is a result of factorization:

33 Process dependence of TMDs Operator for TMD is not localized to 1/xp: NOT Localized to the size ~ 1/xp ~ 1/Q extended color flow Strength of the gauge field depends on the gauge: Covariant gauge: transverse link at is not important Light-cone gauge: whole effect of the link is from the transverse link Lattice QCD: Cannot calculate the link at! Bad or advantage? Definitely an advantage! Plot calculated TMDs as a function of x + QCD color confinement TMDs should reach a stable value when x + reaches the range of color force

34 Measure TMDs Sivers effect Sivers function: Hadron spin influences parton s transverse motion Collin s effect Collin s function: Transversity Parton s transverse spin affects its hadronization Need TMD factorization to quantify parton transverse motion! Two-scale problem in QCD: Q 1 Q 2 Λ QCD Separation of different effects?

35 ElC is ideal for studying TMDs SIDIS has the natural kinematics for TMD factorization: (s e )+p(s p ) + h(s h )+X Natural event structure: high Q and low p T jet (or hadron) Separation of various TMD contribution by angular projection: Lepton plane vs hadron plane

36 Critical test of TMD factorization Parity and time-reversal invariance: Drell-Yan: Collins; Kang, Qiu Sivers functions change sign! Collins et al, 2006 Kang, Qiu, 2009 Z 0 :

37 TMD factorization to collinear factorization: A N (Q 2,p T ) p T Q TMD Transition from low p T to high p T Q s Collinear factorization: p T Q p T Collinear Factorization Ji,Qiu,Vogelsang,Yuan, Koike, Vogelsang, Yuan Two factorization are consistent in the overlap region where Λ QCD p T Q Efremov, Teryaev, 82; Qiu, Sterman, 91, etc. 2 p, s k σ(q, s) t 1/Q = σ LP (Q, s)+ Q s Q σnlp (Q, s)+... σ(s T ) T (3) (x, x) ˆσ T D(z)+δq(x) ˆσ D D (3) (z,z)+... T (3) (x, x) D (3) (z,z) Qiu, Sterman, 1991, Kang, Yuan, Zhou, 2010

38 SSA from quark-gluon correlation (FermiLab E704) (RHIC STAR) Kouvaris,Qiu,Vogelsang,Yuan, 2006 Nonvanish twist-3 function Nonvanish transverse motion

39 Universality of correlation functions: P, s ψ(0)γ + ψ(y ) P, s P, s ψ(0)γ + γ 5 ψ(y ) P, s Global QCD analysis for SSA P, s ψ(0)γ + P, s ψ(0)γ + αβ s T α ig αβ s T α dy ψ(y 2 F + ) P, s β (y 2 ) dy 2 F + β (y 2 ) ψ(y ) P, s Same replacement for the gluons Kang, Qiu, 2009 Scaling violation of correction functions: Leading order evolution kernels for all channels have been derived! What are urgently needed: NLO partonic contributions to SSA of all measureable observables! A completely new domain to test QCD! Kang, Qiu, 2009 Yuan, Zhou, 2009 Braun et al, 2009 Vogelsang, Yuan, 2009 From paton s transverse motion to direct QCD quantum interference EIC is complementary to RHIC, but, better in separation of sources of SSA!

40 Summary After 35 years, we have learned a lot of QCD dynamics, but, only at very short-distance - less than 0.1 fm, and limited information on non-perturbative parton structure EIC with polarization provide a new program to do the new frontier research of QCD dynamics key to the visible matter Understanding proton spin could provide the first complete example to describe the fundamental properties of hadrons The program of measuring transverse spin asymmetries at EIC, which is complementary to RHIC, provides a new domain to test QCD dynamics, in particular, the parton s transverse motion Thank you!

41 Backup slices

42 Matter in our universe Energy distribution: Visible matter Dark matter Dark energy Visible matter: Proton and neutron are building blocks of all elements make up more than 95% mass of all visible matter But, proton and neutron themselves are not elementary made of quarks and gluons of QCD

43 GPDs and parton/color distribution Spatial dependent quark distribution: Burkardt, NPA711, 2002 EIC is a place to measure GPD s, but, extraction is still challenging