Theory Introduction to Semi-Inclusive Physics Jianwei Qiu Brookhaven National Laboratory Jefferson Lab (Jlab) 2014 Joint Hall A/C Summer Meeting JLab, Newport News, VA, June 4-5, 2014

DIS vs. SIDIS  E E’ Inclusive DIS – one scattering plane: Localized probe:  E E’ Two independent variables: Semi-inclusive DIS (SIDIS) – two scattering planes: Leptonic plane: Hadronic plane: Path of the color flow Angle between two planes:

Semi-inclusive DIS Naturally, two scales: Spin-motion correlation: high Q – localized probe To “see” quarks and gluons Low pT – sensitive to confining scale To “see” their confined motion Theory – QCD TMD factorization Confined motion Spin-motion correlation: 4 spin combinations Various TMDs: vector, axial vector, tensor Needs 4 spin combinations

TMDs – role of spin and motion Rich quantum correlations: 8 leading power (twist) quark TMDs: Similar for gluons

Quantum correlation between hadron and parton Sivers effect – between hadron spin and parton motion: Hadron spin influences parton’s transverse motion Sivers function o Observed particle Parton’s transverse spin influence its hadronization Collins function Transversity Collins effect – between parton spin and hadronization: Observed particle JLab12, COMPASS, and low energy EIC for valence, EIC@US covers the sea and gluon!

SIDIS – the best for probing TMDs Naturally, two planes: Separation of TMDs: Collins frag. Func. from e+e- collisions Very hard, if not impossible, to separate TMDs in hadronic collisions Using a combination of different observables (not the same observable): jet, identified hadron, photon, …

QCD corrections Sources of parton kT at the hard collision: Gluon shower Confined motion Emerge of a hadron hadronization Parton kT generated by the shower caused by the collision: Has very little to do with the kT in hadron wave function – hadron structure At large Q2 and collision energy (large phase space), the shower generated kT could be perturbative Q2 – evolution of the cross section “True” parton structure: Input distribution for the Q2 evolution - nonperturbative

Factorization for SIDIS TMD fragmentation Leading power contribution: Soft factors Low PhT – TMD factorization: TMD parton distribution High PhT – Collinear factorization: PhT Integrated - Collinear factorization:

Modified Universality of TMDs TMD distributions with non-local gauge links: Parity + Time-reversal invariance: The sign change is a critical test of TMD factorization approach

Evolution of TMDs Evolution in the b-space – Fourier transform of kT: RG equations: Boer, 2001, 2009, Idilbi, et al, 2004 Aybat, Rogers, 2010 Kang, Xiao, Yuan, 2011 Aybat, Collins, Qiu, Rogers, 2011 Sun, Yuan, 2013 … Evolution equations for Sivers function: CS: RGs:

Numerical “prediction” for evolution Aybat, Prokudin, Rogers, 2012: Huge Q dependence Sun, Yuan, 2013: Smaller Q dependence No disagreement on evolution equations! Issue: extrapolation to non-perturbative large b-region choice of the Q-dependent “form factor” – more work needed!!!

SIDIS Drell-Yan e–e+ to pions World effort on TMDs proton lepton EIC BNL JPARC FNAL proton lepton antilepton proton lepton pion SIDIS Drell-Yan BESIII Partonic scattering amplitude Fragmentation amplitude Distribution amplitude electron positron pion Test of the sign change! e–e+ to pions

Transition from low pT to high pT TMD factorization to collinear factorization: Two factorization are consistent in the overlap region where TMD Collinear Factorization Quantum interference – high pT region (integrate over all kT): Non-probabilistic quark-gluon quantum correlation Single quark state quark-gluon composite state (Spin flip) interfere with Kang, Yuan, Zhou, 2010

Twist-3 correlation functions Twist-2 parton distributions: Kang, Qiu, PRD, 2009 Unpolarized PDFs: Polarized PDFs: Two-sets Twist-3 correlation functions: Role of color magnetic force!

Evolution of twist-3 correlation functions Kang, Qiu, 2009 Closed set of evolution equations (spin-dependent): Plus two more equations for: and

Sample scale dependence of twist-3 correlations Kang, Qiu, 2009 Follow DGLAP at large x Large deviation at low x (stronger correlation) Matching between low pT (resum) and high pT (fixed) Kang, Xiao, Yuan, 2011

Single-spin asymmetry in hadronic collisions Consistently observed for over 35 years! ANL – 4.9 GeV BNL – 6.6 GeV FNAL – 20 GeV BNL – 62.4 GeV BNL – 200 GeV Definition:

Do we understand it? Early attempt: QCD factorization at twist-3: 2 Kane, Pumplin, Repko, PRL, 1978 Early attempt: 2 Cross section: Asymmetry: Too small to explain available data! QCD factorization at twist-3: Qiu and Sterman, NPB, 1991 Sivers - type Collins - type

A sign “mismatch” if keeps only Sivers-type Sivers function and twist-3 correlation: Kang, Qiu, Vogelsang, Yuan, 2011 + UVCT “direct” and “indirect” twist-3 correlation functions: Calculate Tq,F(x,x) by using the measured Sivers functions direct direct indirect indirect Metz & Pitonyak, 2013 Important role of Collins’ effect to single pion production – twist-3 FFs SIDIS – separate two effects by difference in angular distribution

Flavor structure of the proton sea The proton sea is not SU(3) symmetric! Violation of Gottfried sum rule Confirmed by Drell-Yan exp’t Why ? Why does change sign?

Challenges for d(x) – u(x) All known models predict no sign change! Meson cloud Chiral-quark soliton model Statistic model Future experiments: Fermilab E906 Very important non-perturbative physics What is the ratio as x increases?

Asymmetry between strange and up/down sea? LO and NLO QCD global fitting to DIS data: with for x > 0.1 New LHC data on W/Z data: HERMES data: Does not follow the shape of u(x) + d(x)? Why strange sea behave so different? Need FFs PT-integrated SIDIS:

Hadronization puzzle Strong suppression of heavy flavors in AA collisions: Emergence of hadrons: How do hadrons emerge from a created quark or gluon? How is the color of quark or gluon neutralized? Need a femtometer detector or “scope”: Nucleus, a laboratory for QCD Evolution of partonic properties

Nucleus as a “detector” The “vertex” detector At a fermi scale Nucleus in SIDIS is an ideal “vertex” detector Need a good control of the kinematics of fragmenting parton Almost impossible for a hadron machine

Color neutralization – energy loss Unprecedented ν range at EIC: D0 Control of ν and medium length! Heavy quark energy loss: Mass dependence of fragmentation pion D0 semi-inclusive DIS π Need the collider energy of EIC for heavy flavors

PT broadening of leading hadron in SIDIS Definition:

Color fluctuation – azimuthal asymmetry Preliminary low energy data: Hicks, KEK-JPAC2013 Contain terms in cos(φpq) and cos(2φpq) only statistical uncertainties shown Classical expectation: Any distribution seen in Carbon should be washed out in heavier nuclei Surprise: Azimuthal asymmetry in transverse momentum broadening Spin-”orbital” correlation + soft multiple scattering Qiu & Pitonyak In preparation

SIDIS’ role in probing the gluon saturation Strong suppression of dihadron correlation in eA@EIC: Theory Simulation ϕ12 Never been measured! Directly probe Weizsacker-Williams (saturated) gluon distribution in a large nucleus A factor of 2 suppression of away-side hadron-correlation! No-sat: Pythia + nPDF (EPS09)

Summary SIDIS in eP offers many more better controlled observables to probe QCD’s confining features and hadron’s partonic structure From 3D confined motion to quantum interference of different parton states Best channel for probing TMDs SIDIS in eA collision is ideal for probing “hadronization”, “color neutralization”, QCD energy loss, … JLab12 is excellent for the valence region, while a future EIC will cover the sea and gluon A future EIC@US could help continue to keep the US’s leadership position in nuclear physics and … Thanks!

Electron-Ion Collider (EIC) A giant “Microscope” To “see” quarks and gluons A sharpest “CT” To “cat-scan” nucleons and nuclei