Partonic Structure of Hadrons

Theory

Jianwei Qiu Brookhaven National Laboratory

The International Conference on Electromagnetic Interactions with Nucleons and Nuclei (EINN 2013)

October 28 – November 02, 2013, Pafos (Cyprus)

Pre-workshop lecture (10/28/2013)

Nobel Prize 2013 - discovery of Higgs boson

"for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider"

François Engler Peter W. Higgs

mq ~ 10 MeV

mN ~ 1000 MeV

But, the Higgs mechanism generates

Too little to be relevant for

the mass of our world of visible matter!

Outline

q Summary

q Why do we care about the structure?

Structure leads to the revolution in knowledge

q How to “see” hadron’s partonic internal structure?

QCD factorization links hadron cross sections to parton structures

q Hadron properties and partonic structures

Proton spin, mass, radius (EM charge, color, quark, gluon), …

q Nucleon is not point-like and has internal structure

Birth of QCD, partons (quarks and gluons) and their dynamics

Atomic structure

q  Revolution in our view of atomic structure (100 years ago):

J.J. Thomson’s plum-pudding model

Atom:

Modern model Quantum orbitals

Discovery of Quantum Mechanics,

and the Quantum World!

q  Completely changed our view of the visible world:

² Mass by “tiny” nuclei – less than 1 trillionth in volume ² Motion by quantum probability – the quantum world!

² Nano materials, quantum computing, …

q  Provided infinite opportunities to improve things around us:

Rutherford’s planetary model

Discovery of nucleus A localized

charge/force center A vast

“open” space

1911

Nuclear structure and nuclear physics

q  Since the Rutherford exp’t,

Nuclear Binding Energy

q  Origin of nuclear force?

Nucleon-nucleon, multi-nucleon, …?

Hadrons – building blocks

q  Protons, neutrons, and pions:

q  “Historic” – as bound state:

Fermi and Yang, 1952; Nambu and Jona-Lasinio, 1960 (dynamics) Yang-Mills theory, SU(2) Non-Abelian Gauge theory (1953)

Nucleon structure

q  Nucleon is not elementary:

Magnetic moment: gproton �= 2 gneutron �= 0

q  The zoo of particles:

Nobel Prize, 1969

Quark Model

Proton Neutron

A complete example: Proton

q  Flavor-spin part:

q  Normalization:

q  Charge:

q  Spin:

Magnetic Moments

q  Quark’s magnetic moment:

Assumption: Constituent quark’s magnetic moment is the same as that of a point-like, structure-less, spin-½ Dirac particle

for flavor “i”

q  Proton’s magnetic moment:

q  Neutron’s magnetic moment:

If

How to “see” nucleon’s structure?

Deep inelastic scattering (DIS)

q  Discovery of spin ½ quarks: SLAC 1968

θ E E’

The birth of QCD (1973)

Quark Model + Yang-Mill gauge theory

Nobel Prize, 2004

QCD Landscape of the nucleon and atomic nuclei?

q  Nucleon structure is complicate:

Probing momentum

Q (GeV)

200 MeV (1 fm) 2 GeV (1/10 fm)

Color Confinement Asymptotic freedom

Quantum Chromodynamics (QCD)

A quantum field theory of quarks and gluons

q  Fields: Quark fields: spin-½ Dirac fermion (like electron) Color triplet: Flavor:

Gluon fields: spin-1 vector field (like photon) Color octet:

q  QCD Lagrangian density:

q  QED Lagrangian density – force to hold atoms together:

LQED(φ, A) =�

f

ψf[(i∂µ − eAµ)γ

µ −mf ]ψf − 1

4[∂µAν − ∂νAµ]

2

QCD is much richer in dynamics than QED

Gluons are dark, but, interact with themselves, NO free quarks and gluons

Role of QCD in the formation of hadronic matter

QCD influenced how the universe evolve §  the dynamics of early universe §  the emergence of nucleons, and nuclei

Accelerator technology allows us to: §  recreate the condition of early universe §  repeat the formation of hadronic matter

QCD and hadron mass spectrum

13

q Lattice QCD calculation of hadron masses:

Hadrons are made of quarks and gluons bound together by QCD

H0

Heavy flavors – new challenges

q  Particles discovered in 1964 – Now:

q  New X, Y, Z particles:

H0

Heavy flavors – new challenges

q  Particles discovered in 1964 – Now:

q  New X, Y, Z particles:

See talk by Yuan, …

States outside Quark Model

q  Charmonium quantum numbers:

The complete list of allowed quantum numbers, , has gaps!

q  Exotic JPC :

q  Charmonium hybrids:

– States with an excited gluonic degree of freedom

²  Link QCD dynamics of quarks and gluons to hadrons beyond the Quark Model – new insight to the formation of hadrons

²  Why one “quasi-stable” gluon? What is the penalty to have more?

q  If it exists,

Questions?

17

How to probe or “see” what is inside a hadron?

Sub-femtometer scope?

Need a well-controlled “tool” or ”probe” at sub-fermi scale!

QCD Asymptotic Freedom

q  ΛQCD:

μ2 and μ1 not independent

Controllable QCD dynamics at short-distance (large momentum transfer)!

Weak coupling Reliable QCD perturbation theory (perturbative QCD)

q  BUT:

The challenges

Detectors only see hadrons and leptons, not quarks and gluons!

Cross section involving identified hadron(s) is not infrared safe and is not perturbatively calculable!

q  Facts:

Hadronic scale ~ 1/fm ~ ΛQCD is non-perturbative

q  Solution – QCD Factorization:

²  Isolate the calculable dynamics of quarks and gluons

²  Connect quarks and gluons to hadrons via non-perturbative but universal distribution functions – provide information on the partonic structure of the hadron

How to probe quark-gluon structure of hadron without seeing them?

Sub-femtometer “scope”

q  New DIS “Rutherford” experiment:

Q > 2 GeV ∆r < 10−1 fmQ2 = 4EE� sin2(θ/2) xB =

Q2

2mNνν = E − E�, ,

q  QCD Factorization - theory development in last thirty years:

Parton in a hadron Asymptotic freedom Cross section

ke(l)

h(p)e(l�) 2

≈e(l)

e(l�) 2h(p)

2

⊗

Sub-femtometer probe The structure

Factorization (theoretical advances in recent years!)

xp, kTxp, kT

An example: Inclusive DIS

q Process:

e(k) +N(p) −→ e�(k�) +X

Q2 = 4EE� sin2(θ/2) xB =Q2

2mNνν = E − E�, ,

y =q · pk · p

Cross section structure functions PDFs

q Spin-averaged cross section:

FL(x,Q2) = F2(x,Q

2)− 2xF1(x,Q2)

+O(αs) +O(1/Q2)

QCD Factorization!

q Spin-averaged cross section:

Helicity PDFs

QCD Factorization!

A few steps of details (3 slides)

Hadronic tensor and structure functions

q  Hadronic tensor:

EM current

4 †1( , , ) e , ( ) (0) ,4

iq zS S SW q p d z p J z J pµν µ νπ⋅= ∫

q  Structure functions:

Wµ! = ! gµ! !qµq!q2

"

#$$

%

&''F1 xB ,Q

2( )+ 1p (q

pµ ! qµp (qq2

"

#$

%

&' p! ! q!

p (qq2

"

#$

%

&'F2 xB ,Q

2( )

+iM p!µ"#$q!

S!p.qg1 xB ,Q

2( )+p.q( )S! ! S.q( ) p!

p.q( )2

g2 xB ,Q2( )

)

*

+++

,

-

.

.

.

q  Spin and polarization:

σ =1

2[σ(s) + σ(−s)] ∆σ =

1

2[σ(s)− σ(−s)]Spin-avg: Spin-dep:

Approximation and factorization

q  Collinear approximation, if Q ! xp !n ! kT , k 2

Parton’s transverse momentum is integrated into parton distributions, and provides a scale of power corrections

q  DIS limit: 2 whil, , e fixedBQ xν →∞

Feynman’s parton model and Bjorken scaling 2QCD2 2

2 2( )( , ) ( )QB B sf f B

fF x Q xx e O Oαϕ

⎛ ⎞Λ= + + ⎜ ⎟⎜ ⎟

⎝ ⎠∑

Scheme dependence

≈2

2TkOQ⎛

+⎞

⎜ ⎟⎝ ⎠

⊗ +UVCT

– Lowest order:

Same as elastic x-section

Factorization – two or more indentified hadrons

DIStotσ : ⊗

1 OQR⎛ ⎞

+ ⎜ ⎟⎝ ⎠

q  One hadron:

Now Hard-part

Past Parton-distribution

Connection Power corrections

�+ h(p) → �� +X

q  Two hadrons:

DYtotσ : ⊗

1 OQR⎛ ⎞

+ ⎜ ⎟⎝ ⎠

s

h(p) + h�(p�) → V (γ∗, Z0, ...) +X

Predictive power: Universal Parton Distributions

Parton distribution functions (PDFs)

q  Two parton correlations:

�p,�s|ψi(0)Γij ψj(y−)|p,�s�

�p,�s|F+i(0)F+j(y−)|p,�s� f ij

q  Parity and time-reversal invariance:

�p,−�s|O(ψ, Aµ)|p,−�s� = �p,�s|PT O†(ψ, Aµ)T −1

P−1

|p,�s�

q  Cross section – Factorization:

Factorized partonic part is independent of hadron spin

σ(Q,�s)± σ(Q,−�s) ∝ �p,�s|O(ψ, Aµ)|p,�s�± �p,−�s|O(ψ, Aµ)|p,−�s�

q  Good operators:

�p,�s|PT O†(ψ, Aµ)T −1

P−1

|p,�s� = ±�p,�s|O(ψ, Aµ)|p,�s�

Operator gives “+”: contribute to spin-averaged cross section Operator gives “–”: contribute to spin asymmetries

Collinear quark and gluon distributions

q  Quark distributions – leading power spin projection:

Transversity

Net helicity

Number density

q  Gluon distributions – leading power spin projection:

O(ψ, Aµ) =1

xp+F+i(0)

�δij

�F+j(y−) ⇒ G(x)

O(ψ, Aµ) = ψ(0)γ+γ · s⊥ψ(y−) ⇒ δq(x) → h(x)

O(ψ, Aµ) = ψ(0)γ+γ5 ψ(y−) ⇒ ∆q(x)

O(ψ, Aµ) = ψ(0)γ+ ψ(y−) ⇒ q(x)

O(ψ, Aµ) =1

xp+F+i(0)

�iεij

�F+j(y−) ⇒ ∆G(x) Net helicity

Number density

q  All operators for collinear PDFs are “local”:

U†−(∞, 0)U−(∞, y−) = exp

�−ig

� y−

0dy

�−A+(y�−)

�

All operators are localized to “1/xp ~ 1/Q” (Not true for TMDs!)

q  Physical cross sections should not depend on the factorization scale

22

22 ( , ) 0BFF

d F x Qd

µµ

=

( ) ( )2 2 2 22 2 2 2

2 2

, , , , , , 0F FB

F FF F F

f f f ff f

sF

Bs

d x Q x Q dC x C xd x x d

µ ϕ µ µα α ϕ µµ µ µ µ

⎡ ⎤⎛ ⎞ ⎛ ⎞⊗ + ⊗ =⎢ ⎥⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎣ ⎦∑ ∑

Evolution (differential-integral) equation for PDFs

DGLAP evolution equation:

2/

2 22 ( , ) ( ', ),

'i i j jF F s FF j

xPx

x xµ ϕ µ α ϕ µµ

⎛ ⎞⎜= ⎟⎝ ⎠

∂⊗

∂ ∑

q  PDFs and coefficient functions share the same logarithms

PDFs:

Coefficient functions:

( ) ( )2 2 2 20 QCDlog or logF Fµ µ µ Λ

( ) ( )2 2 2 2log or logFQ Qµ µ

Scaling violation – “see” dark gluon

Global QCD analysis – test of QCD

Input DPFs at Q0

{ }( ), jf h x aϕ

DGLAP

( )f h xϕ at Q>Q0 Comparison with Data at various x and Q

Minimize Chi2 Vary { }ja

QCD calculation

Procedure: Iterate to find the best set of {aj} for the input DPFs

Successes of QCD factorization

Measure e-p at 0.3 TeV (HERA)

q  Predict hadronic collisions at 0.2, 1.96, and 7 TeV:

Universal PDFs

Puzzles and new challenges

31

How to descript hadron properties

in terms of parton dynamics?

How to explore hadron structure beyond

1-D parton distributions?

The hadron mass puzzle

32

q  Generation of mass: from QCD dynamics?

mq ~ 10 MeV

mN ~ 1000 MeV

q How does QCD generate energy for the proton’s mass?

C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227

Mass from nothing!

Quark mass ∼ 1% proton’s mass

mG2(k2)  ≈  mG

4/(k2+mG2)  

Qin et al., Phys. Rev. C 84 042202 (Rapid Comm.)

²  BSE calculation results confirmed by lattice simulation

²  Light-quark mass comes from a cloud of soft gluons

² Gluon is massless in UV, but “massive” in IR

Higgs mechanism is not enough!!!

The hadron mass sum rule

33

q Decomposition:

q  QCD definition: Ji, 1994

QCD energy-momentum tensor:

²  None of these terms is a “direct” physical measurable (e.g. cross section)!

Can we “measure” them with controllable approximation?

Can we “measure” them by lattice calculation, or other approaches?

q  Proton spin sum rule:

The proton spin puzzle

S(µ) =1

2µ ⇒ ∞

q Proton – composite particle of quarks and gluons:

Spin = intrinsic (parton spin) + motion (orbital angular momentum)

q Over 20 years effort (following EMC discovery)

How to explore the “full” gluon and sea quark contribution? How to quantify the role of orbital motion? How to calculate them on the lattice?

²  Quark (valence + sea) helicity: of proton spin

²  Gluon helicity (latest RHIC data): from limited x range ∼ 30%

∼ 20%

S(µ) =�

f

�P, S|Jzf (µ)|P, S� =

1

2≡ Jq(µ) + Jg(µ) =

1

2∆Σ(µ) + Lq(µ) +∆G(µ) + Lg(µ)

Decomposition is useful if, only if, each term can be related to physical observables with controllable approximation

The nucleon structure

35

q 3D imaging of sea and gluons (EIC@US, no spin@LHeC):

²  TMDs – confined motion in a nucleon (semi-inclusive DIS)

²  GPDs – Spatial imaging of quarks and gluons (exclusive DIS)

5D

3D

1D

JLab12 COMPASS

HIAF for

Valence

JLab12 COMPASS

HIAF

q A unified view – Wigner distributions:

Parton distributions

QCD Collinear factorization for

Cross sections with one large momentum transfer

HERA data alone leads to precise PDFs

Polarized EIC should pin down proton helicity distributions

See talks by Jansen, Lorce, Surrow, …

Flavor structure of the proton sea

q The proton sea is not SU(3) symmetric!

37

Violation of Gottfried sum rule Confirmed by Drell-Yan exp’t

Why ?

d(x)− u(x)

d(x) �= u(x)

Why does change sign?

NMC: SG = 0.235± 0.026

q Future experiments:

38

Challenges for d(x) – u(x)

q All known models predict no sign change!

Meson cloud Chiral-quark soliton model Statistic model

Fermilab E906

What is the ratio as x increases?

Very important non-perturbative physics

Asymmetry between strange and up/down sea?

q LO and NLO QCD global fitting to DIS data:

39

for x > 0.1 s(x) = s(x) =κ(x)

2

�u(x) + d(x)

�κ(x) ∼ 0.5

q New LHC data on W/Z data:

with

q HERMES data:

Does not follow the shape of u(x) + d(x)?

Why strange sea behave so different?

Non-perturbative origin of s(x) differing from s(x)?

TMDs

QCD TMD factorization for

Cross sections with one large and one small momentum transfers

“Picture” of confined parton motion inside a hadron

Quantum correlation between hadron property and parton motion,

Parton properties influence hadronization

…

See talks by Jen-Chieh Peng, …

Transverse momentum dependent PDFs (TMDs)

q  Two parton correlations – like PDFs:

Without integrating over kT

=

�d2k⊥ f(x, k⊥)

Need two-scale observables – to be sensitive to kT

q  Averaged kT effect – twist-3 correlation functions:

No probability interpretation - Quantum interference of single/double states

∼�

d2k⊥ k⊥ f(x, k⊥)

An example: Sivers effect

q  Single-spin asymmetry:

More sensitive to the role of quantum correlation!

q  Quantum correlation between hadron spin and parton motion:

Hadron spin influences parton’s transverse motion

Sivers effect – Sivers function o Observed particle

q  Consistently observed for almost 40 years – vanish without kT!

TMDs – Link hadron property to parton motion

q  TMDs - rich quantum correlations:

Leading twist TMDs

Similar for gluons

43

q  DIS, naturally, has two scales and two planes: ²  Two scales: high Q - localized probe Low pT - sensitive to confining scale

²  Two planes: angular modulation to separate TMDs

Hard to separate TMDs in hadronic collisions

Non-locality of TMD parton distributions

q  TMD distributions with non-local gauge links:

q  Parity + Time-reversal invariance:

The sign change is a critical test of TMD factorization approach

SIDIS: DY:

Extract Sivers function from SIDIS

q  SIDIS and DY cover both double-scale and single-scale cases: AN (Q2, pT )

pT

pT ∼ QpT � Q

∼ Qs

TMD Collinear Factorization

q  SIDIS:

Precise PT –dependence? – motion?

Importance of the evolution

q  Aybat, Prokudin, Rogers, 2012:

q  Sun, Yuan, 2013:

Huge Q dependence

Smaller Q dependence

No disagreement on evolution equations!

Issue: Extrapolation to non-perturbative large b-region Choice of the Q-dependent “form factor”

GPDs

QCD collinear factorization for

Cross sections of exclusive processes with small t

EM charge radius

To

Proton’s quark radius, gluon radius

as a function of x!

…

See talks by Frank Sabatie, …

How is color distributed inside the proton?

q  The “big” question:

How color is distributed inside a hadron? (clue for color confinement?)

q  Electric charge distribution:

Elastic electric form factor Charge distributions

q

p'p

q  But, NO color elastic nucleon form factor! Hadron is colorless and gluon carries color

Parton density’s spatial distributions – a function of x as well (more “proton”-like than “neutron”-like)

Spatial imaging of quarks and gluons

q  Partonic structure – spatial distributions of quarks and gluons:

²  Need a localized probe

²  Scan in transverse direction

²  Partonic structure Exchange of colorless object

q Need exclusive processes – diffractive scattering

+ + +...

But, every parton can participate – need a “localized” probe! Q >> |t| !!!

No factorization for hadron-hadron diffractive scattering !

dσ

dxBdQ2dt

ξ = (P � − P ) · n/2Quark spatial distributions Proton’s “quark radius”

F.T. of t-dep

t-dep

Hq(x, ξ, t, Q), Eq(x, ξ, t, Q), ...

GPDs q Deep virtual Compton scattering (DVCS):

Proton’s “gluon radius”

q  Exclusive vector meson production:

t-dep

J/Ψ, Φ, …

dσ

dxBdQ2dtQ

²  Fourier transform of the t-dep

Spatial imaging of glue density

²  Resolution ~ 1/Q

pxp

1

Q

Images of gluons from exclusive J/ψ production

q  Gluon imaging from simulation:

Model dependence – parameterization?

EIC-WhitePaper

Proton’s “gluon radius”

Natural of pion cloud?

New facilities

arXiv:1212.1701

Proposed (or talked about) Future EICs

52

HERA@DESY LHeC@CERN eRHIC@BNL MEIC@JLab HIAF@CAS ENC@GSI

ECM (GeV) 320 800-1300 45-175 12-140 12 à 65 14

proton xmin 1 x 10-5 5 x 10-7 3 x 10-5 5 x 10-5 7 x10-3

à3x10-4 5 x 10-3

ion p p to Pb p to U p to Pb p to U p to ~ 40Ca

polarization - - p, 3He p, d, 3He (6Li) p, d, 3He p,d

L [cm-2 s-1] 2 x 1031 1033 1033-34 1033-34 1032-33 à 1035 1032

IP 2 1 2+ 2+ 1 1

Year 1992-2007 2022 (?) 2022 Post-12 GeV 2019 à 2030? upgrade to FAIR

q  Electron-Ion Colliders in the world:

²  High luminosity – sufficiently high energy (100-1000 x HERA)

²  High energy polarized electron + polarized proton beam

²  High energy heavy ion beams (large number of A’s)

q  Common features (differences from HERA):

Nuclear structure

Nuclear landscape =\= Superposition of nucleon landscape!

See talks by Kawtar Hafidi, …

² Overlapping of pion cloud?

² Overlapping of sea quarks?

² Overlapping of soft gluons?

Nature of nuclear force?

An “easiest” measurement

q  EMC effect, Shadowing and Saturation:

q  Questions:

Why nuclear structure function suppressed at small x?

Will the suppression/shadowing continue to fall as x decreases?

An “easiest” measurement

q  EMC effect, Shadowing and Saturation:

Color range ~ size of nucleon

Long range color coherence ~ size of nucleus (a bigger nucleon at small-x?)

Immediate impact on our understanding of neutron stars

q Role of color in nuclear binding:

Colored metal/crystal or condensed “gas”

Summary

q Advances in QCD factorization in last 15 years,

Advances of our knowledge in 3D structure of nucleon/nucleus might give us enough hints to explore the nature of confinement and dynamical chiral symmetry breaking, neither of which is apparent in QCD Lagrangian

Thanks!

q QCD is very successful in the asymptotic regime (< 1/10 fm):

But, we have learned very little about hadron structure and its formation

q Newly proposed EIC facilities would make it possible to “see” 3D QCD landscape/structure of nucleon/nucleus

TMD factorization for two-scale observables, Collinear factorization for exclusive processes with a small t,

Allow us to probe nucleon/nucleus structure beyond 1D PDFs