Xiangdong JiUniversity of Maryland

—Hadronic and Electroweak Physics at MIT Bates:Retrospective and future prospects, Sept. 28, 2006 —

Gluons in the protonGluons in the proton

Outline

1. Introduction2. Gluon rules in the QCD vacuum!3. The mass of the proton: how much of it is

glue?4. Polarized gluon distribution: a feeble

response to the quark effectData and model calculations

5. Strange anomalous magnetic moment:what’s in the sign?

6. Summary

Introduction

The gluon is an integral part of QCD and the structure of the proton.

Without gluons, quarks in the proton will fly apart.Without gluons, the mass of the proton will be just the sum of quark masses.Dominant mechanism for SM Higgs production

However, it is actually hard to “see” the glue in the proton directly

Does not couples to electromagnetism Gluon degrees of freedom “missing” in hadronicspectrum.… Where is the glue?

Gluon Dominance in the vacuum

QCD vacuum has interesting non-perturbativestructures,

Color confinementChiral symmetry breaking

These properties are large due to strong fluctuation gluon fields in the vacuum as in pure glue QCD.

J.Negele et al

Large Nc limit

The gluon dominance may be caricaturized by a theory with Nc quark colors, where Nc is large. A scalar gluon operator of GG types goes like Nc

2 in the vacuum, because there are Nc2-1

gluons (the majority wins!).

Gluons in a proton

The proton matrix element of the gluon operators goes like Nc.

Introduction of valence quarks yields a relatively small change in the background gluon field!Gluon distribution in the nucleon goes like

g(x) = Nc2 f(Ncx) : fraction of nucleon momentum

carried by gluon is a constant!

Gluon Parton Distribution

Interesting physics happens at small-x «1/Nc /high-energy (parton saturation): gauge aspects of gluons

Nucleon Mass

The hamiltonian of QCD comes from traceless and trace part of the energy momentum tensor

The traceless part gluon energy contributes (~Nc) about 320 MeV/c2 to the mass. The trace part contributes (Nc) about 200 MeV/c2

(dominated by gluon condensate in large Nc limit)

X. Ji, Phys.Rev.Lett.74:1071-1074,1995

MIT bag constant

Color Electric & Magnetic Fields

One can solve the color electric and magnetic fields in the nucleon from the above

The color electric field is stronger in the proton than that in the vacuum (strong coulomb field?)The color magnetic field produced by the motion of valence quark is also strong, with the surprising feature that it almost cancels that field in the vacuum. (A key to color confinement?)

Polarized gluon distribution ∆g(x)

The polarized gluon matrix elements go like Nc0

1 in the large limit. Thus the polarized part of the gluon field is

1/Nc suppressed relative to the measurable gluon field in the proton. 1/Nc

2 suppressed relative to the gluon fields in the vacuum. Δg(x) = Nc h(Ncx)

The total gluon helicity in the light-cone gauge A+ = 0 is

g PS E A PSΔ = ×

Experimental progress…

Two leading-hadronproduction in semi-inclusive DIS

Q-evolution in inclusive spin structure function g1(x)

Experimental progress

production in polarized PP collision at RHIC

Two jet production in polarized PP collision at RHIC

Calculating ∆g(x) in Models

Since the quarks are the primary constituents of a proton, the ∆g(x) effect is small in large Nclimit, one may regard its presence as a response due to polarized constituent quarks. Thus the polarized gluons may be calculated from

The dominant gluon responsible for the motions of the quarks have no pol. effect.Non-linear effects are usually ignored.

D G jμν νμ =

Total gluon helicity: positive?

There was a calculation by Jaffe (PRB365, 1996), showing a negative result in NR quark and bag models (two-body contribution)However, there is also the one-body contribution

Part of the one-body contribution cancels the two-body one, a positive residue remains.

Barone et al., PRB431,1998

x-dependence

No model calculation for x-dependent ∆g(x) has ever reported in the literature so far. A calculation is in progress in NR quark model and MIT bag model (P. Chen, X. Ji, D. Toublan)

Prelimary results show that the distribution is positive at all x.

Fit to data

Δg = 0.31 ± 0.32 type-1= 0.47 ± 1.0 type-2= —0.56 ± 2.16 type-3

Type-3 fit assumes gluon polarizationis negative at smallx.

Hirai, Kumano,Saito, hep-ph/003213

Sizing gluon polarization

Thought to be large because of the possible role of axial anomaly –(αs/2 )Δg (Altarelli & Ross, 1988)

2-4 units of hbar!Theoretical controversy…

Of course, the gluon contribute the proton spin directly.

∆q + ∆g + Lz = 1/2Naturalness?if ∆g is very large, there must be a large negative

Lz to cancel this---(fine tuning!)

Other processes sensitive to polarized gluon fields

Single-spin asymmetryColor-field polarizabilitiesMagnetic moment of the strange sea?…

Single Spin Asymmetry

In a polarized nucleon, the color electric field is polarized in a plane perpendicular to the direction of the polarization.This color electric field is at the origin of the single spin asymmetry in electron-hadron and hadron-hadron scattering.

Second moment of g2

Strange contribution to proton’s magnetic moment

A wonderful and clean probe of the QCD vacuum polarization effects. Bates SAMPLE experiment ushered in a new era in proton structure study.Current world data suggest that it is small and perhaps positive.Hard to calculate in theory, so “What is the crisp question that it answers?”

World Data near Q2 ~0.1 GeV2

Caution: the combined fit is approximate. Correlated errors and assumptions not taken into account

Preliminary

GMs = 0.28 +/- 0.20

GEs = -0.006 +/- 0.016

~3% +/- 2.3% of proton magnetic moment

~0.2 +/- 0.5% of electric distribution

HAPPEX-only fit suggests something even smaller:

GMs = 0.12 +/- 0.24

GEs = -0.002 +/- 0.017

Strangeness Models (as/of 2000)

Leading moments of form factors:

μs = GMs (Q2=0)

ρs = ∂GEs/∂τ (Q2=0)

Lattice QCD—Direct Calculations

Involving calculating quark loops on lattice. Very expensive!

Kentucky group (K. F. Liu et. al., hep-lat/0011015)163 X 24 lattices with lattice spacing 0.1fmμs = − 0.28±0.10

Lewis, Wilcox, and Woloshyn (PRD67,2003)203 X 32 lattices with lattice spacing 0.1fmChiral extrapolation to physical quark massμs = 0.05±0.06

Lattice QCD---An Indirect Approach

D. B. Leinweber et. al. PRL94, 212001 (2005)Find two expressions

• They assume 0<R<1, and henceGs must be negative!• From a model, they findR= 0.139, hence μs = -0.046!• However, R could be a number less than 0, if R=−0.5, Gs = 0.2!

R is the ratio of strange to down quark sea contribution.

MM as a function of quark mass

Heavy Quark

Light-by-light scattering

Gluon matrix element

Muon contribution to electron’s MM

Understanding EFT calculation

Proton matrix element

Contribution is positive at large M

Ji & Toublan

Where does the transition happen?

It is difficult to estimate where the transition happen in QCDHowever, lattice calculation seems to indicate that sharp transition occurs at relatively small quark mass.

Contribution is positive at large M

Ji & Toublan

Conclusion

Gluons play a critical role in QCD. They dominate in the vaccum and high-energy. Although they are less visible in hadronicphysics at low-energy, their contribution to the mass and spin of the proton is as important as the quarks. The polarized gluons effects in the proton are small. However, precision experimental data allow us to learn their effects through QCD analysis.