Transverse Nucleon Structure and Chiral Symmetry Breaking C

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Transverse nucleon structure and chiral symmetry breaking C. Weiss (JLab), Penn State HEP/Astrophysics Seminar, 17–Apr–13 JHEP 1301 (2013) 163

• Nucleon structure in QCD Perturbative Dynamicalχ SB Hadronic QCD size R Scale Parton model QCD radiation, factorization 0.1 fm 1 fm

• Chiral symmetry breaking in QCD valence Non–perturbative scale ρ ≪ R

sea ρ Eﬀective description: Constituent quarks,

... Goldstone bosons R P • Eﬀect on partonic structure

pT (sea) ≫ pT (valence) Short–range correlations of partons

Q: How does χSB scale • Experimental tests ρ ∼ 0.3 fm express itself in Single–particle inclusive PT,h distributions nucleon’s partonic structure? HERMES, COMPASS, JLab12, EIC → Intrinsic transverse momenta Correlations current ↔ target regions EIC → Parton correlations Multiparton interactions Tevatron, LHC Nucleon structure: Parton model

• Q,2 W Hadron as composite system Pointlike constituents with = pz xP interactions of ﬁnite range µ µ ∼ µ Relativistic, can create/annhilate particles pT Interactions System moves with P ≫ µ P Constituents’ momenta longitudinal pz = xP transverse pT ∼ µ xf(x) σ ∼ Bjorken T Q2 scaling • Scattering process Q2,W 2 ≫ µ2

Electron scatters from quasi–free constituent with momentum fraction 2 2 2 2 2 f(x) = d pT f(x, pT ) x = Q /(W − MN + Q ) Z Parton density in Transverse momenta integrated over, longit. momentum integral converges pT ∼ µ Nucleon structure: QCD • QCD radiation

Real emissions with pT from ∼ µ to Q ... Virtual radiation renormalizes couplings • Factorization 2 2 p ∼ Q Separation of scales in regime Q ≫ µ ... T Inclusive scttering γ∗N → X: ∼ µ pT Net radiation eﬀect simple Factorization well understood non−pert. interactions ∗ ′ Semi-inclusive γ N → h(low PT )+ X : Radiation eﬀect more complex Final–state interactions of struck parton Factorization more challenging Much progress: Collins 11 → Seminar T. Rogers

Parton density as N| QCD–operator |N, universal, process–independent σT ∼ [parton density] ∼ µ Collins, Soper 82, . . . × [radiation] • Parton transverse momentum × [scattering process] ∼ Q pT ∼ Q pert. QCD, calculable pT ∼ µ nonpert. interactions ← this talk! Chiral symmetry breaking: Physical picture

• Chiral symmetry breaking in QCD L R pert. . Pert. interactions conserve quark chirality L, R . non−pert. LL Non-pert. gluon fields can flip chirality Topological gauge fields, instantons R R L R Condensate of qq¯ pairs ψ¯LψR + ψ¯RψL, ρ ~ 0.3 fm pion as collective excitation Order parameter, Goldstone boson Dynamical mass generation: condensate Constituent quarks, hadron structure

... Euclidean correlation functions → Lattice, analytic methods ...... • Short–range interactions ρ ∼ 0.3 fm New dynamical scale ρ ≪ R Shuryak; Diakonov, Petrov 80’s dynamical mass Gauge–invariant measure of qq¯ pair size ψ¯∇2ψ/ψψ¯ ∼ 1 GeV2 “average virtuality” Lattice: Teper 87, Doi 02, Chiu 03. Instantons: Polyakov, CW 96 valence • How does it aﬀect partonic structure? sea ρ

... Valence quark mostly in conﬁgurations of size ∼ R R P Sea quarks in correlated pairs of size . ρ

Can we quantify it? . . . Dynamical model! Chiral symmetry breaking: Dynamical model

• Effective description of χSB Diakonov, Eides 83; Diakonov, Petrov 86 . . . chiral field Constituent quarks/antiquarks with dynamical mass M ∼ 0.3-0.4 GeV M dynamical mass Coupled to chiral field (Goldstone boson) with eff. coupling M/fπ = 3–4 strong!

−2 ¯ − iγ5τπ/fπ Valid up to χSB scale ρ : Leﬀ = ψ i∂/ Me ψ Matching with QCD quarks/gluons

Field theory, solved non–perturbatively in 1/Nc expansion

classical field • Nucleon as chiral soliton ... Diakonov, Petrov, Pobylitsa 88; Kahana, Ripka 84

Classical chiral ﬁeld “Hedgehog” π r in rest frame, cf. skyrmion

Binds valence quarks, creates quark–antiquark pairs Relativistic mean–ﬁeld approximation binds valence creates quark− quarks antiquark pairs Field theory: Completeness, conservation laws, positivity ρ−2 ≫ M2 No Fock space truncation! → PDFs, sea quarks Chiral symmetry breaking: Parton distributions

2 • - - Parton densities in model valence x (u + d - u - d ) Diakonov, Petrov, Pobylitsa, Polyakov, CW 96+; Wakamatsu et al. 97+ sea 2 x (u- + d- ) q † 1.5 f (x, pT ) = N| a a(xP, pT ) |NP →∞ q¯ † f (x, pT ) = b b ) x

( Chiral quark-

1 1 soliton model x f Quark/antiquark number densities at P → ∞ equivalent to light–cone correlation function ψ...ψ¯

0.5 −2 pT integral convergent due to cutoﬀ ρ

0 Intrinsic pT distributions, not “TMDs” no FSI! 0 0.2 0.4 0.6 0.8 1 x • Interpretation

x and pT distribution of constituent 1 Q2 = 54 GeV2 quarks and antiquarks eﬀective DOF

u Matching with QCD quarks, antiquarks

− χQSM −2 d 0.5 and gluons at scale ρ + QCD evol. PDF ﬁts show 30% of nucleon momentum carried by gluons 2 2 anti at µ ∼ 0.5 GeV : “Accuracy” of model E866 0 • Flavor asymmetries 0 0.1 0.2 0.3 Describes well measured d¯− u¯ E866 Drell-Yan x Predicts sizable ∆¯u − ∆d¯ → DSSV, RHIC W Partonic structure: pT distributions

• Valence quarks q − q¯

10 −1 valence u + d − u- − d- pT ∼ R , approximate Gaussian shape sea u- + d- 2 2 pT ≈ 0.15 GeV , weakly x–dependent 1 x = 0.1 ] 2 − M • Sea quarks q¯ ) [ T

p 0.1 ,

x q¯ 2 ( d Power-like tail f (x, pT ) ∼ C(x)/pT

+ −2 u

1 up to cutoﬀ scale ρ f 0.01 Structure determined by low–energy M = 0.35 GeV chiral dynamics, model–independent 0.001 0 5 10 2 −2 2 2 pT ∼ ρ : Some model dependence pT [M ] from UV cutoﬀ

Similar tail in ∆¯u − ∆d¯

Sea quark pT distribution qualitatively diﬀerent from valence quarks! • Qualitative diﬀerence

Generic feature, rooted in dynamical scale ρ ≪ R Partonic structure: Short–range correlations

• Parton short–range correlations valence sea Sea quarks in nucleon LC wave function partly classical ρ chiral in correlated pairs of size ρ ≪ R field Explains high-momentum tail of pT distribution R P Pairs have distinctive spin-isospin structure: Scalar–isoscalar Σ, pseudoscalar–isovector Π

Restoration of chiral symmetry at high pT : 2 2 2 −2 2 |ΨΣ| = |ΨΠ| at pT ∼ ρ ≫ M Large eﬀect: Fraction of correlated sea is O(1) Mean field • Cf. NN short–range correlations in nuclei Short−range correlation N Mean ﬁeld Ψ(r1, ...rN ) ≈ i Φ(ri)

Rare conﬁgs with |ri − rj| ≪Q average experience short-range NN interaction, generate high momentum components

Indirect probes: Momentum distributions, x > 1 Direct probes: (e, e′NN) in special kinematics JLab Hall A, CLAS, Hall C at 12 GeV Parton SRCs as imprint of χSB on partonic structure . . . What about parton correlations? Measurements: Single–particle inclusive

z, PT, h • Hadron PT,h distributions in SIDIS

. Intrinsic pT in WF . x, p Final–state interaction Observable PT,h T Parton fragmentation ) soft FSI . . x , P ' External handles: z ↔ x, z ↔ PT,h F T To be explored with CLAS12: Kinematic coverage

• Separate valence and sea quarks in target

Charge separation with pions N ()P T,h from + − 2 2 ¯ valence N(π − π ) ∝ eu(u − u¯) − ed(d − d) + − 2 2 ¯ N(π + π ) ∝ eu(u +u ¯)+ ed(d + d) from sea Charge separation with kaons: u dominance, s =s ¯ fragmentation PT,h N(K+) ∝ u mostly valence N(K−) ∝ u¯

Sea quarks contribute only at x ∼ 0.1 Different widths of valence/sea affect Intrinsic pT manifest only at z > 0.5 flavor separation if P coverage incomplete 12 GeV kinematics probably marginal. T,h Schweitzer, Strikman, CW 12; simulations in progress Frankfurt et al. 89; Christova, Leader 01 Measurements: Correlations • Hadron correlations between current and target fragmentation regions

Unravel SIDIS mechanism: What balances observed P ? current target T,h

y • Kinematics for nonperturbative correlations

Suﬃcient separation in rapidity 2 2 2 ∆y ≈ ln[W /(PT,h + mh)] & 4 Moderate virtuality to avoid pQCD radiation Q2 ∼ few GeV2 current Momentum fractions of nonperturbative sea Parton SRC x ∼ 0.05–0.1 target → “Kinematic window” at W 2 ≈ 30 GeV2, 2 2 PT,h ≈ 0.5 GeV COMPASS: Detection of target fragments? EIC: Medium energiesideal JLab12: Probably marginal, but should be explored

• Other option: Exclusive meson production “Knockout” of correlated qq¯ pairs. Many possibilities with JLab12! Measurements: Multiparton processes in pp

• −1 Double dijet rate parametrized by σeff 2 Mean field σeff = πR13 avg distance btw collision points. Calculable from transverse distributions

−1 2 σeff (mean field) = d bP12(b) P34(b) x1 x2 b Z x3 x4 • Observed enhancement dynamical correlations? CDF/D0 3jet + γ rate two times larger than mean field with ρ2(x ∼ 0.1)

Possible explanation: Parton correlations FSW, Annalen Phys. 13 (2004)

Perturbative vs. nonperturbative correlations? Higher–order vs. mulitparton processes? σ(12; 34) 1 Many challenges. Blok, Dokshitzer, Frankfurt, Strikman 11 = σ(12)σ(34) σeﬀ • LHC: High rates for multijet events f(x1, x3)f(x2, x4) × f(x1)f(x2)f(x3)f(x4) Background to new physics processes Detailed studies of parton correlations New ﬁeld of study. Great interest! MPI@TAU Tel Aviv 2012 Summary

• Dynamical χSB in QCD creates short–distance scale ρ ≪ R ∼ 1 fm

Natural scale for separating soft wave function ↔ pQCD radiation

• Qualitatively diﬀerent pT distributions of valence and sea quarks −1 Valence quarks pT ∼ R −1 Sea quarks “tail” pT . ρ

• Parton short–range correlations in nucleon Imprint of QCD vacuum on partonic structure

• Experimental tests Separate valence and sea quarks in single–particle inclusive DIS: Charged pions, kaons. Details simulations in progress.

Correlations between current and target fragmentation regions: Kinematic window for non–perturbative correlations. Ideal for medium-energy EIC

Exclusive meson production: Knockout of correlated qq¯ pair. Exploratory studies in progress.

Multiparton interactions in high–energy pp collisions