The proton remains puzzling Proton mass, spin and charge radius Haiyan Gao Duke University H. Gao 1 QCD: still unsolved in non-perturbative region Gauge bosons: gluons (8) • 2004 Nobel prize for ``asymptotic freedom’’ • Non-perturbative region QCD ????? • One of the top 10 challenges for physics! • QCD: Important for discovering new physics beyond SM • Nucleon structure is one of the most active areas H. Gao 2 Lepton scattering: powerful microscope! • Clean probe of hadron structure • Electron (lepton) vertex is well-known from QED • One-photon exchange dominates, higher-order exchange diagrams are suppressed (two-photon physics) • Vary the wave-length of the probe to view deeper inside 2 ' " 2 2 % dσ α E GE +τGM 2 θ 2 2 θ = $ cos + 2τGM sin ' 2 2 2 4 θ τ = −q / 4M dΩ 4E sin E # 1+τ 2 2 & 2 Virtual photon 4-momentum! q = k − k' = (q,ω) Q2 = −q2 1 k’ α = 137 H. Gao 3 k € What is inside the proton/neutron? 1933: Proton’s magnetic moment 1960: Elastic e-p scattering Nobel Prize Nobel Prize In Physics 1943 In Physics 1961 Otto Stern Robert Hofstadter "for … and for his thereby achieved discoveries "for … and for his discovery of the magnetic concerning the structure of the nucleons" moment of the proton". g =2 Form factors Charge distributions 6 ! 1969: Deep inelastic e-p scattering 1974: QCD Asymptotic Freedom Nobel Prize in Physics 1990 Nobel Prize in Physics 2004 Jerome I. Friedman, Henry W. Kendall, Richard E. Taylor David J. Gross, H. David Politzer, Frank Wilczek "for their pioneering investigations concerning "for the discovery of asymptotic deep inelastic scattering of electrons on freedom in the theory of the strong protons …". slide credit: Jian-Wei Qiu H. Gao interaction". 4 The Proton remains puzzling: spin, mass and charge radius Quark Quark Energy Mass 33! 11! Trace Gluon Anomaly Energy 22! 34! β(g) N | GαβγGγ m qq | N M < αβ + ∑ q >= N 2g u,d ,s, Image credit: fineartamerica.com H. Gao 5 The Committee on U.S.-Based Electron Ion Collider Science Assessment • Finding 1: An EIC can uniquely address three profound questions about nucleons—neutrons and protons—and how they are assembled to form the nuclei of atoms: • How does the mass of the nucleon arise? • How does the spin of the nucleon arise? • What are the emergent properties of dense systems of gluons? EIC NSAC NAS White LRP Report Paper 2015 2018 2015 citation: National Academies of Sciences, Engineering, and Medicine. 2018. An Assessment of 55 U.S.-Based Electron-Ion Collider Science. Washington, DC: The National Academies Press. 56 https://doi.org/10.17226/25171 H. Gao 6 Proton: a fascinating many-body relativistic system Higgs discovery almost irrelevant to proton mass Proton rest frame Gao, Liu et al. (2015) Quark Quark !Decomposition of Proton mass [ X. Energy Mass Ji PRL 74 1071 (1995)Quark energy ] Trace 33! 11! Quark mass Anomaly CM frame Gluon energy Trace Gluon 2 Quark MS@1 GeV Anomaly Energy Trace anomaly Quark Energy Sets the scale for the Hadron mass! 22! 34! H. Gao Mass X. Ji PRL 74 1071 (1995) 7 From Cross section to the Trace Anomaly D. Kharzeev. Quarkonium interactions in QCD, 1995 * NNJ/ D. Kharzeev, H. Satz, A. Syamtomov, and G. Zinovjev, Eur.Phys.J., C9:459–462, 1999 γψ+→+ Heavy quark – dominated by two gluons • VMD relates photoproduction cross section to quarknium-nucleon scattering amplitude • Imaginary part is related to the total cross section through optical theorem • Real part contains the conformal (trace) anomaly; Dominate the near threshold region and constrained through dispersion relation A measurement near threshold could allow access to theH. Gao trace anomaly 8 Charm @ SoLID and Beauty @ EIC SoLID with J/ψ EIC with Upsilon Total elastic electro and photo-production of J/psi Total elastic electro and photo-production of Upsilon Trace of energy-momentum tensor proportional to quarkonium-proton scattering amplitude to be measured at JLab with J/psi at SoLID or Upsilon at EIC Both SoLID and EIC are needed to confirm the trace anomaly extraction and could lead to a solution of the nucleon mass puzzle H. Gao 9 Solenoidal Large Intensity Device (SoLID) Physics SoLID provides unique capability: " high luminosity (10 37-39) 2) Precise determination of the electroweak couplings " large acceptance with full φ coverage à A search for new physics in the 10-20 TeV region, complementary to the reach at LHC. # multi-purpose program to maximize the 12-GeV science potential Quark Quark Energy Mass 1) Precision in 3D momentum space imaging of the nucleon 3) J/ψ production cross section 33! 11! Trace Gluon Anomaly Energy 22! 34! à Constrain the QCD trace anomaly contribution to the proton H. Gao mass budget10 Spin structure of the nucleon $1980s: “Proton spin crisis” (original EMC result from CERN) H. Gao 11 Impressive experimental progress in QCD spin physics in the last 30+ years ! Inclusive spin-dependent DIS ➥ CERN: EMC, SMC, COMPASS ➥ SLAC: E80, E142, E143, E154, E155 ➥ DESY: HERMES ➥ JLab: Hall A, B and C ! Semi-inclusive DIS ➥ SMC, COMPASS ➥ HERMES, JLab ! Polarized pp collisions ➥ BNL: PHENIX & STAR ➥ FNAL: POL. DY ! e+e- collisions ➥ KEK: Belle ➥ BaBar ➥ BESIII 12 Adapted from Z. Meziani’s Global Analysis: Polarized PDF Global analysis of spin-dependent parton distribution functions (µ2 =1 GeV2) J.J. Ethier et al. (JAM Collaboration), Phys. Rev. Lett. 119, 132001 (2017). 13 Measurement of the gluon polarization Δg at RHIC Dominates Dominates at low pT at high pT D. de Florian et al, PRL 113 (2014) 012001 E. Nocera et al, NPB 887 (2014) 276 Phys. Rev. D 90 (2014) 012007 Phys. Rev. Lett. 115 (2015) 092002 1 2 2 +.06 ʃdxΔg(x,Q =10GeV ) = 0.20 -.07 DSSV++ 0.05 0.2 Surrow et al on sea quark spin 2 2 ʃdxΔg(x,Q =10GeV ) = 0.17+-0.06 NNPDFpol1.1 from W production at RHIC 0.05 0.8 2 2 H. Gao ʃdxΔg(x,Q = 1 GeV ) = 0.5+-0.4 JAM15 14 Results from PHENIX , 40% gluon to 1/2 0.001 Gluon Spin From Lattice QCD First lattice QCD calculation of the gluon spin in the nucleon µ2 =10 GeV2 µ2 =10 GeV2 p = 0 mπ = 0.139 GeV 2 2 ΔG ≈ Sg (|p|→∞) : 0.251(47)(16) (µ =10 GeV ) 50(9)(3)% of the total proton spin Y.-B. Yang et al. (χQCD Collaboration), Phys. Rev. Lett. 118, 102001 (2017). 15 The incomplete nucleon: spin puzzle Jaffe-Manohar, 90 Ji, 96 1 1 = ⌃ +∆G +(L + L ) 2 2 q g Proton Spin Quark helicity Best known Gluon helicity Orbital Angular Momentum Start to know of quarks and gluons Little known 30% ⇠ 40% 20%(STAR Data) Net effect of partons’ ⇠ transverse motion? Maybe even more from Lattice H. Gao 16 Nucleon Structure from 1D to 3D Generalized parton distribution (GPD) Focus on Transverse momentum dependent parton distribution (TMD) in this talk H. Gao 17 Nucleon Spin Leading Twist TMDs Quark Spin Quark polarization Un-Polarized Longitudinally Polarized Transversely Polarized ⊥ h1 = U f1 = Boer-Mulder g = L 1 ⊥ h1L = Helicity h1T = Transversity Nucleon Polarization ⊥ T f 1T = ⊥ g1T = ⊥ Sivers h1T = Pretzelosity H. Gao 18 Access TMDs through Hard Processes FNAL JPARC EIC BNL lepton lepton proton lepton proton pion proton antilepton SIDIS Drell-Yan Partonic scattering amplitude BESIII Fragmentation amplitude electron pion Distribution amplitude ⊥⊥qq ff11TT(SIDIS)=− (DY) hh⊥⊥(SIDIS)=− (DY) positron pion 11 e–e+ to pions H. Gao 19 Separation of Collins, Sivers and pretzelocity effects through angular dependence ↑↓ ll 1 NN− AUT(,ϕϕ h S )= P N ↑↓+ N Collins Sivers =++AUT sin(φφhS )AUT sin( φφhS− ) Pretzelosity +AUT sin(3φφhS− ) Collins ⊥ AhHsin( ) Collins frag. Func. UT∝ φ h+φ S UT ∝ 11⊗ from e+e- collisions ASivers sin( ) f ⊥ D UT ∝−φφhSUT ∝ 1T ⊗ 1 APretzelosity sin(3 ) h⊥⊥H UThST∝ φ −∝⊗φ UT 11 2 SIDIS SSAs depend on 4-D variables (x, Q , z and PT ) Large angular coverage and precision measurement of asymmetries in 4-D phase space is essential. H. Gao 20 SIDIS @ SoLID SoLID (SIDIS He3) SoLID (SIDIS NH3) EM Calorimeter EM Calorimeter (forward angle) (forward angle) Scint Scint EM Calorimeter EM Calorimeter (large angle) (large angle) GEM GEM Scint Scint Target Target Beamline Beamline Collimator Coil and Yoke Coil and Yoke 1 m Light Gas Heavy Gas 1 m Light Gas Heavy Gas Cherenkov Cherenkov Cherenkov Cherenkov E12-10-006: Single Spin Asymmetries on Transversely Key of SoLID-spin program: Polarized 3He @ 90 days, rating A Large acceptance, full azimuthal E12-11-007: Single and Double Spin Asymmetries on coverage Longitudinally Polarized 3He @ 35 days, rating A + High luminosity E12-11-108: Single Spin Asymmetries on Transversely # 4-D mapping of asymmetries Polarized Proton @120 days, rating A # Tensor charge, TMDs … Run group experiments approved for TMDs and GPDs # Lattice QCD, QCD dynamics, models. H. Gao 21 SoLID SIDIS Projection Compare SoLID with World Data Transversity Sivers SoLID(Baseline) vs. World Fit Collins and Sivers SoLID(Baseline) vs. World (systematic uncertainty included) 0.4 (systematic uncertainty included) 0.04 asymmetries in SIDIS and e+e- annihilation 0.2 0.02 ) x ) ( x ( World data from (1) 1 0.0 T ? 1 0.00 HERMES, COMPASS xh and JLab-6 GeV xf 0.2 − 0.02 − e+e- data from BELLE 0.4 and BABAR − 0.04 50 − 50 u Monte Carlo method with u 40 d nested sampling 40 SoLID d algorithm is applied 30 SoLID Error 30 / Error 20 / World 20 Including both systematic World Error 10 and statistical uncertainties Error 10 0 0.0 0.2 0.4 0.6 0.8 1.0 0 x 0.00 0.25 0.50 0.75 1.00 x Ref: Z.