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 QiuH. 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. Ye et al, Phys. Lett. B 767, 91 (2017) SoLID baseline used H. Gao 22 SoLID Impact on Tensor Charge
Definition
• A fundamental QCD quantity: Dyson-Schwinger equation Lattice QCD Models matrix element of local operators. Phenomenology Future experiment gd gu T T • Moment of the transversity Wang et al. (2018) Yamanaka et al. (2013) distribution: valence quark Bhattacharya et al. (2016) Abdel-Rehim et al. (2015) Gockeler et al. (2005) dominant. Cloet et al. (2008) Wakamatsu (2007) • Calculable in lattice QCD. Pasquini et al. (2005) Gamberg, Goldstein (2001) Schweitzer et al. (2001) • Quark tensor charge also connects Ma, Schmidt (1998) Barone et al. (1997) Schmidt, Soffer (1997) to quark electric dipole moment He, Ji (1996) Kim et al. (1996) Kang et al. (2016) Radici et al. (2015) Goldstein et al. (2014) Anselmino et al. (2013) JLab12 SoLID Baseline
Including both -0.5 0 0.5 1 1.5 2 2.5 systematic and statistical SoLID baseline uncertainties used H. Gao 23 Neutron Electric Dipole Moment (EDM)
d u s dn = δT du +δT dd +δT ds - +
d•E s = 1/2
• If neutron possesses EDM, in an electric field, ! ! Hamiltonian H = − d σ •E € n – changes sign under T (P) symmetry operation
• d n is more sensitive to the θ term than to δCKM • Sensitive to new CP-violating mechanism(s) beyond SM Quark EDM appears only at the three-loop level€ H. Gao 24 € Constraint on Quark EDMs d u s dn = δT du +δT dd +δT ds Constraint on quark EDMs with combined proton and neutron EDMs
du upper limit dd upper limit
-24 -24 Current gT + current EDMs 1.27×10 e cm 1.17×10 e cm -25 -24 SoLID gT + current EDMs 6.72×10 e cm 1.07×10 e cm -27 -28 SoLID gT + future EDMs 1.20×10 e cm 7.18×10 e cm Include 10% isospin symmetry breaking uncertainty Sensitivity to new physics
Three orders of magnitude Probe to 30 ~ 40 times higher scale improvement on quark EDM limit
Current quark EDM limit: 10-24e cm ~ 1 TeV
Future quark EDM limit: 10-27e cm 30 ~ 40 TeV
H. Gao, T. Liu, Z. Zhao, PRD 97, 074018 (2018)
Proton Charge Radius • An important property of the nucleon – Important for understanding how QCD works – Challenge to Lattice QCD (exciting new results, Alexandrou et al.) – An important physics input to the bound state QED calculations, affects muonic H Lamb shift (2S 1/2 – 2P 1/2) by as much as 2%
• Electron-proton elastic scattering to determine electric form factor (Nuclear Physics)
2 2 dG(q ) < r > = −6 | 2 dq2 q =0
• Spectroscopy (Atomic physics) – Hydrogen Lamb shift – Muonic Hydrogen Lamb shift H. Gao 27
p GE Pt E + E0 ✓ p = tan (1) GM Pl 2M 2
A a b Gp /Gp R = 1 = 1 1 · E M (2) A A a b Gp /Gp 2 2 2 · E M
p 2 p p 2⌧vT 0 cos ✓⇤GM +2 2⌧(1 + ⌧)vTL0 sin ✓⇤ cos ⇤GM GE Aexp = PbPt Electron-protonp 2 elasticp 2 scattering(3) (1 + ⌧)pvLGE +2⌧vT GM • Unpolarized elastic e-p cross section (Rosenbluth separation) G and G d ↵2 cos2 ✓ E Gp 2 + ⌧Gp 2 ✓ E M = 2 0 E M +2⌧Gp 2 tan2 d⌦ 4E2 sin4 ✓ E 1+⌧ M 2 2 ! (4) 1 2 ✓ = f A + B tan M rec 2 ✓ ◆ One-photon-exchange • Recoil proton polarization measurement (pol beam only) p p GE Pt E + E0 ✓ GE Pt E + E0 ✓ p p= tan p = tan(1) (1) G G Pl P 2EM+ E 2G✓ Pl 2M 2 M E = t 0 tan M (1) Gp P 2M 2 • AsymmetryM (super-ratio)l measurement p p p p (pol beamA1 and apol1 target)b1 G E/GM A1 a1 b1 GE/GM RA = = · pRpA p=p = · p (2)p (2) A2A a2 a b2 bG G/G/G A2 a2 b2 G /G R = 1 = 1 · 1 ·E E M M · E (2)M A A a b Gp /Gp 2 2 2 · E M p 2 p 2 p p p p 2⌧vT 0 cos ✓⇤GM +2 2⌧2(1⌧v +T 0⌧cos)vTL✓⇤0GsinM ✓⇤+2cos 2⇤⌧G(1M +GE⌧)vTL0 sin ✓⇤ cos ⇤GM GE Aexp = PbPt Aexp = PbPt (3) (3) 2⌧v cos ✓ Gp 2 +2 p2⌧2(1 + ⌧)v p sin2 ✓ cos pG2 p Gp p 2 T 0 ⇤(1M + ⌧)pvLGE +2⌧vT GTLM0(1 + ⌧⇤)pvLG⇤E M+2E⌧vT GM Aexp = PbPt p 2 p 2 (3) C. Crawford(1 et +al.⌧ PRL98,)pvLGE 052301+2⌧ v(2007)T GM H. Gao 28 d ↵2 cos2 ✓ E Gpd2 + ⌧G↵p22cos2 ✓ E Gp 2✓+ ⌧Gp 2 ✓ = 2 0 E = M +22⌧Gp0 2 tanE2 M +2⌧Gp 2 tan2 2 2 4 ✓2 ✓ p 2 p 2 4 ✓ M M d⌦d 4E ↵sincos E E0 Gd⌦1++⌧4⌧EG2 sin E 1+2 ✓ ⌧ 2 = 2 2 E M +22 ⌧G p 2 tan2! (4) ! (4) d⌦ 4E2 sin4 ✓ E 1+⌧ M 2 1 2 2 ✓ 1 2 ✓ ! (4) = M frec A + B tan = M frec A + B tan 1 22 ✓ 2 = f ✓ A + B tan◆ ✓ ◆ M rec 2 ✓ ◆
1
1 1 1 Hydrogen Spectroscopy
The absolute frequency of H energy levels has been measured with an accuracy of 1.4 part in 1014 via comparison with an atomic cesium fountain clock as a primary frequency standard.
Yields Rydberg constant R∞ (one of the most precisely known constants)
Comparing measurements to QED calculations that include corrections for the finite size of the proton can provide very precise value of the rms proton charge radius Proton charge radius effect on the muonic hydrogen Lamb shift is 2%
H. Gao 29 Muonic hydrogen Lamb shift at PSI (2010, 2013)
2010 value is rp = 0.84184(67) fm H. Gao 30 2013 PSI results reported in Science
H. Gao 31 2013: rp = 0.84087(39) fm, A. Antognini et al., Science 339, 417 (2013) The situation on the Proton Charge Radius in 2013
This proton charge radius puzzle triggered intensive experimental and theoretical efforts worldwide in the last decade or so H. Gao 32 How to resolve the puzzle? - Incomplete list • Revisit of the state of the art QED calculations: E. Borie (2005), Jentschura (2011), Hagelstein and Pascalutsa (2015) • Contributions to the muonic H Lamb shift: Carlson and Vanderhaeghen,; Jentschura, Borie, Carroll et al, Hill and Paz, Birse and McGovern, G.A. Miller, J.M. Alarcon, Ji, Peset and Pineda…. • Higher moments of the charge distribution and Zemach radii, Distler, Bernauer and Walcher (2011), de Rujula (2010, 2011), Cloet and Miller (2011) • Extrapolation in electron scattering: Higinbotham et al. (2016), Griffioen, Carlson and Maddox (2016) • Reanalysis of ep elastic data: Distler, Walcher, and Bernauer (2015), Arrington (2015), Horbatsch and Hessels (2015), T. Hayward, K. Griffioen (2018),….. • Discrepancy explained/somewhat explained by some but others disagree: Lorentz et al., Ronson, Donnelly et al. • New physics: new particles, Barger et al., Carlson and Rislow; Liu and
Miller,….New PV muonic force, Batell et al.; Carlson and Freid; Extra
dimension: Dahia and Lemos; Quantum gravity at the Fermi scale R. Onofrio • New experiments: Mainz, JLab (PRad), MUSE at PSI, Japan, France, CERN; H spectroscopy (Germany, France, Canada), … H. Gao 33 The Proton Charge Radius Puzzle in 2018
5.6 σ CODATA-2014
µp 2013 e-p scattering (CODATA-2014)
µp 2010 H spectroscopy (CODATA-2014)
H spectroscopy 2018 H spectroscopy 2017 0.8 0.82 0.84 0.86 0.88 0.9 0.92 Proton charge radius R (fm) p
Electron scattering: 0.879 ± 0.011 fm (CODATA 2014) Muon spectroscopy: 0.8409 ± 0.0004 fm (CREMA 2010, 2013) H spectroscopy (2017): 0.8335 ± 0.0095 fm (A. Beyer et al. Science 358(2017) 6359) H spectroscopy (2018): 0.877 ± 0.013 fm (H. Fleurbaey et al. PRL.120(2018) 183001)
not shown: ep scattering (ISR, 2017): 0.810 ± 0.035stat. ±0.074syst. ±0.003 (delta_a, delta_b) (Mihovilovic PLB 771 (2017); 0.870 ± 0.014stat. ±0.024syst. ±0.003mod. (Mihovilovic 2019) H. Gao 34 The PRad Experiment in Hall B at JLab
% High resolution, large acceptance, hybrid HyCal calorimeter (PbWO4 and Pb-Glass) % Windowless H2 gas flow target % Simultaneous detection of elastic and Moller electrons % Q2 range of 2x10-4 – 0.06 GeV2 % XY – veto counters replaced by GEM detector % Vacuum chamber
Spokespersons: A. Gasparian (contact), Mainz low Q2 data set H. Gao, D. Dutta, M. Khandaker Phys. Rev. C 93, 065207, 2016 35 Analysis – Event Selection Event selection method
1. For all events, require hit matching between GEMs and HyCal
2. For ep and ee events, apply angle dependent energy cut based on kinematics 1. Cut size depend on local detector resolution
3. For ee, if requiring double- arm events, apply additional cuts 1. Elasticity 2. Co-planarity 3. Vertex z
H. Gao 36 Analysis – Background Subtraction • Runs with different target condition taken for background subtraction and studies for the systematic uncertainty • Developed simulation program for target density (COMSOL finite element analysis) Pressure: ~470 mTorr
~3 mTorr
< 0.1mTorr
H. Gao DNP2019 37 Analysis – Background Subtraction at 2.2 GeV • ep background rate ~ 10% at forward angle (<1.3 deg, dominated by upstream collimator), less than 2% otherwise • ee background rate ~ 0.8% at all angles ep Background Contribution ee Background Contribution 0.12 bg run, gas in, cell in bg run, gas in, cell in total total 0.014 /N /N bg run, gas out, cell out bg run, gas out, cell out bg run, gas out, cell in 0.1 bg run, gas out, cell in 0.012 residual hydrogen gas contribution residual hydrogen gas contribution background background N N 0.08 0.01 2.2 GeV data 2.2 GeV data 0.008 0.06 0.006
0.04 0.004
0.02 0.002
0 0 −3 −2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 10 10 2 2 Q (GeV ) One of scattered electron polar angle, θe1 (deg)
H. Gao DNP2019 38 Analysis – elastic cut and inelastic contribution • Using Christy 2018 empirical fit to study inelastic ep contribution • Good agreement between data and simulation o • Negligible for the PbWO4 region (<3.5 ), less than 0.2%(2.0%) for 1.1GeV(2.2GeV) in the Lead glass region
o o 2 2 o spectrum for 3.0 < θ < 3.3 ( Q ~ 0.014 GeV ) spectrum for 6.0 < θ < 7.0o ( Q2 ~ 0.059 GeV2)
300 data data simulation 80 simulation Inelastic ep (Christy 2018) Inelastic ep (Christy 2018) 250 70 counts/MeV PbWO counts/MeV 200 4 60 Lead glass region 50 region 150 40
100 30
20 50 elasticity cut 10 elasticity cut 0 0 1600 1700 1800 1900 2000 2100 2200 1600 1700 1800 1900 2000 2100 2200 2300 2400 E' (MeV) E' (MeV) M.E. Christy and P.E. Bosted. PRC 81, 055213 (2010) H. Gao DNP2019 39 Extraction of ep Elastic Scattering Cross Section
• To reduce the systematic uncertainty, the ep cross section is normalized to the Møller cross section:
• Event generators for unpolarized elastic ep and Møller scatterings have been developed based on complete calculations of radiative corrections 1. A. V. Gramolin et al., J. Phys. G Nucl. Part. Phys. 41(2014)115001 2. I. Akushevich et al., Eur. Phys. J. A 51(2015)1 (beyond ultra relativistic approximation)
• A Geant4 simulation package is used to study the radiative effects:
• Iterative procedure applied for radiative correction
H. Gao 40 Radiative corrections ep cross section / ee cross section ratio ratio
1.1 GeV 2.2 GeV
• Event generators for ep and ee elastic scattering developed based on complete calculation of radiative correction beyond URA1 • Cross checked with results from second generator2 • Include hard emission radiative photons for full correction of radiative effect with HyCal • Include effect from two photon exchange3 1. I. Akushevich et al., Eur. Phys. J. A 51(2015)1 3. O. Tomalak, Few Body Syst. 59, no. 5, 87 (2018) 2. A. V. Gramolin et al., J. Phys. G Nucl. Part. Phys. 41(2014)115001 H. Gao DNP2019 41 Elastic ep Cross Sections
• Differential cross section v.s. Q2, with 2.2 and 1.1 GeV data
• Statistical uncertainties: ~0.15% for 2.2 GeV, ~0.2% for 1.1 GeV per point
• Systematic uncertainties: 0.3%~1.1% for 2.2 GeV, 0.3%~0.5% for 1.1 GeV (shown as shadow area)
Systematic uncertainties shown as bands 42 Proton Electric Form Factor GE
1.05 1.05 1.1 GeV data 2.2 GeV data 1 1
0.95 0.95 p E p E G G 0.9 0.9 1.1 GeV data 2.2 GeV data 0.85 0.85
0.8 0.8 0.01 0.02 0.03 0.04 0.05 0.06 2×10−4 10−3 2×10−3 10−2 2×10−2 Q2 [(GeV/c)2] Q2 [(GeV/c)2]
First experiment to complete post Jlab 12-GeV upgrade – only to achieve the Lowest Q2 ever from ep elastic scattering
H. Gao 43 Introduction | PRad and Apparatus | Analysis | Result Searching the Robust fitters • Various fitters tested with a wide range of GE parameterizations, using PRad kinematic range and uncertainties: • X. Yan et al. Phys. Rev. C98, 025204 (2018) • Rational (1,1), 2nd order z transformation and 2nd order continuous fraction are identified as robust fitters with also reasonable uncertainties
2nd order z transformation ' !"(1 + !%) + !') )
, + &' − , − , ) = - - " ' ,- + & + ,- − ,"
2nd order continuous faction 1 !" ' !%& 1 + ' 1 + !'&
H. Gao 44 Proton Electric Form Factor G’E (Normalized)
• n1 and n2 obtained by fitting PRad GE to
• G’E as normalized electric Form factor:
2 • PRad fit shown as f (Q ) rp = 0.831 +/- 0.007 (stat.) +/- 0.012 (syst.) fm
n1 = 1.0002 +/- 0.0002(stat.) +/- 0.0020 (syst.), n2 = 0.9983 +/- 0.0002(stat.) +/- 0.0013 (syst.) H. Gao 45 PRad result on the radius
• PRad result: 0.831 +/- 0.007 (stat.) +/- 0.012 (syst.) fm
Antognini 2013 (µH spect.) CODATA-2014
Pohl 2010 (µH spect.) CODATA-2014 (ep scatt.)
Beyer 2017 (H spect.) CODATA-2014 (H spect.)
Fleurbaey 2018 (H spect.)
Bernauer 2010 (ep scatt.)
PRad exp. (ep scatt.)
0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 Proton charge radius r [fm] p
Xiong et al., Nature 575, 147–150 (2019) 46 Rapid Progress • The latest result published in Science on September 9, 2019 from H Lamb Shift: 0.833 +/- 0.010 fm
• CODATA released online their revised 2018 value of rp: 0.8414 +/- 0.0019 fm
Antognini 2013 (µH spect.) CODATA-2014
Pohl 2010 (µH spect.) CODATA-2014 (ep scatt.)
Beyer 2017 (H spect.) CODATA-2014 (H spect.)
CODATA-2018 Fleurbaey 2018 (H spect.)
Bezginov 2019 (H spect.) Bernauer 2010 (ep scatt.)
Mihovilovic 2019 PRad exp. (ep scatt.) (ep scatt.)
0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 Proton charge radius r [fm] p
Bezginov et al., Science 365, 1007-1012 (2019) Xiong et al., Nature 575, 147–150 (2019) 47 CODATA has also shifted the value of the Rydberg constant. Future Outlook for PRad – PRad-II
Upgrade HyCal to be replace all lead- glass modules with PbWO4 modules to have uniform high resolution (desired)
Convert to FADC based readout of HyCal Add a second GEM plane between HyCal and vacuum chamber to further reduce the backgrounds and improve vertex resolution.
Goals: improve the precision of rp measurements and start a new program of high precision measurements using the PRad method 48 PRad Collaboration Institutional List % 17 collaborating universities and institutions:
Thomas Jefferson National Accelerator % Graduate (``thesis”) Facility students: North Carolina A&T State University Duke University and TUNL Idaho State University Chao Peng (Duke) Weizhi Xiong (Duke) Mississippi State University Li Ye (MSU) University of Virginia Xinzhan Bai (UVa) Argonne National Laboratory University of North Carolina at Abhisek Karki (MSU) Wilmington % Postdocs: Kharkov Institute of Physics and Technology Chao Gu (Duke) MIT Xuefei Yan (Duke) Old Dominion University Mehdi Meziane (Duke) ITEP, Moscow, Russia Zhihong Ye (Duke) University of Massachusetts Amherst Maxime Lavilain (NC A&T) Hampton University Krishna Adhikari (MSU) College of William & Mary Rupesh Silwal (MIT) Norfolk State University Yang Zhang (Duke Ph.D. student) Yerevan Physics Institute H. Gao DNP2019 51 Summary and outlook • The proton remains puzzling after years of studies, but major progress made in resolving the charge radius puzzle • The Jlab 12-GeV and the future Electron-Ion-Collider are expected to solve the proton spin and mass puzzle • The PRad collaboration carried out a first electron- scattering experiment using a non magnetic spectrometer approach – calorimeter and GEM – Lowest 4-momentum transfer squared ever reached 10-4 (GeV/c)2 – Novel use of an internal cryogenically cooled hydrogen gas target – Simultaneous measurements of ep and ee scattering to reduce systematics • The PRad result supports the smaller value of the proton charge radius • Precision e-p scattering: PRad-II and more
Acknowledgement: The JLab SoLID collaboration, the PRad collaboration, and may others; supported in part by NSF MRI PHY-1229153 and the U.S. Department of Energy under contract number
DE-FG02-03ER41231 H. Gao 52