Experimental investigation of the nucleon transverse structure

Transcription

1 Electron-Nucleus Scattering XIII Experimental investigation of the nucleon transverse structure Silvia Pisano Laboratori Nazionali di Frascati INFN.

2 The unsolved proton How do the lagrangian degrees of freedom relate to the hadrons we observe? How the spin and the mass of the nucleon emerge from its constituens characteristics? How do the nucleon picture change with the resolution of the hard probe (evolution)? What part of the nucleon spin is due to gluons and sea quarks? What is the role of the s-quark in the nucleon? Valence description Valence + sea quarks + gluons

3 Electromagnetic form factors and elastic scattering The response of the nucleon to the elastic scattering, as encoded in the electromagnetic form factors, is still not clear: two different behaviours depending on the method adopted in the measurement Scaling behaviour SLAC, Rosenbluthlike extractions New through Polarization Transfer

4 The partonic substructure: Deep-Inelastic Scattering By increasing the virtuality of the virtual photon, i.e. by improving the spatial resolution of the probe, the Deep-Inelastic Scattering regime is entered. The partonic substructure is resolved SCALING BEHAVIOUR point-like constituents are identified (no Q 2 dependence) The nucleon is described in terms of collinear partons sharing its momentum:

5 Longitudinal view of the nucleon Longitudinal Parton Distribution Functions q x : number density of an unpolarized quark in an unpolarized nucleon q x : number density of longitudinally polarized quark in a longitudinally polarized nucleon δq x : number density of transversely polarized quarks in a transversely polarized nucleon transversity first extraction by Anslmino et al., arxiv:

6 The proton spin puzzle Σ = u + d + s

7 From longitudinal to transverse view Why do we extend the description to a transverse view? 1. new degrees of freedom explored, that offer new insights into the nucleon structure 2. can help in addressing important open questions To study the Orbital Angular Momentum transverse momenta and positions have to be considered what is the role of the parton Orbital Angular Momentum (OAM)? s-quark content of the nucleon through the fragmentation process q b T p T what other contributions have to be included in the computation of the nucleon spin? we need to extend the simple, longitudinal picture and allow transverse degrees!

8 5D mapping of the nucleon Wigner «Mother» functions are quantumphase distributions of quarks not directly accessible, we can only extract their 3D reductions Picture by A. Bacchetta

9 GPDs&TMDs: 3D reductions of the Wigner functions Wigner Functions: quantum phase-space quark distributions in the nucleon W Γ r, k = dk 2π 2 W Γ r, k TMDs: 3D imaging in the momentum space GPDs: 3D imaging in the coordinate space integrated over spatial coordinates: Tranverse Momentum Distributions accessed through Semi-Inclusive Deep Inelastic Scattering integrated over momentum space: Generalized Parton Distributions measured through exclusive reactions

10 Transverse Momentum Dependent PDFs 8 leading-twist TMDs They depend on the parton longitudinal fraction x and on its transverse momentum k T full 3D dynamics Two natural momentum scales: Q 2 &p T, the transverse p of the produced hadron 3 survive the k T -integration and reduce to the longitudinal, 1D PDFs Off-diagonal elements interference among wave function of different angular momenta (OAM, spin-orbit effect)

11 Tranversely pol. target Longitudinally pol. target Unpolarized target Experimental access to TMDs through SIDIS Semi-Inclusive Deep-Inelastic Scattering: (at least) one hadron observed in the final state with the outgoing electron Structure Functions TMDxFFxC it also brings information on the fragmentation process, important to understand HADRONIZATION

12 The nucleon content through the fragmentation process In the structure functions TMDs are coupled to the Distribution Functions they allow to understand how we go from the Lagrangian degrees of freedom quarks and gluons to the hadrons we observe can shed light on the flavour content of the nucleon

13 Transverse correlations inside the nucleon through TMDs Three transverse degrees of freedom appear: the nucleon transverse spin S N the quark transverse spin s q 3. the quark transverse momentum k q Correlations explored through specific TMDs, i.e. specific modulations in the crosssection Transversity correlation among s q and S N Sivers function correlation between k q and S N Boer-Mulders correlation among s q and k q observable also with an unpolarized target

14 3D in the coordinate space: Generalized Parton Distributions Generalized Parton Distributions transverse spatial images of quarks and gluons as a function of their longitudinal momentum fraction 4 GPDs for any quark flavor: 2 helicity-conserving and 2 helicity-flipping H, vector E, tensor x t = p p 2 ξ x B 2 x B H, axialvector E, pseudoscalar

15 Exploring the Orbital Angular Momentum through GPDs Under specific kinematical conditions, GPDs relate to PDFs and FFs. Optical theorem: forward GPDs DIS x-integral Form Factors Second x- moment Ji s sum rule

16 Accessing GPDs: Deeply-Virtual Compton Scattering In the Deeply-Virtual Compton Scattering an incident electron exchanges a virtual photon with a quark of the proton. An emission of a real photon from the target follows. The process, under appropriate kinematic conditions, gives access to the GPDs. Q 2 = e e 2 x B = Q2 2mν t = p p 2 x B ξ 2 x B ν = E e E e

17 Accessing GPDs through DVCS observables The following observables are sensible to different combinations of Compton Form Factors and electromagnetic Form Factors: 1. Beam-Spin Asymmetry: σ LU sin φ Im F 1 H + ξ F 1 + F 2 H + kf 2 E dφ 2. Target-Spin Asymmetry: σ UL sin φ Im F 1 H + ξ F 1 + F 2 H + kf 2 E dφ Im H p, H p, E p Im H n, H n, E n Im H p, H p, Im H n, E n, E n 3. Double-Spin Asymmetry: σ LL (A + Bcos φ) Re F 1 H + ξ F 1 + F 2 H + x B 2 E dφ Re H p, H p, Re H n, E n, E n 4. Transverse Target-Spin Asymmetry: σ UT sin φ Im k(f 2 H F 1 E) + dφ Im H p, E p Im H n

18 The ideal experiment to map the nucleon Both TMDs&GPDs need specific experiment characteristics to be explored: 1. Beam energy high enough to reach hard regime 2. large kinematic coverage for full mapping 3. polarized beams&targets to access ALL the modulations in the cross-sections 4. Different Targets as H 2, D 2, NH 3, ND 3 with longitudinal/transverse polarizations 5. High luminosity to extract small cross sections in a fully differential analysis 6. Hermetic detectors (to ensure exclusivity for DVCS) and excellent hadron identification (fragmentation in SIDIS) F. Gross, «Making the case for Jefferson Lab» The first decade of Science at Jefferson Lab JoP, Conf. Series 299 (2011)

19 Worldwide facilities (a non exhaustive map) SIDIS in fixed-target experiments e-p: Hermes JLab (Hall-A, B, C) Compass Fragmentation in e + e annihilations: BaBar@SLAC Belle@KeK

20 A joint venture to explore the phase-space

21 Thomas Jefferson National Accelerator Facility (aka JLab) The Continous Electron Beam Accelerator Facility (CEBAF) is installed in the Thomas Jefferson National Accelerator Facility (Newport News, VA, USA). It provides a continous electron beam with a duty factor ~ 100%; with a beam energy up to 6 GeV; has a good energy resolution ( σ E E ~10 5 ); and the beam has a polarization ~ 85%

22 Jefferson Lab in the 6 GeV era Hall-A 1. Very-high luminosity 2. test of kinematic approximations (scaling) 3. Transverselypolarized 3 He target Hall-B 1. High luminosity 2. Large acceptance 3. Unpolarized 2 H Longitudinallypolarized 3 NH target Hall-C 1. Very-high luminosity 2. systematics tests 3. high-precision measurements

23 The 12-GeV upgrade 4 experimental halls with a longitudinally-polarized electron beam of E e up to 12 GeV.

24 Generalized Parton Distributions 1. Does the theoretical description encoded in the Handbag Diagram apply to the kinematics explored with fixed-target experiments? test of SCALING in Hall- 2. DVCS Beam-Spin Asymmetries and transverse spatial distributions of the quarks A LU in Hall-B@JLab Selected results 3. Phenomenological constraints on the OAM from DVCS measurements neutron A LU & proton A UT in Hall- B@JLab Transverse Momentum Dependent Distributions 1. Does the target polarization affect the quark momentum distributions? & Hermes 2. Is the flavour content of the nucleon as explored through fragmentation consistent with expectations? & Hermes

25 Scaling test for DVCS in Hall-A Beam-polarized and unpolarized cross sections with high precision at different electron-beam energies to test the scaling Q 2 dependence of dσ at fixed x B σ LU sin φ Im F 1 H + ξ F 1 + F 2 H + kf 2 E dφ Large Q 2 region explored with high statistics

26 High-statistics A LU extraction@hall-b in the 6 GeV era First CLAS DVCS devoted experiment F. X. Girod et al., Phys. Rev. Lett. 100, (2008).

27 GeV: High-statistics BSA - E σ LU sin φ Im F 1 H + ξ F 1 + F 2 H + kf 2 E dφ

28 From GPDs to quark spatial distributions arxiv: M. Guidal, H. Moutarde, M. Vanderhaeghen t dependence of the imaginary part of the GPD H can be translated into the spatial charge density

29 Quark orbital angular momentum & GPD E To access E u &E d both E p &E n are needed. Proton GPD E p : cos φ modulation in σ UT on proton Neutron GPD E n : A LU on the neutron E A UT on proton H, E u ξ, ξ, t = H, E p ξ, ξ, t H, E n ξ, ξ, t H, E d (ξ, ξ, t) = H, E n ξ, ξ, t H, E p ξ, ξ, t E A LU on neutron

30 Spin-Orbit information through the Sivers Function A. Bacchetta, Conti, Guagnelli, Radici, arxiv:1003:1328 Non-zero Sivers distribution of quarks in transverse momentum affected by the direction of the nucleon s spin

31 Collins Function: the kaon puzzle and the role of the s-quark Scattering on u-quark dominate same Fragmentation behaviour expected for pions and kaons k + Collins bigger than π + one what is the role of the s-quark?

32 Looking the nucleon at a higher resolution With an increasing Q 2, both sea-quarks and gluons degrees of freedom start to play a more and more important role. Jefferson Lab and Hermes explored the valence-quark region, while COMPASS moved toward the sea-quark one. What about the gluon-dominated regime? What it the spatial distributions of sea-quarks and gluons? How do gluon contribute to the nucleon spin? Where the saturation of gluon densities begins? How does the nuclear environment affect the parton distributions? EIC White Paper

33 Electron-Ion Collider A collider is needed to reach the gluonsaturated domain electron probe will provide the unmatched precision of the electromagnetic probes dynamical interplay between sea quarks & gluons through their distributions change of distributions when going from small to large x, to relate sea and valence quarks dependence on the quark flavours

34 EIC candidates

35 Conclusions Despite being a building block of the observed matter, the nucleon protons and neutrons is far from being fully understood The mechanisms leading from its constituents to its macroscopic characteristics, as its mass and spin, are not clear To shed light on these aspects it is needed to access nucleon transverse degrees of freedoms, both in momentum (TMDs) and in coordinate (GPDs) space Semi-Inclusive Deep-Inelastic Scattering provides access to the correlations among the transverse degrees of freedom, and allows to explore the fragmentation mechanism the role of the s-quark in the nucleon is still unclear Fragmentation Functions can bring information on the role this flavour plays inside the proton new data are coming in the close (JLab12&COMPASS) and far (EIC) future Stay tuned!

36 backup

37 Sentisivity to GPDs in observables - Compton Form Factors Only (ξ, t) are experimentally accessible, not x. GPDs will enter in the observables through The two parts will be accessible through observables sensible to the imaginary (A LU, A UL ) or the real part (A LL, A BeamCharge ) of the amplitude. The following Compton Form Factors are introduced (experimentally observable): ReH q = e 2 1 qp H q x, ξ, t H q ( x, ξ, t) 0 ImH q = πe 2 q H q ξ, ξ, t H q ( ξ, ξ, t) 1 1 ξ x ξ+x dx

38 Deep Inelastic Scattering

39 Tranversely pol. target Longitudinally pol. target Unpolarized target Semi-Inclusive DIS cross-section 18 structure functions appear in the cross-section F ij,k DF FF They can be identified through specific modulations It is important combine measurements with unpolarized/longitudinally/trans versely-polarized beam&targets

40 Upgraded GeV Hall-A Hall-A - SoLID High Resolution Spectrometer (HRS) pair and specialized large installation experiments Hall-C Hall-B Super High Momentum Spectrometer (SHMS) at high luminosity and forward angles CLAS12: large acceptance, high luminosity

41 Deeply-Virtual Compton Scattering & GPD knowledge DVCS data in the valence region Hall-A: unpolarized and beam-polarized cross-section Hall-B: beam-spin asymmetries, longitudinally-polarized target spinasymmetries HERMES: beam-charge, beam-spin and target-spin asymmetries All included in CFFs extractions H Im CFF constrained at the level of 15% Wanted: 1. more observables 2. more precise data 3. larger phase-space coverage COMPASS: DVCS program (2016) 160 GeV muon beam (recoil detector for full exclusivity): x B = region explored JLAB12: Hall-A, B, C high-statistics in a wide kinematics

42 12-GeV DVCS program nucleon polarization unpolarized longitudinallypolarized transverselypolarized Sensitivity to GPDs H, H, E H, H, E E, H E : Hall-A, p E : Hall-B, p E : Hall-B, n E : Hall-C, p PR : Hall-B, p (DVMP - π 0, η) E : Hall-B, p (NH 3 ) LOI : Hall-B, p (HD) Good mapping in the x B, Q 2, t bins big impact in constraining CFFs

43 Deeply-Virtual Compton JLab Two processes contribute to the same (e, p, γ) final state: Bethe-Heitler and Deeply-Virtual Compton Scattering. σ = BH 2 + I BH DVCS + DVCS 2 I BH DVCS gives rise to spin asymmetries, which can be connected to combinations of GPDs

44 Semi-Inclusive with 12 GeV Three halls involved ALL Beam/Target combinations explored Different targets for FLAVOR SEPARATION multi-d mapping N/q U L T U f 1 h 1 L g 1 h 1L T f 1T g 1T h 1, h 1T proton (H 2, NH 3, HD) deuterium (D 2, ND 3 ) 3 helium ( He) E : π +, π, π 0 E : k +, k, k 0 E : π +, π, k +, k C : π 0 E : π +, π, π 0 E :k +, k, k 0 C (SoLID) PR : π +, π, π 0, k +, k, k 0 PR : di-hadron SIDIS E : π +, π, π 0, k +, k, k 0 E : π +, π, k +, k C : π 0 E07-107: π +, π, π 0 E09-009: k +, k, k 0 E : π +, π E10-006: π +, π (SoLID) E : π +, π, k +, k (SBS)

45 Physics in the 12-GeV era Elba XIII Workshop June 23th - 27th, 2014

46 JLab12 impact on Im H &Re(H) M. Guidal, H. Moutarde, M. Vanderhaeghen: hep-ph > arxiv:

47 Hall-A setup: SBS (hadrons) & BB (electron) 3 He 60-cm long target Projected luminosity: 2x10 37 electron nucleon cm 2 s 1 (2x10 36 electron polarized neutron cm 2 s 1 )

48 SBS for SIDIS experiments

49 BigBite 1. tracker 2. gas Cherenkov counter 3. two-layer electromagnetic calorimeter 4. scintillator hodoscope