GPDs at an Electron Ion Collider Salvatore Fazio

GPDs at an Electron Ion Collider Salvatore Fazio Brookhaven National Laboratory Upton, New York (for the BNL EIC Science Task Force) DIFFRACTION 2012 Puerto del Carmen, Lanzarote – Canary Islands September 10 -15, 2012

The EIC project Electron Ion Collider project (EIC) ‐> 2 options: Brookhaven National Laboratory (e. RHIC) Thomas Jefferson National Laboratory (ELIC) ELIC e. RHIC Center mass energy range: √s=28 -200 Ge. V High beam polarization for both hadrons and electrons Mission: Studying the Physics of Strong Color Fields September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 2

The e. RHIC idea (Existing) Electron accelerator (to be build) Unpolarized and polarized leptons 5 -20 (30) Ge. V p e- Polarized protons 75 -250 (325) Ge. V Light ions (d, Si, Cu) e- Heavy ions (Au, U) 50 -100 (130) Ge. V/u e+ Polarized light ions (He 3) 215 Ge. V/u Center mass energy range: √s=28 -200 Ge. V September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 3

EIC/e. RHIC – experimental features e. RHIC detector Why EIC is unique: REAR FORWARD q 5 - 30 Ge. V electrons on 75 -250 Ge. V (50100 Ge. V) protons (nuclei). Polarization of electrons and protons (nuclei) q Lumi: ~1034 cm-2 s-1 Important for exclusive DIS: • Dedicated forward instrumentation • High tracker coverage • Very High lumi! What are the detector requirements: Important for exclusive diffraction: • Hermetic Central Tracking Detector • Good EM calorimeter resolution with fine granularity • Preshower em cal p 0 background • Very forward calorimetry • Roman pots (and with excellent acceptance) September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote e (k) ’) e’(k Q 2 *(q) VM, W P (p) IP t P’(p’ ) 4

Direct |t| measurement – Roman Pots Accepted in“Roman Pot”(example) at s=20 m 5 x 100 Ge. V Quadrupoles acceptance 20 x 250 Ge. V 5 x 100 Ge. V Simulation based on e. RHIC 10 s from the beam‐pipe • high‐|t| acceptance mainly limited by magnet aperture • low‐|t| acceptance limited by beam envelop (~10σ) • |t|‐resolution limited by – beam angular divergence ~100μrad for small |t| – uncertainties in vertex (x, y, z) and transport – ~<5‐ 10% resolution in t (RP at STAR) September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 5

(2+1)-Dimensional imaging of the proton Open questions: PDFs do not resolve transverse coordinate or momentum space In a fast moving nucleon the longitudinal size squeezes like a `pizza’ but transverse size remains about 1 fm Goal: nucleon tomography! Proton imaging what is the spatial distribution of quarks and gluons in nucleons/nuclei Possible window to orbital angular momentum September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 6

Accessing the GPDs Dominated by H slightly dependent on E Angle btw the production and scattering planes Angle btw the scattering plane and the transverse pol. vector Requires a positron beam at e. RHIC Dominated by H slightly dependent on E sin(FT-f. N) governed by E and H September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 7

Deeply Virtual Compton Scattering γ* VM (ρ, ω, φ, J/ψ, Υ) V γ* DVCS (γ) IP p p Scale: Q 2 + M 2 γ Q 2 DVCS properties: • Similar to VM production, but γ instead of VM in the final state • Very clean experimental signature • Not affected by VM wave-function uncertainty • Hard scale provided by Q 2 • Sensitive to both quarks and gluons (via evolution) September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 8

DVCS phase-space 20 x 250 Ge. V Stage 2 5 x 100 Ge. V Stage 1 EIC: the first machine to measure xsec. and asymmetries HERA results limited by lack of statistics September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 9

Scanning the phase space… EIC lumi: ~10 fb‐ 1/year @ stage 1 – 5 x 100 ~100 fb‐ 1/year @ stage 2 – 20 x 250 5 X 100 – stage 1 Acceptance criteria EIC willpots: provide • for²Roman 0. 03<sufficient |t| < 1. 5 lumi Ge. V 2 in multi‐dimensions • 0. 01 to < ybin < 0. 85 2 • h <² 5 wide x and Q range needed to extract GPDs ØBH rejection criteria (applied to x-sec. measurements) 20 X 250 – stage 2 • y < 0. 6 • (θel-θg) > 0 • Eel>1 Ge. V 2; Eg>1 Ge. V 2 Ø Events smeared for expected resolution in t, Q 2, x Ø Systematic uncertainty assumed to be ~5% Ø Overall systematic uncertainty from luminosity measurement not taken into account … we can do a fine binning in Q 2 and W… and even in |t| September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 10

BNL EIC Science Task Force ds/d|t| 20 x 250 dσ/d|t| b=5. 6 |t|‐differential cross section is a very powerful tool Ø Gives precise access to GPD H Ø Fourier transform ‐> direct imaging in impact parameter space • |t|‐binning –> 3 * resolution (or higher) • Statistical error down to 1% EIC lumi: ~10 fb‐ 1/year @ stage 1 – 5 x 100 ~100 fb‐ 1/year @ stage 2 – 20 x 250 September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 11

20 x 250 5 x 100 Ge. V ‐ 1 Lumi=10 fb Lumi=100 fb‐ 1 BNL EIC Science Task Force ds/d|t| ‐ 4 dσ/d|t| - large |t| EIC lumi: ~10 fb‐ 1/year @ stage 1 – 5 x 100 ~100 fb‐ 1/year @ stage 2 – 20 x 250 Dependence at large‐|t| still unknown Measurements possible also at large‐|t| with a sufficient precision Very important to constrain GPDs September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 12

Asymmetries Beam long. and transverse polarization beam helicity asymmetries (AUL, ALU, AUT) Unpolarized positron beam charge asymmetry (Ac) GPD H GPD E ~ GPD H The complex Amplitude can be accessed September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 13

Transverse target-spin asymmetry Different assumptions for E sin(FT-f. N) governed by E and H Gives access to GPD E September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 14

Imaging Ø A global fit over all mock data was done, based on the GPDs‐based model: [K. Kumerički, D Müller, K. Passek‐ Kumerički 2007] Ø Known values q(x), g(x) are assumed for Hq, Hg (at t=0 forward limits Eq, Eg are unknown) Shift due to GPD E er uri September 10 -15, 2012 Fo r rie Fou Unpolarized sea-quarks Fo ur ie r Polarized sea-quarks S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote Impact of e. RHIC: ü Excellent reconstruction of Hsea, and Hg (from dσ/dt) ü Reconstruction of GPD E(connection to the orbital momentum g‐sum role) gluons 15

All details and more to appear in: g n i m Co September 10 -15, 2012 … n o so S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 16

J/ψ *p ‐> J/y p Fourier Øpseudo-data generated using a version of Pythia tuned to J/y data from HERA Øwave function uncert. (non-relativistic approximation) Ømass provides hard scale • Sensitive to gluons • Both photo- and electro-production can be computed BNL EIC Science Task Force September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 17

J/ψ September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 18

GPDs on nuclear targets q How does the nuclear environment modify parton‐parton correlations? q How do nucleon properties change in the nuclear medium? Nuclear GPDs ≠ GPDs of free nucleon • Diffraction in e+p: ‣ coherent ⇔ p intact ‣ incoherent ⇔ breakup of p ‣ 15% of all events at HERA September 10 -15, 2012 • Diffraction in e+A: ‣ coherent diffraction (nuclei intact) ‣ breakup into nucleons (nucleons intact) ‣ incoherent diffraction ‣ Predictions: σdiff/σtot in e+A ~25 -40% S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 19

GPDs on nuclear targets Exclusive VMP in e+A f J/y ØLow‐t: coherent diffraction dominates ‐ gluon density ØHigh‐t: incoherent diffraction dominates ‐ gluon correlations Important: need good breakup detection efficiency to discriminate between the two scenarios September 10 -15, 2012 • Coherent events identified by vetoing nuclear break‐up measure emitted neutrons in a ZDC • rapidity gap sufficient to identify coherent events S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 20

Summary Ø A lot of experience carried over from HERA Ø DVCS can be used to drive the requirements for a dedicated new detector Ø Simulation shows how an EIC can much improve our knowledge of GPDs Ø A fine binning of x-sec and symmetries will be possible, uncertainties mostly dominated by systematics Ø Large potential for an accurate 2+1 D imaging of the polarized and unpolarized quarks and gluons inside the hadrons (and nuclei!) Brookhaven National Lab ‐ EIC Science Task Force People: Elke Aschenauer, Thomas Ullrich, Thomas Burton, Ramiro Debbe, Jamie Dunlop, Salvatore Fazio, Wlodek Guryn, Matt Lamont, J. H. Lee, Dieter Mueller, Hubert Spiesberger, Marco Stratmann, Tobias Toll, Liang Zheng Working groups: ep, e. A, detector and machine design Web‐page: https: //wiki. bnl. gov/eic/index. php/Main_Page September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 21

Back up September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 22

The RHIC site @ BNL 12 o’clock proposed PHOBOS PHENIX LIN AC RHIC v = 0. 99995⋅ c = 186, 000 miles/sec STAR EBIS BOOSTER BRAHMS RF ERL Test Facility AGS TANDEMS September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 23

(2+1)-D imaging of the proton Longitudinal momentum & Wigner Distributions helicity distributions transverse charge & current densities Fourier trf. transverse momentum distributions (TMDs) semi−inclusive processes parton densities inclusive and semi−inclusive processes Wigner Distribution W(x, r, kt) September 10 -15, 2012 generalized parton distributions (GPDs) exclusive processes impact parameter distributions form factors elastic scattering generalized form factors lattice calculations 3 D picture in coordinate space generalized parton distributions exclusive reaction like DVCS and VMP S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 24

Vector Meson Production W & t dependences: probe transition from soft hard regime r f J/Y U s ~ Wd s steep ~ e-b|t| energy dependence of s inuniversality presence of the hard scale of b-slope parameter: point-like configurations dominate September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 25 25

MC simulation Written by E. Perez, L Schoeffel, L. Favart [ar. Xiv: hep-ph/0411389 v 1] The code MILOU is Based on a GPDs convolution by: A. Freund and M. Mc. Dermott [All ref. s in: http: //durpdg. dur. ac. uk/hepdata/dvcs. html] üGPDs, evolved at NLO by an indipendent code which provides tables of CFF - at LO, the CFFs are just a convolution of GPDs: üprovide the real and imaginary parts of Compton form factors (CFFs), used to calculate cross sections for DVCS and DVCS-BH interference. -> The B slope is allowed to be costant or to vary with Q 2: ü üProton dissociation (ep → eγY) can be included üOther non-GPD based models are implemented like FFS, D D September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 26

Data simulation & selection Acceptance criteria • for Roman pots: 0. 03< |t| < 0. 88 Ge. V 2 • for |t| > 1 Ge. V 2 detect recoil proton in main detector • 0. 01 < y < 0. 85 Ge. V 2 • h<5 The code MILOU by E. Perez, L Schoeffel, L. Favart [ar. Xiv: hep-ph/0411389 v 1] is Based on a GPDs convolution by: A. Freund and M. Mc. Dermott [http: //durpdg. dur. ac. uk/hepdata/dvcs. html] ØBH rejection criteria (applied to x-sec. measurements) • y < 0. 6 • (θel-θg) > 0 • Eel>1 Ge. V 2; Eel>1 Ge. V 2 Ø Events smeared for expected resolution in t, Q 2, x Ø Systematic uncertainty assumed to be ~5% (having in mind experience from HERA) 0. 01 < |t| < 0. 85 Ge. V 2 (Low-|t| sample) • Very high statistics • Systematics will dominate! • Within Roman pots acceptance 1. 0 < |t| < 1. 5 Ge. V 2 (Large-|t| sample) • Xsec goes down exponentially • requires a year of data taking • Main detector can be used in measuring |t| Ø Overall systematic uncertainty from luminosity Stage 1: 5 X 100 Ge. V ~10 fb‐ 1 (~ 10 months) measurement not taken into account Stage 2: 20 X 250 Ge. V ~100 fb‐ 1 (~ 1 year) September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 27

DVCS - BH DVCS e BH e p p DVCS cross section: BH becomes background ‐> must be removed Uncertainty on proton form factor uncertainty on BH xsec ~ 3% (at LO) Asymmetry measurement -> BH is the vehicle to study interference term September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 28

q vs E 10 X 100 September 10 -15, 2012 S. Fazio: DIFFRACTION 2012 - Puerto del Carmen, Lanzarote 29