INT workshop on gluons and the quark sea at high energies, INT Seattle, Sep-Nov, 2010 Delia Hasch hunting the OAM a very brief review of the spin sum rule observables of OAM some attempts to quantify OAM conclusion
the spin puzzle nucleon spin: 1 1 = 2 2 n q g q s z = q + L q z + G + Lz = J + 30% zero J g W. Vogelsang [week 1] global fits for extraction of helicity distributions: [e.g. DSSV 2008] π,k inclusive DIS classical NLO analyses semi -inclusive DIS flavour tagging polarised pp scattering flavour tagging, gluon polarisation
polarised pdfs: q results driven by inclusive DIS [DSSV (2008,9)] DSSV DSSV+1 DSSV 2% DNS GRSV std [1996] Q 2 =10GeV 2 GRSV val
polarised pdfs: q π,k results driven by inclusive and semi -inclusive DIS [DSSV (2008,9)] striking impact of SIDIS data Q2=10GeV2
Q 2 =10GeV 2 polarised pdfs: G results driven by inclusive DIS & pp-scattering data impact of pp scattering data: x RHIC range 0.05 < x < 0.2
polarised pdfs pdfs: q & G global analysis of polarised DIS & pp-scattering data contributions to nucleon spin: Q 2 =10GeV 2 f 1 dx f x min ( x) s receives large negative contribution @small x g: hughe uncert. below x 0.01 1 st moment undetermined [DSSV, PRL101(2008),072001 and 0904.3821] call for new facilities: high energy polarised ep collider needed! week 6/7
the spin budget contribution of quarks 25-35% : 1 2 h 1 Σ 2 u 1 Σ s 1 2 Σ d 2? where are the missing 70%? g surprisingly small in measured range (0.05 < x g < 0.2) significant contribution of gluons and/or sea quarks @low x? golden measurement for EIC on its own week 6/7 what about the orbital angular momentum (OAM)? new concepts: GPDs & TMDs week 8/9
parton OAM studying effects of OAM: TMDs & spin-orbit correlations L=1 Sivers fct. L=1 Boer-Mulders fct. role of different orbital angular momentum components in nucleon wave-fct fct. L=2 pretzelosity
parton OAM studying effects of OAM: TMDs & spin-orbit correlations L=1 Sivers fct. L=1 Boer-Mulders fct. role of different orbital angular momentum components in nucleon wave-fct fct.. L=2 pretzelosity quantifying the quark & gluon OAM: [X. Ji, 1997] J q 1 1 q 1 = Σ + L = 2 2 xdx t 1 [ ] q q H ( x, ξ, t) + E ( x, ξ, t) = 0 J g = ~ M. Burkardt week 8 9
TMDs in SIDIS σ h XY ˆ σ f part pdf ( x) q,g h frag ( z) σ XY beam: target: λ S L,S T
leading-tw distribution functions σ h XY f ˆ σ part q,g h pdf (x) frag ( z) Boer-Mulders Sivers pretzelosity chiral-odd pdf & Collins FF [ Amsterdam notation]
signals of OAM
Sivers fct. G. Schnell [week 1] spin-orbit correlations & role of OAM [PRL2009]
Boer-Mulders fct fct. G. Schnell [week 1]
Boer-Mulders fct role of kaons (no sign change ) : fct. G. Schnell [week 1] h + h -
pretzelosity h 1T -- role of different orbital angular momentum components in nucleon n wave-fct fct. -- measures deviation of the nucleon shape from a sphere pretzel, bagel, peanut [G. Miller, M. Burkardt] requires presence of nucleon wave-fct components with L=2 e.g. s-d wave interference or quadratic in p-wave component in some quark models: measure of relativistic effects: h ( x, pt ) = q( x, pt ) h1 ( x, p (1) q q 1T T ) L q z = dx (1) q h 1 ( x) T light-cone SU(6) quark-diquark model [She, Zu, Ma 2009] bag model [Avakian et al. 2010] inclusion of gluons spoils the relations nevertheless, let s s have a look: covariant parton model [Efremov et al. 2009]
pretzelosity expected to be suppressed w.r.t. Sivers & Collins amplitudes
pretzelosity expected to be suppressed w.r.t. Sivers & Collins amplitudes ± positivity
pretzelosity -- model calculations & predictions -- ~ h1 T f 1 H D 1 1 down up π +
pretzelosity -- model calculations & predictions -- ~ h1 T f 1 H D 1 1 π + 0.1 x
signals of OAM Wigner distribution: ( mother function) W(k,b) B. Pasquini [week 1] d 3 b d 2 k dbl TMD spin-orbit correlations GPD direct access to OAM relations between TMDs and GPDs (model dependent): q(n) q(n) f1 T ( x) ~ E ( x,0,0) f q 1T q ~ κ [Burkardt 2002] [Burkardt, Hwang 2003] [Diehl, Haegeler 2005] ecc.
intuitive picture of Sivers effect FT (GPD) : momentum space impact parameter space: [M. Burkardt, M. Diehl 2002] distribution of partons in plane transverse to longitudinal momentum x polarised nucleon: spin-orbit correlations (TMDs)
intuitive picture of Sivers effect FT (GPD) : momentum space impact parameter space: [M. Burkardt, M. Diehl 2002] distribution of partons in plane transverse to longitudinal momentum x polarised nucleon: spin-orbit correlations (TMDs) Sivers fct.. from lattice [Hägler et al.]
GPDs & OAM J q, g 1 1 = xdx t 2 [ ] q, g q, g H ( x, ξ, t) + E ( x, ξ, t) = 0 1 [X. Ji, 1997] E q 0 requires orbital angular momentum proton helicity flipped but quark helicity conserved
what do we know about GPDs? Q 2 ξ ~ x Bj Q 2 >>, t<< x +ξ x ξ appear in factorisation theorem for hard exclusive processes form factors q e dx H ( x, ξ, t) = F1 ( t) q q t x x Bj H ( x, ξ, t) ξ ~ xbj E, E ~ PDFs, H q g ~ ( x,0,0) = q( x) q, ( x,0,0) = q ( x ) H g : nucleon helicity flip don t appear in DIS new information!
GPDs: : caveats x + ξ x ξ CFF hard scatt. part GPD x is mute variable (integrated over): apart from cross-over trajectory (ξ=x) GPDs not directly accessible extrapolation t 0 is model dependent
GPDs: : caveats x + ξ x ξ CFF hard scatt. part GPD x is mute variable (integrated over): apart from cross-over trajectory (ξ=x) GPDs not directly accessible extrapolation t 0 is model dependent cross sections & beam-charge asymmetry ~ Re(T DVCS ) beam or target-spin asymmetries ~ Im(T DVCS ) double DVCS: x < ξ evolution
Q 2 attempts to constrain J q J q 1 1 = lim xdx t 0 2 1 [ H ( x,, t) E ( x,, t) ] q q ξ + ξ GPD models: J q free parameter in ansatz for E x + ξ t x ξ
Q 2 attempts to constrain J q J q 1 1 = lim xdx t 0 2 1 [ H ( x,, t) E ( x,, t) ] q q ξ + ξ GPD models: J q free parameter in ansatz for E x + ξ t x ξ observables sensitive to E : DVCS Α UT A UT : HERMES ndvcs A LU : Hall A excl. ρ 0 A UT : HERMES, COMPASS beam target U, L U, T A UT (cross sections) in exclusive VM prod. ω, φ, ρ +, K *0 Unpolarised Longitudinally Transversely polarised
deeply virtual compton scattering DVCS Bethe-Heitler @HERMES, JLab: ~ H,E,H ~, E DVCS << Bethe-Heitler dσ 2 2 * τbh + τdvcs + (τbhτdvcs + τ * DVCS τ BH )
DVCS interference term dσ 2 2 * τbh + τdvcs + (τbhτdvcs + τ * DVCS τ BH ) different charges: e + e polarisation observables: beam spin asymmetry A LU : longitudinal target spin asymmetry A UL : transverse target spin asymmetry A UT : [F 1, F 2 : Pauli and Dirac FF, : Compton FF : moments of corresponding GPDs ]
DVCS A UT sensitivity to E (J q ) from both interference and DVCS 2 term: analogous modulations for DVCS 2 term n = 0, 1 terms found to be most sensitive to values of J u
attempts to constrain J q J q free parameter in ansatz for E separate contributions from DVCS 2 and interference terms: [JHEP06(2008)] [VGG] J d =0
attempts to constrain J q Hall-A J q free parameter in ansatz for E difference of polarised cross sections on LH 2 & LD 2 ndvcs: [PRL99(2007)] p target: ~ n target: ~ F 1 small cancellation between u and d quark pol. pdfs in
attempts to constrain J q Hall-A J q free parameter in ansatz for E difference of polarised cross sections on LH 2 & LD 2 ndvcs: [PRL99(2007)] VGG : tw-2 CFF
attempts to constrain J q Hall-A J q free parameter in ansatz for E difference of polarised cross sections on LH 2 & LD 2 ndvcs: [PRL99(2007)] VGG
an infamous step further J q free parameter in ansatz for E highly model dependent extraction!!! [VGG] [NOTE: uncorrected Dual!] data are free to be reused at any time with new models
exclusive VM production
exclusive VM production flavour separation: ρ 0 2u d ρ + ω 0 d u 2u + d
exclusive ρ 0 production after the full glory of transverse SDME extraction [formalism: M. Diehl (2007)] : * ( γ L 0 ρ ) : L [PLB679(2009)] 0 ρ νν ' n µµ ' * γ µ,ν = 0, ±1 long.pol: 0 transv.pol: ±1
exclusive ρ 0 production after the full glory of transverse SDME extraction [formalism: M. Diehl (2007)] : * ( γ L 0 ρ ) : L [PLB679(2009)] 0 ρ [GPD model: Ellighaus et al. (2004)] νν ' n µµ ' * γ µ,ν = 0, ±1 long.pol: 0 transv.pol: ±1 more data coming: COMPASS, CLAS12 with transverse target more models: Goloskokov, Kroll (09)
exclusive ρ 0 production more models: [Goloskokov, Kroll 0809.4126] [variant 4: extreme case: β u val >> βd val ]
GK: valence gluon/sea φ cross section probes gluon/sea contributions [Goloskokov, Kroll 0809.4126]
GK: valence gluon/sea φ cross section probes gluon/sea contributions ρ, ω, K *0 A UT probes valence contributions [Goloskokov, Kroll 0809.4126] data needed! : JLab12, EIC
from GPD E J q, J g [Goloskokov, Kroll 0809.4126]
from GPD E J q, J g Goloskokov,, Kroll model [0809.4126] large J u and J g small J d and J s variants for GPD E
from GPD E J q, J g Goloskokov,, Kroll model [0809.4126] large J u and J g small J d and J s variants for GPD E lattice calculations [P. Hägler et al. 2009] J u = 0.236 J d = 0.0018
lattice s opinion about J q [P. Hägler et al. 2009]
lattice s opinion about J q L q [P. Hägler et al. 2009] [HERMES]
GPD observables @EIC 10-3 10-1 0.2-0.5 HERA-collider HERMES / JLab sea quarks & gluons (valence) quarks Compass JLab12GeV EIC x Bj topic of week 8/9 [C. Weiss]
GPD observables @EIC 10-3 10-1 0.2-0.5 HERA-collider HERMES / JLab sea quarks & gluons (valence) quarks Compass JLab12GeV EIC x Bj topic of week 8/9 DVCS: as many observables (charge & polarization dependent) as possible over wide kinematic range [Kumericki, Mueller 2007,8 ]
GPD observables @EIC 10-3 10-1 0.2-0.5 HERA-collider HERMES / JLab sea quarks & gluons (valence) quarks Compass JLab12GeV EIC x Bj topic of week 8/9 DVCS: as many observables (charge & polarization dependent) as possible over wide kinematic range excl. meson production & flavour separation: diffractive channels (J/Ψ, φ, ρ 0, DVCS): gluon imaging high energies non-diffractive channels (π, ρ +, K, K *, ): flavour decomposition medium/low energies
conclusion presence of OAM w/o debate golden topic how to transform in a golden measurement?
conclusion presence of OAM w/o debate golden topic how to transform in a golden measurement? contribution to nucleon spin: determination of Σ and G missing piece attributed to OAM quest for G: from scaling violation of g 1 charm production & high pt hadrons over wide x B range EIC @highest possible energies
conclusion presence of OAM w/o debate golden topic how to transform in a golden measurement? contribution to nucleon spin: determination of Σ and G missing piece attributed to OAM quest for G: from scaling violation of g 1 charm production & high pt hadrons over wide x B range EIC @highest possible energies direct measurement via Ji-SR (GPDs) spin-orbit correlations from TMDs EIC @modest energies, high lumi (symmetric beams) JLab12