Progress Report on FL and Diffractive Physics Program to Measure Gluon Distributions in Nuclei

Transcription

1 Progress Report on FL and Diffractive Physics Program to Measure Gluon Distributions in Nuclei Thomas Ullrich (BNL) EICAC Meeting, JLAB November -3, 009

2 The Big Questions NSAC Long Range Plan 07- Overarching Question: What is the role of gluons and gluon self-interactions in nucleons and nuclei? Studying gluons implies measurements of: 1. gluon momentum distributions G(x,Q ). gluon space time distribution Incremental in ep, transformational in ea Main Focus (Discovery Potential) Establishment/Clarification of saturation and validity of CGC approach one of the fundamental outstanding problems in QCD

3 Gluon Distributions and Saturation How to probe saturation? G(x,Q ) is not an observable! Measurement σ(x, Q, A, t, W,...) Structure Function F, FL, F D, FL D, Dipole dσ/db,... Linear QCD Models (DGLAP, BFKL) Non-Linear QCD Higher Twist, saturation models, CGC comparison G(x,Q ) model dependent 3

4 Gluon Distributions and Saturation How to probe saturation? G(x,Q ) is not an observable! Measurement σ(x, Q, A, t, W,...) Structure Function F, FL, F D, FL D, Dipole dσ/db,... Linear QCD Models (DGLAP, BFKL) Non-Linear QCD Higher Twist, saturation models, CGC comparison G(x,Q ) model dependent 3

5 Gluon Distributions and Saturation How to probe saturation? G(x,Q ) is not an observable! Measurement σ(x, Q, A, t, W,...) Structure Function F, FL, F D, FL D, Dipole dσ/db,... Linear QCD Models (DGLAP, BFKL) Non-Linear QCD Higher Twist, saturation models, CGC comparison G(x,Q ) model dependent Comparison (to constrain/reject models) requires lever arm in x, Q, A,... complementary measurements (incl., semi-incl., excl., DIS & diffractive, varying probes,...) 3

6 Measurements & Techniques Gluon Distribution G(x,Q ) Scaling violation in F: δf/δlnq FL ~ xg(x,q ) +1 jet rates Diffractive vector meson production ([xg(x,q )] ) Space-Time Distribution Exclusive diffractive VM production (J/ψ, φ, ρ) Deep Virtual Compton Scattering (ngpds) Structure functions for various mass numbers A and its impact parameter dependence Ongoing studies On To-Do List 4

7 Saturation & Kinematic Range $ & % %'()* & +!,!!"#$%&'()*+$,,(*$-.*/0",$%$-)* 34+*566)*677868*9766:;;<* =>?0&@"*0@*$%A)*34+*BCD677667<* >?"/!"#$%&'()*E0$-0F)* 34G*H:D55C66I (Q A s ) A cq 0 %%$ & :;< %%$ & :;= 3%'4) Nuclear Enhancement of Qs 1/3 ~6 for Au/U at fix Q translates into huge increase in x (~500) pp, pa, AA: Qs,g DIS (ep, ea): Qs,q x,-!!, &!,.!, /!, 0!, 1!"# 5

8 Saturation & Kinematic Range $ & % %'()* & +!,!!"#$%&'()*+$,,(*$-.*/0",$%$-)* 34+*566)*677868*9766:;;<* =>?0&@"*0@*$%A)*34+*BCD677667<* >?"/!"#$%&'()*E0$-0F)* 34G*H:D55C66I (Q A s ) A cq 0 %%$ & :;< %%$ & :;= 3%'4) Nuclear Enhancement of Qs 1/3 ~6 for Au/U at fix Q translates into huge increase in x (~500) pp, pa, AA: Qs,g DIS (ep, ea): Qs,q x,-!!, &!,.!, /!, 0!, 1!"# x, Q kinematics: x = 10-3 : Q = GeV s = GeV 5

9 Saturation & Kinematic Range $ & % %'()* & +!,!!"#$%&'()*+$,,(*$-.*/0",$%$-)* 34+*566)*677868*9766:;;<* =>?0&@"*0@*$%A)*34+*BCD677667<* >?"/!"#$%&'()*E0$-0F)* 34G*H:D55C66I (Q A s ) A cq 0 %%$ & :;< %%$ & :;= 3%'4) Nuclear Enhancement of Qs 1/3 ~6 for Au/U at fix Q translates into huge increase in x (~500) pp, pa, AA: Qs,g DIS (ep, ea): Qs,q x,-!!, &!,.!, /!, 0!, 1 Ee + EA (GeV) s (GeV) !"# x, Q kinematics: x = 10-3 : Q = GeV s = GeV x = 10-4 : Q = GeV s = GeV 5

10 New Hints from RHIC: Saturation at x=10-3? Disappearance of angular correlations in Run 8 dau data at forward rapidities (log x ~.5-3) Low gluon density (pp): pqcd predicts process back-to-back di-jet q side view q-jet g g-jet beam view High gluon density (pa): 1 ( many) process mono-jet Mono-jet p T balanced by many gluons beam view pp dau peripheral dau central 6

11 Measuring F with the EIC d ep ex σ = 4πα 1 y + y dxdq xq 4 F (x,q ) y F L (x,q ) Inclusive DIS: F is day 1 measurement 4 & CF B4& 3 %"& %!"$!"# %"& %!"$!"#!"#$%&'$()*$+$&''$()*,-./$$0/<A-)--@BC-D8 E% % %! %! & %! ' ()!"!!!# ()!"!!# ()!"!& *+,-./ :;<-=><;? ()!"& % %! %! & %! ' G & -.7;H & 5 Assumptions: 10 GeV GeV/n s = 63 GeV Ldt = 4/A fb equiv. to L = cm - s, T = 4 weeks, duty cycle: 50% Detector: 100% efficient Q up to kin. limit s x see talk by Elke Statistical errors only Note: L ~ 1/A 7

12 Measuring F with the EIC d ep ex σ = 4πα 1 y + y dxdq xq 4 4 & CF B4& 3 %"& %!"$!"# %"& %!"$!"# F (x,q ) y F L (x,q )!"#$%&'$()*$+$&''$()*,-./$$0/<A-)--@BC-D8 E% ()!"!!!# ()!"!!# ()!"!& *+,-./ :;<-=><;? ()!"& *+, - #.'"%/ 01 # :8;9 '"$ '"# 4*56!/ '"!!"&!"%!"$!"#!"! '! ($ '! () '! (# '! (' ' Initial state effects in pa, AA relevant for heavy ion program! % %! %! & %! ' % %! %! & %! ' G & -.7;H & 5 7

13 Measuring F with the EIC d ep ex σ = 4πα 1 y + y dxdq xq 4 4 & CF B4& 3 %"& %!"$!"# %"& %!"$!"# F (x,q ) y F L (x,q )!"#$%&'$()*$+$&''$()*,-./$$0/<A-)--@BC-D8 E% ()!"!!!# ()!"!!# ()!"!& *+,-./ :;<-=><;? ()!"& antishadowing *+, - #.'"%/ 01 # :8;9 '"$ '"# 4*56!/ '"!!"&!"%!"$!"#!"! '! ($ '! () '! (# '! (' ' Initial state effects in pa, AA relevant for heavy ion program! % %! %! & %! ' % %! %! & %! ' G & -.7;H & 5 7

14 Measuring F with the EIC d ep ex σ = 4πα 1 y + y dxdq xq 4 4 & CF B4& 3 %"& %!"$!"# %"& %!"$!"# % %! %! & %! ' F (x,q ) y F L (x,q )!"#$%&'$()*$+$&''$()*,-./$$0/<A-)--@BC-D8 E% ()!"!!!# ()!"!!# ()!"!& sweet spot (R=1)? (bulk at RHIC) *+,-./ :;<-=><;? ()!"& % %! %! & %! ' G & -.7;H & 5 antishadowing *+, - #.'"%/ 01 # :8;9 '"$ '"# 4*56!/ '"!!"&!"%!"$!"#!"! '! ($ '! () '! (# '! (' ' Initial state effects in pa, AA relevant for heavy ion program! 7

15 Measuring F with the EIC d ep ex σ = 4πα 1 y + y dxdq xq 4 4 & CF B4& 3 %"& %!"$!"# %"& %!"$!"# % %! %! & %! ' F (x,q ) y F L (x,q )!"#$%&'$()*$+$&''$()*,-./$$0/<A-)--@BC-D8 E% ()!"!!!# ()!"!!# shadowing LHC η=0, RHIC η=3 ()!"!& sweet spot (R=1)? (bulk at RHIC) *+,-./ :;<-=><;? ()!"& % %! %! & %! ' G & -.7;H & 5 antishadowing *+, - #.'"%/ 01 # :8;9 '"$ '"# 4*56!/ '"!!"&!"%!"$!"#!"! '! ($ '! () '! (# '! (' ' Initial state effects in pa, AA relevant for heavy ion program! 7

16 Measuring FL with the EIC F L ~ α s G(x,Q ) : the most direct way to G(x,Q ) F L runs at various s longer program d ep ex σ = 4πα 1 y + y dxdq xq 4 F (x,q ) y F L (x,q ) In order to extract F L one needs at least two measurements of the inclusive cross section with wide span in inelasticity parameter y (Q = sxy)! 0!1& 0" Coverage in x and Q for inclusive cross section measurements y > 0.4 *+,-! ". 0"1& 0# 3 (1/ (1. (1- (1, (1+ (1* (1" (1) ( ) (1 (1/ (1. (1- (1, 0 (1+ (1* (1" (1) ( ( ) " " * +, #$%&'! -. / 0#1& 0$ 0$1&! " # $ % & ' ( ) *+,-!/ # ". Plots for 4 GeV electrons on GeV protons

17 Measuring FL with the EIC Assumptions: Ldt = 4/A fb (10+100) GeV = 4/A fb (10+50) GeV = /A fb (5+50) GeV Detector: 100% efficient Q up to kin. limit s x Statistical errors only 1. G Pb (x)/g d (x) Q : HKM Color Glass Condensate Statistical errors for FGS Ldt = 10 fb year running Q Q reflects kinematic limits LHC RHIC x x

18 Measuring FL: Uncertainties F L Au /FL D F L Au /FL D First attempt to get a feeling for systematic uncertainties 1% energy-to-energy normalization (can we do better?) EIC GeV 1 10 x= x= syst. uncertainties nds EKS CGC x=0.00 x= Q (GeV ) Q (GeV ) Conclusion from this study: Dominated by sys. uncertainties It makes little sense to collect more statistics when dominated by systematical errors Depending on x and Q might be able take a hit in luminosity need more detailed studies (detector simulations) 10

19 FL for Staged EIC: Ee = 4 GeV FL for electron energy fixed at 4 GeV and proton energies: 50, 70, 100, 50 GeV (4fb each) ) * +, -)*. ) * +, -)*.!%#! "%' "%&!%#! "%' ()"%""#*! ()"%""&& The magenta lines shows the statistical and systematic error (1% uncertainty in normalization) added in quadrature. "%& ()"%"#$ ()"%'!!" #!"! " #$%&' " ( $!"!!" #!"! " #$%&' " ( $!" 11

20 FL for Staged EIC: Ee = 4 GeV FL for electron energy fixed at 4 GeV and proton energies: 50, 70, 100, 50 GeV (4fb each) ) * +, -)*. ) * +, -)*.!%#! "%' "%&!%#! "%' ()"%""#*! ()"%""&& The magenta lines shows the statistical and systematic error (1% uncertainty in normalization) added in quadrature. Again, the extraction of FL is dominated by systematic uncertainties "%& ()"%"#$ ()"%'!!" #!"! " #$%&' " ( $!"!!" #!"! " #$%&' " ( $!" 11

21 Extracting G(x,Q ) from Diffractive Events General Assumption: Diffractive processes are the most sensitive means to probe G(x,Q ) and saturation since σ G(x,Q ) Note: quadratic dependence not for all processes Caveats: Theoretical How to extract G from σ? At what scale (Q ) and what x are we probing G? Experimental Detecting diffractive ea events? testing breakup of nuclei versus rapidity gap Separating coherent from incoherent processes How to detect breakup of nuclei? How to measure t? 1

22 Extracting G(x,Q ) from Diffractive Events Smoking Gun (?): exclusive diffractive vector meson production pqcd: Brodsky et al. Frankfurt,Koepf,Strikman but: only valid at large Q (Q MV ) 13

23 Extracting G(x,Q ) from Diffractive Events Smoking Gun (?): exclusive diffractive vector meson production pqcd: Brodsky et al. Frankfurt,Koepf,Strikman but: only valid at large Q (Q MV ) Dipole model: dσ γ p pv T,L dt = 1 16π dr(πr) 1 0 dz 4π Kowalski,Motyka,Watt db(πb)(ψ V Ψ) T,L J 0 (b )J 0 ([1 z]r ) dσ q q d b [ )] dσ q q d b = 1 exp ( π r α S (µ )xg(x, µ )T (b). N c Glauber-Mueller 13

24 Modeling Diffractive VM Production Implemented various dipole models (b-sat, b-cgc) in a single program (xdvmp) for ep and recently for ea. Various VM wave functions are implemented. The implementation of the pqcd model is underway. (Dipole: H. Kowalski, L. Motyka, G. Watt, PhysRev D74, , arxiv:hep-ph/06067v; Henri Kowalski, Derek Teaney, PRD68:114005, hep-ph/ ; H. Kowalski, T. Lappi, R. Venugopalan, PRL100:0303, arxiv: [hep-ph] pqcd: S. Brodsky et al., Phys.Rev.D50:3134,1994, e-print: hep-ph/94083; L. Frankfurt et al., Phys. Rev. D 54, (1996); L. Frankfurt et al., Phys.Rev.D57:51,1998, hep-ph/97016) The dipole model describes VM (J/ψ, φ, ρ) production at HERA very well. Both will be used to test sensitivity to different G(x,Q ) and can be used in detector simulations. 14

25 First Lessons Learned for EIC Cross-section for production of final state VM: dσ γ p Ep T,L dt 0.05 dz (!_V!) (r/) " L = 1 16π A γ p Ep T,L Amplitude Overlap Function J/ψ Q =.4 GeV Q = 3. GeV Q = 0.05 GeV = 1 16π b /d qq d! d r 1 0 dz 4π Dipole Cross-Section b-sat b = 0 GeV b = 1 GeV b = GeV b = 3 GeV b = 4 GeV b = 5 GeV d b (Ψ E Ψ) T,L e i[b (1 z)r] dσ q q d b Overlap between Dipole photon and VM Cross-Section wave function b /d qq d! b-cgc b = 0 GeV b = 1 GeV b = GeV b = 3 GeV b = 4 GeV b = 5 GeV r (fm) r (GeV dσ q q d b = [ 1 exp ) r (GeV ( π N c r α S (µ )xg(x, µ )T (b) ) )]. 15

26 First Lessons Learned for EIC Cross-section for production of final state VM: Overlap function (and thus σ) vanishes for large dz (!_V!) (r/) " dσ γ p Ep T,L dt 0.05 L = 1 A γ p Ep T,L = π 16π d dz r d b (Ψ E 0 4π Ψ) T,L e i[b (1 z)r] dσ q q dipole radii where saturation kicks in (Q ~ 1/r) d b Overlap between The J/ψ Amplitude seems too small to probe Dipole photon saturation and VM physics Cross-Section wave function Overlap Function φ looks better, ρ is ideal.5 Q =.4 GeV Dipole Cross-Section J/ψ b-cgc.5 Q = 3. GeV Problem is that the wave b-sat functions for ρ, φ are less b = 0 GeV b = 1 GeV Q = 0.05 GeV b = 0 b = GeV known (can - in principle 1.5 b = - 1 GeVbe solved) 10 1 r (fm) b /d qq d! 1.5 b = GeV b = 3 GeV r (GeV ) b /d qq d! b = 3 GeV b = 4 GeV b = 5 GeV b = 4 GeV 1 b = 5 GeV 1 Measuring VM other than J/ψ l + l - requires particle 0.5 ID capabilities (K, π) 0.5 of the detector over a wide pt range dσ q q d b = [ 1 exp r (GeV ( π N c r α S (µ )xg(x, µ )T (b) ) )]. 15

27 From ep to ea... (All xdvmp) ep b /d qq d! b = 0 GeV b = 1 GeV b = GeV b = 3 GeV b = 4 GeV b = 5 GeV ) d!/dt (nb/gev Q Q Q Q = 0 GeV = 3.1 GeV = 6.8 GeV = 16 GeV ea Note: ea is less b dependent than ep (which is good) b /d qq d! r (GeV b = 0 GeV b = 1 GeV b = 4 GeV b = 8 GeV b = 16 GeV b = 3 GeV ) ) d!/dt (nb/gev t (GeV ) Q = 0 GeV Q = 3.1 GeV Q = 6.8 GeV Q = 16 GeV r (GeV ) t (GeV 16 )

28 Diffractive Physics is Experimentally Hard Scattered Electron θ(p) GeV GeV Stringent constraints on detector: Need to measure electrons (PID + p) down to very low angles (up to 1 o off the beam line) need dipole magnet(s) to bend e in sane region 17

29 Identifying Diffractive Events Beam angular divergence limits smallest outgoing p(a) angle that can be measured Cannot measure coherent diffraction in heavy ions (small t) using forward spectrometry (Roman Pots) separate ion only if pt > pt,min possible for p and light ions Can determine t in exclusive production from e, e, X e d! D /dt (fm /GeV ) q Lappi, Kowalski, Venugopalan, PRL 100, (a)!*(q ) 0.1 e! Ca, with breakup Ca, no breakup p p (x 40) t (GeV ) species (A) pt min (GeV/c) d () 0.0 Si (8) 0. Cu (64) 0.51 In (115) 0.9 Au (197) 1.58 U (38) 1.90 p, P W x IP " t P!,p! # $ % $ & X (M X ) Largest rapidity gap in event or breakup of A # $ % $ & Y (M Y ) 18

30 Identifying Diffractive Events Beam angular divergence limits smallest outgoing p(a) angle that can be measured Cannot measure coherent diffraction in heavy ions (small t) using forward spectrometry (Roman Pots) separate ion only if pt > pt,min possible for p and light ions Can determine t in exclusive production from e, e, X d! D /dt (fm /GeV ) Lappi, Kowalski, Venugopalan, PRL 100, (a) Ca, with breakup Ca, no breakup p p (x 40) t (GeV ) Need to rely on rapidity gap method simulations look good high efficiency, high purity possible with gap alone ~1% contamination, ~80% efficiency depends critically on hermeticity of detector improve further by veto on breakup of nuclei (DIS) Very critical: Mandatory to detect nuclear fragments from breakup n: Zero-Degree Calorimeter p, Afrag: Forward Spectrometer New idea: Use U instead of Au (fission) 18

31 New: Probing Gluonic Structure of Nuclei Basic Idea: Studying diffractive exclusive J/ψ production at Q =0 (photo-production) (H. Kowalski & A. Caldwell) Ideal probe large photo-production cross sections t can be derived from e, e, and J/ψ 4-momentum no measurement of ion momentum necessary beam electron pt < 1 MeV (0. with cooling MeV) for E < 5 GeV scattered electron can be detected in the forward detector (beam optic needs to be studied) J/ψ has small width well separated from background J/ψ dipole interacts only by g exchange at low x process is well understood in QCD 19

32 Probing Gluonic Structure of Nuclear Forces Simplified assumption for proof of principle: Random and uncorrelated distribution of nucleons within the nucleus Shape of the nucleus given by the Woods-Saxon distribution ρ(bt) Average (sum) over all configurations Fourier transform the average dσ A /dt Promising method to measure gluon form factor Fg in nuclei d&/dt (nb/gev ) !*A "#J/$ A Q = 0 incoherent Au R A 0.9 % 0.8 Crucial: Need to suppress background by factor 100 Dynamics of nuclear disintegration? studies underway (QMD?) easier with Uranium? coherent t (GeV ) 0

33 Summary Study of measurements of G(x,Q ) in progress F (existing studies but not updated yet) FL (EIC & staged EIC) +1 jets (EIC & staged EIC) [not shown, see add. material] Diffractive VM production - no error evaluation yet but all we need is there 1

34 Summary Study of measurements of G(x,Q ) in progress F (existing studies but not updated yet) FL (EIC & staged EIC) +1 jets (EIC & staged EIC) [not shown, see add. material] Diffractive VM production - no error evaluation yet but all we need is there New promising idea to measure gluonic structure of nuclear forces (Gluonic formfactor of nuclei) Diffractive exclusive J/ψ production at Q =0 (photo-production) 1

35 Summary Study of measurements of G(x,Q ) in progress F (existing studies but not updated yet) FL (EIC & staged EIC) +1 jets (EIC & staged EIC) [not shown, see add. material] Diffractive VM production - no error evaluation yet but all we need is there New promising idea to measure gluonic structure of nuclear forces (Gluonic formfactor of nuclei) Diffractive exclusive J/ψ production at Q =0 (photo-production) Next Steps Further investigate nuclear breakup Simulation on diffractive VM Run measurements through detector simulation (see Elke s talk) 1

36 Additional Slides

37 Gluon Distribution from Jet Analysis at EIC Jets: window to partons, DIS is a clean environment +1 jets becomes more interesting x p jet a jet a ŝ Main formula: Technique: d σ +1 dx p dq = α [ s ag(xp,q )+bq(x p,q ) ] 1. a and bq: matrix elements & quark piece from Monte Carlo ( ). x p = x 1+ ŝ Q 3. Extract the gluon distrib: g extr. = 1 (σ meas. b MC q) a MC 3

38 Results from Jets Experimental cuts: Outgoing electron energy: E min Minimal jet pt : pt,min Azimuthal separation between the jets: φ > π ε (in the Breit frame ensures that the jets come from the hard scattering) Clustering: kt algorithm with R=1 (large but OK in DIS) Cross-section for gluon-initiated dijet events (obtained with LEPTO) d!/(dx g dq ) (nb/gev ) Q E = GeV E" min = 0.5 GeV p t,min = GeV LEPTO d!/(dx g dq ) (nb/gev ) P = 100 GeV k t, R = 1 E = 0 GeV E" min = GeV p t,min = GeV x g x g 4

39 Results from Jets Experimental cuts: Outgoing electron energy: E min Minimal jet pt : pt,min Azimuthal separation between the jets: φ > π ε (in the Breit frame ensures that the jets come from the hard scattering) Clustering: kt algorithm with R=1 (large but OK in DIS) Stat. errors assuming 1 fb 1 of data: Statistical errors assuming 1 fb statistical error for fb of data P = 100 GeV k t, R = 1 E = GeV E! min = 0.5 GeV p t,min = GeV x g LEPTO statistical error for fb of data E = 0 GeV E! min = GeV p t,min = GeV x g Q

40 Diffractive Structure Function F D at EIC d 4 eh exh σ dxdq dβdt = 4πα e.m. 1 y + y β Q 4 F D y F L D = x/x IP x IP = momentum fraction of the pomeron w.r.t the hadron Distinguish between linear evolution and saturation models Insight into the nature of pomeron Curves: Kugeratski, Goncalves, Navarra, EPJ C46, 413 5

41 Deep Inelastic Scattering (DIS) e(k) P(p)! " (q) e(k ) X(p ) Resolution power ( Virtuality ): Q = q = (k k ) # e Q = 4E e E e sin ( θ e Inelasticity: y = pq pk = 1 E e E e cos ) ( θ e ) p fraction of struck quark x = Q pq = Q sy d ep ex σ dxdq = 4πα e.m. 1 y + y xq 4 F (x,q ) y F L (x,q ) quark+anti-quark momentum distributions gluon momentum distribution 6

42 Hard Diffraction in DIS at Small x Cyrille Marquet e! e q!*(q ) is the momentum fraction of the struck parton w.r.t. the Pomeron xip = x/β momentum fraction of the exchanged object (Pomeron) w.r.t. the hadron The measured cross-section: p, P W x IP " t P!,p! # $ % $ & X (M X ) Largest rapidity gap in event or breakup of A # $ % $ & Y (M Y ) The dipole picture: Here inclusive DIS overlap of splitting functions dipole-hadron cross-section Tq q = dipole scattering amplitude 7