Parton flavor separation at large fractional momentum

Transcription

1 Parton flavor separation at large fractional momentum Alberto Accardi Hampton U. & Jefferson Lab Pavia U. 13 July 2010

2 Outline Introduction Quark, gluons and nucleons Parton distributions Global fits Why large fractional momentum (x) Up and down: the CTEQ6X fit Gluons, intrinsic charm Outlook: the Electron Ion Collider 2

3 Quarks, gluons and nucleons

4 Hadrons are made of quarks nucleons 6 flavors (and 3 colors): up, down, strange charm, bottom, top light heavy confined in colorless hadrons mesons 2 quarks baryons 3 quarks tetraquarks (?) pentaquarks (???) 4

5 Nucleons are made of 3 quarks... Fractional momentum: x= p+ parton p+ nucleon 1 p = p (p0 p3 ) 2 5

6 Nucleons are made of 3 quarks... Fractional momentum: x= p+ parton p+ nucleon 1 p = p (p0 p3 ) 2 6

7 ... and gluons, sea quarks... Fractional momentum: x= p+ parton p+ nucleon 1 p = p (p0 p3 ) 2 7

8 ... and gluons, sea quarks... Fractional momentum: x= p+ parton p+ nucleon 1 p = p (p0 p3 ) 2 8

9 ... spinning and orbiting around!... but this is another story... 9

10 Probing the nucleon parton structure Need a large momentum transfer Q2=q q to resolve the parton structure Example 1: Deep Inelastic Scattering (DIS) 2 Q = 2 p ;Z 10

11 Probing the nucleon parton structure Need a large momentum transfer Q2=q q to resolve the parton structure Example 2: Drell Yan lepton pair creation (DY) Q2 = (p` + p ¹ )2 11

12 Probing the nucleon parton structure Need a large momentum transfer Q2=q q to resolve the parton structure Example 3: jet production in p+p collisions 2 Q2 = Ejet 12

13 Factorization of hard scattering processes perturbative QCD factorization of short and long distance physics d¾hadron = X f1 ;f2 ;i;j f1 f2!ij Áf1 ¾ ^ parton Áf2 Parton Distribution Fns (from inclusive DIS) pqcd cross section Universality: PDF from DIS describe also DY, p+p jets+x,... 13

14 Factorization of hard scattering processes Hard scattering, computable in pqcd e.g., in DIS (at Leading Order) 1³ q¹ qº 2 ³ q2 = g¹º 2 ef ± q 2k q ³ e2 ³ k q ³ q2 f + k¹ q¹ 2 ¹$º ± 1+ q k q 2k q PDF field theoretical definition (at Leading Order) 14

15 Global PDF fits Problem: we need a set of PDFs in order to calculate a particular hard scattering process Solution: Choose a data set for a choice of different hard scattering processes Generate PDFs using a parametrized functional form at initial scale Q0; evolve them from Q0 to any Q using DGLAP evolution equations Use the PDF to compute the chosen hard scatterings Repeatedly vary the parameters and evolve the PDFs again Obtain an optimal fit to a set of data. Examples: CTEQ6.6, MRST2008 for unpolarized protons DSSV, LSS for polarized protons For details, see J. Owens' lectures at the 2007 CTEQ summer school 15

16 Global PDF fits as a tool Test new theoretical ideas e.g., constrain amount of intrinsic charm Phenomenology explorations e.g., can CDF / HERA excesses be at all due to glue/quark underestimate at large x? Test / constrain models e.g., by extrapolating d/u at x=1 Possibly, constrain nuclear corrections Limitations existing data experimental errors theoretical errors 16

17 Why large x?

18 Why large x? Large uncertainties in quark and gluon PDF at x 0.4 e.g., CTEQ6.1 PDF errors propagation of exp. errors into the fit statistical interpretation reduced by enlarging the data set Theoretical errors often poorly known difficult to quantify can be dominant 18

19 Why large x? Large uncertainties in quark and gluon PDF at x 0.4 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Lumi monitoring at high mass (Z,W cross section) Example: Z' production M Z0 & 200 GeV mt y x= p e s x 0:02 (LHC); 0:1 (Tevatron) but recent work raises the bar: MZ 0 & 900 MeV 19

20 Why large x? Large uncertainties in quark and gluon PDF at x 0.4 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Lumi monitoring at high mass (Z,W cross section) NLO state of the art at the time Kuhlmann et al. PLB476(00) Example 2: 1996 CDF pt excess Kuhlmann et al. PLB409(97) enhanced glue at large x (compatible with older data)... or valence u... 20

21 Why large x? Large uncertainties in quark and gluon PDF at x 0.5 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Luminosity monitoring at high mass Z,W cross sections non perturbative nucleon structure e.g., d/u at x 1 21

22 Why large x? Large uncertainties in quark and gluon PDF at x 0.5 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Luminosity monitoring at high mass Z,W cross sections non perturbative nucleon structure e.g., u/u, d/d at x 1 22

23 Why large x? Large uncertainties in quark and gluon PDF at x 0.5 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Luminosity monitoring at high mass Z,W cross sections non perturbative nucleon structure spin structure of the nucleon at small x 0 ¾(p~ p! ¼ X) / q(x1 ) g(x2 )^ ¾ x2 x1 qg!qg ¼0 Dq (z) pt y x1» p e s pt y x2» p e s 23

24 Why large x? Large uncertainties in quark and gluon PDF at x 0.5 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Luminosity monitoring at high mass Z,W cross sections non perturbative nucleon structure spin structure of the nucleon at small x 0 ¾(p~ p! ¼ X) / q(x1 ) g(x2 )^ ¾ x2 x1 qg!qg p s = 500 GeV pt pt 2:5 GeV x1» p s x1 ¼ 0:06 ¼0 Dq (z) ey pt y xx ¼» 0:01p e 1 2 s x1 ¼ 0:3 ¼ rapidity: j j 0:35 = 1:0 3:0 = 3:1 3:9 24

25 Why large x? Large uncertainties in quark and gluon PDF at x 0.5 Precise PDF at large x are needed, e.g., at LHC, Tevatron 1) QCD background in high mass new physics searches 2) Luminosity monitoring at high mass Z,W cross sections non perturbative nucleon structure spin structure of the nucleon at small x neutrino oscillations 25

26 Why large x...and low Q2? JLab and SLAC have precision DIS data at large x, BUT low Q2 need of theoretical control over 1) 2) 3) 4) higher twist 2 Q2 target mass corrections (TMC) xb2 mn2 Q2 heavy quark mass corrections mq2 Q2 nuclear corrections this talk 5) jet mass corrections (JMC) mj2 Q2 6) large x resummation 7) large x DGLAP evolution 8) quark hadron duality 9) parton recombination at large x 10) perturbative stability at low Q2 11)... 26

27 Up and down: the CTEQ6X fit Accardi, Christy, Keppel, Melnitchouk, Monaghan, Morfín, Owens, Phys. Rev. D 81, (2010)

28 Collaboration and goals JLab / Fermilab/ Florida State U. collaboration A. Accardi, Accardi E. Christy, C. Keppel, W. Melnitchouk, P. Monaghan, S.Malace, J. Morfín, J. Owens Initial Goals: Extend PDF global fits to larger values of xb and lower values of Q Wealth of data from older SLAC experiments and newer Jlab, DY see if PDF errors can be reduced using new JLAB data 28

29 CTEQ6X vs. CTEQ CTEQ Q2 4 GeV2 W 2 12:25 GeV2 Green: BCDMS Black: NMC Blue: SLAC Red: JLab not so large x, not too low Q2 hope 1/Q2 corrections not large CTEQ6X TMC, HT, deuteron corrections Progressively lower the cuts: CTEQ cut0 cut1 cut2 cut3 Q2 [GeV2 ] W2 [GeV2 ] CTEQ cut1 cut2 cut3 Better large x, low Q2 coverage 29

30 CTEQ6X vs. CTEQ CTEQ Q2 4 GeV2 W 2 12:25 GeV2 Green: BCDMS Black: NMC Blue: SLAC Red: JLab not so large x, not too low Q2 hope 1/Q2 corrections not large CTEQ6X TMC, HT, deuteron corrections Progressively lower the cuts: CTEQ cut0 cut1 cut2 cut3 Q2 [GeV2 ] W2 [GeV2 ] CTEQ cut1 cut2 cut3 Better large x, low Q2 coverage 30

31 Target mass corrections 2xB p < 1 at xb = 1 Nachtmann variable:» = xB mn =Q Standard Georgi Politzer (OPE) [Georgi, Politzer 1976; see review by Schienbein et al. 2007] [see also Leader, d'alesio, Murgia, 2009] leads to non zero structure functions at xb>1 (!) Collinear factorization [Accardi, Qiu, JHEP 2008; Accardi, Melnitchouk 2008] Structure fns as convolutions of parton level structure fns and PDF FT;L (xb ; Q2 ; mn ) = P f Z» xb» respects kinematic boundaries scaling, uses CF with xmax = 1 dx f ³» 2 ht;l ; Q 'f (x; Q2 ) x x [Aivazis et al '94; Kretzer,Reno '02] (0) nv FT;L (xb ; Q2 ; mn ) FT (»; Q2 ) leads to non zero structure functions at xb>0 (!) 31

32 Higher-Twists parametrization Parametrize by a multiplicative factor (same for p and n, for simplicity): with µ C(xB ) F2 (data) = F2 (T M C) 1 + Q2 C(xB ) = a xb (1 + c x) Important: C(xB) includes ¹ A DA Ãjpi ) dynamical higher twists (parton correlations, e.g., hpjãd all uncontrolled power corrections: TMC model uncertainty, Jet Mass Corrections NNLO corrections (power like at small Q) large x resummation... 32

33 Deuterium corrections Nuclear Smearing Model [Kahn et al., PRC79(2009) Accardi,Qiu,Vary, in preparation] nucleon Fermi motion and binding energy p use non relativistic deuteron wave function finite Q2 corrections F2A (xb ) = Z A xb n D dysa (y; ; xb )F2T MC+HT (xb =y; Q2 ) q = 1 + 4x2B m2n =Q2 xb q2 = y 2pN q off shell effects can be included in SA 33

34 Reference fit vs. CTEQ6.1 SLAC, E866 Reference fit: cut0, no corrections PDF errors with =1 DIS W asym + jet. DY W E866 jet +jet data (JLab) SLAC NMC BCDMS H1 ZEUS E605 E866 CDF '98 (`) CDF '05 (`) D0 '08 (`) D0 '08 (e) CDF '09 (W ) CDF D0 D0 CTEQ6.1 NO NO p p p p p NO p NO NO NO NO p p NO 34

35 CTEQ6X vs CTEQ6.1 CTEQ6X fit: cut3, TMC+HT deuteron corrections TMC, HT compensate each other u quark: almost unchanged d quark suppressed due to deuteron corrections Reduced PDF errors about 30 50% 35

36 CTEQ6X vs CTEQ6.1 CTEQ6X fit: cut3, TMC+HT deuteron corrections TMC, HT compensate each other u quark: almost unchanged d quark suppressed due to deuteron corrections Reduced PDF errors about 30 50% 36

37 Deuterium corrections d quarks are very sensitive to deuterium corrections Off shell corrections completely absorbed by the d quark free dens nuc offsh = free p+n = density model corrections = WBA smearing model = off shell corrections [Melnitchouk et al., '94] 37

38 Impact on LHC 1 Parton luminosities: Li;j (M ) = S Z 1 M 2 =s dx qi (x; M 2 )qj (M 2 =(xs); M 2 ) x Nuclear model uncertainty ~10% at large x: dominates Z cross sections used as luminosity monitor [Alekhin PRD63 (2001)] LHC exp Deut. Corr. RS MC exp RS MC TS SS TS SS = experimental = renorm. scale = charm mass = charm threshold = strangeness suppr. 38

39 d-quarks at large x Large theoretical undertainties on d quark at large x coming from deuteron corrections (no deuteron d unconstrained at large x) unavoidable at the moment: model dependent How to progress? Avoid them Free nucleon targets not enough data so far Constrain them Q2 dependence of D/p ratios at large x (maybe) Use quasi free nucleon targets Use ratio of 3He 3H mirror nuclei 39

40 Free nucleon targets Constraints on large x d quarks from p p(¹ p)! ¹+ ¹ X p+p(bar) : DY at large xf p+p(bar) : W asymmetry at large rapidity [D0 and CDF] +p and bar+p p p(¹ p)! W X º(¹ º ) p! l X WA21 already has data (but hard to reconstruct cross-sections from published quark distributions ) MINER A with a hydrogen target ~el (~er ) p! e X Parity Violating DIS * L/R electron asymmetry /Z interference d/u Charged current structure functions [H1 and ZEUS] e p! º X * planned for Jlab at 12 GeV 40

41 HERA combined data [JHEP 1001,2010] H1 and ZEUS combined data on e+ p and e p collisions, NC & CC Reaches into the critical x range Too limited x coverage 41

42 HERA combined data [JHEP 1001,2010] These data alone insufficient for d quark at large x combine with deuterium data, cross check nuclear corrections 42

43 Constraining the nuclear corrections Quasi free nucleon targets * n [BONUS, E and EG6 at JLab 6 GeV] e A! e (A 1) X D X p He 3H mirror nuclei * 3 3 H n 2 + p=n ¼ 3 He p 2 + n=p * planned for Jlab at 12 GeV 43

44 Gluons

45 Observables for gluons Jets in p+p collision CT09 limited statistics only very large Q2, and smallish x df2 / d(ln Q2) indirect limited leverage at large x, large errors Longitudinal FL directly sensitive to gluons so far not many data points JLab / JLab12 will improve large x coverage, but low Q2 45

46 FL HT and perturbative stability HT for FL have little constraints from theory, some guidance from renormalon calculations Perturbatively unclear at large x When fitted, large at NLO, decrease at NNLO The high x and low Q2 domain is 'dangerous'. This is another reason, along with target mass, to avoid fitting data in this region Alekhin, HT(2) HT(L) [Martin, Stirling, Thorne, PLB635(06)] Should we dare more? NOTE: H2 (x) = C(x)F2 (x) [see e.g., Alekhin et al., arxiv: ] 46

47 Target Mass Corrections Difference between Coll. Fact. [Accardi,Qiu] and OPE [Georgi,Politzer] for F2 different slope in Q2 different gluons from df2/d(ln Q2)! Accardi, Qiu JHEP '08 MRST2002 Accardi, Qiu JHEP '08 MRST

48 Target Mass Corrections Very different FL correction Can the differences be absorbed in HT terms? Play FL and F2 off each other can differentiate TMC method?? Accardi, Qiu JHEP '08 Accardi, Qiu JHEP '08 R= MRST2002 ¾L ¾T MRST

49 Intrinsic charm

50 Intrinsic vs. radiative charm Usual assumption in global fits: at threshold c(x; Qc ¼ mc ) = 0 Pumplin, PRD73(06), Brodky et al., PRD73(06) + references teherein charm generated during DGLAP evolution Melnitchouk,Thomas, PLB414(97) but QCD predicts intrinsic charm a c cbar pair fluctuation already exists, peaked at large x~0.4 fully participates in DGLAP evolution c, cbar asymmetry: NLO (pqcd) or large (nonpert. models) 50

51 Phenomenological implications SM and beyond at Tevatron and LHC Higgs and single top production sensitive to heavy quarks Novel Higgs production mechanisms at large xf [Brodsky et al. PRD73(06), NPB907(09)] [Nadolsky et al. PRD78(08)] ¾tot (pp! (W! e ºe )X) nb W production + + ¾totPavia (pp!u., (W13! ºe )X) nb Jule

52 Indications from global fits [Pumplin, Lai, Tung, PRD75(07)] 3 models at = mc [see Pumplin PRD 73(06) for review of models] 1) Brodsky Hoyer Peterson Sakai [PLB c(x) = c¹(x) 2 = Ax 93 (80)] 2 6x(1 + x) ln x + (1 x)(1 + 10x + x ) 2) meson cloud model [Navarra et al '96, '98; Melnitchouk,Steffens,Thomas '97,'99] c(x) = Ax1:897 (1 x)6:095 ¹ 2:511 (1 x)4:929 c¹(x) = Ax 3) phenomenological sea like ¹ +u c(x) = c¹(x) / d(x) ¹(x) 52

53 Indications from global fits [Pumplin, Lai, Tung, PRD75(07)] All models allow IC = 0 3% intrinsic charm Evolution redistributes IC to lower x, but large x peak persists sea like spread out over x BHPS model meson cloud sea like 53

54 Experimental evidence - D0 D0 measured excess of +charm jets compared CTEQ6.6 [D0, PRL102(09)] g + Q! =Z + Q ¹ q + q¹! =Z + g! =Z + QQ D0 PRL102(09) Difference due to intrinsic charm? c? underestimate of g! c¹ 0.01<x<0.3 and 103<Q2<104 54

55 How to measure hadronic collisions /Z + charm jet ¹ sensitive to g + Q! =Z + Q and q + q¹! =Z + g! =Z + QQ y yjet > 0 and y yjet < 0 sensitive to different x1, x2 allows constraints on Q, Qbar, and gluons angular dependence to distinguish above sub processes Also, 55

56 How to measure DIS HERA charm and bottom events already included in the fits c dominates over c! c X most data at small x, where g! c¹ needs larger x JLab 6/12 Ideally placed across the charm threshold D+ vs. D sensitive to c/cbar asymetry EIC (LHeC??) jet measurements are possible larger Q2 range than Jlab, larger x than HERA 56

57 Target and heavy-quark mass corrections DIS in collinear factorization: [Accardi, Qiu JHEP '08] currently being revisited FT;L (xb ; Q2 ; mn ) = P f Z xmax f xmin f dx f ³»f ht;l ; Q2 'f (x; Q2 ) x x f parton mass Nachtmann variable "»f =» 1» 2 m2f x2 Q2 # 1 mf!0!» MN!0! xb Q + (c 1)m + [m ; Q ; cm mf!0 MN!0 f f f] min xf =»!»! xb 2Q Q =x + 3m + [m ; Q ; Q (1=xB 1)] mf!0 B MN!0 f f max xf =»!»=x! 1 B 2Q2 q p [a; b; c] = a + b + c 2(ab + bc + ca)» = 2xB = xB MN =Q 57

58 Outlook: the Electron-Ion Collider 58

59 The EIC for dummies Future US based e+p (e+a) collider 2 designs: BNL erhic: Ee=5 30 GeV Ep=250 GeV L ~1034 cm 2/s 1 Jlab MEIC: Ee=3 11 GeV Ep=60 GeV L ~1034 cm 2/s 1 59

60 The EIC for dummies Future US based e+p (e+a) collider 2 designs: BNL erhic: Ee=5 30 GeV Ep=250 GeV L ~1034 cm 2/s 1 Jlab MEIC: Ee=3 11 GeV Ep=60 GeV L ~1034 cm 2/s 1 proton deuteron - much less data 0.04 < y < 0.8 MEIC will probe lower x in the shadowing region, and higher Q2 at large x. 60

61 Projected Results - F2p Relative Uncertainty [Accardi, Ent, in progress] MEIC year of running (26 weeks) at 50% efficiency, or 230 fb-1 Solid lines are statistical errors, dotted lines are stat+syst in quadrature For MeRHIC the luminosity is probably down by a factor of ~10, so these error bars will go up ~50% Huge improvement in Q2 coverage and uncertainty Will, for instance, greatly aid global pdf fitting efforts proton only stat. errors on projected results 61

62 Projected Results - F2d Relative Uncertainty [Accardi, Ent, in progress] MEIC year of running (26 weeks) at 50% efficiency, or 35 fb-1 Even with a factor 10 less statistics for the deuteron the improvement compared to NMC is impressive EIC will have excellent kinematics to measure n/p at large x! only stat. errors on projected results 62

63 Impact on global fits Sensible reduction in PDF error, likely larger than shown if energy scan is performed 63

64 Structure functions at the EIC Bread and butter: inclusive DIS Electroweak structure functions Detailed rates: F2 and FL, p and D charm and bottom str.fns.? Impact on global fits: large-x, small-x and saturation flavor separation, charge symmetry violation, new spin str.fns. requires high luminosity needed rates under study Spectator tagging will open up an exciting physics program Ongoing detector design angular & momentum resolution Rate estimates needed p vs. n tagging: effective neutron target control nuclear effects on an effective proton Tagging with 4He targets??? EMC effect 64

65 Conclusions Flavor separation at large x important to understand the nucleon structure for phenomenological applications but needs theoretical corrections target/hadron/quark mass, HT, nuclear corrections,... u, d quarks: ongoing CTEQ6X studies Gluons: will be included in the CTEQ6X global fit Intrinsic charm: interesting direction for the future Lots of progress available at the EIC The future is bright... and busy! 65

66 BACKUP SLIDES

67 Effects of corrections on reference fit Apply the theoretical corrections one at a time 2 important lessons: cut0 removes TMC+HT (as desired) nuclear corrections are large starting from x > 0.5!! ( safe cuts aren't safe everywhere) 67

68 Stability of the d-quark fit Relatively stable against kinematic cuts, but the d quark suppression is lessened by the less restrictive cuts effect still sizable at x= in the nominal range of validity of cut0 68

69 TMC vs HT Extracted twist 2 PDF much less sensitive to choice of TMC fitted HT function compensates the TMC except when no TMC is included Inclusion of TMC allow for economical HT parametrization (3 params) 69

70 TMC vs HT Extracted higher twist term depends on the type of TMC used Q2 > 1.69 GeV2 and W2 > 3 GeV2 (referred to as cut03 ) lower cuts xb < 0.85 compared to xb < 0.7 in CTEQ/MRST No evidence for negative HT 70

71 Off-shell corrections F2p 4 d = x u(1 + ) 9 4u no corrections F2d 5 d = x u(1 + ): 9 u O.S. corrections ±d 4 ±F2d 1 = (1 + ): d d 3 F2 d=u 1.5% on F2d 40% on d quark!!! d quark is strongly correlated to choice of Off Shell correction! on shell or mild off shell correction d quark suppression might as well be enhanced... Need to constrain the models! see later 71

72 Experimental uncertainties: PDF errors PDF errors at large x are reduced by lowering the cuts Note: these are exp. errors propagated in the fit nuclear correction uncertainty for d quarks likely larger than this! 72

73 Quasi-free nucleon targets BONUS and E experiments at JLab n DIS on deuterium with tagged proton X tagged proton momentum is measured neutron off shellness can be reconstructed D p Study the off shell dependence of F2(n) and quark PDFs q qd (x; Q2 ; p2 ) Extrapolate to a free neutron target p2 Mn2 73

74 D/p ratios Strong Q2 dependence of nuclear smearing use fixed xb data up to larger Q2 needs resonance region quark hadron duality off shell corrections can't be constrained Jlab E

75 Projected Results IIa - F2p with CTEQ6X PDFs Ee = 4 GeV, Ep = 60 GeV (s = 1000) larger s (~4000 MeRHIC, or ~2500 MEIC) would cost luminosity < y < 0.8 Luminosity ~ 3 x year of running (26 weeks) at 50% efficiency, or 230 fb 1 Somewhat smaller Q2 reach and large luminosity is better choice at large x, ~ (1 x)3 only stat. errors on projected results 75

76 Projected Results IIb - F2d Ee = 8 GeV, EN = 30 GeV (s = 1000) Luminosity ~ 3.5 x 1033 (scales with synchrotron limit) Smaller neutron str. fn. + reduced luminosity = factor of 10 loss in rate. One year of running (26 wk) at 50% efficiency, or 35 fb 1 Can tag spectator proton, measure neutron, concurrently only stat. errors on projected results 76