Lectures on the Longitudinal Spin Structure of the Nucleon. Marco Stratmann

Transcription

1 Lectures on the Longitudinal Spin Structure of the Nucleon Marco Stratmann

2 Outline of the lectures Lecture 1: some fundamentals about spin; helicity sum rule ; helicity parton distributions; evolution and angular momentum Lecture 2: inward bound: femto-spectroscopy Lecture 3: longitudinal spin physics at RHIC part I Lecture 4: longitudinal spin physics at RHIC part II Disclaimer: 4 hours are barely enough to discuss the main principles, recent experimental findings, and theoretical foundations & developments June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 2

3 Lectures 3 & 4 longitudinal spin physics at RHIC June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 3

4 main theme of today s lectures: What can we learn about the nucleon spin structure - in particular the gluon polarization from very inelastic polarized proton-proton collisions? June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 4

5 found at homepage of R.D. Ball (Edinburgh) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 5

6 pqcd and hadron-hadron colliders collider experiments are QCD laboratories... vast source of information about hadronic structure complementary to lepton-proton experiments gluons are often key players challenge our understanding of strong interactions motivation to perform more and more refined calculations... a success story ever since June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 6

7 pqcd approach to hard scattering if hardness of probe is large enough (α s (Q) <<1), perturbative QCD can be used to make quantitative predictions (exploiting asymptotic freedom of QCD) Gross, Wilczek; Politzer starting point: factorization theorem & universality of pdfs Libby, Sterman; Ellis et al.; Amati et al.; Collins et al.;... example : (un)polarized inclusive high-p T pion production June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 7

8 colliders: one (of many) examples high transverse momentum p T jet production at the TeVatron: cross section described over many orders of magnitude similar for other final-states: photons, W-bosons, heavy quarks June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 8

9 main objective with long. polarization we want to understand the nucleon s spin budget in terms of total spin polarizations Δf(x,μ) dx orbital angular momenta of quarks and gluons to achieve this goal we have to extract the fully x-dependent helicity parton densities Δf(x,μ) from experiment important test of QCD: understanding of hadron structure hard scattering QCD dynamics factorization & universality June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 9

10 milestone of RHIC spin program (as far as possible) a model independent determination of Collins, Soper; Manohar features: gauge link interpretation as diff. of number operators only in A + =0 gauge all n=2 moments, x n-1... dx, give local operators but there is no gauge-invariant local gluonic operator for n=1 in A + =0 gauge the 1 st moment also collapses into a local operator and has the interpretation as gluon contribution to the spin sum rule June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 10

11 before we turn to the phenomenology of Δg in polarized high-energy pp scattering let s have a quick look at available model estimates for Δg June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 11

12 What can we learn from models? well, as often, not too much... non-relativistic constituent quark models give boundary condition for evolution at μ GeV size of effect: M Δ M N M N /3 two contributions for ambient glue o Jaffe (only 1 st term relevant): Δg(μ 0 ) = -0.8 negative o Barone, Calarco, Drago (both terms incl.): Δg(μ 0 ) = positive bag model estimates o Jaffe : Δg(μ 0 ) = -0.2 o Lee, Min, Park, Rho, Vento: Δg(μ 0 ) = +0.2 recent update: hep-ph/ Chen, Ji Δg(1GeV) +0.3 (shape like GRSV std) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 12

13 What can we learn from models? QCD sum rule estimate o Mankiewicz, Saalfeld, Piller: Δg(1GeV) = 2 ± 1 o Balitsky, Ji: J g (1GeV) 0.25; expect(unless strong cancellations) Δg<0.5 helicity retention, color coherence o Brodsky, Burkardt, Schmidt: Δg(1GeV) 0.5; Δg/g 1 as x 1 lattice calculation?? (not a model) recall: Δg non-local operator except for A + =0 gauge nevertheless an attempt by Mandula (1990!): 3α s /(2π) Δg 0.05 all interesting efforts, but we better get it from data... June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 13

14 What should we measure at RHIC? with long. polarized protons we can perform four different experiments: which combination measures our parton helicity densities Δf?? to figure this out, first recall that in a proton with helicity + we can find partons with helicity + and - : June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 14

15 What should we measure at RHIC? (cont.) next, we can decompose each of the hadronic cross sections dσ(±,±) into four partonic reactions, e.g., dσ(+,+) and similarly for dσ(+,-), dσ(-,+), and dσ(-,-) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 15

16 What should we measure at RHIC? (cont.) simplification: strong interactions invariant under parity parity flips helicity find that is the relevant cross section June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 16

17 the strategy to go after Δg is simple... e.g. pp πx: measure! from global analysis new d(δ)σ ' learn about hadronic/spin structure compute as a power series in α s in pqcd June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 17

18 but it is an intricate problem: recall information on long-distance physics inside complicated convolutions & summed over many partonic subprocesses no 1:1 correspondence between data and parton densities or frag. fcts. information on momentum fractions smeared over significant range ex.: pp πx at p T = 2.5 GeV June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 18

19 theoretical calculations depend on unphysical scales a measurable cross section d(δ)σ has to be independent of μ r and μ f leads to renormalization group eqs. like, e.g., DGLAP evolution if we truncate the series after the first N terms, there will be a residual scale dependence of order (N+1) theory error there is no such thing like the right scale (not even μ=q in DIS) the harder we work, the less the final result should depend on these artificial scales a powerful gauge of the reliability of a pqcd calculation June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 19

20 example: single-jet production at RHIC taken from B. Jäger, MS, W. Vogelsang p T /2 < μ r,f < 2p T going beyond the LO is a must for any quantitative study June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 20

21 The science and art of choosing scales let us look at the most transparent example: e + e - hadrons QCD corrections can be expressed as an power series: in lowest order we have no clue what the scale is in higher orders both α s and the coeff. fct. depend logarith. on the scale: cancellations!! & μ r should be of the order of s June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 21

22 Choosing scales (cont.) lessons to learn: (applies in general, also for μ f ) arbitrary scales should be of the order of the hard scale characterizing the process (here s) to avoid large logs in the coeff. fcts. which might spoil the perturbative series we cannot say more & errors due to our choice are difficult to estimate example June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 22

23 Choosing scales (cont.) numerical example (again e + e - hadrons): from Dave Soper s CTEQ lectures have to think about the theor. error caused by truncation of the series Δ N=1 (μ r ) error estimate: Δ N=2 (μ r ) central μ r value: much smaller μ r dependence p error band: vary μ r by factor 2 around centr. value June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 23

24 Choosing scales (cont.) How good is such an error estimate? add another order (N=3) and zoom in... Δ N=3 less scale dep. as expected Δ N=2 (μ r ) Δ N=3 (μ r ) Δ N=1 (μ r ) p two places where μ r -dep. stationary take average as new central value error estimate was slightly off June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 24

25 going beyond the LO is in every aspect a major enterprise LO NLO NNLO number of final-state partons complexity of calculation rough estimate start of precision physics... pushes math. tools & computer algebra to their limits June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 25

26 Cross sections: Born approximation June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 26

27 LO cross sections: kinematics June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 27

28 Cross sections: computation (basic steps) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 28

29 Diracology June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 29

30 Partonic spin asymmetries at LO analyzing power June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 30

31 NLO pqcd in a nutshell need loop and real emission corrections to LO diagrams encounter singularities sing. config. of a three parton final-state dimensional regularization, soft: cancel in sum + collinear: absorb into def. of phenomenological inputs (parton densities & fragmentation fcts.) a meaningful observable is insensitive to these long-dist. effects infrared safety June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 31

32 how can we make use of pqcd to probe all aspects of helicity pdfs, in particular Δg? plenty of options at RHIC... June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 32

33 tremendous progress on NLO calculations for RHIC-spin available: hadrons jets photons heavy flavors Drell Yan Jäger,Schäfer, MS, Vogelsang; de Florian Jäger,MS,Vogelsang; Signer et al. Gordon,Vogelsang; Contogouris et al.; Gordon, Coriano Bojak, MS Weber; Gehrmann; Kamal; Smith et al. work in progress: particle-correlations for RHIC (hadron-hadron, hadron-photon, heavy-flavor) new Jäger, Owens, MS, Vogelsang; Riedl, MS June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 33

34 Unpolarized benchmark results before one can go after some new unknown quantity like Δg it is important to have an adequate and proven theoretical framework relevance of unpol. benchmark results demonstrate applicability of pqcd methods (or map out the regions where they fail!!) measurements at 200 GeV (and 500 GeV) never done before!! energy dependence of cross sections at a given p T : (fixed target) RHIC SPS TeVatron LHC valuable source of information also about unpol. pdfs and frag. fcts unpol. measurements should always precede A LL measurements June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 34

35 this is a strength of the RHIC spin program pqcd challenged by experiment latest from RHIC (arxiv: ) vs. NLO pqcd Jäger, MS, Vogelsang find (jets, pions, photons, ) perfect agreement over many orders of magnitude foundation/baseline for: polarized pp collisions at RHIC interpretation of heavy-ion results P π [GeV] much less clear at fixed-target exp. gluons are key players June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 35

36 data probing Δg are rolling in now... pp: lp: PHENIX, STAR HERMES, COMPASS, SMC What do they imply? How to analyze them properly? Potential problems & limitations? June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 36

37 what do RHIC data already tell us? June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 37

38 current probes at RHIC: single-inclusive hadrons & jets PHENIX, STAR at moderate p T and mid-rapidity η relevance of different subprocesses: gluon induced processes dominant sensitivity to Δg but at central rapidities hadron/jet (η'0) x 1 x 2 probe Δg(x 1 ) Δg(x 2 ' x 1 ) (taken from Jäger,MS,Vogelsang) sign deadlock June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 38

39 indeed single-incl. A LL vs. NLO calc. for very diff. gluon polarizations Δg spin asymmetry A LL but beyond that?? PHENIX arxiv π 0 STAR jets major result: very large (& 2 units of ~) anomaly-inspired Δg dead June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 39

40 experiments now do their own theory analysis Q: how robust are these results? [heavily biased by GRSV framework? ; x-range? ; 1 st moment? ; ] June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 40

41 data x-range probed can we figure out which hxi is probed? difficult! example: x-range spreads out significantly MS, Vogelsang depends on unknown Δg complication: possible oscillations obscure hxi June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 41

42 a closer look for GRSV standard diff. subprocesses populate different x-ranges gg vs. qg interplay explains all: large pos. Δg pronounced gg peak small pos. Δg double peak not too large neg. Δg oscillations estimates of x±dx very difficult w/o knowing Δg June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 42

43 important disclaimer RHIC data so far are sensitive to a rather limited x-range x. 0.2 full moment 01 dx Δg(x,μ) still a long shot (i.e., depends on assumed shape for Δg) [also Gehrmann-Stirling gluons pick up a large small-x contribution!!] data small values of x can be crucial for 1 st moment!! need a much more precise x-mapping June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 43

44 other issues to worry about June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 44

45 how do quarks & gluons hadronize? key phenomenological input for all calculations of meson/baryon production plenty of experimental information but we know much less about hadronization than about hadron structure - why? many short-comings of available models revealed by RHIC data, e.g.: general trend: Kretzer below data (STAR, PHENIX, BRAHMS) no reliable charge/flavor separation (STAR, BRAHMS: π + vs. π - yields, ) we must do better! NLO calc.: Jäger,Schäfer, MS, Vogelsang June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 45

46 1 st global analysis of e + e - and ep, pp data de Florian, Sassot, MS: hep-ph/ (PRD) main features: handle on gluon fragmentation flavor separation uncertainties via Lagrange multipl. describes all current data June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 46

47 can one assume that ΔΣ is known? NO, it is misleading to extract only Δg w/o refitting the quarks: considerable variation of quark singlet at input GRSV std constraint from DIS June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 47

48 can I use MCs to extract Δg? Δg extraction through signal/background separation based on MC e.g., lp HX fractions from MC MC crucial to model experiment but cannot replace a full global analysis: requires kind of mean-value theorem as (also note that ) MC hadronization not compatible with collinear pqcd which defines pdfs MC neither LO nor NLO (parton showers,...) in general, expect: Δg(MC) Δg(NLO pqcd analysis) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 48

49 can I make a K-factor approx.? NO! June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 49

50 20 years of experience in analyzing unpolarized data: DFLM,, GRV, MT, MRS,, MSTW, CTEQ, learning about nucleon structure requires a global QCD analysis even more true for the spin structure due to lack of HERA-like DIS data none of the current analyses is a full global analysis June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 50

51 global analysis outline of pdf analysis: unpolarized pdfs: CTEQ, MRST gluon constrained by scaling-violations 2 nd moment constrained (mom. sum) pp data only for fine-tuning pdfs K-factor approx., etc. often reasonable polarized pdfs: completely different situation! gluon largely unconstrained by existing DIS data no momentum sum rule; pol. pdfs can have nodes pp data determine Δg and other aspects of pdfs full NLO global analysis mandatory; approximations often misleading June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 51

52 with latest data from RHIC a global analysis starts to make sense... the work just started D. de Florian, R. Sassot, MS, W. Vogelsang in the long-run a CTEQ-like collaboration is desirable June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 52

53 Δg: where do we stand now? Δg dx thought to be large: 2-4 ~ in the aftermath of the EMC result Altarelli, Ross;... due to axial anomaly (very controversial Jaffe; Ji;... ) dark ages : several model calculations: 95 Brodsky, Burkardt, Schmidt: Δg(1GeV) 0.5 ~ (hel. retention, color coh.) 97 Balitsky, Ji: J g (1GeV) 0.25; expect Δg<0.5 ~ (QCD sum rules) 98 Barone, Calarco, Drago: Δg = 0.24 ~ (quark model) 00 Lee, Min, Park, Rho, Vento: Δg 0.2 ~ (bag model)... time now around/after 2000: several DIS fits: Δg largely unconstrained Δg(x) is not large and positive at x ' ; still a long way for full moment Δg dx but anomaly scenario (2-4 units of ~) excluded GRSV, BB, AAC,... PHENIX, STAR, HERMES, COMPASS June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 53

54 Δg semantics we always talk about things like large Δg - but what does it mean? we should probably compare with ½ - the spin of the proton RHIC data: Δg(GRSV input). 0.5 still pretty large!! anomaly inspired Δg s are really large: Δg(input) & 2.0 (but they are now excluded) beware of pqcd evolution: small Δg can turn asymptotically into large Δg however, only J g = Δg + L g is gauge-invariant Ji June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 54

55 some future avenues for Δg and the Δq s at RHIC June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 55

56 RHIC/RHIC-II 500 GeV collisions (smaller x), more luminosity (rare probes) prompt photons: rare, but gold-plated probe of sign through heavy flavors: mass allows (?) pqcd at small p T probes smaller x particle correlations: better control of kinematics = x-range and sign idea: forward-central correlations particle 1 (η 1 ' 0) x 1 x 2 particle 2 (η 2 = 3 4) x 1 À x 2 0 central 3 4 forward rapidity strongly asym. kinematics: x 1 >> x 2 qg-scattering q(x 1 ) g(x 2 ) important NLO 2-hadrons just completed & pheno. studies under way: Jäger, Owens, MS, Vogelsang June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 56

57 high-p T prompt photons expectations for spin asymmetries: unpol. benchmark works out: Run5 preliminary indeed: clean tool to get the sign of Δg at all p T June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 57

58 heavy flavors (prospects for near future) quick & dirty study J. Riedl, MS gg scattering dominant sign of Δg is an issue A LL very small difficult charm detection (c e, ) not yet included pqcd at work? stay tuned for heavy quark correlations charge asymmetry June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 58

59 unpolarized benchmark for 2-hadrons Jäger, Owens, MS, Vogelsang confidence in A LL measurements & interpretation never measured at collider energies test of QCD factorization doable both at STAR and PHENIX preliminary NLO corrections & scale dependence are substantial scan in p T of central hadron June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 59

60 kinematics is as expected: x 1 log 10 x 2 central-forward particle 1 (η 1 ) x 1 x 2 particle 2 (η 2 ) x 1 À x 2 June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 60

61 sensitivity to Δg (sign!) 1 st moment assumed at input scale qg-fraction strongly depends on Δg NLO corrections large, in particular, for small std-like Δg preliminary expected A LL s are only a few 10-3 June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 61

62 new kid on the block: 62.4 GeV data explores larger x values pqcd at the edge? testing ground for resummations qg scattering more relevant sign! could be interesting/important to collect more data at 62 GeV June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 62

63 W-boson production at RHIC Δq weak interactions violate parity conservation single-spin asymmetry 0 (in QCD where parity is conserved : A L =0) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 63

64 u unpol. large scale Q~M W : pqcd complementary to SIDIS, cleaner (no fragmentation) large asymmetries guaranteed (at large x) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 64

65 Hermes 243 pb -1 will get only small part of first moments of pdfs to test model predictions, x-dependence actually more relevant PHENIX 800 pb -1 ultimately, become part of global analysis of all RHIC data June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 65

66 best developed theory tool: RhicBos Monte-Carlo integrator with NLO and NNLL q resummation accuracy P.Nadolsky, C.P.Yuan LO: δ(q ) HO: find: NLO relatively important, resummation moderately so important for RHIC (acceptance): leptonic decays fully included June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 66

67 the future (?): 10 GeV electrons 250 GeV protons erhic (one possible design option) June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 67

68 closer look opportunities with erhic first polarized ep collider: polarized quark & gluon distribution at very low x better understanding of spin sum rule (extrapolation uncertainty) precision measurement of α s through Bjorken sum exclusive processes & generalized parton densities angular momentum contribution to proton spin sum single transverse spin asymmetries transversity and transverse momentum dependent distributions photoproduction processes exploring the spin structure of the photon... also the first electron - heavy ion collider! partonic matter under extreme conditions F 2p vs. F 2A ; color glass condensate, all unique measurements June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 68

69 one highlight: Δg down to x ' from scaling violations in DIS another: SIDIS simulation by A. Brull, R. Ent June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 69

70 fundamental test: Bjorken sum rule erhic should be able to determine pol. pdfs down to x' much reduced extrapolation uncertainties for 1 st moments Bj-sum: Kodaira; Gorishny, Larin; Larin, Vermaseren quote from the Particle Data Book: Theoretically, this sum rule is better for determining a s because the perturbative QCD result is known to higher order (O(a s4 )), and these terms are important at low Q 2... Should data at lower x become available, so that the low x extrapolation is more tightly constrained, the Bj sum rule method could give the best determination of a s June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 70

71 other future facilities with (?) polarization: J-PARC in Japan: already under construction 50 GeV proton beam; polarized option currently under discussion GSI in Germany: program with several stages most promising option would be an anti-symmetric p-pbar collider both facilities will have small c.m.s. energies (applicability of pqcd not a priori guaranteed) but very interesting measurements can be carried out June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 71

72 A guide to further reading see, e.g., N. Craigie et al., Spin Physics at Short Distances, Phys. Rept. 99 (1983) 69 M. Anselmino et al., The Theory and Phenomenology of Polarized DIS, Phys. Rept. 261 (1995) 1 B. Lampe and E. Reya, Spin Physics and Polarized Structure Functions, Phys. Rept. 332 (2000) 1 V. Barone et al., Transverse Polarization of Quarks in Hadrons, Phys. Rept. 359 (2002) 1 E. Leader, Spin in Particle Physics, CUP, 2001 C. Aidala et al., Research Plan for Spin Physics at RHIC, 2005, June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 72

73 from the preface of The Story of Spin Sin-Itiro Tomonaga It is a mysterious beast, and yet its practical effect prevail the whole of science. The existence of spin, and statistics associated with it, is the most subtle and ingenious design of Nature - without it the whole universe would collape. June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 73

74 conclusions we have just explored the tip of the iceberg you are here many avenues for further important measurements and theoretical developments June 25 & 27, 2007 Longitudinal Spin Structure of the Nucleon 74