1. J. G. ContrerasCTEQ School 2005 1 Small x Physics in Deep Inelastic Scattering Puebla May 20, 2005 J. G. Contreras ● Cinvestav Mérida ►Motivation: Limits of pQCD, High density pQCD ►The proton at small x: F 2, F L, F 2 c ►Looking for saturation: Forward Jets Geometric Scaling Heavy ion physics ►Summary: Very exciting field

2. J. G. ContrerasCTEQ School 2005 2 Motivation What are we made of ? What is the most fundamental structure of matter ? What is the structure of the proton in terms of quark and gluons? Long time ago … Today … Homework 1: and tomorrow?

3. J. G. ContrerasCTEQ School 2005 3 DIS: The basic idea Need a microscope to see inside the proton High energy: ►Good resolution (Deep) ►Proton breaks (Inelastic) An accelerated electron … … produces light to see inside a proton Microscope components: ► Accelerators: Fixed Target, HERA ► Detectors: H1, Zeus, …

4. J. G. ContrerasCTEQ School 2005 4 HERA: the only ep collider ► Asymmetric accelerator using superconducting technology ► Operating since 1992 ► 300 GeV CMS energy ► 6.3 Km of circumference ► At DESY in Hamburg

5. J. G. ContrerasCTEQ School 2005 5 H1 and Zeus ►Both big universal detectors with excellent tracking and calorimetry ►Built and maintained by large collaborations, each of ~ 350 scientists and around 40 institutes from around the world ►Each with more than 100 articles and several thousand citations ►Taking new data as we speak! Open detectors Note the scale Note the cables ….

6. J. G. ContrerasCTEQ School 2005 6 DIS in pQCD and Experiment incoming electron outgoing electron struck quark collision proton remnant incoming proton

7. J. G. ContrerasCTEQ School 2005 7 Description of DIS in pQCD ► Proton “=“ Σ free partons (careful with the frame) ► Two variables to describe the process to be choosen from: x: parton energy (0<x<1) Q 2 : resolution s: energy of CMS y: inelasticity (0<y<1) W: energy of γ*p process

8. J. G. ContrerasCTEQ School 2005 8 The structure of the proton according to DIS/pQCD Experiment pQCD: General theory requirements

9. J. G. ContrerasCTEQ School 2005 9 The limits of pQCD Perturbative solution: ►Needs small parameter ►Not all terms considered ►Free partons? Expansion parameter: ►α s (only QCD parameter) ►Its value depends on a scale (asymptotic freedom) ►In inclusive DIS scale is Q 2 Resummation of ►( α s ) m log n (Q 2 /Q o ) (DGLAP) or ►( α s ) m log n (1/x) (BFKL)

10. J. G. ContrerasCTEQ School 2005 10 The Nobel Prizes in DIS and pQCD DIS: ►1990 to Friedman, Kendall and Taylor Experiments at the end of 60s, early 70s ►Their results motivated the development of the quark model of the strong interaction pQCD: ►2004 to Gross, Politzer and Wilczek Theoretical work (1973), foundation of pQCD ►Discovery of asymptotic freedom (btw: read Politzer Nobel lecture!) Homework 2: You are next …

11. J. G. ContrerasCTEQ School 2005 11 Where are we? Where are we going? (I) Where are we? ►Basic idea of DIS and pQCD understood ►Want to explore limits of pQCD, specifically high density of partons and α s small Where are we going? ►A first look at data ►A closer look at the theory ►A second look at data the data

12. J. G. ContrerasCTEQ School 2005 12 Experiment: phase space in x and Q 2 Huge phase space covered: ►x from almost 1 to ≈ 10 -6 ►Q 2 from less than 0.1 to almost 10 5 GeV 2 Several overlapping regions permit cross checks between different accelerators different experiments Note the correlation between x and Q 2 at small x … … smallest x outside pQCD?

13. J. G. ContrerasCTEQ School 2005 13 The first HERA F 2 at small x Before HERA no data at small x … but many predictions based on extrapolations of existing data In 1992 the first HERA data became available: F 2 rises at small x … … and rises quite fast … lets look at it in some detail …

14. J. G. ContrerasCTEQ School 2005 14 Describing F 2 behavior with partons Lots of partons at small x!

15. J. G. ContrerasCTEQ School 2005 15 F 2 (x,Q 2 ) today Impressive amount of data Precision better than few % Perfect agreement between ►Hera and Fix target experiments ►Between Hera experiments Dramatic violation of Bjorken scaling Data described by fits based on DGLAP pQCD

16. J. G. ContrerasCTEQ School 2005 16 From F 2 to pQCD partons See Stump’s talk! H1 and Zeus fits agree: ► independent data ► same theory ► different implementation … Different physics at ► large x: valence quarks ► small x: gluons and sea (note the scale factor!) Small x: ► rise dominated by gluons ► x small → log(1/x big) …

17. J. G. ContrerasCTEQ School 2005 17 pQCD evolution of F 2 : The basic idea In pQCD, F 2 is computed from perturbative expansion in α s subject to constraints (RGE) → linear integro-differencial equations PDFs: ►DGLAP: log(Q 2 ), but not log(1/x) ►BFKL: log(1/x), but ‘fixed’ Q2 Need a boundary condition to be taken from data. Given F 2 in one point, one gets it at another point in phase space Both are pQCD, i.e. weak coupling needed, so none of them should work at very small Q2 …

18. J. G. ContrerasCTEQ School 2005 18 pQCD evolution of F 2 in pictures Initial structure ← exp One emission … … and another … and … BFKL: big steps in x diffusion in Q 2 DGLAP: small steps in x big steps in Q 2 Structure after emissions 1 1 2 2 2 2 3 3 3 We are interested in this region … but there is no scale in plot … 4 4 1

19. J. G. ContrerasCTEQ School 2005 19 High gluon density and saturation Small x, means high gluon density. The gluons are inside the proton At some point they start to overlap (the proton ‘saturates’) When they overlap, they interact, ► they are not ‘free’ anymore ► F 2 stops growing ► non linear equation needed

20. J. G. ContrerasCTEQ School 2005 20 Where are we? Where are we going? (II) Where are we? ►free parton (DGLAP) pQCD works even at small x (where are BFKL effects?) ►Small x, means high gluon density and at some point (where?), saturation Where are we going? ►A second look at data: behavior at small x and Q 2 ►Look ‘directly’ at the gluon: F L and F 2 C

21. J. G. ContrerasCTEQ School 2005 21 The Q 2 dependence of the rise of F 2 At small x pQCD predicts F 2 ~x -λ... but λ varies from BFKL expectation to those from non-perturbative QCD

22. J. G. ContrerasCTEQ School 2005 22 F 2 and the limit Q 2 → 0 Remember: W 2 is energy of γ*p system At small x: W 2 ~Q 2 /x → high energy Remember x and Q 2 correlated at HERA At very small Q 2 : F 2 ~Q 2 But σ γ*p ~ F 2 /Q 2, so at small Q 2 : σ γ*p ~ constant, i.e. stops growing … We look for something like this at high Q 2

23. J. G. ContrerasCTEQ School 2005 23 Extraction of F L : the basic idea Look at high y Compare cross section to F 2 ~x -λ Assign difference to F L (,Q 2 ) DGLAP pQCD describes data …

24. J. G. ContrerasCTEQ School 2005 24 F 2 c and the gluon A small x gluon fluctuates into a charm quark-antiquark The virtual photon interacts with one of them The struck charmed parton is kicked out of the proton It fragments into a charmed hadron, which then decays Reconstruct the hadron using specific signatures Extract F 2 C ~ charm PDF

25. J. G. ContrerasCTEQ School 2005 25 F 2 c : the data Lots of data High precision Big phase space Strong rise … Described by DGLAP pQCD

26. J. G. ContrerasCTEQ School 2005 26 Where are we? Where are we going? (III) Where are we? ►free parton pQCD works also for the gluon at small x ►no real need of BFKL up to now: where are the log(1/x)? ►No real need to go beyond free partons where is saturation? Where are we going? ►looking for BFKL effects: Forward jets ►looking for high density effects: Geometric scaling

27. J. G. ContrerasCTEQ School 2005 27 Forward Jets: the basic idea ► Enhance BFKL: big step in x ► Suppress DGLAP: no step in Q 2 ► Experimentally look in small x for a jet at high x and with k 2 jet =Q 2 ► i.e. Forward jets

28. J. G. ContrerasCTEQ School 2005 28 Forward Jets as seen by the detector Initial electron and proton Scattered electron Emissions along the ladder Forward Jet Proton remnant … very difficult measurement 1 1 2 4 3 5 2 3 4 5

29. J. G. ContrerasCTEQ School 2005 29 Forward Jets: the data ► DGLAP do not describe the measurement at small x ► ‘BFKL-like’ models describe the data, but … ► Other models also do … ► pure LL-BFKL too steep, but works with smaller ‘intercept’ Furthermore, extending BFKL beyond leading log(1/x) presents some problems … ► Anyway, strong hint of something beyond DGLAP

30. J. G. ContrerasCTEQ School 2005 30 Geometric Scaling From 2 variables to 1 !

31. J. G. ContrerasCTEQ School 2005 31 Geometric Scaling and Saturation Why is geometric scaling interesting? ► It is an impressive phenomena ► It happens at small x ► Collapse of data points at different scales in a single curve is known to happen in phase transitions at a critical point ► Saturation may be thought as something like a phase transition: from free to strongly interacting partons from a low to a high density system ► Some of the QCD based nonlinear equations proposed for saturation accept naturally solutions with geometric scaling behavior

32. J. G. ContrerasCTEQ School 2005 32 Where are we? Where are we going? (IV) Where are we? ►Inclusive and exclusive observables point to a world beyond DGLAP ►Hints of BFKL and saturation? Need denser system, still with weak coupling!! Where are we going? BEYOND  ►Small x physics with nuclei ►A few words on nonlinear equations ►A final look at data

33. J. G. ContrerasCTEQ School 2005 33 Small x Physics and Heavy Ions Looking for a source of very dense (small x) gluons at a sizable Q 2 There are many small x gluons in a proton, what about nuclei? (nuclei: lots of p’s and n’s compressed in a tight space) ► Naively expect gluon density to scale as A 1/3 (high A=heavy ion) ► If energy high enough, it is possible to reach small x in the pQCD regime ► Need accelerator of ions ► Need forward detectors ► Need to disentangle all other effects Is all this possible? … let’s try and see!

34. J. G. ContrerasCTEQ School 2005 34 Heavy ions facilities: today and tomorrow Rich history of heavy ions accelerators and experiments: AGS and SPS Today RHIC plus its detector produce beautiful data PHENIX STAR BRAHMS pp2pp In the near future, at even higher energy, LHC and ALICE

35. J. G. ContrerasCTEQ School 2005 35 Color Glass Condensate: The basic idea It is a classical effective field theory of QCD with quantum evolution Valence partons act as a static random source of dynamic sea partons (Born-Oppenheimer separation based on their time scales) Static random source evolves in a time scale much larger than the natural scale like a spin glass. Lots of bosons together condensate. The new degree of freedom is the classical gluon. Gluons are colored, so call it CGC Add the corresponding RGE: Get the JIMWLK equations Limits: DGLAP, BFKL, BK eqs Phenomenology: F 2, geometric scaling and …

36. J. G. ContrerasCTEQ School 2005 36 Small x in heavy ion collisions deuterongold b Centrality = impact parameter High η = small x in Gold Many handels: ► Ion species ► centrality ► CMS energy ► different x ranges For each, measure as many details as possible ► Multiplicity ► 4-momentum ► Type of particle ► Correlations ► … Here only a bit of dA

37. J. G. ContrerasCTEQ School 2005 37 x dependence of R dA R dAu = d 2 N/dp T d  (d+Au) N Coll d 2 N/dp T d  (p+p) Relative measurement ↔ normalization 1 = no change in physics pp vs dAu Concentrate in the higher pt values There is a x dependence …

38. J. G. ContrerasCTEQ School 2005 38 R cp: x and centrality dependence R cp = Normalize central against peripheral events Study it as a function of rapidity as a function of centrality at high pt

39. J. G. ContrerasCTEQ School 2005 39 Heavy Ion Physics CGC ideas quantitatively compatible with dA R cp data Much more data (see Seto’s talk!) CGC seems to be the right way to go, but … ► many other effects are expected to contribute ► difficult to disentangle and them ► some surprise also A bright future at RHIC and then at LHC!

40. J. G. ContrerasCTEQ School 2005 40 Where are we? Where are we going? (V) Where are we? (almost!) at the end of the talk... ►Small x physics is a very active field of research accelerators producing tons of exciting data NOW theoreticians coming up with lots of attractive ideas ►Many interesting open questions both for theory and experiment alike Where are we going? ►questions, answers… ►Next talk … ►Dinner … and beyond! THANK YOU! HOMEWORK 3