1. 1 Introduction to Deep Inelastic Scattering (DIS) Rik Yoshida Argonne National Laboratory CTEQ summer school 07 May 30, 2007

2. 2 Some preliminary remarks This is not a historical review – for a very nice historical review see EnricoTassi’s lectures from 2003: http:://www-zeus.desy.de/~tassi/cteq2003.ppt Nor a review of experimental status Enrico’s second lecture (same place) Max Klein’s DIS lecture from CTEQ 2006 Nor a theoretical discussion –Morning lectures from George Sterman Aim: to leave you with some intuitive feeling for what is happening in Deep Inelastic Scattering (DIS). Going to stick to electron- (positron-) proton DIS

3. 3 Partons in the proton Feynman’s parton model: the nucleon is made up of point- like constituents (later identified with quarks and gluons) which behave incoherently. The probability f(x) for the parton f to carry the fraction x of the proton momentum is an intrinsic property of the nucleon and is process independent. If I were thinking about an experiment where we collide protons with protons at, say, 14 TeV: then this is great! Because: -Protons are just a “beam of partons” (incoherent) -The f(x)s, the “beam parameters”, could be measured in some other process. (process independent)

4. 4 Quarks and Gluons as partons ∫x[u(x)+u(x)+d(x)+d(x)+s(x)+s(x)+….]dx = 1 u(x) : up quark distribution u(x) : up anti-quark distribution etc. Momentum has to add up to 1 (“momentum sum rule”) Quantum numbers of the nucleon has to be right ∫[u(x)-u(x)]dx=2∫[d(x)-d(x)]dx=1 ∫[s(x)-s(x)+……]dx=0 So for a proton:

5. 5 DIS kinematics ep collision proton in “∞” momentum frame √s = ep cms energy Q 2 =-q 2 = 4-momentum transfer squared (or virtuality of the “photon”) No transverse momentum x = fractional longitudinal momentum carried by the struck parton 0 ≤ x ≤ 1

6. 6 DIS kinematics ep collision Q 2 =-q 2 =-(k-k’) 2 =2E e E’ e (1+cosθ e ) x =Q 2 /2Pq = E e E’ e (1+cosθ e ) E P 2E e -E’ e (1-cosθ e ) Initial electron energy Final electron energy Initial proton energy Electron scattering angle Everything we need can be reconstructed from the measurement of E’ e and θ e. (in principle)

7. 7 Deep Inelastic Scattering experiments Fixed target DIS at SLAC, FNAL and CERN completed ~ 10-20 years ago HERA collider: H1 and ZEUS experiments 1992 – 2007 (will complete July 2, 2007)

8. 8 e - p Neutral Current (NC) cross-section: d 2 σ 2πα 2 dxdQ 2 xQ 4 [Y + F 2 (x,Q 2 )-y 2 F L (x,Q 2 )+Y - xF 3 (x,Q 2 )] = y=Q 2 /xs 0 ≤ y ≤ 1 “inelasticity”Y ± =1±(1-y) Has to do with Z 0 exchange: small for Q<<M Z Has to do with long. photon. Only large at largest y We’ll come back to these d 2 σ 2πα 2 dxdQ 2 xQ 4 = Y + F 2 (x,Q 2 ) So for now: F 2 = x∑(q + q) e q + Z-exchange quark charge quark and anti-quark distributions 2

9. 9 The partons are point-like and incoherent then Q 2 shouldn’t matter.  Bjorken scaling: F 2 has no Q 2 dependence. IF, proton was made of 3 quarks each with 1/3 of proton’s momentum: F 2 = x∑(q(x) + q(x)) e q no anti-quark! F2F2 1/3 x q(x)=δ(x-1/3) or with some smearing Let’s look at some data  2

10. 10 Proton Structure Function F 2 F2F2 Seems to be….NOT

11. 11 So what does this mean..? QCD, of course: quarks radiate gluons q q q q gluons can produce qq pairs gluons can radiate gluons!

12. 12 r≈ hc/Q = 0.2fm/Q[GeV] r γ*(Q 2 ) Virtuality (4-momentum transfer) Q gives the distance scale r at which the proton is probed. ~1.6 fm (McAllister & Hofstadter ’56) CERN, FNAL fixed target DIS: r min ≈ 1/100 proton dia. HERA ep collider DIS: r min ≈ 1/1000 proton dia. e e’ Proton HERA: E e =27.5 GeV, E P =920 GeV

13. 13 Higher the resolution (i.e. higher the Q 2 ) more branchings to lower x we “see”. So what do we expect F 2 as a function of x at a fixed Q 2 to look like? F2F2

14. 14 1/3 F 2 (x) x x x Three quarks with 1/3 of total proton momentum each. Three quarks with some momentum smearing. The three quarks radiate partons at low x.

15. 15 Proton Structure Function F 2 How this change with Q 2 happens quantitatively described by the: Dokshitzer- Gribov- Lipatov- Altarelli-Parisi (DGLAP) equations

16. 16 DGLAP equations are easy to “understand” intuitively First we have the four “splitting functions” zzz z 1-z P ab (z) : the probability that parton a will radiate a parton b with the fraction z of the original momentum carried by a.

17. 17 = α s [q f × P qq + g × P gq ] Now DGLAP equations (schematically) dq f (x,Q 2 ) d ln Q 2 convolution strong coupling constant Change of quark distribution q with Q 2 is given by the probability that q and g radiate q. dg(x,Q 2 ) = α s [∑q f × P qg + g × P gg ] d ln Q 2 Same for gluons: o o o o

18. 18 DGLAP fit (or QCD fit) extracts the parton distributions from measurements. (Lectures by Jeff Owens next week) Here’s a 1 min description: Step 1: parametrise the parton momentum desity f(x) at some Q 2. e.g. u v (x) u-valence d v (x) d-valence g(x) gluon S(x) sum of all “sea” (i.e. non valence) quarks Step 2: find the parameters by fitting to DIS (and other) data using DGLAP equations to evolve f(x) in Q 2. “The orginal three quarks” f(x)=p 1 x p2 (1-x) p3 (1+p 4 √x+p 5 x)

19. 19 Sea PDF x xS At x<<1/3, quarks and (antiquarks) are all “sea”. Since F2 = e q ∑x(q + q), xS is very much like F 2 Fractional uncertainty 2

20. 20 Gluon PDF x xg Gluons, on the other hand, are determined from the scaling violations dF 2 /dlnQ 2 via the DGLAP equations. Uncertainties are larger. Scaling violations couple α s and gluon g Fit with α s also a free param.

21. 21 So far: F 2 ~ ∑(q+q) ≈ S (sea quarks) measured directly in NC DIS Scaling violations dF 2 /dlnQ 2 ~ α sg Scaling violations gives gluons (times α s ). DGLAP equations. What about valence quarks? ∑(q-q) = u v + d v can we determine them separately? Can we decouple α s and g ?

22. 22 Return to Neutral Current (NC) cross-section: d 2 σ(e ± p) 2πα 2 dxdQ 2 xQ 4 [Y + F 2 (x,Q 2 ) Y - xF 3 (x,Q 2 )] = Y ± =1±(1-y) ± Now write out the e + p and e - p separately xF 3 = ∑(q(x,Q 2 )-q(x,Q 2 )) xB q ~The valence quarks! B q = -2e q a q a e χ Z + 4v q a q v e a e χ Z 2 χ Z = ( ) Keeps xF 3 small if Q<M Z 1 Q 2 sin2θ W M Z +Q 2 2 (keep ignoring F L for now..) B q = -2e q a q a e χ Z + 4v q a q v e a e χ Z 2

23. 23 Return to Neutral Current (NC) cross-section: d 2 σ(e ± p) 2πα 2 dxdQ 2 xQ 4 [Y + F 2 (x,Q 2 ) Y - xF 3 (x,Q 2 )] = Y ± =1±(1-y) ± Now write out the e + p and e - p separately xF 3 = ∑(q(x,Q 2 )-q(x,Q 2 )) xB q ~The valence quarks! B q = -2e q a q a e χ Z + 4v q a q v e a e χ Z 2 (keep ignoring F L for now..) B q = -2e q a q a e χ Z + 4v q a q v e a e χ Z 2 e q : electric charge of a quark a q v q : axial-vector and vector couplings of a quark a e v e : axial-vector and vector couplings of an electron γ-Z interferenceZ-exchange

24. 24 Return to Neutral Current (NC) cross-section: d 2 σ(e ± p) 2πα 2 dxdQ 2 xQ 4 [Y + F 2 (x,Q 2 ) Y - xF 3 (x,Q 2 )] = Y ± =1±(1-y) ± Now write out the e + p and e - p separately xF 3 = ∑(q(x,Q 2 )-q(x,Q 2 )) xB q ~The valence quarks! (keep ignoring F L for now..) Let’s look at the “reduced NC cross-section” σ NC ± = F 2 (x,Q 2 ) (Y-/Y+)xF3(x,Q2) ± Note the change of sign from e + p to e - p

25. 25 σ NC± x Measurements are at relatively high x Reduced Neutral Current Cross-section

26. 26 Recent (Spring 07) preliminary result from HERA

27. 27 Charged Current Cross-Sections dσ CC (e ± p) G F M W dxdQ 2 2πx M W +Q 2 = [ ] 2 σ CC± 2 22 Skip a few steps…. σ CC+ = x [u + c + (1 - y) 2 (d + s)] ~ d σ CC- = x [u + c + (1 – y) 2 (d + s)] ~ u charm

28. 28 σ CC± Reduced Charged-Current Cross-Section x σ CC+ ~ d σ CC- ~ u Now let’s look at the valence quarks from the QCD fits 

29. 29 Valence PDFs x xf The momenta from valence quarks are producing gluons and sea quarks at low x

30. 30 Jet production in DIS (HERA) Sensitive to α s Sensitive to gluon ~10 -3 < x < ~10 -2 Sensitive to quarks ~10 -2 < x < ~10 -1 complementary to gluon from F 2 Same range as NC and CC σ jet ~ α s f(x)

31. 31 No E T in Breit Frame Jet production cross-section used in QCD fit  Jet measurements in Breit frame

32. 32 Gluon distributions x x Using only HERA (ZEUS) data including NC,CC and jets Using HERA (ZEUS) F 2 data and FNAL, CERN fixed tgt

33. 33 Finally…

34. 34 Proton Structure Function F 2 F2F2 Now we understand what is happening here.

35. 35 Some remarks about DGLAP equations: But now parton densities must be “evolved” in Q 2. What does this mean?  The “incoherence” of the original parton model is preserved. i.e. a parton doesn’t know anything about its neighbor. never happens The “process independent” partons also survive.

36. 36 A parton at x at Q 2 is a source of partons at x’ Q 2. x Q2Q2 Q’ 2 x’ In fact, any parton at x > x’ at Q 2 is a source. To know the parton density at x’, Q’ 2 it’s necessary (and sufficient) to know the parton density in the range: x’ ≤ x ≤ 1 at some lower Q 2. 1 measured known unknown What does this mean for the LHC?  If you know the partons in range x’ ≤ x ≤ 1 at some Q 2, then you know the partons in the range x’ ≤ x ≤ 1 for all Q’ 2 > Q 2.

37. 37 Fixed target DIS HERA DIS Tevatron jets ~safe Q 2 “known”

38. 38 24 parton1(x 1 ) + parton2(x 2 )  State with mass M LHC (or hadron-hadron) parton kinematics x 1 = (M/√s) exp (y)x 2 = (M/√s) exp (-y) y= ln( ) 1 E+P Z 2 E-P Z rapidity: pseudo-rapidity: η=-ln tan(θ/2) angle wrt beam

39. 39 24 So if I want to predict Z or W production cross-section at LHC at some rapidity y, say, -4: q,q(x 1 =10 -4,Q 2 =M W,Z )q,q(x 2 =0.3,Q 2 =M W,Z ) need 22 and σ (pp  W,Z+X) ~ q,q(x 1,M W,Z ) × q,q(x 2,M W,Z ) × σ (qq  W,Z) 22

40. 40 xf(x) xS(x) xg(x) “measured” “evolved” xg(x) xS(x) Evolving PDFs up to M W,Z scale

41. 41 -66 σ(arb. scale) η Z production at LHC Uncertainty ~5% A. Cooper-Sarkar (HERA-LHC workshop 2007) Jet production at LHC Examples of predictions for LHC using partons from DIS

42. 42 Final remarks I We’ve just gone through an informal tour of QCD-improved parton model and its application to data from ep Deep Inelastic Scattering. Some health warnings: –Most of what I talked about is a leading-order picture. In practice, most things are done at least to next-to-leading order. At NLO, the interpretation of the results are not as straight-forward. –Many people worry about whether we are not missing something fundamentally with the picture of DGLAP equations. Much of the data are at very low x: DGLAP is a lnQ 2 approximation. Why aren’t ln(1/x) terms important…or are they?  BFKL equations. The density of the partons, especially that of the gluons is getting very high. When and where should we worry about “shadowing”, “gluon recombination” etc. The idea of incoherence of partons may be breaking down in some kinematic regions: phenomenon of “hard diffraction” is difficult to understand in terms of partons without correlations to each other.

43. 43 Final remarks II There are many other DIS physics topics I did not cover here. Electoweak physics Heavy quark production Diffraction, Vector Meson production, low Q 2 physics Beyond the SM searches. Polarized DIS … I hope I have refreshed your memory about some familiar DIS physics, and got you ready for the rest of the school. Thanks to the organizers for their kind invitation. Thanks to Claire Gwenlan for preparing some of the plots animation for me. –You can find the animated gifs in: http://www.hep.anl.gov/ryoshida/animated_proton.htm

44. 44 Extras (F L )

45. 45 F L =(Q 2 /4π 2 α) σ L Longitudinal cross-section

46. 46 QCD predicts a relationship between scaling violations and FL through the gluon density. increasing y

47. 47 You can determine F L from a NLO DGLAP fit to NC cross-section. x Indeed, we also only determine F 2 the same way, in principle: We measure this only

48. 48 C. Diaconu: DIS 07 conference April 07 HERA measurement of FL on-going now Normally 920 GeV