Deep Inelastic Scattering DIS

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1 Deep Inelastic Scattering DIS Burkard Reisert Max-Planck-Institut für Physik München Historical Prelude Introduction to DIS and proton structure Impact of recent results from HERA

Prelude: Antic Gedankenexperiment Popular science book by Leon Ledermann

for ever or do we end up with some smallest unit? Demokrit ( 460-371 v.

void, and also in reality we know nothing, since the truth is at bottom.

2 Prelude: Antic Gedankenexperiment Popular science book by Leon Ledermann The God Particle : Slicing of Feta cheese: Could we continue the slicing for ever or do we end up with some smallest unit? Demokrit ( v.chr.): By convention hot, by convention cold, but in reality atoms and void, and also in reality we know nothing, since the truth is at bottom. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

3 In search of the smallest particle Human ~2m More than 2400 years after Demokrit we still ask the same question. Employing the experimental methods of modern physics in search for answers. Crystal Molecule Atom Nucleus Nucleon Quark Electron Focus of Deep inelastic scattering Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

4 It all began with Ernest Rutherford The mother of all scattering experiments gold foil α-source scintillating screen Count rate α + Au dσ 2 c 1 ( zzα) = dω 4E 4 kin sin θ/2 2 ( ) Scattering angle Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

5 Ernest Rutherford Interpretatio Thomson s old plum pudding model Rutherford s new planetary model E. Rutherford Nobel prize 1908 in Chemistry (not for this ingenious idea!) Halo of electrons surrounding a point like core, i.e. nucleus Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

Pioneer of Electron Scattering: Robert Hofstadter Nobelpreis 1961 Electrons: -Elementary particle - Only sensitive to the charge distribution of the target - Easy to produce, accelerate and detect

6 Pioneer of Electron Scattering: Robert Hofstadter Nobelpreis 1961 Electrons: -Elementary particle - Only sensitive to the charge distribution of the target - Easy to produce, accelerate and detect Rule of thumb: Resolution hc = 200 [MeV fm] Typical design of an electron scattering experiment: Beam of electron hits on a fixed target Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

7 Graphs from R. Hofstadter s Nobel-Lecture, Dez. 11, 1961 Count rate: electrons (420 MeV) scattering off carbon Elastic Scattering: dip structure finite nuclear radius dσ dσ E θ = dω d E Ω 2 Ruth Charge distribution E k k 2 2 cos ( ) Fq θ E q = k k form factor Fourier transformed of form factor Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School Angle Radius [ fm]

8 Something is wrong with the proton dσ dσ E θ q θ = cos + sin dω d E 2 2M 2 Ω Ruth Cross section for electron scattering on a spin 1/2 Dirac proton the proton has an anomalous magnetic structure (NOT a Dirac particle) beam energy too small to resolve the proton structure Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

9 Pioneers of High Energy Physics E e (multi GeV) J. Friedman R. Taylor H. Kendall Stanford Linear Accelator SLAC Proton is made of Quarks! ( ) Nobelpreis 1990 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School Endstation A spectrometers

10 Resolving the Structure of the Protons In order to resolve even smaller struktures even higher energies are necessary So far: Electron beams on fixed targes (+μ,ν, on p,d,fe ) e ± E k θ E Increasing the available centre-of-mass energy Colliding beams P k e ± P Recycle particle beams Storage Ring, Collider. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

HERA ep Collider: 1992-2007 Longitudinally polarised e Two colliding beam experiments: H1 and ZEUS ~0.

11 HERA ep Collider: Longitudinally polarised e Two colliding beam experiments: H1 and ZEUS ~0.5 fb -1 collected per experiment approximately same amount of collisions with electrons and positrons of Left- and right-handed polarisation E e = 27.5GeV, E p = 920 GeV dedicated low Ep runs Ep = 460GeV,575 GeV Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

12 H1 & ZEUS Collaborations Collaborations of Physicists, at ~40 Institutes of ~15 Countries Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

13 Partons in the proton Feynman s parton model: the nucleon is made up of pointlike 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 (7)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) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

14 Quarks and Gluons as partons u(x) : up quark distribution u(x) : up anti-quark distribution etc. Momentum has to add up to 1 ( momentum sum rule ) x[u(x)+u(x)+d(x)+d(x)+s(x)+s(x)+.]dx = 1 Quantum numbers of the nucleon has to be right So for a proton: [u(x)-u(x)]dx=2 [d(x)-d(x)]dx=1 [s(x)-s(x)+ ]dx=0 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

$DIS kinematics ep collision proton in momentum frame No transverse momentum 0 x 1 x = fractional longitudinal momentum carried by the struck parton s = ep$

15 DIS kinematics ep collision proton in momentum frame No transverse momentum 0 x 1 x = fractional longitudinal momentum carried by the struck parton s = ep cms energy Q 2 =-q 2 = 4-momentum transfer squared (or virtuality of the photon ) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

16 DIS kinematics ep collision Final electron energy Initial electron energy Q 2 =-q 2 =-(k-k ) 2 =2E e E e (1+cosθ e ) x =Q 2 /2P q = E e E e (1+cosθ e ) E P 2E e -E e (1-cosθ e ) Initial proton energy Electron scattering angle Everything we need can be reconstructed from the measurement of E e and θ e (in principle). Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

17 Deep Inelastic Scattering experiments Fixed target DIS at SLAC, FNAL and CERN completed ~ years ago Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

Deep Inelastic Scattering experiments HERA collider: H1 and ZEUS experiments 1992 2007 (data

18 Deep Inelastic Scattering experiments HERA collider: H1 and ZEUS experiments (data analysis ongoing) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

19 e ± p Structure Functions within the Quark-Parton-Model DIS = k k x P electron scatters off a charged constituent (parton) of the proton (= elastic scattering) identify the charged partons with QUARKS (= spin 1/2 fermions) Quark-Parton-Model (QPM) γ e ± X 2 ± d σ ( e p) 2 2πα = Y F dx dq xq QPM: F 2 F x 2 ( ) e xq ( x) 2 i i i= u, d = 0 1 x 0 1 x 1/3 2 y FL parton densities xq ( x ) i (pdf) P Gluons F = L x 1/3 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

20 IF, proton was made of 3 quarks each with 1/3 of proton s momentum: F 2 2 F 2 = x e q q(x) q(x)=δ(x-1/3) or with some smearing 1/3 x The partons are point-like and incoherent then Q 2 shouldn t matter. Bjorken scaling: F 2 has no Q 2 dependence. Let s look at some data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

21 Results from SLAC-MIT experiment Seems to be. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

22 Proton Structure Function F 2 F 2 Seems to be. NOT Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

23 So what does this mean..? QCD, of course: q q quarks radiate gluons q q gluons can produce qq pairs gluons can radiate gluons! Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

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

25 F 2 The higher the resolution (i.e. higher the Q 2 ) the 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? Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

26 F 2 (x) Three quarks with 1/3 of total proton momentum each. F 2 (x) 1/3 x Three quarks with some momentum smearing. F 2 (x) 1/3 x The three quarks radiate partons at low x. 1/3 x Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

27 Proton Structure Function F 2 How this change with Q 2 happens quantitatively described by the: Dokshitzer- Gribov- Lipatov- Altarelli- Parisi (= DGLAP) equations Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

28 DGLAP equations are easy to understand intuitively First we have the four splitting functions z z z z 1-z 1-z 1-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. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

29 Now DGLAP equations (schematically) dq f (x,q 2 ) d ln Q 2 convolution = α s [q f o P qq + g o P gq ] strong coupling constant Change of quark distribution q with Q 2 is given by the probability that q and g radiate q. Same for gluons: dg(x,q 2 ) d ln Q 2 = α s [ q f o P qg + g o P gg ] Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

30 Structure Function F 2 HERA I F = xe q x + q x 2 2 q ( ( ) ( )) q H1 & ZEUS extended fixed target kinematic regime in x and Q 2 by 2 Orders Described by DGLAP Scaling violations rise at low x drop at high x Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

31 DGLAP fit (or QCD fit) extracts the parton distributions from measurements. Step 1: parameterise the parton momentum density f(x) at some Q 2, e.g.: f(x)=ax B (1-x) C (1+Dx+Ex 2 ) u v (x) d v (x) g(x) S(x) u-valence d-valence gluon sum _ of _ all _ sea (i.e. _ non valence) quarks (or U=u+c(+t) & D=d+s+b) The original three quarks Step 2: find the parameters by fitting to DIS (and other) data using DGLAP equations to evolve f(x) in Q 2. 2 _ Caveat! Not as easy: fit 4 PDFs (or 5), input one F 2 =Σe q (q+q) (+ F 2 / lnq 2 ~ α s g(x)) different measurements needed, e.g. fix target data ( global PDF fits) or see next slide Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

32 HERA high Q 2 Data Neutral Current Wirklichkeit times 2 for e+p and e-p Z R Charged Current DESY PR Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

33 Neutral Current Cross Section Generalized structure functions: Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

34 Charged Current Cross Section e + /e - sensitive to different quark densities: CC reduced cross section CC gives sensitivity to different combinations of quarks as NC. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

35 Electroweak Unification γ NC: CC: W ± EW component of SM: NC and CC cross sections are similar at Q 2 M Z2,M W 2 difference in e + and e - for NC in high Q 2 region comes from contribution of Z exchange Z 0 Data compared with SM Good agreement over full range Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

36 Charged Current Cross Sections e + p Results from entire HERA-II data set e - p Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

37 Quark Antiquark Decomposition H1 Preliminary σ% CC CC σ% ZEUS x x Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

38 Quark Antiquark Decomposition Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

39 Neutral Current: xf 3 NC cross section: dominant contribution to xf 3 : Sensitivity to valence quarks e _ e + Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

40 PDF Fits on HERA I Data Standalone PDF Fits HERAPDF 0.1 Impressive reduction of uncertainties of combined analysis Model uncertainty: variation of charm and bottom mass, starting scale Q 02, Q 2 min of included data, strange and charm fraction at starting scale Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

41 Comparison to Global Fits HERAPDF 0.1 HERAPDF 0.1 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

42 Deep Inelastic Scattering Second Lecture Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

43 2 nd Lecture: Outline Yesterday: Developed a picture of the proton (PDFs and DGLAP evolution) Today: Explore validity of this picture Ultimate precision of the HERA measurements Additional constraints on PDFs from HERA: Jets, FL, Heavy Quarks Relation to Tevatron and LHC Polarized CC & NC (if time allows, beautiful physics!) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

44 HERA s Surprise: The Strong Rise of F 2 towards low x scaling violations λ HERA at low x : F x λ Q 2 2 ( ) 0 x 1/6 Transition from the perturbative to the non-perturbative regime Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

45 Low x, Large Parton Densities and Saturation at fixed resolution scale (Q 2 ) go to very large hadronic center of mass energy low x x = Q 2 Q + W 2 2 ultimately expect partons to overlap ( saturation ) Rise of PDFs should flatten with decreasing x λ 1 1 ln x x No saturation observed at HERA Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

46 Combination of H1 and ZEUS Measurements χ 2 definition backup slides Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

47 Results of Combining H1 and ZEUS F 2 ~ [JHEP01 (2010) 109] Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

48 HERA I +II Combined NC Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

49 HERA I+II Combined CC Without HERA II data With HERA II data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

50 QCD Analysis Framework Data Sets - HERA I combined data [JHEP01 (2010) 109] - add HERA-II data (NC+CC high Q2, low Ep, F2cc, ) TR TR Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

51 Sources of PDF uncertainties at HERA Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

52 HERAPDF1.5 vs. HERAPDF1.0 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

53 Fits to New Combined HERA data: HERAPDF1.5 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

54 Fits to New Combined HERA data: HERAPDF1.5 NC & CC inclusive Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

~10-1 ~10-3 < x < ~10-2 complementary Same range as NC and CC to gluon

55 Jet production in DIS (HERA) Sensitive to α s σ jet ~ α s f(x) Boson Gluon Fusion (BGF) Sensitive to quarks Sensitive to gluon ~10-2 < x < ~10-1 ~10-3 < x < ~10-2 complementary Same range as NC and CC to gluon from F 2 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

56 Jet measurements in Breit frame No E T in Breit Frame Jet production cross-section used in QCD fit Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

57 Gluon distributions Using only HERA (ZEUS) data including NC,CC and jets x x Using HERA (ZEUS) F 2 data and FNAL, CERN fixed tgt Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

58 Photon Proton Scattering DIS ep scattering may be interpreted as scattering of an virtual photon off an proton The virtual photon may be transversely or longitudinally polarized γ σ σ γp Cross Sections: σ σ γ p T γ p L γ p L γ p T 4π α 4πα = 2 xf 2 1 = F 2 2 F Q Q 2 ( ) 4πα 4πα = 2 ( F 2 2 xf1) = F 2 Q Q = R = F F L F L L L Quark Parton Model (QPM) 1 2 F1 ( x) = eq xq( x) q 2x 2 F x = e xq( x) 2 ( ) ( ) F x = F 2xF = 0 L q q 2 1 Callan Gross relation Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

59 Longitudinal Structure Function F L QPM QCD Scattering of longitudinally polarized photons on quarks in helicity frame Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School access to gluon density

60 Measurement of FL 2 y σ = F2 x, Q F x, Q 2 2 ( ) ( ) Measure cross sections r L Y at same x and Q 2 but different y = Q 2 + /x s vary s HER MER LER Change proton beam energy to change cms energy - E p = 920 GeV, High Energy Run (HER) - E p = 575 GeV, Medium Energy Run (MER): - E p = 460 GeV, Low Energy Run Large lever arm in y 2 /Y + Measure at high y in LER Extended measurement to high y region y = 1-E e /E e (1-cosθ) high y means low E e Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

61 Combined low E p Cross Sections σ r x ZEUS Range of ZEUS measurement x Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

62 Extracted F L and F 2 ZEUS Most precise F 2 measurement from ZEUS in kinematic region studied First F 2 measurement without assumptions on F L Data support a non-zero F L Predictions for F 2 and F L are consistent with data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

63 Extracted F L medium & high Q 2 Medium Q2 published in Phys. Lett. B665, p. 139 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

64 Extracted F L Low Q 2 F L measured down to Q 2 = 2.5 GeV 2! Data are consistent with R~0.25 (F L =0.2 F 2 ) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

65 H1 + ZEUS Combined F L ZEUS measurements Good agreement between data and predictions for Q 2 >10 GeV 2. F L at low Q 2 above prediction using HERAPDF1.0 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

66 HERAPDF including low E p data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

67 Variants of Predictions for F L Higher Order calculation Variation of heavy flavour treatment Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

68 Heavy Quarkproduction in DIS Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

69 Heavy Flavour Tagging Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

70 H1 + ZEUS Charm Measurements Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

71 Measurement: Visible Cross Section Example: Semileptonic decays into μ Simultaneous extraction of charm and beauty cross sections Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

72 Charm Structure Function: F 2 cc Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

73 cc Combined F 2 to individual measurements Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

74 Combined F 2 cc vs. various Theories Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

75 H1-ZEUS combined F 2 cc vs. HERAPDF1.0 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

76 cc Adding combined F 2 to HERAPDF1.0 Fit Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

77 Q 2 A parton at x at Q 2 is a source of partons at x < x at Q 2 > Q 2. Q 2 unknown x known measured x 1 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. 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. What does this mean for the LHC? Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

78 known Tevatron jets HERA DIS Fixed target DIS ~safe Q 2 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

79 LHC (or hadron-hadron) parton kinematics rapidity: 1 E+P Z y= ln( ) 2 E-P Z pseudo-rapidity: η=-ln tan(θ/2) 2 4 angle wrt beam parton1(x 1 ) + parton2(x 2 ) State with mass M x 1 = (M/ s) exp (y) x 2 = (M/ s) exp (-y) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

80 σ (pp W,Z+X) ~ q,q(x 1,M W,Z ) q,q(x 2,M W,Z ) σ (qq W,Z) 2 2 So if I want to predict Z or W production cross-section at LHC at some rapidity y, say, -4: and need q,q(x 1 =10-4,Q 2 =M W,Z ) q,q(x 2 =0.3,Q 2 =M W,Z ) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

81 Predictions for LHC using partons from DIS Examples: σ(arb. scale) Uncertainty ~5% -6 η 6 (nb/gev) dσ/de T Fractional Uncertainty 10 1 NLO QCD (JETRAD) PDF: ZEUS-JETS PDF: HERA-II PROJECTION pp Jet + X s = 14 TeV JETCLU Cone R= < η Jet < < η Jet < 2 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School < η Jet < Jet production at LHC (GeV) Inclusive Jet E T Exciting times ahead, LHC experiments started to do these measurements

82 HERAPDF1.0 vs. Tevatron Data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

83 HERAPDF1.0 vs. Tevatron Data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

84 If time allows: Deep Inelastic Scattering with Polarized Leptons: Demonstration of the chiral structure of electroweak interactions Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

85 Charged Current Cross Section e + /e - sensitive to different quark densities: CC reduced cross section CC gives sensitivity to different combinations of quarks as NC. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

86 Polarized Charged Current cross section Linear dependence of σ CC on P e Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

Total Charged Current Cross Section Linear dependence of σ CC on P e e - p SM: weak CC interactions: only left handed particles (right handed anti-particles)

87 Total Charged Current Cross Section Linear dependence of σ CC on P e e - p SM: weak CC interactions: only left handed particles (right handed anti-particles) interact e + p ZEUS and H1 in agreement with SM SM: No right-handed weak currents Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

88 Polarised CC Cross Sections e _ p e + p LH RH RH LH zeus-pub Predictions of SM give good description of data Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

89 Neutral Current Cross Section Generalized structure functions: Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

90 Polarized NC measurements The charge dependent polarization asymmetries in neutral currents direct measure of EW effects Polarization asymmetries (A) sensitive to ratio of γz interference term to F 2 A is proportional to a e v q combination HERA II data neglecting Z term, the generalized structure function F 2 is expressed: At LO: Data well described by SM Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

91 Combined EW and QCD Fits Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

92 Summary What have we learnt from DIS in the last 30-35years? Verified the basic idea of QPM Established QCD as the theory of the strong interaction Measurement of essential parameters: Parton Distribution Functions, αs(mz ) and the running of α s Discovery of neutral currents Vivid demonstration of the unification of weak interaction and electromagnetism at high Q2 Verification of the chiral structure of electroweak interactions (polarized cross sections) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

93 Final Remarks There are many other DIS physics topics I did not cover here. Electoweak physics (?) Jet physics (algorithms, substructure, running of α s, ) Polarized DIS (polarized targets) Diffraction, Exclusive Vector Meson production low Q 2 physics, transition to non-perturbative QCD Beyond the SM searches Future machines (LHeC) 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. New fixed target experiments High x, nuclear corrections, 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. Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

94 Backup Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

95 χ 2 Definition χ M 2 i i,true i M M M + Δ α j j 2,true ex p (, ) = α Δ i j M Δ α j i σ i j σ α i σ i measured central values statistical and uncorrelated systematic uncertainties α 2 j j σ α j M α M j i i,true i M Δα j α j correlated uncertainty Sensitivity of the data to the systematic source j Fitted H1-ZEUS combined cross section Fitted shift of the I data due to the systematic source j If Δ = 0 it coincides with a standard average α j Caution: Most errors are provided as relative errors, a smaller value of cross section has smaller absolute error bias toward smaller averages Can be avoided by modified χ 2 definition: insert itrue, Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet M i Summer School 2010 M 95

96 Modified χ 2 definition Caution: Most errors are provided as relative errors, a smaller value of cross section has smaller absolute error, bias toward smaller averages Can be avoided by modified χ 2 definition: Normalization uncertainty is clearly a relative (multiplicative). Are other systematic errors as additive or multiplicative errors? Choice of best treatment is debatable. Does it matter? Impact is mostly negligible, except at very large Q2 and x where statistical errors and fluctuation are largest. How to deal with this freedom in systematic error treatment? Additional correlated uncertainty of averaged data points Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

97 F 2 at medium Q 2 New measurement (L = 22pb -1, 2000) combined with published results (96/97) s r ~ F 2 (12 < Q 2 < 150GeV 2, y<0.6) impressive accuracy 1.3-2% Steep rise described by QCD X Rise compatible with Effect of Gluon dynamics well described by fit Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

98 NC Measurement at low Q 2 Measurement presented as effective γ p cross section precision of combined measurements better than 2% Smooth transition from perturbative to non-perturbative regime at Q 2 ~ 1GeV 2 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

tot γ p γ p DL98: Donnachie Landshoff, Phys Lett.

99 Total Photon-Proton Cross Section Measurements at 3 proton energies Slope with W γp locally extracted σ = AW + BW 2η + 2ε tot γ p γ p DL98: Donnachie Landshoff, Phys Lett. B296, 227 Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

$Diffraction: A New Class of Events at$ $Diffractive Event Burkard Reisert, Deep$

100 Diffraction: A New Class of Events at HERA Rapidity Gap η max DIS event Diffractive Event Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

101 Diffraction: Further constituents in the proton? x = Q 2 Q + W 2 2 β = Q 2 Q + M 2 2 X W 2 2 Q + M x X P = 2 2 x (DIS) β (Diff. DIS) Q + W momentum fraction of color singlet exchange relative to the proton leaves a rapiditiy gap between M X and p colorless exchange emitted particle: Pomeron 2 t = ( p p ) (momentum transfer) 2 at proton vertex Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

102 Diffractive vs Inclusive DIS: x-dependence β (Diff. DIS) x (DIS) weak dependence on β, similar to the photon (few partons?) Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

103 Partonic Structure of Diffraction 2 Q NLO M 12 z P M X x P z P = Q Q + M MX Gluon momentum fraction: ( 70 ± 5)% Diffraction is gluon-dominated Fit B: simple gluon Burkard Reisert, Deep Inelastic Scattering, CTEQ/MCnet Summer School

The MINERνA Experiment

The MINERνA Experiment -Brian G Tice- Rutgers, The State University of New Jersey On behalf of the MINERνA collaboration MINERνA Workshop on Electron-Nucleus Scattering XII Marciana Marina, Isola d Elba