Presentation is loading. Please wait.

Presentation is loading. Please wait.

1 Vector and Axial Form Factors and Inelastic Structure Functions Arie Bodek University of Rochester Lecture.

Similar presentations


Presentation on theme: "1 Vector and Axial Form Factors and Inelastic Structure Functions Arie Bodek University of Rochester Lecture."— Presentation transcript:

1

2 1 Vector and Axial Form Factors and Inelastic Structure Functions Arie Bodek University of Rochester http://www.pas.rochester.edu/~bodek/CTEQ04.ppt Lecture Given in CTEQ04 Summer School, Madison Wed. June 23,2004 (4pm-5pm) Plus Three Problems for Students to work out together as a team. Email solution -bodek@pas.rocherster.edu end of week-bodek@pas.rocherster.edu

3 2 1. Bubble Chamber language. - Exclusive final states 2. Quasi+Resonan - Excitation Form Factors (to nucleons and resonances) 3. Deep Inelastic Scattering -PDFs and fragmentation to excl. final states Note 2 and 3: Form Factors can be converted to PDFs  /E E (GeV) -------- 1 Pion production ---- Quasielastic W=Mp 1100.1 ------total  -------- DIS W>2GeV 

4 3 MIT SLAC e-p DATA 1970 e.g. E0 = 4.5 and 6.5 GeV e-P scattering A. Bodek PhD thesis 1972 [ PRD 20, 1471(1979) ] Proton Data Electron Energy = 4.5, 6.5 GeV Data ‘ The Deep Inelastic Region is the “ Rutherford Experiment ” of the proton. The electron scattering data in the Resonance Region is the “ Frank Hertz Experiment ” of the Proton. SAID V. Weisskopf * (former faculty member at Rochester and at MIT when he showed these data at an MIT Colloquium in 1971 (* died April 2002 at age 93 ) What do The Frank Hertz” and “Rutherford Experiment” of the proton’ have in common? A: Quarks! And QCD

5 4 Fixed W scattering - form factors (the Frank Hertz Experiment of the Nucleon ) OLD Picture fixed W: Elastic Scattering, Resonance Production. Electric and Magnetic Form Factors (G E and G M ) versus Q 2 measure size of object (the electric charge and magnetization distributions). Elastic scattering W = M p = M, single final state nucleon: Form factor measures size of nucleon.Matrix element squared | | 2 between initial and final state lepton plane waves. Which becomes: | | 2 q = k1 - k2 = momentum transfer G E (q) =  {e i q. r  (r) d 3 r } = Electric form factor is the Fourier transform of the charge distribution. EXERCISE 1 FOR STUDENTS - SHOW THIS (non-relativsitically) By end of CTEQ4 Week. <<<<<<<<< Similarly for the magnetization distribution for G M Form factors are relates to structure function by: 2xF 1 (x,Q 2 ) elastic = x 2 G M 2 elastic (Q 2 )  x-1) Resonance Production, W=M R, Measure transition form factor between a quark in the ground state and a quark in the first excited state. For the Delta 1.238 GeV first resonance, we have a Breit- Wigner instead of  x-1). 2xF 1 (x,Q 2 ) resonance ~ x 2 G M 2 Res. transition (Q 2 ) BW  W-1.238) e +i k2. r e +i k1.r r Mp Mp q Mp MRMR e +i k1. r e +i k2. r

6 5 A REVIEW OF EXPERIMENTAL DATA ON THE PROTON AND NEUTRON ELASTIC FORM-FACTORS. Arie Bodek (Rochester U. ),. UR-1376, ER-40685-826, (Jun 1994). 10pp. Presented at 6th Rencontres de Blois: The Heart of the Matter: from Nuclear Interactions to Quark - Gluon Dynamics, Blois, France, 20-25 Jun 1994. In *Blois 1994, The heart of the matter* 255-264. Scanned Version (KEK Library) - Start with Electron Scattering For elastic scattering No structure cross section

7 6 Gep, Gen = electric form factors for proton and neutron Gmp, Gmn = magnetic form factors for proton and neutron Normalization at Q2=0: electric charge (Ge) Q2=0 Anomalous magnetic moment (Gm) Q2= 0 Axial ga(w) = -1.267 (neutron lifetime) Q2= axial ga(Z0) hard to measure Q2 Dependence--> How are Electric, Magnetic and Axial Weak charge as probed by photon, W and Z bosons distributed? Or how are u, d, s, ubar, dbar, sbar distributed?

8 7 New polarization transfer method measure Ge/Gm ratio Separation of Ge, Gm requires cross section+ Rosenbluth method (rad cor)

9 8 1

10 9 Neutrino Quasi- Elastic scattering Note in electron scattering this is called Elastic. The term Quasi for used for scattering from bound nucleons in nuclei

11 10 Electric vector Pseudo-scalar ~(m-lepton) Magnetic vector Axial (W) Dipole Form

12 11 Most up to date Constants 2003-BBA-Form Factors and constants (Bodek, Budd Arrington)

13 12 Neutron G M N is negative Neutron (G M N / G M N dipole ) At low Q2 Our Ratio to Dipole similar to that nucl-ex/0107016 G. Kubon, et al Phys.Lett. B524 (2002) 26-32 Neutron (G M N / G M N dipole )

14 13 Neutron G E N is positive New Polarization data gives Precise non zero G E N hep-ph/0202183(2002) Neutron, G E N is positive - Imagine N=P+pion cloud Neutron (G E N / G E P dipole ) Krutov (G E N ) 2 show_gen_new.pict Galster fit Gen

15 14 Functional form and Values of BBA Form Factors G E P.N (Q 2 ) =  {e i q. r  (r) d 3 r } = Electric form factor is the Fourier transform of the charge distribution for Proton And Neutron (therefore, odd powers of Q should not be there at low Q) EXERCISE - 2 FOR STUDENTS - SHOW that Odd powes of Q should not be there near Q2=0.<<<<<<<

16 15 The dotted curve shows their calculation using their fit value of 1.07 GeV They do unbinned likelyhood to get M A No shape fit Their data and their curve is taken from the paper of Baker et al. The dashed curve shows our calculation using M A = 1.07 GeV using their assumptions The 2 calculations agree. If we do shape fit to get M A With their assumptions -- M A =1.079 GeV We agree with their value of M A If we fit with BBA Form Factors and our constants - M A =1.055 GeV. Therefore, we must shift their value of M A down by -0.024 GeV. Baker does not use a pure dipole The difference between BBA-form factors and dipole form factors is -0.049 GeV Determining m A, Baker et al. – BNL deuterium

17 16 Summary of Results

18 17 Hep-ph/0107088 (2001) Difference in Ma between Electroproduction And neutrinos is understood For M A from QE neutrino expt. On free nucleons No theory corrections needed 1.11=M A -0.026 -0.028 Neutrinos 1.026+-0.021-=M A average From Neutrino quasielasti c From charged Pion Electroproduction Average value of 1.069->1.014 when corrected for theory hadronic effects to compare to neutrino reactions =1.014 when corrected for hadronic effect to compare to neutrino reactions Ma=1.06+-0.14 (using dipole FF) from K2K goes down to 1.01 with BBA form factors For updated M A expt. need to be reanalyzed with new g A, and G E N More correct to use 1.00+-0.021=M A

19 18 We solve for F A by writing the cross section as a(q 2,E) F A (q 2 ) 2 + b(q 2,E)F A (q 2 ) + c(q 2,E) if (d  /dq 2 )(q 2 ) is the measured cross section we have : a(q 2,E)F A (q 2 ) 2 + b(q 2,E)F A (q 2 ) + c(q 2,E) – (d  /dq 2 )(q 2 ) = 0 For a bin q 1 2 to q 2 2 we integrate this equation over the q 2 bin and the flux We bin center the quadratic term and linear term separately and we can pull F A (q 2 ) 2 and F A (q 2 ) out of the integral. We can then solve for F A (q 2 ) Shows calculated value of F A for the previous experiments. Show result of 4 year Miner a run Efficiencies and Purity of sample is included. Measure F A (q 2 )

20 19 For Miner a - show G E P for polarization/dipole, F A errors, F A data from other experiments. For Miner a – show G E P cross section/dipole, F A errors. Including efficiencies and purities. Showing our extraction of F A from the deuterium experiments. Shows that we can determine if F A deviates from a dipole as much as G E P deviates from a dipole. However, our errors, nuclear corrections, flux etc., will get put into F A. Is there a check on this? F A /dipole - Current versus future data

21 20 d(d  /dq 2 )/dff is the % change in the cross section vs % change in the form factors Shows the form factor contributions by setting ff=0 At Q 2 above 2 GeV 2 the cross section become insensitive to F A Therefore at high Q 2, the cross section is determined by the electron scattering data and nuclear corrections. Anti-neutrino data serve as a check on F A. Do we get new information from anti-neutrinos?

22 21 The Structure of the Nucleon 3 decades of investigation 1973-2004 A personal historical view Arie Bodek, University of Rochester As the majority of advances in High Energy Physics, progress in this area was accomplished by: 1.Higher Energies (new accelerators and machines) And more importantly in combination with 2.Higher Precision (new experimental techniques) 3.Better understanding (new theoretical tools) 4.Higher Luminosities (more statistics) 5.Different probes (new beams) But most important - Mentor new graduate students and postdocs

23 22 The Structure of the Nucleon 3 decades of investigation 1973-2004 Arie Bodek, University of Rochester In the beginning there was hadron Spectroscopy and quarks were only mathematical objects and then came the MIT-SLAC electron scattering experiments 1967- 1973 And Quarks became Real Particles by 2000: Nucleon Structure is well understood and NNLO QCD works from Q 2 =1 GeV 2 to the highest values currently accessible in hadron colliders. How did we get there?

24 23 A : Nobel Prize 1990 - Friedman, Kendall, Taylor for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics.” (1967-73) Front row: Richard Taylor, Jerome Friedman, Henry Kendall. Second row: Arie Bodek, David Coward, Michael Riordan, Elliott Bloom, James Bjorken, Roger (Les) Cottrell, Martin Breidenbach, Gutherie Miller, Jurgen Drees, W.K.H. (Pief) Panofsky, Luke Mo, William Atwood. Not pictured: Herbert (Hobey) DeStaebler Graduate students in italics Described in detail in "The Hunting of the Quark," ( Simon & Schuster) Michael Riordan AIP Science Writing Award 1988 & AIP Andrew Gemant Award 2003 Important to share the excitement of science with the public

25 24 N =d d u + sea 1/3 1/3 2/3 P = u u d + sea 2/3 2/3 1/3 Large x N/P -> 0.25 Explained by valence d/u PARTONS ARE QUARKS ! [ (1/3) / (2/3)] 2 =1/4 Small x : N/P=1 explained by sea quarks F2PF2P F2NF2PF2NF2P xx 1/4 2/3 Scaling-> Point like PARTONS 1968 - SLAC e-p scaling ==> Point like Partons in the nucleon 1970-74 - Neutron/Proton ratio - Partons are fractionally charged (quarks ) COMPARISONS OF DEEP INELASTIC ep AND en CROSS-SECTIONS AB et al Phys. Rev. Lett. 30: 1087,1973. (SLAC Exp. E49 PhD thesis)-First result Next Step higher precision THE RATIO OF DEEP - INELASTIC en TO ep CROSS-SECTIONSINTHE THRESHOLD REGION AB et al Phys.Lett.B51:417,1974 ( SLAC E87) PRL referees - nothing substantially new over 1973

26 25 RPRP R=  L /  T (small) quarks are spin 1/2 ! EXTRACTION OF R =  L/  T FROM DEEP INELASTIC eP AND eD CROSS-SECTIONS. E. Riordan, AB et al Phys.Rev.Lett.33:561,1974. EXPERIMENTAL STUDIES OF THE NEUTRON AND PROTONELECTROMAGNETI C STRUCTURE FUNCTIONS. AB et al Phys.Rev.D20:1471- 1552,1979. BUT what is the x and Q2 Dependence of R? What is x, Q2 dependence of u, d, s, c quarks and antiquarks?

27 26 Integral of F2(x) did not add up to 1.0. Missing momentum attributed to “gluons”. GLUONS “DISCOVERED” BUT what is their x Distributions? Like Pauli’s missing energy in beta decay attributed to neutrinos *Gluons were “Discovered” in 1970, much before PETRA. Scatter shows F 2 (x, Q 2 ) as expected from bremstrahlung of gluons by struck quarks in initial of final states. BUT QCD NOT FULLY FORMALIZED YET F2PF2P F2NF2N F2DF2D

28 27 Next Higher Precision: First observation of Scaling Violations SLAC E. M. Riorday, AB et al TESTS OF SCALING OF THE PROTON ELECTROMAGNETIC STRUCTURE FUNCTIONS Phys.Lett.B52:249,1974 (more detail in AB et al Phys.Rev.D20:1471-1552,1979 Note in 2000. We show that Higher Twist come from Target Mass + NNLO QCD STUDIES OF HIGHER TWIST AND HIGHER ORDER EFFECTS IN NLO AND NNLO QCD ANALYSIS AB, UK Yang. Eur. Phys. J. C13 (2000) 241 245. F 2 P Extracted from Rosenbluth separations Scaling violations SEEN in 1974, Are they deviations from Parton Model e.g. from “gluon” emission, or are they just at Low Q2 1974: PRL Referees - obviously these are uninteresting low Q2 effects

29 28 How are Parton Distributions (PDFs) Extract from various data at large momentum transfer (e/  / and other expts.) d/u PDF(x)= Valence and sea Also Drell Yan, jets etc H and D

30 29 "Physics is generally paced by technology and not by the physical laws. We always seem to ask more questions than we have tools to answer. Wolfgang K. H. Panofsky Questions in 1972-2000 Anti-quarks, strange, charm quarks in nucleons, individual PDFs (u,d,qbar,gluons Q2,x dependence) R= longitudinal structure function (x,Q2), quarks in nuclei, origin of scaling violations- low Q2 higher twist or QCD?, A Detailed understanding of Nucleon Structure Required Initiating Measurements at Different Laboratories, New Detectors, New Analysis Techniques and Theoretical Tools - AND also sorting out which experiments are right and which experiments are wrong - incremental but steady progress. Meanwhile: the J/Psi was discovered in 1974 ---> and the age of Spectroscopy returned; and then came the Upsilon and there was more spectroscopy to be done.

31 30 Conclusion Fermilab CCFR/NuTeV v-N Expt.  -N (data ) CDF Collider Expt MINERvA Expt J-lab e-N (Data) JUPITER Expt. SLAC ESA SLAC NPAS programs e-N Data KEK AMY @ TRISTAN JHF CERN  -N, v-N (data) CMS Collider Rochester

32 31 Also thanks to our Collaborators over the past 3.5 decades +FUTURE ( Blue awarded Panofsky Prize) The Electron Scattering SLAC-MIT collaboration at SLAC End Station A (E49, E87) with Kendall, Friedman, Taylor, Coward, Breidenbach, Riordan, Elias, Atwood& others (1967-1973) The Electron Scattering E139, E140, E140x, NE8 collaboration at SLAC ESA/ NPAS injector at SLAC (with Rock, Arnold, Bosted, Phillipone, Giokaris & others) (1983-1993) The E379/E595 Hadronic Charm: with Barish, Wojcicki, Merrit. Fisk, Shaevitz& others) Production collaboration at Fermilab lab E (1974-83) The AMY e+e- Collaboration at TRISTAN/KEK (with Steve Olsen& others) (1982-1990) The CCFR-NuTeV Neutrino Collaboration at Fermilab Lab E (with (1974-2004) Barish, Sciulli, Shaevitz, Fisk, Smith,Merritt, Bernstein, McFarland and others) The CDF proton-antiproton Collaboration at Fermilab (1988- And in particular I thank the graduate students and 2004) postdocs over the years, and Rochester Senior Scientists Budd, deBarbaro Sakumoto. +more progress to be made with collaborators at the CMS-LHC experiment,(1995-->) The New Electron Scattering JUPITER Collaboration at Jefferson Lab,& the new MINERvA Neutrino (1993--> Collaboration at Fermilab (McFarland, Morfin, Keppel, Manly),

33 32 Neutrino Experiments REQUIRE good Hadron Calorimetry and Muon Energy calibration (~0.3%) 10 cm Fe Sampling, NuTeV simultaneous neutrino running and hadron and muon test beams D.A. Harris (Rochester), J. Yu et al NuTeV PRECISION CALIBRATION OF THE NUTEV CALORIMETER. UR-1561 Nucl. Inst. Meth. A447 (2000) W.K. Sakumoto (Rochester), et al. CCFR CALIBRATION OF THE CCFR TARGET CALORIMETER.Nucl.Instrum.Meth. A294:179-192,1990. CCFR Developed Fe-scintillator compensating calorimeter. 3mx3m large counters with wavelength shifting readout

34 33 B: Hadronic Charm Production -Lab E Fermilab E379/E595 Single muons from charm, dimuons from Drell-Yan, vary target density to determine rate of muons from pion decays (1974-1983 Jack L. Ritchie, HADRONIC CHARM PRODUCTION BY PROTONS AND PIONS ON IRON. UR-861 (1983) Ph.D. Thesis (Rochester). Dexter Prize, U of Rochester - Now Professor at UT Austin Hadronic Charm Production is about 20 mb. Distribution is peaked at small Feynman x and is dominated by quark-quark and gluon-gluon processes. No Intrinsic Charm quarks in the nucleon - in contradiction with ISR results. Intrinsic C(x) = 0 B: Are there charm quarks in nucleon ?

35 34 C: Strange Quarks in the Nucleon - Caltech-Fermilab - -> CCFR (Columbia -Chicago- Fermilab-Rochester) and - Later- NuTeV Neutrino Collaborations at Fermilab LAB E. Dimuon event Karol Lang, AN EXPERIMENTAL STUDY OFDIMUONS PRODUCED IN HIGH-ENERGY NEUTRINO INTERACTIONS. UR-908 (1985) Ph.D. Thesis (Rochester) Now Professor at UT Austin Most recently M. Goncharov and D. Mason (NuTeV PhDs) The Strange Sea Anti-quarks are about 1/2 of the average of u and d sea - i.e Not SU3 Symmetric. K

36 35 H. Kim (CCFR Columbia PhD); D.Harris (Rochester) et. al. MEASUREMENT OF  S (Q 2 ) FROM THE GROSS- LLEWELLYN SMITH SUM RULE. Phys. Rev. Lett. 81, 3595 (1998) W.G. Seligman et al. (CCFR Columbia PhD), IMPROVED DETERMINATION OF  S FROM NEUTRINO NUCLEON SCATTERING. Phys. Rev. Lett. 79 1213 (1997) Precision High Statistics Neutrino Experiments at Fermilab - Valence, Sea, Scaling Violations, gluons F 2 xF 3, Precise  s GLS sum rule (Q 2 dependence) GLS( q2) dependence  s

37 36 Precision Neutrino Experiments CCFR/NuTeV Un Ki Yang UR-1583,2000 Ph.D. Thesis, (Rochester) Lobkowicz Prize, U of R; URA Best Thesis Award Fermilab 2001 (now at Univ. of Chicago) Un-Ki Yang et al.. MEASUREMENTS OF F 2 AND XF 3 FROM CCFR -FE DATA IN A PHYSICS MODEL INDEPENDENT WAY. By CCFR/NuTeV Phys.Rev.Lett.86, 2742,2001 Experiment vs Theory: Ratio of F 2 (neutrino)/F 2 (muon ) Resolved 10% to 20% difference between and  data Same PDFs should describe all processes

38 37 D Quark Distributions in Nuclei - New Parallel Program at SLAC AB, J Ritchie FERMI MOTION EFFECTS IN DEEP INELASTIC LEPTON SCATTERING FROM NUCLEAR TARGETS, Phys.Rev.D23:1070,1981; Phys.Rev.D24:1400,1981. 1983 (conference proceeding) surprising report of difference between Iron and Deuterium muon scattering data from the European Muon Collaboration (EMC) Disagreement with Fermi Motion Models. AB, EMPTY TARGET SUBTRACTIONS AND RADIATIVE CORRECTIONS IN ELECTRON SCATTERING EXPERIMENTS, Nucl. Inst. Meth. 109 (1973). - factor of 6 increase in rate of empty target data by making empty target same radiation length as H2 and D2 targets; - used in SLAC E87 - more payoff later ELECTRON SCATTERING FROM NUCLEAR TARGETS AND QUARK DISTRIBUTIONS IN NUCLEI. AB et al Phys.Rev.Lett.50:1431,1983.. - Use Empty Target Data from SLAC E87 (1972)(initially rejected by Phys. Rev, Letters) A COMPARISON OF THE DEEP INELASTIC STRUCTURE FUNCTIONS OF DEUTERIUM AND ALUMINUM NUCLEI. AB et al Phys.Rev.Lett.51:534,1983. Use empty target data from SLAC E49B (1970)

39 38 Quark Distributions in Nuclei AB et al Phys. Rev. Lett. 51: 534, 1983 (SLAC Expt. E49, E87 empty tgt data 1970,1972) EMC PRL Referees: (1) How can they claim that there are quarks in nuclei + (2) Obviously uninteresting multiple scattering of electrons in a nucleus- --> later accepted by PRL editors.

40 39 D. Back to SLAC using High Energy Beam and the Nuclear Physics Injector NPAS - SLAC E139, E140, E140x, E141, NE8 R.G. Arnold et al., MEASUREMENTS OF THE A- DEPENDENCE OF DEEP INELASTIC ELECTRON SCATTERING FROM NUCLEI Phys. Rev. Lett.52:727,1984; (initial results incorrect by 1% since two photon external radiative corrections for thick targets not initially accounted for. Found out later in SLAC E140) J. Gomez et al., MEASUREMENT OF THE A-DEPENDENCE OF DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.D49:4348-4372,1994. Back to SLAC End Station A to measure effect on various nuclei

41 40 SLAC E140, E140x -. New Precision Measurement of R and F2, and Re- Analysis of all SLAC DIS data to obtain 1% precision. The issues: (1) Precise Values and Kinematic dependence of R needed to extract F2 from all electron muon and neutrino experiments. (2) Precise normalization of F2 needed to establish normalization of PDFs for all DIS experiments to 1%. Solution--> SLAC E140 - New hardware, new theoretical tools 1 month run worth years of data, IMPACT all DIS Experiments Past and Future. (1)Upgrade Cerenkov Counter for ESA 8 GeV spectrometer - N2 with wavelength shifter on phototube (2)Upgrade Shower Counter from lead-acrylic (to segmented lead glass) (3)Upgraded tracking (wire chambers instead of scintillator-hodoscope) (4)Upgraded Radiative Corrections - Improved treatment using Bardin, Complete Mo-Tsai, test with different r.l. targets ( to 0.5%) (5)Cross normalize all previous SLAC experiment to SLAC E140 by taking data in overlap regions.(Re-analysis with upgraded rad corr).

42 41 Sridhara Rao Dasu, PRECISION MEASUREMENT OF X, Q2 AND A-DEPENDENCE OF R =  L/  T AND F2 IN DEEP INELASTIC SCATTERING. UR-1059 (Apr 1988). Ph.D. Thesis. (Rochester) SLAC E140 - winner of the Dexter Prize U of Rochester 1988 (now Professor a U. Wisconsin, Madison) S. Dasu (Rochester PhD )et al., MEASUREMENT OF THE DIFFERENCE IN R =  L/  T, and  A/  D IN DEEP INELASTIC ed, eFE AND eAuSCATTERING. Phys.Rev.Lett.60:2591,1988; S. Dasu et al., PRECISION MEASUREMENT OF R =  L/  T AND F2 IN DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.Lett.61:1061,1988; S. Dasu et al., MEASUREMENT OF KINEMATIC AND NUCLEAR DEPENDENCE OF R =  L/  T IN DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.D49:5641-5670,1994. L.H. Tao (American U PhD) et al., PRECISION MEASUREMENT OF R =  L/  T ON HYDROGEN, DEUTERIUM AND BERYLLIUM TARGETS IN DEEP INELASTIC ELECTRON SCATTERING. Z.Phys.C70:387,1996 L.W. Whitlow (Stanford PhD), et al., A PRECISE EXTRACTION OF R =  L/  T FROM A GLOBAL ANALYSIS OF THE SLAC DEEP INELASTIC ep AND ed SCATTERING CROSS- SECTIONS. Phys.Lett.B250:193-198,1990. L.W. Whitlow, et. al., PRECISE MEASUREMENTS OF THE PROTON AND DEUTERON STRUCTURE FUNCTIONS FROM A GLOBAL ANALYSIS OF THE SLAC DEEP INELASTIC ELECTRON SCATTERING CROSS-SECTIONS. Phys.Lett.B282:475-482,1992.

43 42 Provided normalization and shape at lower Q2 for all DIS experiments- constrain systematic errors on high energy muon experiments - Perturbative QCD with and without target mass (TM) effects

44 43 SLAC E140 and the combined SLAC re-analysis provided the first precise values and kinematic dependence of R Related to F 2 /2xF 1 for use by all DIS experiments to extract F2 from differential cross section data R

45 44 Proton-Antiproton (CDF/Dzero) collisions are actually parton- parton collisions (free nucleons ) This is why it is important to know the nuclear corrections for PDFs extracted from nucleons bound in Fe (neutrino) or in Deuterium (d versus u), when the PDFs are used to extract information from collider data In 1994 uncertainties in d/u from deuteron binding effects contributed to an uncertainty in the W mass (extracted from CDF or Dzero Data of order 75 MeV. By introducing new techniques, CDF data can provide independent constraints on free nucleon PDFs. CONSTRAINTS ON PDFS FROM W AND Z RAPIDITY DIST. AT CDF. AB, Nucl. Phys. B, Proc. Suppl. 79 (1999) 136-138. In *Zeuthen 1999, Deep inelastic scattering andQCD* 136-138.

46 45 E: Proton-Antiproton (CDF/Dzero) collisions are actually parton- parton collisions (free nucleons )

47 46 Mark Dickson, THE CHARGE ASYMMETRY IN W BOSON DECAYS PRODUCED IN P ANTI-P COLLISIONS. (1994) Ph.D.Thesis (Rochester). (now at MIT Lincoln Labs) Qun Fan, A MEASUREMENT OF THE CHARGE ASYMMETRY IN W DECAYS PRODUCED IN P ANTI-P COLLISIONS. Ph.D.Thesis (Rochester) (now at KLA- Tenor Proton-antiproton collisions (CDF)- Measurement of d/u in the proton by using the W+- Asymmetry

48 47 Need to measure the W Decay lepton Asymmetry at high rapidity where there is no central tracking Unfortunately W’s decay to electrons and neutrinos - Decay lepton asymmetry is a convolution of the W production Asymmetry

49 48 A NEW TECHNIQUE FOR DETERMINING CHARGE AND MOMENTUM OF ELECTRONS AND POSITRONS USING CALORIMETRY AND SILICON TRACKING. AB and Q. Fan In *Frascati 1996, Calorimetry in HEP*553- 560 (First used in AMY) Use silicon vertex detector to extrapolate electron track to the forward shower counters. Compare the extrapolated location to the centroid of the EM shower in a segmented shower counter. Energy of electron determined by the shower counter, Sign is determined by investigating if the shower centeroid is to the left or right of the extrapolated track, All hadron collider physics (Tevatron, LHC) with electrons and positrons can be done better without a central tracker. No Track misID Need Just silicon tracking and segmented EM +HAD calorimetry

50 49 The d/u ratio in standard PDFs found to be incorrect. Now all new PDF fits include CDF W Asymmetry as a constraint. PDF error on W mass reduced to 10 MeV by using current CDF data.

51 50 With this new technique, one can also significantly reduce the QCD background for very forward Z Bosons. Jinbo Liu, Measurement of d  /dy for Drell-Yan e+e Pairs in the Z Boson Region Produced in Proton Anti-proton Collisions at 1.8 TeV. UR-1606, 2000 - Ph.D. Thesis (Rochester). (now at Lucent Technologies) T. Affolder et al. (CDF- article on Rochester PhD Thesis), MEASUREMENT OF d  / dY FOR HIGH MASS DRELL-YAN E+ E- PAIRS FROM P ANTI-P COLLISIONS AT 1.8-TEV. Phys.Rev.D63:011101,2001. NLO QCD describes Z -y distributions better than LO QCD

52 51 F : Phenomenology: PUTTING it ALL TOGETHER The Great Triumph of NNLO QCD Origin of Higher Twist Effects, d/u and PDFs at large X – PARTON DISTRIBUTIONS, D/U, AND HIGHER TWIST EFFECTS AT HIGH X. AB, UK Yang Phys.Rev.Lett.82:2467-2470,1999. STUDIES OF HIGHER TWIST AND HIGHER ORDER EFFECTS IN NLO AND NNLO QCD ANALYSIS OF LEPTON NUCLEON SCATTERING DATA ON F(2) AND R =  (L) /  (T). AB, UK Yang Eur.Phys.J.C13:241-245,2000 NNLO QCD +target mass corrections describes all of DIS data for Q 2 >1 GeV2 with NO Need for Higher Twists. GREAT TRIUMPH for QCD. Most of what was called low Q 2 higher Twist are accounted for by higher order QCD.

53 52 NNLO QCD+TM black Great Triumph of NNLO QCD. AB, UK Yang Eur.Phys.J.C13:241-245,2000 Size of the higher twist effect with NNLO analysis is very small a2= -0.009 (in NNLO) versus –0.1( in NLO) - > factor of 10 smaller, a4 nonzero NNLO QCD+Tgt Mass works very well for Q2>1 GeV2 F2PF2P F2DF2D R

54 53 Great Triumph of NNLO QCD. AB, UK Yang Eur.Phys.J.C13:24,2000 First extraction of (NNLO PDFs)/(NLO PDFs) ratio For High Statistics Hardon Collider Physics (run II, LHC), the next step is to extract NNLO PDFs. So declare victory and let theorists and PDF Professionals (MRST and CTEQ) make progress towards the next generation NNLO PDF fits for Tevatron and LHC High x NNLO PDFs 10% lower than NLO PDFs Low x NNLO PDFs 2% higher than NLO PDFs

55 54 F 2, R comparison of NLO QCD+TM+HT black (Q 2 >1) (use QCD Renormalons for HT vs NLO QCD+TM only green AB, UK Yang Phys.Rev.Lett.82,1999 PDFs and QCD in NLO + TM + QCD Renormalon Model for Dynamic HT describe the F2 and R data very well, with only 2 parameters. Dynamic HT effects are there but small NLO QCD + Target Mass + Renormalon HT works. A GREAT QCD TRIUMPH

56 55 2000-2004->2010 (The high Energy Frontier): For Tevatron and Run II and LHC, the path to greater precision is using: NNLO QCD fits with both Q2>1 GeV 2 DIS data & very high Q2 Collider Data.-Good for theorists 2000-2004->2010 (The Low Energy Frotier) Applications to Neutrino Oscillations at Low Energy (Nucleon and Nuclear Structure down to Q2=0) Here the best approach is to use a LO PDF analysis (including a more sophisticated target mass analysis) and include the missing QCD higher order terms in the form of Empirical Higher Twist Corrections. * Vector Part well understood - Phenomenology AB+U K Yang (2002-2004) - Axial Part needs further investigation - future Data 2004-2008 (JUPITER, e-N at Jlab) MINERvA, v-N at Fermilab)

57 56 Original approach (NNLO QCD+TM) was to explain the non-perturbative QCD effects at low Q 2, but now we reverse the approach: Use LO PDFs and “effective target mass and final state masses” to account for initial target mass, final target mass, and missing higher orders Modified LO = Pseudo NNLO approach for low energies Applications to Jlab and Neutrino Oscillations P=M q m f =M* (final state interaction) Resonance, higher twist, and TM  w  = Q 2 +m f 2 + A M (1+(1+Q 2 / 2 ) ) 1/2 +B Xbj= Q 2 /2 M K factor to PDF, Q 2 /[Q 2 +C] A : initial binding/target mass effect plus higher order terms B: final state mass m f 2,  m  and photo- production limit ( Q 2 =0) MODELING DEEP INELASTIC CROSS-SECTIONS IN THE FEW GEV REGION. AB, UK Yang Nucl.Phys.Proc.Suppl.112:70,2002

58 57 Initial quark mass m I and final mass,m F =m * bound in a proton of mass M Summary: INCLUDE quark initial Pt) Get  scaling (not x=Q 2 /2M ) for a general parton Model  Is the correct variable which is Invariant in any frame : q3 and P in opposite directions P= P 0 + P 3,M P F = P I 0,P I 3,m I P F = P F 0,P F 3,m F =m * q=q3,q0 Most General Case: EXERCISE - 3 FOR STUDENTS - SHOW )<<<<<<  ‘ w = [Q’ 2 +B] / [ M (1+(1+Q 2 / 2 ) ) 1/2 +A] (with A=0, B=0)  where2Q’ 2 = [Q 2 + m F 2 - m I 2 ] + { ( Q 2 +m F 2 - m I 2 ) 2 + 4Q 2 (m I 2 +P 2 t) } 1/2  Bodek-Yang: Add B and A to account for effects of additional  m 2  from NLO and NNLO (up to infinite order) QCD effects. For case  w with P 2 t =0  see R. Barbieri et al Phys. Lett. 64B, 1717 (1976) and Nucl. Phys. B117, 50 (1976) Special cases: (1) Bjorken x, x BJ =Q 2 /2M , -> x  For m F 2 = m I 2 =0 and High 2, (2) Numerator m F 2 : Slow Rescaling  as in charm production (3) Denominator : Target mass term  =Nachtman Variable  =Light Cone Variable  =Georgi Politzer Target Mass var. ( all the same  )

59 58 Describes all vector structure functions from Q2=0 to 100,000 GeV 2

60 59

61 60

62 61 MODELING DEEP INELASTIC CROSS-SECTIONS IN THE FEW GEV REGION. A. Bodek, U.K. Yang Presented at 1st Workshop on Neutrino - Nucleus Interactions in the Few GeV Region (NuInt01), Tsukuba, Japan, 13-16 Dec 2001. Nucl.Phys.Proc.Suppl.112:70-76,2002 e: hep-ex/0203009 HIGHER TWIST, XI(OMEGA) SCALING, AND EFFECTIVE LO PDFS FOR LEPTON SCATTERING IN THE FEW GEV REGION. A Bodek, U.K. Yang Proceedings of 4th International NuFact '02 Workshop (Neutrino Factories Workshop on Neutrino Factories, London, England, 1-6 Jul 2002. J.Phys.G29:1899-1906,2003 MODELING NEUTRINO AND ELECTRON SCATTERING INELASTIC CROSS- SECTIONS IN THE FEW GEV REGION WITH EFFECTIVE LO PDFS IN LEADING ORDER. A. Bodek, U.K. Yang. 2nd International Workshop on Neutrino - Nucleus Interactions in the Few GeV Region (NUINT 02), Irvine, California, 12-15 Dec 2002. Nucl.Phys.Proc.Suppl. hep-ex/0308007 Invited Article to be published in Annual Review of Particle and Nuclear Science 2005 Applications to Neutrino Oscillations at Low Energy

63 62 G: Next: JUPITER at Jlab (Bodek,Keppel) will provided electron-Carbon (also e-H and e-D and other nuclei such as e-Fe) data in resonance region, and final states (Manly)-summer 04 +05. G : Next: MINERvA at FNAL (McFarland, Morfin) will provide Neutrino-Carbon data at low energies. G: CDF Run II (now) and CMS, high statistics W’s Z’s and Drell Yan Phenomenology: Low energy Axial structure functions and resonance fits for both electrons/neutrinos Maintaining the colorful Program

64 63 CONCLUSION: Progress is made in finite incremental steps as new techniques and methods lead to greater precision (making what was impossible -> possible) A factor of 2 reduction in error each generation (either statistical or systematic) is worth it, and one can always go back and re-analyze old data with better corrections to reduce systematic errors In 4 generations of experiments (2) 4 = 16 fold reduction in errors 2000: Nucleon Structure well understood. NNLO QCD works from Q 2 =1 to the highest values currently accessible. Hadron colliders are actually quark and gluon colliders with known and well understood PDFs.

65 64

66 65

67 66


Download ppt "1 Vector and Axial Form Factors and Inelastic Structure Functions Arie Bodek University of Rochester Lecture."

Similar presentations


Ads by Google