HERA Collider Physics Summer Student Lectures August 2003 Hans-Christian Schultz-Coulon Universität Dortmund [H1 Collaboration] [e-mail: coulon@mail.desy.de]
Overview on topics covered (or touched) in this lecture A. Introduction Elastic en-scattering Inelastic Scattering Quark-Parton-Model Structure Functions B. HERA Experiments The HERA Collider H1 & ZEUS C. Proton Structure F 2 measurement Parton densities α s and the Gluon D. (Di)-Jet Production E. Photon Structure Scale Problem DGLAP & BFKL Concept of Photon Structure F. Diffraction Introduction Inclusive Diffraction Exclusive Final States G. Heavy Flavour Physics Quarkonia Production Open Charm & Bottom H. Electroweak Aspects ep Cross Section EW Unification PDFs at High x, Q 2 I. Searches Direct Searches Indirect Searches J. HERA II Upgrade Experimental Setup Physics Prospects not covered not covered not covered
Elastic Scattering Cross Section e (k ) e + N e' + N' i dσ dω ------- M if 2 ρf f phase space Fermi s Golden Rule e(k) Nucleus at rest q = k k' q = υ, q N(N ) M if M if = = M if ψ * f V( r)ψ i dτ e i q r V( r)d 3 r F( q) perturbing potential Form Factor [describes structure of target] Elastic scattering on a nucleus with charge distribution ρ( ): r dσ dω ------- = F 2 ( q) dσ dω ------- Rutherford pointlike scattering (no spin) F( q) = ρ()e r i q r d 3 r
Form Factor Properties e (k ) A. Describes the difference between scattering on extended objects with respect to pointlike target B. For q 0 also e -iqr 1 and lim q 0 F( q) = ρ( r)d 3 r = 1 e(k) Probed Target q ~ 1/λ [Resolving Power] C. If 1/q ~ r, small changes of q imply large changes of e -iqr. D. For 1/q << r, i.e. qr >>1 the expression e -iqr oscillates fast. Hence lim F( q) 0 q E. For a spherical charge distribution one gets F( q) = F( q 2 ) = 1 1 --q 2 r 6 2 Determination of elastic form factor possible Elastic cross section vanishes [DIS-Region] Proton: r 2 Proton m 10 15 To resolve proton structure one needs Q 2 >> 0.04 GeV 2 HERA: max. Q 2 = 10 5 GeV 2 probing down to 10-18 m
Relation of ρ( r) and F( q) ρ(r) F(q 2 ) --------- δ( r) 4π 1 ----- a 3 e ar 8π 1 q 2 2 + ----------- a 2 h 2 ----- a 2 32 / a 2 r --------- 2 2 e 2π q 2 exp -------------- 2a 2 h 2 ----- 3 R 3 θ( R r) 4π ------------------------------------------ 3( sinα αcosα) α 3 with α = fr ( ) ----------------------- 1 1+ e r ----------- R a
Nuclear Form Factors Experimental Results ~ 450 MeV e- From difference of position of minima 48 40 R Ca > R Ca Charge distribution of atomic nuclei
Elastic en-scattering e (k ) Fixed target experiment [Lab frame] q = k k' = υ, q with υ = E E ' e(k) Nucleus at rest γ Q 2 q 2 -- h λ 2 = Resolving power of the photon P = ( M i N, 0) P f = ( M N + υ, q) Target stays intact (elastic scattering): cross section p f 2 M N 2 M N 2 = = = M N 2 ( + υ) 2 q 2 M N + 2M N υ + υ 2 q 2 Expect: narrow peak at x=1 υ = Q ------------- 2 2M N -Q 2 x = Q 2 -------------- 2M N υ 1 X
Fixed Target Experiments [Example: DESY Strahl 22] Electrons from DESY Spectrometer T: Target Qx: Quadrupoles H: Collimator V: Collimator Mx: Dipoles C: Cherenkov Counter Sx: Scintillators
First DIS Result [DESY 1968] d 2 σ --------------- de'dω [nb GeV -1 sr -1 ] E = M p E/[E(1-cosθ)+M p ] E ~ 4.5 GeV using: Q 2 = 2EE (1-cosθ) Q 2 = 2M p ν [and M p = 1 GeV] E = 4.9 GeV θ =10 o E
Observed Cross Section dependence at lower x. [schematic diagram] Hofstatter experiment cross section 1956 (e-he Scattering) Expected if proton consists out of quarks with effective mass m q = 1/3 M p x = Q 2 -------------- 2M N υ
Naive QPM Model [Feynman 1969] u flat, frozen Proton consists out of partons Interaction due to interaction of partons Hadronic structure defined by distribution of partons at any given time 2r p u P changes in number and momenta of partons should be small during time they are probed d x i P Σ x i = 1 0 < x i < 1 Infinite momentum frame: Proton is moving with infinite momentum; proton mass can be neglected. Partons frozen during interaction time Can be treated as free during short time of interaction Photon-Proton interactions can be expressed as sum of incoherent scattering from point-like partons Partons identified with Quarks
Electron DIS Kinematics k' = ( E', k' ) p k = ( E, k) Deep-Inelastic Scattering: Extra degree of freedom Relation between Q 2 and υ no longer valid P' q 2 Proton = = = = = = ( q+ xp) 2 2xPq Q 2 0 γ Q 2 = -(k k') 2 P= xp W 2 ( P+ q) 2 P 2 q 2 2 + + 2Pq M P q P' q Q 2 + 2Pq x = Q --------- 2 2Pq [Bjorken-x] elastic: M x = M p inelastic: M x = W W extra degree of freedom!! elastic: Q 2 = inelastic: 2Pq fixed target =2M P υ Q 2 = 2 2Pq + M P W 2
DIS Kinematics Summary of Relevant Kinematic Variables s = (k+p) 2 = 4E e E p Q 2 = -q 2 = (k-k ) 2 = 2E e E e (1-cosθ e ) υ = q.p/m p υ max = s/(2m p ) y = (q.p)/(k.p) = υ/υ max x = Q 2 /(2q.p) W 2 = (p+q) 2 = M p - Q 2 + 2M p υ Centre-of-mass energy squared Negative squared four momentum transfer Energy transfer in proton rest frame Maximum energy transfer Fraction of energy transfer Bjorken scaling variable Invariant mass of total hadronic system k k' Q 2 =sxy At fixed s only two independent variables p = (E p,0,0,e p ) k = (E e,0,0,-e e ) k = (E e,0,e e sinθ e,-e e cosθ e ) Q 2 xp P' q p
e Electron-Quark scattering (spinless case) q Structure Function F 2 γ e q dσ( eq) -------------- dq 2 = 4πα ----------e 2 2 q 4 q Rutherford scattering on pointlike target dσ( ep) -------------- dq 2 xq(x) 1/3 4πα = ---------- 2 [ 2e2 u + e2 d ] = q 4 Naive QPM x p = uud > x = 1/3 4πα ---------- 2 q 4 With quark-quark interactions xq(x) dσ( ep) -------------- dq 2 = 4πα ----------e 2 [ 2 q 4 u ux ( ) + e 2 d dx ( ) + ] = 4πα ---------- 2 F 2 ----------- ( x) q 4 x QPM: Structure Function F 2 independent of Q 2 1/3 x
Scaling [SLAC 1972] F 2 Q 2 [GeV 2 ]
Scaling Violations [1990++] SLAC 1972
DGLAP Evolution Intuitive picture
F 2 at Low Bjorken-x [Pre-HERA Knowledge] DGLAP: No prediction for the x-dependence of F 2 [except asymptotic behaviour] A. De Rujula et.al. 1974 Fixed Target Measure!! Remark: Accessing low x offers possibility to determine g(x,q 2 ) [see later]
Selected List of Fixed Target Experiments [Mostly Pre-HERA] Experiment Year Reaction Beam Energy SLAC - MIT 1968 ep, ed 4.5-20 GeV CDHS, CHARM <1984 ν µ Fe <260 GeV FMMF <1988 ν µ <500 GeV CCFR 1979-1988 ν µ Fe <600 GeV BCDMS 1981-1985 µp, µd 100-280 GeV EMC <1983 µp, µd <325 GeV NMC 1986-1989 µp, µd 90-280 GeV E665 1987-1992 µp, µd 90-470 GeV NuTeV 1996-1997 ν µ Fe <600 GeV Electron energy limited by synchrotron radiation Muon beam experiments Different processes Universality of parton density functions
Q 2 10 4 10 3 10 2 Accessing Lower Bjorken-x HERA Experiments Fixed Target Experiments Q 2 =sxy access to highest Q 2 y = 1 [HERA: s ~ 10 5 GeV 2 ] y = 1 [Fixed Target: s < 10 3 GeV 2 ] Fixed Target: 10 1 accessing lower x at fixed Q 2 needs higher s s = 2M p E e s = 10 5 GeV E e = 50 TeV ep-collider: 10-1 access to lowest x at very low Q 2 10-6 10-5 10-4 10-3 10-2 10-1 1 x s = 4E p E e E e = 30 GeV E p = 900 GeV s = 10 5 GeV
The HERA Accelerator Complex e Halle Nord H1 e p 360m R=797m p Halle Ost HERMES NW e p HERA- Halle West N NO Halle West HERA-B HERA 360m Stadion Stellingen W Kältehalle PETRA Magnet- Testhalle H -Linac DESY II/III PIA + e -Linac e --linac O Trabrennbahn p e Proton ring: Energy*: 920 GeV Mag. Field: 4.682 T Current: ~ 100 ma * before 1998: 820 GeV ZEUS Halle Süd SW Electron ring: Energy: 27.5 GeV Mag. Field: 0.164 T Current: ~ 40 ma General: Proton bypass SO Energy in cms: 318 GeV Circumference: 6.3 km BX rate: 10.4 MHz Lumi: 1.5. 10 31 cm -2 s -1
View into the Tunnel
Luminosity Ṅ L σ N = σ L dt σ L : integrated Luminosity = N L Φ a N = ----- a = n A a v a Φ a : flux n a : density of particle beam v a : velocity of beam particles Ṅ = Φ a N b σ b N : reaction rate N b : target particles within beam area σ b : effective area of one single scattering centre L = Φ a N b L : Luminosity Collider experiments: Φ a HERA: N x ~ 10 10 A ~ 0.01 mm 2 n ~ 200 f ~ 50 khz Ṅa N ----- a n v U N ---------------------------- a n f = = = ------------------- A A A L f nn a N b nn --------------- f a N = = ------------------ b A 4πσ x σ y L ~ 10 31 cm -2 s -1 N a : number of particles per bunch (beam A) N b : number of particles per bunch (beam B) U : circumference of ring n : number of bunches per beam v : velocity of beam particles f : revolution frequency A : beam cross-section σ x : standard deviation of beam profile in x σ y : standard deviation of beam profile in x
2m 1m 0 Software :SDRC-IDEAS level VI.i Performed by : Carsten Hartmann Status : October 1993
The H1 Detector Puddle Heinz 1: Beam pipe & magnets 2: Central tracking chambers 3: Forward tracking 4: Electromagn. calorimeter 5: Hadronic calorimeter 6 : Superconducting coil 7 : Compensating magnet (PreUpgr.) 8 : Helium cryogenics 9 : Muon chambers 10: Instrumented iron 11 : Muon toroid magnet 12: Backward calorimeter (SpaCal) 13: Plug calorimeter 14: Concrete shielding 15: Liquid argon cryostat
H1 detector in parking position
H1 Collaboration
ZEUS Collaboration
Schematic View of H1 Forward Tracking Central Tracking System Silicon Detectors Digital Muon System e FPS FNC ToF ToF Lumi p Forward Muon System Toroid Solenoid Liquid Argon SpaCal
Large Q 2 range Precision QCD Test of DGLAP evolution Q 2 (GeV 2 ) 10 5 10 4 10 3 HERA Kinematic Coverage H1 ZEUS CDF/D0 Inclusive jets η<0.7 D0 Inclusive jets η<3 Fixed Target Experiments: CCFR, NMC, BCDMS, E665, SLAC Small x range High parton densities Novel quantum system Small Q 2 regime Non-perturbative QCD Confinement Large CMS energy Electroweak Physics Search for new phenomena 10 2 10 1 10-1 10-6 10-5 10-4 10-3 10-2 10-1 1 x