4 Semi-inclusive Kinematics 5 independent variables Detect the scattered electron in coincidence with hadron h: e+p e'+h+X Final state: undetected hadronic final state of mass squared In OPE approximation: Four-momenta in Lab: Initial state:
5 Observables Cross section is described by 4 functions of 4 variables: Azimuthal asymmetries (moments): where J.Levelt & P.Mulders, PRD49 p T -integrated cross section:
6 SIDIS: constant in Current fragmentationTarget fragmentationL.Trentadue & G.Veneziano, PLB323 X.Ji et al., PRD71 J.C.Collins, PRD57 Factorization proved
7 SIDIS: -dependence 1.Cahn effect: 2.Berger effect (Collins fragmentation): 3.Boer-Mulders function h 1 ┴ (TMD) contribution: D.Boer&P.Mulders, PRD57 H 1 ┴ from e + e - collisions R.N.Cahn, PRD40 E.Berger, ZPC4 4.Higher Order pQCD corrections: H.Georgi&H.Politzer, PRL40 hadron wave function
8 Data & pQCD 1.Except for low-x, the difference between data and pQCD is of the order of scale dependence, 2.NLO reproduces better data at low-z, 3.Leaves room for target fragmentation, 4.Calculations depend on the assumption about favored fragmentation (20% effect). CTEQ 5, Kretzer + Q 2 =2.4 GeV 2 Calculations contain current fragmentation only:
9 vs. p T Cahn effect calculations (using k ┴ 2 =0.20 GeV 2 and p ┴ 2 =0.25 GeV 2 from M.Anselmino et al., PRD71) do not reproduce measured and the inclusion of Berger effect contribution does not improve the agreement significantly. =2.2 GeV 2 Data are integrated over x and Q 2 in DIS region.
10 vs. p T Cahn and Berger effect compensate each other to give zero moment. Within systematic errors the data are also compatible with zero, except for low-z. Data are integrated over x and Q 2 in DIS region. =2.2 GeV 2
11 Q 2 -dependence We compared our data on φ- dependent terms with EMC measurement (J.Aubert et al., PLB130) performed at significantly higher Q 2 : curves show Cahn effect prediction corrected for threshold effect: EMC(83)CLAS x=0.24 z>0.2 p T >0.2 GeV and n=1,2
12 Summary 1.We measured 5-fold differential + semi-inclusive electro-production cross sections in a wide kinematical range in all 5 independent variables, 2.Data are in reasonable agreement with naïve current fragmentation pQCD calculations (difference is of the order of systematic errors ~20%), 3.At low-z there is room for the target fragmentation contribution, 4.Measured moment is incompatible with Cahn and Berger effects and in striking disagreement with high Q 2 data, while is compatible with zero in agreement with theory except for low-z region.
14 Graudenz variable Struck quark light cone momentum fraction carried by the detected hadron, used in pQCD calculation, is commonly approximated: D.Graudenz,Fortsch.Phys.45 LO pQCD D(z G ) In e + e - function D(z) is measured as a function of:
15 Machine Upgrade Beam energy increase up to 12 GeV (11 for Halls A,B,C): 5 new cryomodules to each LINAC gain increase up to 1.1 GeV/LINAC one new recirculation arc for Hall-D 85 A maximum beam current maximal beam power 1 MWatt
16 CLAS Upgrade Luminosity up to 10 35 cm -2 s -1 Preshower calorimeter New drift chamber Improved TOF ~50-60 ps High threshold Cherenkov Central detector 40-130 Electromagnetic calorimeter TOF Tracking detector Vertex detector No photon tagger p/p~0.3%+0.1%p ~1mrad, ~5-40 e/ > 10 3 (p<4.8 GeV) p/p~2% ~8 mrad, ~40-135
17 Central detector Superconducting solenoid B~5 Tesla Scintillator counter TOF, t~50 ps Tracking detector gas filled cathode chamber p/p~2.2 % at p=1 GeV Neutron Detector plastic scintillators t~100 ps Silicon strip/MicroMega vertex detector ~100 m Flux return iron
18 CLAS12 - Expected Performance Forward DetectorCentral Detector Angular coverage: Tracks (inbending) 8 o - 37 o 40 o - 135 o Tracks (outbending) 5 o - 37 o 40 o - 135 o Photons 3 o - 37 o 40 o - 135 o Track resolution: p (GeV/c)0.003p + 0.001p 2 p T =0.02p T (mr) 1 5 (mr)2 - 5 2 Photon detection: Energy range > 150 MeV > 60 MeV E/E 0.09 (1 GeV)0.06 (1 GeV) (mr) 3 (1 GeV)15 (1 GeV) Neutron detection: eff 0.5 (p > 1.5 GeV/c) Particle id: e/ >>1000 ( < 5 GeV/c) >100 ( > 5 GeV/c) /K (4 ) < 3 GeV/c0.6 GeV/c /p (4 ) < 5 GeV/c1.3 GeV/c
19 High luminosity gives access to large x Valence quarks only No explicit hard gluons (if observable couples to valence quarks) Hadronic fluctuations of the virtual photon are suppressed x 1 limit, sensitive test for spin-flavor symmetry breaking x>1 region for nuclear targets to probe high density quark matter Polarization: beam, target, recoil Distribution of the spin in the nucleon H1, ZEUS 12 GeV upgrade kinematical reach
20 k T - Dependent Parton Distributions f 1, g 1 studied for decades: h 1 essentially unknown In standard notations Study pQCD evolution in k T : Q 2 =5 GeV 2 Q 2 =10 GeV 2 Q 2 =20 GeV 2 Hadronization model is necessary to obtain information on distributions in quark transverse momentum k T.
24 z-dependence at fixed p T At large p T the suppression of z-distribution is clearly seen, but its contribution to the integral is small (low p T dominates) and modeled by phenomenological transverse momentum distribution: different p T
25 Normalization In e + e - collisions In SIDIS, neglecting target fragmentation contribution Hadron multiplicity: => Cut on x F removes part of the p T region breaking normalization of transverse momentum distribution. =>
26 vs z The same situation. Data are integrated over x and Q 2 in DIS region.
27 vs z The same situation. =2.3 GeV 2 Data are integrated over x and Q 2 in DIS region.
28 Azimuthal angle definition k – initial electron 3-momentum, p h – hadron 3-momentum, q – virtual photon 3-momentum Trento convention
29 p T -dependence Q 2 =2.4 GeV 2, x=0.26, z=0.23 CLAS The same p T behavior for all structure functions => trivial kinematical factors for azimuthal asymmetries and H 3 contribution is negative H 4 is mostly positive Suggest only internal transverse motion of quarks (Cahn)? Structure functions were separated by fitting dependences in each separate kinematical bin. Only bins with complete -coverage were considered. up to p T ~1 GeV
30 e - measurement 1.Cherenkov Counter (CC) uniquely identify electrons up to P~3 GeV 2.Electromagnetic Calorimeter (EC) separates high energy electrons e-e- -- e-e- - +CC noise
31 e - inclusive 1.Inclusive cross sections obtained with the same data are in good agreement with world data. 2.Little effort needed to complete the inclusive data analysis at 6 GeV CLAS E1-6 Bodek fit World
33 + measurement 1.Pions are well identified by Time Of Flight (TOF) measurement in all accessible kinematical range 2.Loss of events in data and Monte Carlo (MC) simulations due to PID cuts was checked in + n peak all positive hadrons selected events + n peak background
34 + semi-inclusive 1.New CLAS data are in agreement with previously published measurements within given uncertainties 2.Comparison also shows non-trivial p T -behavior p T =0.07 GeV/c p T =0 or 0.1
35 + semi-inclusive Kinematics does not match perfectly, some extrapolations have been performed in CLAS data.
36 EMC data EMC, PLB95 Much larger values measured by EMC, but seen to increase rapidly with W.
37 Mass Corrections At low energies masses are not negligible, one has to use correct variables (Mulders, PRD49):
38 x F cut Cut on x F simply remove low-z part of the spectrum. Its application always destroy the good agreement with pQCD calculations in these region. BEBC (CERN), PLB87
41 Parameterization dependence CTEQ 5 LO GRV 98 LO MRST cg LO CTEQ 5 NLO GRV 98 NLO MRST cg NLO 1.Very small uncertainty due to parton distribution function 2.Larger uncertainty due to fragmentation function
42 ZEUS data ZEUS, PLB481 1.The same limitations as for EMC and E665 2.More detailed data sample in hep-ex/0608053 represented in different variables (pseudorapidity and minimum hadronic energy in HCM) and integrated also over neutral hadrons appears hard to compare 0.01
"name": "42 ZEUS data ZEUS, PLB481 1.The same limitations as for EMC and E665 2.More detailed data sample in hep-ex/0608053 represented in different variables (pseudorapidity and minimum hadronic energy in HCM) and integrated also over neutral hadrons appears hard to compare 0.01
43 EMC and E665 data E665, PRD48 EMC, Z.Phys.C34 1.The same limitations also in E665 data 2.Minimum transverse momentum of hadrons is commonly used p T C which can mask possible sign change at low p T 3.Strong x F variation is seen by EMC Q 2 >4 GeV 2 403 GeV 2 100
"name": "43 EMC and E665 data E665, PRD48 EMC, Z.Phys.C34 1.The same limitations also in E665 data 2.Minimum transverse momentum of hadrons is commonly used p T C which can mask possible sign change at low p T 3.Strong x F variation is seen by EMC Q 2 >4 GeV 2 403 GeV 2 1004 GeV 2 403 GeV 2 100
44 EMC data in p T EMC, PLB130 EMC, Z.Phys.C34 1.Summed over all charged hadrons positive and negative, no PID 2.Integrated over all other variables: x, Q 2, z 3.Radiative corrections with Monte Carlo Q 2 >4 GeV 2 40
"name": "44 EMC data in p T EMC, PLB130 EMC, Z.Phys.C34 1.Summed over all charged hadrons positive and negative, no PID 2.Integrated over all other variables: x, Q 2, z 3.Radiative corrections with Monte Carlo Q 2 >4 GeV 2 404 GeV 2 40
46 Kinematical Separation (for ) Separation is possible by means of a cut on the energy flow from the virtual photon to the measured hadron. Current fragmentation Target fragmentation Hadron rapidity Current Target x=0.3, Q 2 =3 GeV 2 Pion electroproduction
48 Longitudinal Momentum ++ p CEBAF beam energy in combination with CLAS acceptance allow to explore current fragmentation for light mesons and target fragmentation for baryons. In DIS Feynman permits to disentangle two regions, however, at small invariant masses W separation is ambiguous. target current 6 GeV beam energy
49 Rapidity gap at CLAS Separation of the current and target fragments: Berger criterion ++ p Useful kinematics Exclusive Boundary M X ~M n DIS only! Q 2 =2 GeV 2 W>2 GeV current
50 CLAS Acceptance 0 Zero-order approximation: φ-constant term Acceptance mixes Fourier coefficients with different n.
51 Fourier analysis of acceptance 100 harmonic expansion: CLAS acceptance is cosine-like. Even number of sectors generate mostly even functions in azimuthal distributions. even (cos nφ)odd (sin nφ) DATA Fourier series DATA Fourier series
53 CLAS Acceptance Only first 10 harmonics are significant, but 20 harmonics are kept in the analysis.
54 Three methods Comparison of the three methods for structure function separation: 1.Fit of φ-distribution 2.Moments method in zero- order approximation 3.Moments method accounting for N=20 harmonics of CLAS acceptance Higher harmonics are important in the extraction of φ–even observables from CLAS data
55 Pseudo-data Cross Check Pseudo-data generated in a limited kinematical area from a known model (different from that used in the reconstruction) were used to check that the two extraction procedures are able to extract correct φ-moments. model
56 Results of Integration Different assumptions yield slightly different results in low-z region. Exponential p T Exponential t Numerical p T integ. Numerical t integ. exact formula no E h /p || correction unphysical high p T tail Correct expression for low energy: LO pQCD
57 Leading Protons at HERA DIS on a Pomeron target parton momentum fraction in Pomeron Chekanov, NPB658
58 Leading Particle Effect Systematic study of different reactions with hadron and lepton beams showed: 1.only particles present in the initial state can be leading particles in the final state, 2.more valence quarks from initial state particles are present in the particle measured in the final state then more likely particle to be leading. Basile, Nuovo Cim.A66 Leading particle is defined as the particle carrying most of the specific jet (current or target) momentum in CM reference frame.
60 Electromagnetic Probe Lepton scattering off a nucleon is the cleanest probe of nucleon internal structure. electron beam with energy E detected electron at angle with momentum E’ produced hadronic system of mass squared virtual photon and target four-momenta: Lorentz invariants: Electromagnetic current inclusive cross section: One Photon Exchange approximation refers to aligned (anti-aligned) spins of incident electron and target nucleon (k) (k’)
61 Inclusive Kinematical Domains elastic peak ep e’p’ nucleon resonances Elastic scattering Inelastic scattering: W<2 GeV - Resonance region W>2 GeV - Deep Inelastic Scattering (DIS) Q 2 <1 GeV 2 † - Non-perturbative Q 2 >1 GeV 2 † - Perturbative Elastic and resonance peaks are due to formation of intermediate particles with a given mass M<2 GeV. inelastic region † Running coupling constant of the strong interaction S (Q 2 ) becomes ~0.3 at Q 2 =1 GeV 2. Furthermore, higher twists are suppressed by powers M 2 /Q 2. Unpolarized electron-proton scattering
62 Perturbative DIS Bjorken limit: and x-fixed Scaling: Parton spin flipping contributions vanish: Callan-GrossWandzura-Wilczek Parton distribution functions Fraction of proton momentum carried by struck parton Neglect parton and target masses. valence sea Valence and sea partons and flavor Singlet and Non-Singlet combinations Incoherent elastic scattering of partons
63 Semi-Inclusive Kinematical Domains elastic peak ep e’p’ resonances Exclusive production Inclusive production: M X <1÷2 GeV - Resonance region M X >1÷2 GeV - Deep Inelastic Scattering (DIS) Q 2 <1 GeV 2 † - Non-perturbative Q 2 >1 GeV 2 † - Perturbative Current fragmentation Target fragmentation inelastic ,, n 00 ep e’p’X ep e’ + X J.P.Albanese et al.,PLB144 Y CMS rapidity
66 Structure Function Separation Two methods of separation: 1.fit of -dependence 2.event-by-event moments
67 p T and t dependences p T dependence cannot be calculated by ordinary pQCD, only TMD-based approach will permit for a complete description of the measurement. One has to integrate the data in p T 2 :
68 Mean transverse momentum Parton model predicts simple z-dependence of measured mean transverse momentum: Kinematical constraints cut transverse momentum distributions at low-z:
70 Leading Particle Effect target jet direction current jet direction Upper limit of 5% on the leading target fragmentation contribution was estimated at lowest z=0.07 where |t|=|t| max is kinematically allowed. Q 2 =2 GeV 2 x=0.24 z=0.18 Approximate integration:
71 Soft Target Fragmentation 1.Most of hadrons have x F ~0 regardless energy of the experiment. No separate peaks for target or current fragmentation. 2.Current fragmentation pQCD fails at backward CM angles EMC, E =280 GeV CLAS, E e =6 GeV LO pQCD
72 Interplay between variables Standard SIDIS variable squeezes backward going hadrons into the very low-z region, where z 0 divergence dominates the total cross section: 1.Commonly used z H variable is not suitable for target fragmentation analysis, 2.Definition of the hadron direction with respect to virtual photon is frame dependent. forward backward