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QCD and FSI at LEP

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Title: QCD and FSI at LEP


1
QCD and FSI at LEP
  • aS measurements
  • event shapes
  • power corrections
  • Colour Reconnection
  • Bose-Einstein Correlations
  • Summary

2
aS Motivation
  • aS the fundamental, universal QCD parameter
  • SM predicts ?s evolution, not absolute value
  • Perturbative effects 1/lnQ
  • Non-perturbative effects 1/Q
  • Test measure different processes, energies
  • Intuitive techniques in ee-
  • Precision low, O() cf. electroweak O(10?5)

3
LEP Luminosity
4
Luminosity at LEP2 Energies
  • 272 Niobium film and 16 Nb bulk Superconducting
    Cavities
  • Average accelerating field 7.5 MV/m

5
ee- ? Hadrons Data
Illustrative numbers, per experiment
  • LEP1
  • High statistics, ? 0 background or ISR
  • LEP 2
  • O(10-3) LEP1 statistics, large 4-fermion
    contamination, ISR effects
  • Variable energy, averaged to nominal ?s

6
aS from Z0 Parameters
  • G(Z?hadrons) sensitive to QCD radiation, gives
  • Inclusive
  • Negligible hadronisation uncertainty
  • Reliable calculations
  • Other variables also affected GZ, ,
  • Combined fit, all EW data for best measurement
  • theory error
    0.002

7
Sensitivity of Z0 Observables
  • most sensitive
  • t hadronic width similar measurement, calculation
  • Non-perturbative effects
  • Estimated OPE 0.0140.005
  • Constrained by mass spectra
  • Precision 0.003 at mZ

8
aS from Event Shapes
  • QCD calcs. divergant for colinear or soft gluon
    emission
  • Use robust observables
  • e.g. thrust
  • Further variables heavy jet mass MH, C-parameter
    C, total and wide jet broadenings BT and BW,
    diff. 2-jet rate (Durham, y3)

9
Measurements
  • Select hadronic final states, rejecting
  • 4-fermion-like
  • Hard ISR
  • Observables formed from charged particles,
    neutrals, or energy flow objects
  • 1-T, MH, BW, BT, y3, C-parameter
  • 4-fermion background subtracted
  • Bin-by-bin corrections
  • Acceptance
  • Resolution
  • ISR contamination
  • Fair description of data by MCs

Correction factor
4-fermion background
(MC-data)/data
error
10
as Fits
  • pQCD predictions corrected for hadronisation
    using MC
  • NLO O(as2) pQCD prediction for event shape
    variables, y
  • Small y behaviour of cumulative cross-section at
    LO
  • Diverges
  • At O(aSn), leading term (aSL2)n ? large!
  • Saved by resummation, NLLA prediction

Leading, sub-leading logs to all orders in aS
11
as2 NLLA Matching
O(aS2 ) calc.
ln R(y)
NLLA calc.
?
  • LogR or R matching avoids double counting of
    terms
  • Use modified matching schemes, ensures L0 for
    yymax

12
Fit Results
Scaled heavy jet mass
Thrust
Total jet B
Wide jet B
L3 data
C-parameter
13
Systematic Uncertainties
  • Experimental (little correlation, full
    covariance)
  • Event selection, particle reconstruction,
    detector corrections vary cuts or models
  • Background subtraction (4-f criteria, sgg , etc.)
  • ISR corrections (LEP2)
  • Typically around 1
  • Hadronisation (moderate correlation, on-diagonal
    covariance)
  • Model comparisons string (Pythia), cluster
    (Herwig), colour dipolestring (Ariadne)
  • Model parameter variation (Pythia)
  • typically around 0.7?1.5
  • Theoretical, pQCD (large correlation, on-diagonal
    only)
  • LEP QCD WG devised new prescription

14
Theoretical Uncertainty
  • Uncertainty band obtained (for fixed as),
    varying
  • Renormalisation scale
  • Rescaling factor
  • L? 1/ln(y.xL)
  • Kinematic limit ymax
  • Modification degree
  • For fixed reference prediction (lnR) find as
    variation which covers this band (within the fit
    range)
  • Typically 3.5 ? 5

BT
15
Combined Result
?s evolution of as
  • LEPQCDWG combination summer 02
  • 6 observables
  • 8 nominal ?s (L3 ISR)
  • 4 experiments
  • Results evolved to MZ

16
Power Law Approach
  • 3 loop level
  • (Landau) Pole at ?sL

17
Power Law Approach
  • Alternative to MC derived hadronisation
    corrections
  • Expect non-pert. effects suppressed 1/Qn
  • Parametrise behaviour of as in non-pert. region
    D-M-W
  • Assumes strong coupling remains finite ?s ? L
  • Predictions of form
  • means
  • distributions

mI 2 GeV a0 universal, same all y
P ? 1/Q Dy differs y shift (T,C,MH2) from
2-j shift/squeeze (BT,BW)
18
Power Law Corrections
  • Updated study (DELPHI)

as(Mz)0.1184 ? 0.0033
(inc. ? 0.0031 (scale))
19
Power Law Corrections
  • Example of fits to total jet broadening
  • Uses data ?s 12-189 GeV
  • Note re-analysed JADE data
  • 1979-1986, MC resurrected

From P.A. Movilla Fernandez et al.,
Eur.Phys.J.C22(2001)1
20
Global (aS,a0) Fit to Means
From P.A. Movilla Fernandez et al.,
Eur.Phys.J.C22(2001)1
?BT?
?1-T?
?MH2/s ?
?C?
?y3?
?BW?
21
Global (aS,a0) Fits
  • Systematic shift, aSpow vs. aSMC from
    distributions
  • Combined results (JADE, prel., summer 02)
  • Universality of a0 at 25 level (1-2 s total
    error)

22
4-jet Rate
  • O(aS3) (NLO) predictions for k? Dixon, Signer,
    Glover, Nagy, Trocsanyi
  • ALEPH (xm1)
  • as(Mz) 0.1170 ? 0.0001 (stat)
  • ? 0.0003 (had.)
  • ? 0.0008 (scale)
  • 0.1170 ? 0.0013
  • xm 0.729 (fit for scale and aS)
  • as(Mz) 0.1175 ? 0.0013

Similar to earlier DELPHI results
High sensitivity to aS at LO
23
Colour Reconnection Motivation
Winter 2003 Summary
  • Single dominant uncertainty
  • Final state interactions
  • WW?qqqq only

?(W?W?) decay vertices ? 0.1 fm hadronic
scale ? 1 fm ? Large spacetime overlap ?
Colour exchangeW??W? ? DMW bias ? 25-300 MeV
  • LEP gives best mW measurement
  • Agreement, direct/indirect

24
Predicted mW bias
  • Comparison of mass bias ADLO
  • Analysis of shared MC sample
  • Consistent results
  • Potentially large problem

25
Example Hadronic B Meson Decay
Gustafson, Petterson, Zerwas Phys.Lett.
B209(1988)90
  • B ? J/Y X
  • Colour suppressed decay

BR.exp 1 BR.fullCR 3-5 BR.noCR 0.3-0.5
c/o P.Abreu
26
Charged Particle Multiplicity
  • CR may alter nch in qqqq
  • W hadronisation modelling
  • Compare qqqq/qqlv
  • More important for low p
  • Studied by all LEP expts.
  • ALEPH update, all data
  • Conclusion only limited sensitivity to CR

D?nch? 4q ? 2(qqlv) 0.31 0.23 0.10
(within acceptance)
27
Particle Flow
  • Motivated by simple string picture of CR
  • Regions of interest
  • Define 4 planes
  • Pair jet-jet ? W
  • Minimise ??(j2-j3)??(j4-j1)
  • Project particles ? planes
  • Compare intra-W ? inter-W
  • ? string effect
  • Define RN ? ? intra-W
  • ? inter-W
  • (away from jet cores)

28
Projection of Particles
  • 4 jets, not coplanar
  • 6 possible jet-jet regions
  • Project onto 4 jet-jet planes intra-W and
    inter-W
  • Consider region away from jet cores

29
Event Selection
  • Topological
  • 4 distinct jets, y34gt0.01
  • 2 angles ? 1000
  • 1000 ? angles ? 1400
  • Large/small not adjacent
  • Good jet-jet ? W
  • Efficiency 15
  • Correct pairing 90
  • W mass
  • Minimise ??(j2-j3)??(j4-j1)
  • Pairing integral to selection
  • Efficiency 85 (A), 40 (O)
  • Correct pairing 75 (A), 90 (O)

30
Particle Density
  • Normalised particle density
  • Effect of CR shown
  • Raw particle density
  • Non-planar
  • 4-jet structure evident

31
Particle Flow
  • Ratio intra-W/inter-W particle density Rflow
  • no-CR models
  • CR models
  • Most sensitivity outside jet cores
  • Statistically limited
  • Combine LEP expts.

extreme case
32
Quantitative Measure
  • Quantify using ratio of sums, RN
  • Different experimental acceptances, normalise to
    shared no-CR MC sample before comparison
  • Very different selections, weight by sensitivity
    for each CR model, i

33
Combination Systematics
  • Each expt. evolves their data to single ?s point
    and averages
  • Systematics considered correlated or uncorrelated
    between expts.
  • WW signal
  • Hadronisation model, spread in predictions of
    Koralw Jt,Hw,Ar
  • BEC, ?intra-W no-BE no evidence for
    inter-W BEC
  • (4-jet) Background subtraction
  • Z ? qq, vary sqq ?10
  • Z ? qqqq, vary sZZ ?15
  • Z ? qq hadronisation models
  • Energy dependence
  • Model dependence of ?s evolution
  • Detector effects

34
LEP CR Combination SK-I model
  • NB Extreme, 100 SK-I
  • Vary reconnected fraction in combination
  • Preferred Preco 49 in data
  • Increases DmW from LEP

r?RN(x)/RN(no-CR)
35
Ariadne and Herwig CR models
r?RN(x)/RN(no-CR)
r?RN(x)/RN(no-CR)
36
CR from Rapidity Gaps
Planar 3-jet event
  • CR reduces particle production in
  • central y region
  • Increased prob. of rapidity gap

CR suppressed O(1/Nc2)
37
CR from Rapidity Gaps
CR and no-CR models describe inclusive data
  • Select ee-?qqg
  • Anti-tag g by b decays
  • 10k g jets, ?Ejet? 23 GeV, P 94

Highest E
Select 4 gluon jets with rapidity gaps
38
CR from Rapidity Gaps
39
Leading Part of Gluon Jet
No. charged particles
  • Isolated, neutral, leading g jet system
  • sensitive to CR
  • and glueball prodn.
  • Unable to tune away effects cannot describe
    inclusive Z0 and rapidity gap data
  • (Current implementation of) Ariadne/Rathsman CR
    models strongly disfavoured

Net charge
40
Bose-Einstein Correlations
  • Enhanced identical boson pairs (?? or ??),
    small Q2 -(p1p2)2
  • Firmly established phenomena, LEP1 and intra-W
  • Studied using 2-particle correlation function
  • R(p1, p2) ?2(p1, p2)/?0(p1, p2) Many
    experimental factors!
  • Essential question do BEC exist between W and
    W ?? 
  • Problem 1
  • Reference ?0 should be identical to ?2,but
    without BEC
  • Unlike-sign data, / ratio of same in
    MC (resonances)
  • Like-sign MC without BEC (MC modelling)
  • Event mixing
  • Problem 2
  • Non-pQCD amplitudes unknown, resort to models
  • Phenomenological parametrisation R(Q) ? 1
    ?exp(-r2Q2)

Source radius
BE strength
41
B-E Analysis Method
  • Idea Chekanov, De Wolf, Kittel,
    Eur.Phys.J.C6(99)403 
  • If W and W decays uncorrelated, 2-particle
    density
  • ?2WW(p1,p2) ?2W(p1,p2) ?2W(p1,p2)
    2?1W(p1) ?1W(p2)
  • Subtract background
  • Form ratio Dlhs/rhs
  • D/ D(data) / D(MC, intra-W BEC) remove
    potential residual bias
  • D ? D/ ? 1 ? non-independent W decays
  • inter-W BEC (or similar effect)

?MIXWW(p1,p2) mix 2 x qql? ? BEC ? 0
Assume ?2W?2W-?2W Estimate from qql?
42
(Final) L3 results
Phys.Lett.B547(2002)139
  • MC tuned to Z-gtqq (udsc)
  • LS/ULS behaviour OK
  • D (ratio data/MC) ? D
  • Enhancement predicted for inter-W BE model
  • No effect seen in data
  • Quantify effect using BE32

Like-sign
Unlike-sign
43
Combination ?s189-207 GeV
  • Fit to
  • L0.008 ? 0.018 ? 0.012
  • k0.4 ? 0.4 ? 0.3 fm
  • Inter-W BE gives
  • L0.098 ? 0.008 (stat.)
  • This model diagrees with data 3.8s
  • BE models a problem...
  • Delphi/L3 not inconsistent
  • Combined LEP results very soon now (D, L so far).

44
Summary
  • as
  • New LEP average, LEP1LEP2 event shapes
  • Improved prescription for theoretical
    uncertainties
  • V. precise as from 4-jet rate, mean valuespower
    corrections
  • Colour Reconnection
  • First combination, Summer 2002, all data
  • Extreme case SKI 100 excluded (favour Preco
    49)
  • Data/models compatible, with/without CR.
  • Impact of qqqq channel on LEP mW 9!
  • New Z0 rapidity gap study, further constrains
    models
  • Bose-Einstein
  • L3 final results, no support for inter-W BEC
  • Delphi/L3 not inconsistent, wait for A/O!

45
Theoretical Uncertainty
  • Thrust has large, well-behaved fit region
  • Uncertainty band obtained (for fixed as) via
    variations
  • Renormalization scale
  • Rescaling factor l1/ln(xL y)
  • kinematic constraint
  • Modification degree
  • For fixed reference prediction (LogR) find as
    variation which covers this band (within the fit
    range)
  • Typically 3.5 ? 5

46
LEP results
47
W Mass
  • Dominant systematics
  • Hadronisation 18MeV
  • Compare models
  • Use LepI data MLBZ D
  • LEP Energy 17MeV ?MWMW?Ebeam/Ebeam
  • Resonant depolarisation, NMR probes/flux loop
  • LEP spectrometer
  • QCD Final State Interactions
  • Colour Reconnection
  • Bose-Einstein Correlations

qqqq channel weight 10!
48
MW, qqqq vs. qqlnl
DMW(qqqq-qqln) 2243 MeV
(in fit neglecting BE/CR effects)
49
WW ? lnl lnl
  • Typical (perfect) event
  • 2 charged leptons
  • ? 2 neutrinos
  • Branching fraction 11
  • Typical efficiency 80
  • purity 90
  • ? Underconstrained, limited impact on mW
    measurements

50
WW ? qqlnl
  • Typical (perfect) event
  • 2 well-separated hadronic jets
  • 1 charged lepton, 1 hard n
  • Branching fraction 44
  • Typical efficiency 85
  • purity 90
  • ? Reconstruct n from (E, p) constraints

51
WW ? qqqq
  • Typical (perfect) event
  • 4 well-separated hadronic jets
  • Branching fraction 45
  • Typical efficiency 87
  • purity 80
  • ? Jet-jet ? W ambiguity
  • ? Colour Reconnection, BEC (FSI)
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