R Scan and QCD Study at BESIII

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R Scan and QCD Study at BESIII

• Haiming Hu
• R Group, IHEP
• January 13-15, 2004, Beijing

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Outline

• Motivation
• R scan
• QCD related topics
• Summary

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Motivation (R value)

• R value is an important parameter in the test of
  the Standard Model .
• In 1998 -1999, two R scans were done in
• 2-5GeV with about error 7 at BES2.
• In order to decrease the uncertainty of the
  calculations of the Standard Model parameters,
  more precision R measurement at BES3 are appealed.

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Motivation (QCD topics)

• QCD is the unique candidate theory of strong
  interaction.
• QCD can describe the evolutions of the quark and
  gluon with large momentum transferring.
• QCD can not give complete calculations from the
  primary qurks and gluons to hadrons.
• The knowledge of hadronization at low energy are
  
• rather poor or even blank.
• The pQCD needs more experiments to test and to
  develop.

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The low energy accelerators in the world
DA?NE (Italy) VEPP2000 (Russian) BEPC3 (China) CLEO-c (US)
Ecm (GeV) 0.5 1.4 0.5 2.0 2 4 3.1 12
Luminosity (1030cm-2s-1) 50 [phone] _at_3.70GeV 500
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R value measurement
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R values between 2-5 GeV at BES2(1998 and 1999)
Broad resonant structure
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R value status at some energy pointsPhys.Rev.Lett
.88,(2002)101802-1
Ecm (GeV) Nhad N??N?? L(nb-1) ?had 1?obs R
2.0 1155.4 19.5 47.3 49.50 1.024 2.18
3.0 2055.4 24.3 135.9 67.55 1.038 2.21
4.0 768.7 58.0 48.9 80.34 1.055 3.16
4.8 1215.3 93.6 84.4 86.79 1.113 3.66
Ecm (GeV) Nhad error () ?trig error () L error () ?had error () 1?obs error () Total
2.0 7.07 0.5 2.81 2.62 1.06 8.13
3.0 3.30 0.5 2.30 2.66 1.32 5.02
4.0 2.64 0.5 2.43 2.25 1.82 4.64
4.8 3.58 0.5 1.74 3.05 1.02 5.14
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QED running coupling constant

decrease
Before BES experiments, the ratio of R error
contribution to ??s) in 2-5 GeV account for about
53.
After BES measurement of R, the ratio of error
contribution reduce to about 30 in 2-5GeV.
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Error estimation of the R measurement in
2004(estimated according to R scan in 1999)blue
figures R99 pink figures R04
In 2004, R value at 2.2 Gev, 2.6GeV, 3.0 GeV will
be measured
Ecm (GeV) Nhad events selct () Lum. () 1d () ehad () error stat () error sys () error total ()
2.2 1,444 2,000 5.54 4.0 2.48 2.2 1.29 1.0 3.49 2.5 2.88 2.2 7.04 5.0 7.61 5.5
2.6 1,734 20,000 4.43 2.0 2.77 1.5 1.26 1.0 3.83 2.0 2.71 0.8 6.50 3.3 7.04 3.5
3.0 2,055 20,000 3.30 2.0 1.70 1.5 1.32 1.0 2.66 2.0 2.49 0.8 5.02 3.3 5.61 3.5

• Hadronic efficiency ehad will be determined by
  using new developed
• detector simulation Monte Carlo (BIMBES) based on
  GEANT3

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The R errors of measured at BESII and the
estimated R error at BESIII
error sources BESII () BESIII ()
Luminosity 2-3 1
Hadronic model 2-3 1-2
Trigger efficiency 0.5 0.5
Radiative correction 1-2 1
Hadronic event selection 3 2
Total systematic error 7 2.5 4
Very rough
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The change of the uncertainty of QED ??s? with
the decrease of R error in 2-5 GeV
(If R error in other energy region fixed)
R error in 2-5 GeV
5.9 0.027610.00036
3.0 0.027610.00030
2.0 0.027610.00029
The aim of the precision of R measurement at BES3
(2-4) is reasonable and hopeful
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Some methods used in R measurement at BESII

• (Some of them may be used at BES3)

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Luminosity

• Two independent ways were used to select
  wide-angle Bhabha events, one sample to calculate
  the luminosity, another to estimate the
  efficiency.
• The main luminosity error was the statistical
  error of the two samples. Large event sample
  will help for reducing the luminosity error.
• Use Bhabha, two-photon and ?? events to analysis
  luminosity and to find systematic errors.

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Integrated luminosity cross check
Ecm (GeV) Lee (nb-1) Lµµ (nb-1) L?? (nb-1)
2.6 292.96.5 268.218.9 266.712.0
3.2 109.33.4 108.9 8.6 106.0 5.9
3.4 135.34.0 125.1 9.8 130.7 7.1
3.55 200.25.2 192.114.5 191.1 9.7
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Backgrounds

• Use M.C to estimate the residual QED backgrounds
• Nll ?ll L ?ll , (le,?,?)
  N????? L ???
• Use vertex-fitting to estimate
• beam-associated backgrounds.
• The better track resolution of
• BES3 is benefit for reducing
• beam associated backgrounds

Gaussian2 order polynomial fitting
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Initial state radiative corrections

• Some schemes are studied
• (1) G.Bonneau, F.Martin
• Nucl.Phys.B27,(1971)381
• (2) F.A.Berends, R.Kleiss
• Nucl.Phys. B178, (1981)141
• (3) E.A.Kureav, S.V.Fadin
• Sov.J.Nucl.Phys.41,(1985)3
• (4) A.Osterheld et.al.
• No.SLAC-PUB-4160(1986) ?(used)
• In BES3 experiments more precision schemes are
  needed

Fenyman figures for ISR (to a3 order)
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Formula used for ISR calculation
The difference of (1??) between scheme (3) and
(4), which is 1 in non-resonant region
The radiative correction factor calculated by
scheme (4)
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Hadronization Picture
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Lund area law
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Lund area law
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Lund area law

• Phase space
• Partition function
• Define n-particle multiplicity distribution
• N and p are two free parameters tuned by data
• Pn is used for controlling fragmentation hadron
  number in MC

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BES raw data spectrum compared with LUARLW
detector simulation at 2.2 GeV
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BES raw data spectrum compared with LUARLW
detector simulation at 2.5 GeV
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BES raw data spectrum compared with LUARLW
detector simulation at 3.0 GeV
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Check RQCD prediction
Central value of Rexp and RQCD agree well. Is
it true or due to error?
RQCD has 1sdeviation from both BES and ??
measurements. Is this the experimental error
or new physics?
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Determination of the running ?s

• R value is predicted by pQCD
• Where,
• Solving the equation
• One may obtain ?s

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Determination of the running ?s
Charged particle differential cross section
q momentum ?ch neutral particle
correction
In QCD
Measure the differential cross section, one may
get ?s
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QCD Related topics
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? Inclusive distribution

• 
  e e-
  ? h X (h p, K etc)
• The inclusive spectrums are governed by
  hadronization dynamics.
• In general, the single particle distributions are
  the function of (s, p// ,p? ) .
• The two questions are needed to answer
• (i) how do the inclusive distributions
  change with (p// ,p?) when s fixed?
• ? depends on the type of the initial state
  and the final state.
• (ii) how do the distributions change with
  the center of mass energy s?
• ? Feynman scaling assume the distributions
  are the function of
• the scaling variable x and p? at
  large energies.
• Scaling assumption is a good approximate behave
  at high energy,
• but it has not been tested precisely at low
  energy.
• The as may be determined by the scaling deviation.

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? ? Spectrum (to be published in PRD)
Variable
Parameters
MLLA Modified leading log approximation LPHD
Local parton and hadronic duality
BES2
BES2
BES data are reasonably well described by
MLLA/LPHD.
?eff from different experiments
Veriation of KLPHD as the function of Ecm
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? Form Factors

• Exclusive cross section is expressed as the
  product of the phase space factor and form
  factor.
• The measurement of the form factor may check the
  phenomenological model, which is also the
  effective method to find short life-time
  particle.
• The following channels may be measured with large
  sample obtained at BES3
• e e-? pp- pp-, pp- pp- p0 ,
• pp- p0p0 , pp-, pp-KK-,
• pp-, KK-, ppbar

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? ee- ?p p- p p- (BES2)
form factor
Phase-space factor
ND, DM2 data
ND, DM2 data
BES data
BES data
Very preliminary
Very preliminary
Cross section (nb)
Form factor
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ee- ?2(p p- ) at BES3
2.2GeV
2.2GeV
BES3 has better momentum resolution and larger
acceptance than BES2, which will be helpful to
the events selection and reduce the backgrounds.
BES3
BES3
BES2
2.6GeV
2.6GeV
BES3
BES3
BES2
Ptotal distribution
M4pdistribution
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? e e- ?p pbar at BES2
Form factor
Form factor by BES2
Form factor combined other experiments
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? e e- ?p pbar ( momentum resolution of BES2
and BES3)
ltBES2gt
lt BES3gt
experiment
Ecm pexp p ?p p ?p
2.0 0.347 0.315 0.022 0.346 0.006
2.2 0.575 0.563 0.024 0.574 0.008
2.4 0.748 0.739 0.027 0.747 0.010
2.6 0.900 0.891 0.032 0.898 0.012
2.8 1.039 1.029 0.038 1.037 0.015
3.0 1.171 1.161 0.039 1.168 0.018
Momentum resolution at BES3 is much better than
BES2
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? e e- ?p pbar (efficiencies of BES2 and BES3)
BES2
BES3
Ecm (GeV) cos?0.75 cos?0.75 cos?0.90
2.0 0.6328 0.3567 0.4288
2.2 0.6752 0.5847 0.7183
2.4 0.6217 0.6067 0.6764
2.6 0.6467 0.6209 0.6937
2.8 0.6248 0.6077 0.6823
3.0 0.6448 0.6014 0.6774
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? Multiplicity Distribution

• The multiplicity is the basic quantity in
  reactions
• multiplicity distribution Pn(s)
• average multiplicity ltnch(s)gt?nPn(s)
• pQCD predicts the ratio of multiplicity of the
  gluon fragmentation to qurk fragmentation
  rltnGgt/ltnFgt ? CA /CF 9/4.
• This may be tested by analyzing
• J/? data (gluon-fragmentation events account
  for 95)
• 3.07 GeV data (gluon events may be neglected).

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Multiplicity Distribution of BES2
(To be published in PRD)
The results of BES2
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? Correlation function

• The measurement of the correlation effects is
  more valid way to abstract the dynamical
  informations from data than from the single
  particle spectrum.
• Correlation function C(x1,x2)CL(x1,x2)CS(x1,x2)
• (x1,x2) kinematical observable for two
  particles,
• CL/CS long/short-range correlation
  functions.

Lund model prediction to C(x1,x2)C
L(x1,x2)CS(x1,x2)
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?The Bose-Einstein correlation

• The identical bosons is symmetric for the
  communication of any two bosons of same kind,
  which leads to the special statistic correlation,
  i.e. Bose-Einstein correlation (BEC).
• BEC contains the space-time information of the
  hadronic sources.
• The space-time properties of hadronic source may
  be inferred by measuring the BEC functions R(Q2 )
  for same charged ?/K pairs, where Q2 (p1 p2 )2
  .
• It is expected that the following subjects may be
  measured
• (a) two-body correlation
• (b) inflections of multi-body correlation
• (c) inflections of the final state
  electromagnetic/strong interactions
• (c) multiplicity dependence of BEC
• (d) space-time form of hadronic source
• (e) BEC in the resonance decay, e.g. in J/?
  decay.

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? Fractal properties at low energy

• One usually paid the attention to averaged
  distributions only.
• The fluctuations are thought as the statistical
  phenomena for the finite particles number.
• The events with abnormal high particle density
  condensed in small phase-space have been observed
  in several kinds of reactions at high energy.
• The important questions to these discover are
• (a) do the anomalous fluctuations have their
  intrinsic dynamics origins?
• (b) is the phase-space of the final state
  the isotropic or not?
• (c) is the phase-space the continuous or
  fractal?
• (d) do the intermittency observed at high
  energy exist at low energy?
• (e) can the intermittency be explained by
  the known theories (cascade , BEC)?

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? Fractal properties at low energy

• The study of this topic has two aspects
• (i) experiment aspect
• - measure the fractal moments
• - measure the Hurst index
• (ii) mechanism problem
• - whether the asymptotic fractal behavior
  in the perturbative evolution of partons may be
  kept after the hadronization processes?
• - and so on

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Summary

• The high luminosity of BEPC2, the large geometry
  acceptance, good space and momentum resolution,
  good particle identification of BES3 will be
  beneficial to the R measurement and QCD studies
  at low energy.
• The goal of the R measurement at BEPC2/BES3 is to
  reach the precision about 2-4.
• Some subjects which are interesting to low energy
  QCD will be studied experimentally with high
  precision.