Jet Production at High Transverse Energies at HERA

1
Jet Production at High Transverse Energies at HERA
Underline
Costas Foudas Imperial College
c.foudas_at_ic.ac.uk Krakow 1.5.2002
(1) Introduction (2) Jet Production in NLO
pQCD (3) Jet Measurements and ?s (4) Summary and
outlook
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Jet Events at HERA
Jet signatures are clearly visible !!!
?jet(-1)ln(tan(?jet/2))
Jet production has been measured at HERA for 0 ?
Q2 ? 104 GeV2 and 4 ? ET ? 100 GeV
3
Jet Production in e-p scattering at HERA
At LO pQCD two processes contribute to Jet
production
Boson-gluon fusion (BGF)
QCD Compton (QCDC)
Q2
q
Q2 -q2
XBJ Q2
Yq.p/p.l
2pq
?s
?s
Sensitive to the gluon parton distribution
function xg(x) and the strong coupling constant
?s. Mainly at low x.
Sensitive to the sea quarks, which are
constrained from measurements of the proton
structure, and ?s.
? x(1 MJJ2/ Q2) Fraction of the protons
momentum carried by the emitted parton.
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Jet Production Cross Sections
The Jet production Cross Section can be written
in terms of the proton Parton Distribution
Functions and the hard Scattering cross section
as
d?(ep? jetjetX) ? ? qi(x,?F,?s)
?i(?R,?s ?F) (1?had)
2 2 2
Factorization Scale
Parton to Hadron Corrections
Renormalization Scale

• The cross section calculation is only
• reliable if
• ?R, ?F Uncertainties are small (what is ?R ?)
• ?had Correction and uncertainty is small
• PDF uncertainties are small

Hence, to test QCD and perhaps make a discovery,
one must measure Jets at High Q2 and high ET
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Renormalization Scale Uncertainties
The uncertainties decrease with Q2 and ET
but they depend upon the choice of ?R (Q2 or ET
or ?)
2
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PDF Uncertainties
Ratios of cross sections are in general less
sensitive to the PDF uncertainty !!!!
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Hadron to Parton Corrections
At low Q2 the corrections depend strongly on
the choice of the jet finder but as Q2 increases
they converge.
In all cases the hadronization corrections
decrease with increasing Q2.
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pQCD Predictions and Asymmetric Jet Cuts
The predictions become unphysical when the two
jets balance in ET !!!
This is because there is no phase space for extra
gluons to be emitted in the final state
Use asymmetric jet cut ETBRE(2) gt 5 GeV and
ETBRE (1) gt 8 GeV
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Jet Data vs Monte Carlo Models
Although the Monte Carlo reproduces well the
shape of the measured cross sections (good
for calculating corrections) It does not
reproduce the jet absolute cross section.
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The DiJet cross section vs Q2
The data agrees well with the predictions of
pQCD within 10 for ?2R Q2
Large scale uncertainty at low Q2. Only for Q2
gt 400 GeV2 does it decrease below 10.
The data are more precise than the predictions.
Need predictions with smaller uncertainty
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DiJet Cross Section vs ?
Within the theoretical and experimental
uncertainties the measured DiJet cross section
agrees with the pQCD predictions using xg(x)
extracted from scaling violations and other data.
Important test of the universality of xg(x)
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Dijet Double Differential Cross Section
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DiJet Cross Sections I
5 ? Q2 ? 5000 GeV2
0.2 ? y ? 0.6
-1 ? ?lab ? 2.5
ET,1ET,2 ?17 GeV
ET,1,2 ? 5 GeV
d?/dMJJ described well except at low Q2
d?/d? is sensitive to the gluon PDF and is
Described well by NLOCTEQ5M1
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DiJet Cross Sections II
d?/d? The NLO corrections are large in the
forward Region at low Q2.
NLO QCD describes d?/d? in the entire kinematical
region
d?/dET described well except at low Q2
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3 Jets Cross Sections
2
3 Jet Cross sections are sensitive to as already
at LO pQCD ? Important test of QCD
The shapes and angular distributions of the cross
sections are sensitive to the dynamics of the
interaction
X4E4/M3jet
X3E3/M3jet
cos?3 (P3?PB)(P4?P5) P3?PB
P4?P5
cos?3 PBP3 PBP3
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3 Jet Cross Section vs Q2
The 3-jet cross section is in good agreement
with the predictions of NLO pQCD including
Hadronization corrections (-18 -22)
?R-uncertainties dominant below 50 GeV2 as
-uncertainties dominate
Sensitivity to as
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3-Jets to 2-Jets Rate
The ratio is described Well by the predictions
of NLO pQCD plus hadronization corr. (-18
-10)
Renoramlization scale Uncertainties
reduced particularly at low Q2
The ratio is sensitive to as but it is
insensitive to the gluon distribution in the
proton.
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3-Jets Cross Sections
The NLO pQCD predictions describe well also the
XBJ and M3jet distributions.
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3-Jets Cross sections vs ?3 and ?3
The shapes of the NLO predictions are different
than those of phase space curves and in agreement
with the data.
Jet 3 prefers the proton Or photon directions.
NLO QCD and Phase Space predictions
have different shape due to the Bremsstrahlung
nature of the process
The data prefers ?3?0 or ?3??
The predictions are in reasonable agreement with
the data !!
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3-Jets Cross Sections vs X4 and X3
The data are well described By the NLO
pQCD predictions
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Measuring aS from the Jet data
ZEUS measured the ratio of dijet (d?21) over the
total cross section (d?tot) and extracted aS by
fitting.
The cross section falls by 4 orders of magnitude
and the predictions of pQCD are in very good
agreement with the data.
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The as evolution with Q2
At ?R MZ these measurements result to
0.00240.0057
?S0.1166?0.0019-0.0033- 0.0044.
(stat.) (exp.) (th.)
Both a precise determination of the strong
coupling constant and a test of its
energy-scale dependence.
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Dijet Cross sections at High Q2
After the fit the cross sections as a function of
the jet pseudorapidity and jet transverse energy
were compared with the NLO pQCD Predictions
using the aS found from the fit.
The measured cross sections agree well with the
NLO pQCD predictions calculated using DISENT
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Extracting as from Inclusive Jets
?s(MZ) 0.1186 ? 0.0059 (tot.) ?s(MZ) 0.1186
? 0.0030 0.0039 0.0033
-0.0045 -0.0023
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Jet Photoproduction at High ET
Direct Photon diagram
Resolved Photon diagram
Scale ETjet
x? ? Ete-?/2yEe Fractional photon momentum
Direct ? x ? 1
Resolved ? x?lt 1
Resolved ?? Direct
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Dijet Photoproduction I
Q2 ? 1 GeV2 0.1 ? y ? 0.9 ETmax ? 25 GeV ETsecond
? 15 GeV -0.5 ? ? ? 2.5
40 from gluons in the proton
The NLO pQCD Calculations using PDFs coming
from F2 at lower scales agree reasonably well
with the data ? Universal PDFs
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Dijet Photoproduction II
The dijet data are shown for two different ET
ranges Representing different factorization
scales for the proton and photon PDFs.
The NLO pQCD predictions agree well with the
data and change very little if the GRV or the AFG
photon PDFs are used.
In contrast the renormalization scale
uncertainties are significant.
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Dijet Photoproduction III
-Difference Between the measured cross Sections
and the NLO pQCD predictions
Correlated uncertainty
Renormalization scale uncertainty
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High Mass Dijets I
47 ? MJJ ? 160 GeV
MJJ 2ET1ET2(cosh(?1-?2)-cos(?1-?2))
The cross section falls by 3 orders of magnitude.
? Renormalization scale uncertainties less
than 15.
? Hadronization uncertainties within 5 !!!
? Uncertainty due to proton and photon PDFs gt
6, 10 (norm)
? The shape of the distributions is described
well by QCD but the data are above the
calculations (still consistent)
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High Mass Dijets II
?1
?
?2
cos? tanh(1/2(?1 -?2))
? (1cos?) /(1-cos?)
Gluon exchange ? uniform Quark exchange ? 1/(1?)
Good agreement ? Dynamics is OK
Renormalization scale uncertainties less than 5.
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Limits for Resonance decaying to Two Jets

Having the experimental and theoretical
uncertainties under control,the dijet data are
then used to search for a resonance P above 60
GeV decaying to two jets ?p ? P X?JetJetX
The d?/dMjj is compared to the NLO QCD
predictions normalized to the data.
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Summary and Outlook

• Jet data at high ET have been used at HERA-I to
  test QCD and make precise measurements of the
  gluons and ?S
• The detector and theory systematic errors have
  been well understood and we have learned that jet
  measurements can be made to better than 10 level
  if the ET is high enough (high Q2 is needed also)
• Low Q2 regime is rich but require more precise
  theoretical calculations.
• HERA II will start soon !! One can expect a
  large increase of the high ET high Q2 samples
  which will enable us to tag the proton PDFs at
  higher x, measure ?S, BFKL, search for new
  physics.