Snmek 1

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The purpose of your RTN
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What do we mean under theoretical uncertainty
of QCD calculations of hard processes?
Jirí Chýla Institute of Physics, Prague
Hard processes like

• Jet production
• Inclusive particle production
• Prompt photon jet production
• Heavy quark production
• Dilepton, W, Z production

are playing central role in the quest for new
physics at HERA and Tevatron and will so even
more so at LHC
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The search for new phenomena requires accurate
theoretical calculations based on the Standard
Model. I will first concentrate on general
discussion of theoretical uncertainties of QCD
calculations because these uncertainties are
soemtimes bigger than experimental errors and
thus prevent unambiguous interpretation of the
comparison of theory with existing data from
HERA, LEP and Tevatron. Then I will illustrate
on the example of top quark production that even
at LHC the theoretical uncertainty of QCD
predictions may be quite large.
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• QCD calculations of physical observable suffer in
  general from uncertainties coming from
• the ambiguities resulting from the inevitable
• truncation of perturbative expansions
• the influence of hadronization effects
• the dependence on the nonperturbative input
  (PDF)

The latter two sources, which would be present
even in the case of all-order calculations, are
reasonably well-defined and under control. On
the other hand the first one is ill-defined and
the single most important source of the
theoretical uncertainty.
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To lump the three sources of theoretical
uncertainties together into one theoretical
error, as is the frequent case, is wrong. The
steady, though very laborious and lengthy
progress with the calculation of higher order
QCD corrections stands in sharp contrast with
often naïve phenomenology. Unfortunately, there
is no easy and unique solution of the problem
caused by the dependence of finite order
approximations on the so called
renormalization and factorization scales and
schemes. As we shall see this problem
significantly restricts the predictive power of
existing QCD calculations for several very
important quantities.
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Huge efforts needed for higher order QCD
calculations
Vermaseren, Moch, Vogt, 2000-2004 (From Vogts
talk at PHOTON2005)
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Phenomenological input
renormalization scheme
colour coupling
renormalization scale
factorization scale
PDF of the proton GRV98, CTEQ6, MRST02
factorization scheme
PDF of the photon AGF94, GRV92, SaS96, GRS99,
CJKL03, AFG05
Fragmentation functions BKK96, KKP2000,
BFGW2001, Kretzer01.
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XS of physical processes can be written as
convolutions of PDF, FF and partonic hard cross
sections
The renormalization scale enters only when
partonic hard scattering cross section is
expanded in PQCD
In defining perturbative calculation the order of
all PDF, FF and hard scattering cross sections
must be specified.
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Hadronization corrections and related effects
What we want to correct?
Standard way of estimating hadronization
corrections to jet observables, i.e. evaluating
the ratio
has only limited relevance for correcting NLO
parton level calculations.
For that purpose all effects absent in hard
partonic calculations should be included.
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But do we understand hadronization?
PYTHIA and PHOJET use the same QED XS, which
dominates at large ET, so what makes such a
dramatic difference?
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Dependence on the choice of PDF
CTEQ MRST two principal groups performing
global fits to hard scattering data. Main
differences - choice of data on hard
processes - definition of acceptable fit -
treatment of systematic errors other recent
ones ALEKHIN, ZEUS, H1 older GRV
Durham HEPDATA database on cross sections
provides also fast interactive tool to estimate
the theoretical uncertainty due to the choice of
PDF. Note the dependence on x!
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Dependence of on the choice of scales/schemes.
Dependence on scales has a clear interpretation,
but their choice is insufficient to specify the
calculations.
has no justification apart from simplicity
(Politzer 87).
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The same choice of the renormalization scale
gives different results in different RS! The
schemes are as important as scales, but there is
no natural RS or FS!
Choice of scales and schemes should be done in
more sophisticated way. This means keeping
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How to choose scales and schemes?
Observable(µ,Mi,RS,FS)
Principle of Minimal sensitivity (P.M. Stevenson,
1980) looks for the point(s) of local stability,
ie. saddle points
Effective charges approach (G. Grunberg,
1984) looks for the points where LONLO
BLM method (Brodsky, Lepage, MacKenzie,
1984) sets the renormalization scale by
mimicking QED not applicable to the
factorization scale/scheme
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Theoretical uncertainty of perturbative
calculations
Conventional way of estimating theoretical
uncertainty due to scale choice, i.e.
identifying all scales with some natural
physical scale Q and plotting the band of
results corresponding to
makes little sense because the results still
depend on selected scheme.
Because of the way the uncertainty due to scale
choice is conventionally defined it should not
be mixed with the other sources of theoretical
uncertainty.
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How to proceed?
We should make a choice of scales and schemes,
based on some general idea, and look whether it
leads to meaningful phenomenology for as wide
range of processes as possible.
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Illustration of the effects of different scale
choice
Single particle production in ?p collisions in
the transition region between photoproduction
(where ET sets the scales) and genuine DIS, where
Q2 is unquestionably the hard scale.
In this region the concept in resolved (virtual)
photon does not have to be introduced, but it
turns out to be very useful phenomenologically.
But, just in this region playing with scales does
wonders and fakes (almost) anything else.
Conventional choice
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Forward jets and single particles at HERA
Mueller 92 best place to look for BFKL effects.
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Daleo, de Florian, Sassot 04 only direct photon
contribution
Difference by a factor of 2 for narrow range of
scales!! Decreases only slowly with increasing Q2
H1 p0

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The most recent analysis of the H1 data on
forward p0 done by Aurenche et al. taking into
account the resolved virtual photon as well.
Calculations done for the common scale set to
Compared to Daleo et al. the common scale is
twice bigger and thus the NLO direct
substantially smaller!
Consequently, also their conclusions are
different.
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Safer bet jet production at the Tevatron
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Heavy quark production
ttbar production at LHC
bbbar production at Tevatron
NLO calculation using code of FrixioneMangano
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Contour plots of the for ttbar produc- tion at
LHC
saddles
curves where LONLO
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30-40!
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Puzzles
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L3
Kniehl et al.
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Puzzling ?? collisions also jets
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Moreover
New L3 analysis confirms their older result
which is in excellent agreement with those of
OPAL and DELPHI.
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Conclusions
In the transition region between photoproduction
and DIS the scale and other uncertainties
prevent us from calculating with (in)accuracy
better than a factor of 2, potentially masking
signals of new physics like BFKL. Work on
NNLO calculations should be accompanied with
systematic investigation of scale and scheme
ambiguities of existing LO/NLO
calculations. In theoretically seemingly clean
case of jet, inclusive hadrons and heavy quark
production in photon-photon collisions we face
serious disagreement with (some?) data which we
do not understand.
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Example