Post on 12-Jan-2016
description
Preparation for measurement of strong coupling constant on CMS
S.Shulga
LPP, JINR (Dubna, Russia)Fr.Skarina Gomel State University, Belarus
International School-seminar “Actual problem of Microworld physics”
Gomel, Belarus23 July – 3 August, 2007
LPP JINR (Dubna, Russia)Fr.Skarina Gomel State University (Belarus)P.Suhoi Gomel State Polytechnical University (Belarus)BLTP, JINR (Dubna, Russia)
Participants:A.Zarubin – CMS HCAL coordinator, head of CMS group in JINR(Dubna)S.Shmatov – head of CMS physics group in JINRS.Shulga – responsible person for task “Alpha_s measurement at CMS”
P.Moissenz – HCAL/JINR group leaderV.Konoplyanikov – leader of Jet physics study in CMS/JINRM.Savina – theoretical group CMS/JINRO.Teryaev – theoretical group CMS/JINRK.Babich – responsible person for full simulation in Jet physics tasks in CMS/JINR physics group
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1
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https://twiki.cern.ch/twiki/bin/view/CMS/MeasurementOfAlpha_s
11,2
11,21
234
“Young scientists from Belarus and from Gomel region
for work at CMS project are invited: Ph.D. positions in Laboratory of Particle Physics JINR”
(S.Shmatov is contact person)
S.Shulga, 24th July, Int.School-seminar, Gomel, 20073
Contents
• Introduction: interplay QCD & experiment• Motivations of measurement• Methods of measurement for inclusive jet observables• Systematic uncertainties• MC tools• Conclusion & plans
ss
S.Shulga, 24th July, Int.School-seminar, Gomel, 20074
Introduction: Jets & pQCDThe applicability of pQCD to an observable depends in general on two assumptions:1. we must neglect hadronization effects;2. the perturbative expansion has to be valid.
This usually means we should1. examine scattering processes with large momentum transfer2. use observables which are relatively insensitive to soft physics.
A Jet, by definition, is a cluster of individual hadrons which are averaged out by the jet algorithm to give a single object with a well defined direction.
The minimal jet transverse-energy cut ensures that there is a substantial momentum transfer.
The averaging over individual hadrons ensures that jet distributions are not sensitive to the behavior of soft QCD radiation.
In order to apply pQCD one can not ask questionabout physics inside jet.
W.T.Giele,E.W.N.Glover, D.Kosower, FERMILAB-CONF-94/350-T
S.Shulga, 24th July, Int.School-seminar, Gomel, 20075
Introduction: Jets & pQCD
N.Glover, Challenges in pQCDDurham, Feb, 2002
S.Shulga, 24th July, Int.School-seminar, Gomel, 20076
Introduction: Jets & pQCD
So, pQCD ensures at conditions listed above :
Davison E. Soper, CTEQ School, June 2007
(renormalization)
S.Shulga, 24th July, Int.School-seminar, Gomel, 20077
Introduction: Renormalization
For example, in Minimal Substraction Renormalization scheme is arbitrary in principle.
In practice is chosen as a physics scale
Physics of scales less then inverseis removed from the perturbative calculation.
Renormalization hides:• Ultra-violet divergences
• and short-distance physics (including new physics:
Quantum Gravitation, Grand Unification,…)
Effects of small time physics are absorbed into the running coupling,
running masses, field operators,…
R
R
.Q
R
S.Shulga, 24th July, Int.School-seminar, Gomel, 20078Davison E. Soper, CTEQ School, June
2007
Introduction: Renormalization
S.Shulga, 24th July, Int.School-seminar, Gomel, 20079
Introduction: Renormalization Scale dependence and independence
Davison E. Soper, CTEQ School, June 2007
Why do we vary renormalization scale ?
•The theoretical predictions used for comparison with experiment should be independent of
• According to equation (2) the change due to varying the scale is formally higher order;
• So, the uncertainty due to varying the renormalization scale is way of guessing the uncalculated higher order contributions
(2)
R
(1)
S.Shulga, 24th July, Int.School-seminar, Gomel, 200710
• fi(x,F) are PDFs– x is parton momentum fraction– PDFs must be measured: can’t
calculate
• is partonic scattering cross section
– Calculate as expansion in s(R)
Strategy is to factorize physical observableinto a calculable Infra-Red Safe part and not calculable but universal part.
Cross-section is convolution the long distance Parton Distribution Functions (PDF)
and short distance hard scattering cross-section:
Introduction: Jet & Factorization
),( Rij s Measure
Calculate perturbatively
ij
)( 1xfi
)( 2xf j
i
j
p
p
X
11 2 2( , )) ((( ) ),ij
i F j Ff x fpp X dx dx x ij X
S.Shulga, 24th July, Int.School-seminar, Gomel, 200711
Introduction: Factorization scale
Davison E. Soper, CTEQ School, June 2007
F is factorization scale
F is boundary which separates long/short distance parts in cross-section.
S.Shulga, 24th July, Int.School-seminar, Gomel, 200712Davison E. Soper, CTEQ School, June
2007
Introduction: Factorization scale dependence and independence
In principle, can take any value:Cross-section should be independent of the choice.
However, for andhard cross-section will contain large logarithms
which will ruin the perturbative expansion.So, not to be much greater than
Choice
Since,
is often taken as a measure of the magnitude of theuncalculated high order terms,
choosing, say
F
F qm qm Qlog
q
Q
m
F .Q, 1F cQ c
1ˆ ˆ( )N
F sF
Oc
1
22
c
S.Shulga, 24th July, Int.School-seminar, Gomel, 200713
Comparison of theory with experiments allows one to fitthe parton distribution function at fixed scale
Once PDFs are determined, they can be used to calculatethe cross-section for other processes
either to test the validity of QCD formalism or to predict the rate or characteristics of new processes
for which the QCD processes are the background.
.F
Introduction: Factorization
Davison E. Soper, CTEQ School, June 2007
S.Shulga, 24th July, Int.School-seminar, Gomel, 200714
“Renormalization” is factorization (of UV divirgences)“Factorization” is renormalization (of soft/colinear div.)
Ultra-violetRenormalization
hides/summarizesour ignorance of
physics at huge scale in
( ), ( ),...s R Rm
Infra-red/collinearFactorization
hides/summarizesnon-perturbative QCD
physics at confinement scale in
( , ), ( , ),...a F a Ff x d x
analogy &correspondences
Introduction: Renormalization & Factorization
Davison E. Soper, CTEQ School, June 2007
The basic idea of factorization of collinear/soft (long-distance) physics
is quite similar to those of renormalization of short distance (ultra-violet) divergences.
S.Shulga, 24th July, Int.School-seminar, Gomel, 200715
Introduction: QCD & experiment
Next steps to study interplay QCD & experiment are
1. Technics of NLO calculation;2. Monte Carlo NLO generators at parton level including parton
level jet finders;3. Full NLO Monte Carlo generators including parton shower, hadronization and particle level jet finders.
These are the topics of separated lecturesat modern specialized HEP schools…
S.Shulga, 24th July, Int.School-seminar, Gomel, 200716
Introduction: experimental determination of s
S.Shulga, 24th July, Int.School-seminar, Gomel, 200717
Motivations( )s
S Bethke Nucl.Phys.Proc.Suppl.121:74-81,2003
S at Q ~ 1 TeV is not measured
Universality of the function provides the most powerful and decisive testof the validity of QCD
W.-M. Yao et al., Journal of Physics G 33, 1 (2006) Review of Particle Physics
S.Shulga, 24th July, Int.School-seminar, Gomel, 200718
Motivations
It is interesting to know S at Q ~ 1 TeV
W.T.Giele, E.W.N.Glower, J.Wu, Determination of a_s at hadron collidersPhys.Rev.D, 1996
S.Shulga, 24th July, Int.School-seminar, Gomel, 200719
S.Kluth, IHEP2006, Proceedings, March 31,
2007.
W.-M. Yao et al., Journal of Physics G 33, 1 (2006) Review of Particle Physics
Motivations
( ) 0,1176 0,0009s ZM
stat. exp. theor.
PDG, 2006:
Rel.err = 0.8%
Rel.err = 5.7%
Rel.err = 4,4%
S.Shulga, 24th July, Int.School-seminar, Gomel, 200720
Methods of measurement of strong coupling constant
Measurements of PDF depend on and on the contrary.An extraction of using a given PDF set can therefore at best return input
valueused in fit of PDF.
s
Method to measure which is independent of the input value of the PDF’s
was pioneered in paper:
ss
sW.T.Giele,E.W.N.Glover, J.Yu, Determination of at hadron colliders. Phys.Rev. D 53. 1996. P.120
S.Shulga, 24th July, Int.School-seminar, Gomel, 200721
(0)
( ) ( ) (0) ( )
( ) ( ) (0) ( )
1
ˆ( ) ( ( ), / )
ˆ( ) ( ( ), / )
ˆ( ) [1 ( ) ( / )]
data pert ms R s R R R
data n pert n m ns R s R R R
ndata n pert n m n l
s R s R l R Rl
O O T K Q
O O T K Q
O O T k Q
01
( ) ( )
( )[( 1 ( / )
ˆ) ( ])n m n l
s R s
data n
l R Rl
R
Ok Q
T
and are calculated in LO and NLO respectivelywith their theoretical uncertainties: - PDF uncertainties - and uncertainty due to scale dependence of finite order (NLO) of calculation.
Parton level generator JETRAD used to calculate T^(0) and k_l.
( / )l R Rk Q(0)T
sW.T.Giele,E.W.N.Glover, J.Yu, Determination of at hadron colliders. Phys.Rev. D 53. 1996. P.120
(1)
(2)
(2’)
(3)
Method of measurement (I)
S.Shulga, 24th July, Int.School-seminar, Gomel, 200722
Method of measurement (I)W
.T.G
iele
,E.W
.N.G
lover, J.Y
u, P
hys.R
ev. D
53
. 199
6.
P.1
20
stat. exp. theor.
CDF
Rel.err = 6,7%
Theor. scale:Rel.err = 4,2%
The error from using different PDF as input isapproximately +/- 0,002 Theor. PDF:
Rel.err = 1,7%
S.Shulga, 24th July, Int.School-seminar, Gomel, 200723
Method of measurement (II)
Similar method used in CDFfor two jet cross section Measurements of strong coupling constant from 2 jet
production cross section in 1.8 TeV proton-antiproton collisions
M. Okabe, Ph.D.Thesis, 1998
(1)
(1)
CDF
S.Shulga, 24th July, Int.School-seminar, Gomel, 200724
M.O
kabe,
Ph.D
.Thesi
, 199
8
Method of measurement (II) CDF
Rel.err = 7,7%
S.Shulga, 24th July, Int.School-seminar, Gomel, 200725
Similar method was studiedby H.Stenzel for inclusive jets
(ATLAS):Determination of using jet cross section parameterizations at hadron colliders
s
H. Stenzel, Max-Planck-Institut fur Physik
Method of measurement (III)
27/03/2001
S.Shulga, 24th July, Int.School-seminar, Gomel, 200726
Normalization procedure:
2 21,
norm
T tot T
d dO
dE d dE d
max max
min min
2' '
' 'T
T
Etot TE
T
ddE d
dE d
Jet Cross Section Parameterization
Normalized differential cross section are parameterized with linear functions in 19 bins of ET. In each bin of ET, the cross section dependence on alpha_s calculated at NLO with package JETRAD for various sets of PDF’s, is fitted with linear functions (hypothesis)
( )theor theor theorT T T s TO E a E b E E
H. Stenzel
data theorT T
s T theorT
O E a EE
b E
( ) ( )theor theor theor dataT T T s T TO E a E b E E O E
Method of measurement (III)
It is the same method as:W.Giele, E. Glower,
hep-ph/9506441v1 July, 1995
S.Shulga, 24th July, Int.School-seminar, Gomel, 200727
Linear parameterization result of the normalized differential cross section in two bins of ET at LHC
200 250TGeV E GeV 300 350TGeV E GeV 310210
H. Stenzel
b~0,5E-2 b~1,65E-3
S.Shulga, 24th July, Int.School-seminar, Gomel, 200728H.Stenzel, ATL-PHYS-2001, 2001
( ) 0,1176 0,0009s ZM PDG, 2007:
Syst. theoretical uncertainty only
Syst.exp. uncertainty for CDF: +/- 0.008(rel.err. = 6,7%)
(W.Giele,e.a. 1996)
For CMS - ?
Method of measurement (III)
NLO scale uncertainty dominatesthe error on alpha_s.
It means that one need NNLOto reduce theor. errors
(rel.err.= 0,1%)
(rel.err.= 6%)
TEVATRON
LHC
(rel.err.= 5%)
S.Shulga, 24th July, Int.School-seminar, Gomel, 200729
LHC
S.Shulga, 24th July, Int.School-seminar, Gomel, 200730
LHC
S.Shulga, 24th July, Int.School-seminar, Gomel, 200731
LHC
S.Shulga, 24th July, Int.School-seminar, Gomel, 200732
CM
S P
hysi
cs T
DR
, V
.II,
20
06
20%
LHC
S.Shulga, 24th July, Int.School-seminar, Gomel, 200733
experimental syst.error :s TE
65 137,0
85 15,3
155 10,2
380 2,6
,TE GeV
dataT
s T theorT
O EE
b E
CDF&LHC
CDF X-sect. 10% rel.err
/ ,%s T s TE E
225 70,3
325 28,8
850 4,8
2250 1,8
,TE GeV
LHCX-sect. 10% rel.err
/ ,%s T s TE E
theorTb E data
TO Eandare taken from
H. Stenzel
For 30% X-sect. rel.error at 1 TeV: and Theor.error ~ 5%
1_
~12%1_s
s
TeV
TeV
LHCPr
elim
inar
y
Prel
imin
ary
S.Shulga, 24th July, Int.School-seminar, Gomel, 200734
CDFWhy go beyond NLO ?
LHC:NLO calculation of inclusive
Jet cross-section will be enough.
But, LHC experimental errors for otherprocesses are often less than
theoretical errors.
S.Shulga, 24th July, Int.School-seminar, Gomel, 200735
Tools: LHApdf-5.3.0 (release 28 June, 2007)
Contains CTEQ6AB with 40 PDF sets alpha_s(M_Z) = 0.110 – 0.126.
J.Pumplin e.a. Hep-ph/0512167v4, 2 Feb 2006
Uncertainties of inclusive jet Xsection Curves are for 0.110(short dash),…, 0.126(long
dash).
y < 10,1 < y < 0,7
The shaden green regionshows the range of
uncertaintydue to source other then
as calculated from eigenvector
basis sets CTEQ6.1 (90% coinfidence range)
( )s
TEVATRON LHC
S.Shulga, 24th July, Int.School-seminar, Gomel, 200736
Nearest plans
JETRAD(2002) installed , tested NLOjet++ installed, tested ?LHApdf-5.3.0 installed, testedfastNLO will be installed soon
JETRAD/LHApdf-5.3.0/User ready NLOjet++/LHApdf-5.3.0/User ? Analysis scripts 30%
Following to references above : 30% ready
28 August 2007 : LPP meeting
Packages
Interfaces,analysis
Tasks:
Talks
We are going to have the studies of alfa_s measurement with new packages:
JETRAD/LHApdf-5.3.0 (and NLOjet++/LHApdf-5.3.0)
S.Shulga, 24th July, Int.School-seminar, Gomel, 200737
Long-term plans NLO jets (partons + shower + hadronization)
GRACE ( j+X, 2j+X, … ) MC@NLO ( j+X, 2j+X will be included at the end
2007 )
Packages
S.Shulga, 24th July, Int.School-seminar, Gomel, 200738
• At the LHC it will be possible to measure up to few TeV by using inclusive jet events and it is a task of first runs;• Uncertainty on existing PDF could lead to 10% on the differential cross section around transverse energy 1 TeV (CMS Physics TDR,2006);• Uncertainty due to dependence on the renormalization and factorization scale is 5% (Stenzel, 2001); A 3% error of the jet energy scale leads to 20% error on the differential jet cross section at 1 TeV (CMS Physics TDR,2006);• A 30% error of the differential cross section leads to 12% relative error on the strong coupling constant (preliminary rough estimation);• For the first LHC runs it is not necessary to use NNLO calculation of inclusive jet cross section because the theoretical error are less then experimental one.
s
Conclusion
Many thanks for attention!
Any new ideas are welcome !
New participants in this business are welcome !