preparation for measurement of strong coupling constant on cms s.shulga lpp, jinr (dubna, russia)...

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

1

1,3

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


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


Introduction: Jets & pQCD

N.Glover, Challenges in pQCDDurham, Feb, 2002


Introduction: Jets & pQCD

So, pQCD ensures at conditions listed above :

Davison E. Soper, CTEQ School, June 2007

(renormalization)


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


Introduction: Renormalization Scale dependence and independence


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)


• 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


Introduction: Factorization scale


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


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



“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


The basic idea of factorization of collinear/soft (long-distance) physics

is quite similar to those of renormalization of short distance (ultra-violet) divergences.


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…


Introduction: experimental determination of s


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

http://www-library.desy.de/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Bethke%2C%20Siegfried%22

http://www-library.desy.de/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Bethke%2C%20Siegfried%22

http://pdg.lbl.gov/2006/html/authors_2006.html







http://www.iop.org/EJ/article/0954-3899/33/1/001/g_33_1_001.html













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.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%





















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


(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)


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%


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


M.O

kabe,

Ph.D

.Thesi

, 199

8

Method of measurement (II) CDF

Rel.err = 7,7%


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


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


It is the same method as:W.Giele, E. Glower,

hep-ph/9506441v1 July, 1995


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 - ?


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%)


LHC


CM

S P

hysi

cs T

DR

, V

.II,

20

06

20%

LHC


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


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.


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


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)


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


• 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 !

preparation for measurement of strong coupling constant on cms s.shulga lpp, jinr (dubna, russia)...

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