Measurement of the Hadronic Cross Section at DA F NE with KLOE Achim G. Denig for the KLOE Collaboration 1. 4. 2004 La Thuile, Vallée d’Aoste XXXIX th.

Measurement of the Hadronic Cross Sectionat DANE with KLOE

Achim G. Denigfor the KLOE Collaboration

1. 4. 2004La Thuile, Vallée d’Aoste

XXXIXth Rencontres de Moriond - QCD

Achim G. Denig Radiative Return @ DANE Moriond -QCD 2004

Outline:

Motivation & Radiative Return Analysis hadr

Results & Outlook


...2/2/)2g(a

newweakhadQEDtheor aaaaa

Motivation: Determination of Hadronic Vacuum Polarization = High Precision Test of the Standard Model:

• Anomalous magnetic moment of the muon a = (g2)

• Running fine structure constant at Z0-mass QED (MZ)

Dirac-Theory: (g 2 ) = 0Quantum corrections: (g 2 ) 0 due to corrections of: - electromagnetic interaction - weak interaction - strong interaction (and maybe NEW PHYSICS ???)

Hadronic Vacuum Polarization

hadrons

+ +

B field

q

q

2nd largest contrib., cannot be calculated in pQCDError of hadronic contribution is dominating total error !

Muon - Anomaly


Hadronic contribution to a can be estimated by means of a dispersion integral:

- K(s) = analytic kernel-function- above sufficiently high energy value, typically 2…5 GeV, use pQCD

Hadronic Cross Section

Input:

a) hadronic electron-positron cross section data

b) hadronic - decays, which can be used with the help of the CVC-theorem and an isospin rotation (plus isospin breaking corrections)

2m4

2

2had

s

)s(K̂)s(Rds

3

ma

)*ee(

)hadronsqq*ee()s(R

tot

tot

H

1 / s2 makes lowenergy contributionsespecially important:

eein the range < 1 GeVcontributes to 70% !


Muon-Anomaly: Theory vs. Experiment

Comparison Experimental Value with Theory - Prediction

a 11 659 000 ∙ 1010

TH

EO

RY

’20/

‘03

e+ e - Data: 2.7 - Deviation

– Data: 1.4 - Deviation

Exp

erim

ent

’20/

‘04 Experiment BNL-E821

Values for +(2002) and -(2004)in agreement with each other.Precision: 0.5ppm

New cross section data have recently lowered theory error:

a) CMD-2 (Novosibirsk/VEPP-2M) channel with 0.6% precision < 1 GeVb) -Data from ALEPH /OPAL/CLEO

Theoretical values taken fromM. Davier, S. Eidelman, A. Höcker,

Z. Zhanghep-ex/0308213


Radiative Return• Standard method for cross section measurement is the energy scan, i.e. the systematic variation of the c.m.s.-energy of the accelerator

• DANE is a - factory and therefore designed for a fixed c.m.s.-energy: s = m = 1.019 MeV; a variation of the energy is not foreseen in near future

Complementary approach:Take events with Initial State Radiation (ISR)

Cross section as a function of the 2-Pion invariant mass s’=M

“Radiative Return” to -resonance: e+ e

d(e+ e )dM

MC- Generator PHOKHARA = NLO

J. Kühn, H. Czyż, G. RodrigoRadiator-Function H(s)

ISR

)(2

2 sdM

dM

H(s)

s’


L

1

1

M

NN

dM

d

..2

bkgobs

2

AcceptSelect

Background Signal

Selections-Efficiency

Luminosity

Acceptance

Analysis

• Final state e+e- relatively easy signature, however cross section measurement on percent level is a challenging task (normalization, efficiencies, background)

• KLOE Detector designed for CP – violation, we are having a high resolution tracking chamber ideal for the measurement of M!

Analysis-Items:


Selection

500< < 1300

< 150 > 1650

Pion tracks at large angles 50o < < 130o

• High statistics for ISR events• Reduced background contamination• Low relative contribution of FSR

Photons at small angles < 15o and > 165o

are shadowed byquadrupoles near the I.P.

Drift ChamberEM Calorimeter

)pp(pp miss NO PHOTON TAGGING


Background

ee

signalregion

MTRK (MeV)

m

tail

0)( 2221

222

222

1 qppMpMpM trktrk

• Rad. Bhabhas e+e-e+e- Pion-Electron-Separation by means of a Particle-ID algorithm using EmC-cluster- signature of tracks and TOF

• e+e-

Kinematic Separation: „Trackmass“

M – dependent MTRK-Cut

• Residual background after cutsFit MC-Spectrum for signal und background with free normalization parameters

m

M GeV2 2( )m


Luminosity

Polar Angle [°] Acoll. [°]Momentum [MeV]

Cut CutCut

55°<<125° p>400MeV Acoll.<9°

MCData

BhabhasBhabhas

Bhabhas

L = NBhabhas / effMC

Experimental precision: Theory precision (radiative corrections):• Large Angle Bhabha Events > 55º• Excellent agreement Data – MC• Background-”free” ( 0.5% )• Experimental uncertainty 0.3%

• BABAYAGA event generator (Pavia group)• systematic comparison among other generators (Berends, KKMC, VEPP-2M), max. =0.7%• Theoretical uncertainty 0.5% (BABAYAGA)


Analysis (e+e-

Background: - e+ e e+ e - e+ e -

Efficiencies:- Trigger & Cosmic veto- Tracking, Vertex- - e- separation- Reconstruction filter- Trackmass-cut- Unfolding resolution- Acceptance

Luminosity:Bhabhas at large angles > 55°, eff = 430 nb,

Statistics: 141pb-1 of 2001-Data 1.5 Million Events

1.0%

0.5%

0.3%exp

0.5%theo

Interference

High Statistics!

High Resolution!

M GeV2 2( )

Errors:


Extraction (e+e- )

Radiator-Function (ISR):- ISR-Process calculated at NLO-level Generator PHOKHARA (Kühn et.al)- Comparison with KKMC (Jadach et.al.) Precision: 0.5%

Radiative Corrections:i) Bare Cross Section divide by Vacuum Polarisation

ii) FSR - Corrections Cross section must be incl. for FSR

M GeV2 2( )

(e+e- )

Vacuum Polarization Cross Section


FSR Corrections

2 approaches for FSR corrections:

• Approach 1: “exclusive NLO-FSR“ - Correcting measured for FSR - Use MC with pure ISR in analysis - Add FSR-contrib. to (ca. 0.8%) by hand

• Approach 2: “inclusive NLO-FSR“ - Correct for „unshifting“, i.e. s‘ M

- Use MC with ISR + FSR in analysis

Both methods in excellent agreement!For the error on the model dependence ofFSR (scalar QED) we take 0.5%

line = approach 1+ = approach 2

M GeV2 2( )

ratio = approach 1 / approach 2

Pion Formfactor after FSR corrections

Suppressed by

Acceptance cutsTo be included !


Muon Anomaly

a= (389.2 0.8stat 4.7syst

3.7theo) 10-10

We have evaluated the dispersions integrals for the 2-Pion-Channel in the energy range 0.35 <M

2<0.95 GeV2

Comparison with CMD-2 in energy range 0.37 <M2<0.93 GeV2

(376.5 0.8stat 5.4syst+theo) 10-10

(378.6 2.7stat 2.3syst+theo) 10-10

KLOE*CMD2

* Error on model dependence FSR and VP not included!

Discrepancy of ca. 10% between e+e- - Data und – Data (ALEPH) for M

2 > 0.6 GeV2

KLOE – data confirms discrepancy with respect to – data !

Explanation: m( m( ???


|F|2

CMD2

— KLOE

0.5 0.7 0.90

20

40

10

30

0M GeV

2 2( )


Summary We have proven the feasibility to use the Radiative Return to perform a high-precision measurement of the hadronic cross section at the -factory DANE

Statistical Error is negligible

In the energy range M2 > 0.6 GeV2 we do reproduce

the large deviation seen by -data with respect to e+e-

Our evaluation of the hadronic contribution of the muon anomaly confirms the deviation btw. Theory and Experiment of about 3 sigma

A draft for a paper is under collaboration-wide review!and in this sense data has still to be considered as PRELIMINARY


Outlook Study events at large photon angles to access lower M

2 region Photon tagging will be possible in this case Use events for normalization advantages from experimental and theoretical point of view

Check FSR parametrization (scalar QED) by testing the Charge Asymmetry

))

)))

(θN(θN

(θN(θNA(θ

ππ

ππ

50 70 90 110 130

-20

-10

0

20

10

Asymmetry [%]

Polar Angle [°]

• Data• MC

K L O EP R E L I M I N A R Y


Work supported by:

Emmy – Noether – Programm

Measurement of the Hadronic Cross Section at DA F NE with KLOE Achim G. Denig for the KLOE Collaboration 1. 4. 2004 La Thuile, Vallée d’Aoste XXXIX th.

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