Measurement of the Hadronic Cross Section via Radiative Return at DA F NE

Achim Denig Radiative Return @ DANE MENU 2004

Measurement of the Hadronic Cross Section

via Radiative Returnat DANE

Achim Denig for the KLOE Collaboration

MENU 2004September 3rd

Beijing, IHEP

Universität KarlsruheInstitut für Experimentelle Kernphysik


hep-ex/0407048, sent to Phys. Lett. B

Outline:

Muon Anomaly Radiative Return at KLOE

Results & Outlook

Further KLOE-Results: St. Müller (Session B2)


...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, almost flat in s- above 2…5 GeV, use pQCD

Hadronic Cross Section

Input Dispersion Integral:

a) hadronic electron-positron cross section data, e.g. e+e + b) hadronic - decays (CVC-theorem, taking into account isospin breaking corrections), e.g. 0

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

a 11 659 000 ∙ 1010

TH

EO

RY

’20/

‘03

Exp

erim

ent

’20/

‘04 Experiment BNL-E821

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

Dispersion integral for hadronic contribution to aevaluated for:

a) e+ e-Data ONLY CMD-2 (VEPP-2M) measured channel with 0.6% precision < 1 GeV 2.7 – Deviation

b) -Data ONLY (if available) ALEPH /OPAL/CLEO 1.4 – Deviation

Theoretical values taken fromDavier, Eidelman, Höcker,

Zhang: hep-ex/0308213

a 11 659 000 ∙ 1010

e+e data and data differ for + channel in a specific energy window

above 0.6 GeV2 (above the -peak)!

Status u

p

to July ‘04


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

ISR

MC- Generator PHOKHARA = NLO

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

)(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 50° < < 130°

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

Photons at small angles < 15° and > 165°

are shadowed byquadrupoles near the I.P.

Drift ChamberEM Calorimeter

)pp(pp miss NO PHOTON TAGGING


Background

ee

signalregion

MTRK (MeV)

m

tail

1) Pion-Electron-Separation Rad. Bhabhas e+ee+eare separated by means of a Likelihood- Method (Signature of EmC-Clusters and TOF of particle tracks)

m

M GeV2 2( )m

0)( 2221

222

222

1 qppMpMpM trktrk

2) Kinematic Separation e+e

using „Trackmass“-variable

M – dependent MTRK-Cut

3) Residual BackgroundFit Trackmass-Spectra for signal and background with free normalization parameters (shape from MC)


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,

0.9%

0.3%

0.3%exp

0.5%theo

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

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

Vacuum Polarization Cross Section

Radiative Return requires ISR photon be inclusive for ISR-FSR-events e+ e ISRFSR

F=1

(

) m

it F

=1

s (GeV2)


Aim: Cross Section e+e-

TOTAL ERROR 1.3%

To be compared with 0.9%CMD-2 Error: exp.+syst.+stat.

2232

2

|)(|3

)(

MFM

ee

Cross Section (e+e-

• Result published now• Considerable improvement in near future


2 Contribution to ahadr

a= (388.7 0.8stat 3.5syst

3.5theo) 10-10

• Dispersions Integral for the 2-Pion-Channel in Energy Range 0.35 <M

2<0.95 GeV2

• Comparison with CMD-2 in the Energy Range 0.37 <M

2<0.93 GeV2

(375.6 0.8stat 4.9syst+theo) 10-10

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

KLOE

CMD2

2

2

GeV95.0

GeV35.0

3 )()ππ(π4/1 sKeedsa

• KLOE data points are not in excellent but in a fair agreement with CMD-2: KLOE higher at low s and lower at large s

1.3% Error0.9% Error

Pion Formfactor

CMD-2KLOE

0.4 0.5 0.6 0.7 0.8 0.9s [GeV]

45

40

35

30

25

20

15

10

5

45

0


Comparison with Data

At large values of s (>m) KLOE & CMD-2 deviate from -Data > 10%

unsufficient understanding of isospin breaking corrections in -Data ?!

Rel. difference of e+e-data with respect to -data (avg.)


Conclusions

M. Davier, A. Höcker @ ICHEP04 Including:

• New KLOE data• New 4th order QED contribution (Kinoshita) hep-ph/0402206• New Light-by-light contribution (Melnikov, Vainshtein) hep-ph/0312226

– data excluded!

Theory (SM) - Experiment a

exp - atheo = ( 25.2 ± 9.2 ) ·10-10

2.7 “standard deviations”

Including KLOE

• Status of the anomalous magnetic moment of the muon today (August ’04):

• KLOE has proven feasibility of the Radiative Return for high-precision hadronic cross section measurements:

New

hep-ex/0407048, sent to Phys. Lett. B


Outlook: KLOE• Measure () in the region close to threshold, M < 600 MeV, responsible for 20% of a

- This region excluded by angular selection in small angle photon approach

- Complementary analysis at large photon angles

• At large photon angles the amount of FSR is large! test model of scalar QED (i.e. poinlike pions) Measure Charge Asymmetry and compare data with MC

Charge asymmetry is due to different C-Parity of ISR- and FSR-amplitudes

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

))

)))

(θN(θN

(θN(θNA(θ

ππ

ππ


Outlook: Muon AnomalyTheory:

• BaBar fills gap between DANE, VEPP-2M ( < 1.4 GeV ) and BES ( > 2 GeV) and will measure all relevant exclusive channels (see e.g. hep-ex/0408078)

• KLOE/CMD-2 threshold region < 0.4 GeV2

• Future measurements at BES, VEPP-2000, CLEO, BELLE, DANE-2?

• “Real Theory“: Rad. corrections, Light-by-light-scattering, Isospin breaking ...

Experiment:

• New beam time for BNL-E821 (still limited by statistics)!?

• Ambitious new project for 5th generation (g-2)experiment at J-PARC

a(theor.) 3…4 · 10-10

a(exp.) < 2…3 · 10-10

Actual Difference: 25 ± 9 · 10-10 Fu

ture


Work supported by:

Emmy – Noether – Programm

Measurement of the Hadronic Cross Section via Radiative Return at DA F NE

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