The Hadronic Cross Section Measurement at KLOE

Marco Incagli - INFN Pisa

on behalf of the KLOE collaboration

EPS (July 17th-23rd 2003) in Aachen, Germany

Still measuring hadronic cross section: why?

The hadronic cross section is a fundamental tool to evaluate the hadronic contributions to a and to (MZ)

These quantities are not evaluable in pQCD, but one can use DATA by means of optical theorem + analyticity:

For example a can be evaluated with the dispersion

integral:

Im[ ] | hadrons |2

ahad =

K(s) ~ 1/s (kernel function)

243

, )()(4

1

m hadree

lohad dssKsa

The factors 1/s and (ee hadr) in the

integrand of the dispersion relation make the

low energy

region and the large resonances

particularly relevant

The ee channel accounts for ~70% of the

contribution both to ahad and to (a

had)

Contributions, as of today, to the error (a

had)

(s<0.5GeV)

(except )

( region)

rest (<1.8GeV)

rest (1.8-5 GeV)

pQCD (>5GeV)

(a(ahadhad))

(from Davier, Eidelman, Hoecker, Zhang)

The role of the

aHAD can also be evaluated

starting from data and using the

(approximate) isospin invariance

The recent very precise

BNL determination of a

and some discrepancies

between the value of aHAD

as evaluatated with ee energy scan and data, make a new measurement relevant

ee

(had) through the radiative return at KLOE

A way to get the hadronic cross section (e+e) vs Q2 at a fixed energy machine: the Radiative Return the Radiative Return

(Binner, Kuehn, Melnikov, Phys.Lett. B 459 (1999) (Binner, Kuehn, Melnikov, Phys.Lett. B 459 (1999) 279)279)

EE

QQ22

Radiation functionH(Q2,) M

s

QsE

s ;

2

2

),,()()( 22

22

MQHee

dQ

eedQ

Radiative ReturN: PROs and CONs

luminosity and energy scale is estabilished at s=M and

applies to all values of M2=Q2

do not need to run the collider at different energies

requires precise understanding of radiative processes

MC used by KLOE : PHOKHARA ver.2.0 (on Tuesday 10, Jul 2003 we have received ver.3.0 which includes FSR!)

DANE e+e- machine at Frascati (Rome)

• e+e s ~ m = 1019.4 MeV

• beams cross at an angle of 12.5 mrad • LAB momentum p ~ 13 MeV/c

BR’s for selected decays

K+K- 49.1%

KSKL 34.1%

+ 15.5%

ee+

KLOE detectorKLOE detector

Cross sections:

3.3 b

eeb

eebeob

b

KLOE detector and Fiducial Volume

Definition of fiducial volume:

50o<<130o

<15o or >165o

where is the two-pion system

This cut enhances the signal wrt ee events in which the photon is radiated from the pion (final state radiation: FSR)

6 m

7 m

The price is that the kinematic region below Q2=0.3GeV2 cannot be probed by these small photon angle events

Getting the cross section

L=140.7pb-1 of data collected in

2001

1.5106 evts ~11000 evts/pb-1

0.35<Q2<0.97 GeV2 (592-985

MeV)

Bin width = 0.01 GeV2 (~7 MeV)

To get the cross section must

evaluate:

background ; efficiencies ;

luminosity

d

dM 2

Nobs N bkg

M2

1

Select.

1

L

Background

Selection efficiency Luminosity

events

M2 (GeV2)

num

ber

of

even

ts (

x10

3)

Background rejection I - e/ separation

e/ separation using a likelihood method:

• electron and pion likelihood definition based on TOF and cluster shape

• the log of the ratio of the two likelihoods is the discriminating variable

eff() ~ 98%

eff(e) ~ 3%log(Lpion/Lelectron)

signal + bkgd events• events• e+e events

Kinematic separation between

signal and background in the

(M2,MTRK) plane where MTRK is

defined as:

(p-p-p)2=p2=0

with: p=( p2+MTRK

2,p)

this cut effects multiphoton

processes (ee)

efficiency evaluated using MC

Background rejection II - closing the kinematics

ee

signalregion

M (GeV2)

MTRK (MeV)

tail

Efficiency of kinematic separation and FSR

The efficiency of the (M2,MTRK) cut

has been evaluated by MCThis efficiency evaluation does not include events with a FSR photon M

TR

K e

ffic

ienc

y

M2(GeV2)

A preliminary run with the new PHOKHARA shows that the FSR contribution is at most 2-3%

As of now, we do not apply any correction for FSR and add a contribution of 2% to the systematic error

M2(GeV2)

1 - )(

)&

(2

2dQISR

ddQ

FSR

ISR

d

• without TrackMass cut• with TrackMass cut

A.Denig, H.Czyz

peak

Luminosity with Large Angle Bhabhas

Luminosity measured with Large Angle Bhabhas: 55o<e<135o

2 independent generators used for radiative corrections: BABAYAGA (Pavia group): eff = (428.80.3stat) nb

BHAGENF (Berends modified): eff = (428.50.3stat) nb

Systematics from generator claimed to be 0.5%

Experimental systematic error determined by comparing data and MC angular and momentum distributions

Systematics on Luminosity

Theory 0.5 %

Acceptance 0.3 %

Background () 0.1 %

Trigger+Track+Clustering 0.2 %

Knowledge of s run-by-run 0.1 %

TOTAL 0.5 % theory 0.4% exp = 0.6 %

Summary of systematics

Experimental Acceptance 0.3% Trigger 0.2% Tracking 0.3% Vertex 1.0% Likelihood 0.1% Track Mass 0.2% BKG subtr. 0.5% Unfolding 0.6%

TOTAL 1.4% (1%)

Theory Luminosity 0.6% Vacum Pol. 0.1%

TOTAL 0.7%

FSR (NNLO processes)2.0%

(<1%)

Systematic error can be reduced to • in a short time scale

Observed cross section

Absolute ee cross section after bkg subtraction

To get (ee) we need the H(Q2) function

eeISR(

Radiation function H(Q2)H(Q2) is obtained from

PHOKHARA MC setting F(Q2)=1

and swithcing off vacuum polarization

(ee) ~

d/d

Q2 (

nb/G

eV2 )

M2 (GeV2)

e

e

F(Q2)

e

e

V.P.

1

1.02

1.04

1.06

1.08

0.2 0.4 0.6 0.8 1.0

Hadronic cross section

Hadronic cross section after dividing by the function H(Q2)The cross section to be inserted in the dispersion integral is the bare cross section

ee

d/d

Q2 (

nb/G

eV2 )

M2 (GeV2)

M2 (GeV2)

Must correct for running of

)()()()(1

)()( 20

2

02 ssss

ss barehadlep

(s)

(co

rrec

tion

tos had(s) from F. Jegerlehner

Preliminary value for ahad

In order to see how our result compares with existing data, we have integrated the bare cross section in the same region covered by CMD2 (0.37<Q2<0.95):

ahad(0.37:0.95) = 374.1 1.1stat 5.2syst 2.6theo (+ 7.5

0.

FSR)

The published CMD-2 result is :

ahad(0.37:0.95) = 368.1 2.6stat 2.2syst+theo

The two numbers are compatible, given the systematic error, but FSR corrections must be included before performing a detailed point to point comparison

Comparison e+e vs data

Q2 KLOEahad CMD2* a

had

0.37:0.6 256.2 4.1 (+5.1-0FSR) 249.7 2.2

0.6:0.95 117.9 2.1 (+2.3-0FSR) 119.8 1.1

10-15% relative difference

The difference with CMD2 value is mostly below the peak

It is very difficult, with our data, to explain the discrepancy between e+e and data in the region above the resonance

* our evaluation based on CMD2 published table

Q2 (GeV2) peak

Summary and outlook

KLOE has shown the feasibility of using initial state radiation to obtain the hadronic cross section at low energies

Measurement using small angle photon events is almost

finalized we have a new MC for a more precise evaluation of FSR

Preliminary result on ahad slightly higher, but compatible with,

CMD2 value

Next steps: Finalize current analysis

Study events at large photon angles which

allow us to cover the region (2m)2<M2<0.35 GeV2

Use events as normalization sample to reduce the systematic error