Fit to theDalitz plot of the final statewith 2001/2002 data

Fit to theDalitz plot of the final statewith 2001/2002 data

S. Giovannella, S.Miscetti

Blessing Meeting – 27 Apr 2006

Related documentation:

KLOE Memo 319 (November 2005) S.Giovannella, S.Miscetti, “Study of the e+e→ process using 2001/2002 data” KLOE Memo 326 (March 2006) S.Giovannella, S.Miscetti, “Fit to the Dalitz plot”

Composition of the final state

Two main contributions to final state @ M:

1. e+e vis() ~ 0.5 nb

S vis() ~ 0.3 nb

Backgrounds:Process S/B

a 8.51

0.06

0.06

0.21

e+e 0.002S= + S

Data and Montecarlo samples

2001+2002 data : Lint = 450 pb─1

Data have some spread aroud the peak + two dedicated off-peak runs @ 1017 and 1022 MeV : All data set divided in 100 keV bins of s

RAD04 MC production: 5 Lint

GG04 MC production: 1 Lint

Improved e+e 0 generator Three body phase space according to VDM from NPB 569 (2000), 158

1(2)

2(1)

Ve+

e─

DATADATA

MC MC

e+e→→events: dataMC comparison

Old exclusive analysis applied on the 2001/2002 data

Old ee 0 MC

Data quality

Runs with the following characteristics removed: Missing beam parameters Not standard EMC trigger thresholds Unexpected event counting for →→ events

→→ Biggest rate in DRN Background free Very simple selection criteria ♦ 7 neutral clusters with 23<<157° ♦ At least 1 photon with E>280 MeV

Number of events normalized using VLAB luminosity and → visible xsec

Central value in good agreement with the expected value: ana×BR(→) = 0.41×0.325 = 0.13

Total: 1.3 pbTotal: 1.3 pb

Sample preselection and kinematic fit

1. Acceptance cut:

5 neutral clusters in TW with E > 7 MeV and |cos|<0.92

[ TW: |Tcl-Rcl/c| < MIN( 5T, 2 ns ) ]

2. Kinematic fit requiring 4-momentum conservation and the

“promptness” of ’s ( TclRcl/c = 0 )

3. Pairing: best ’s comb. for the hypothesis

4. Kinematic fit for both ’s pairing, requiring also constraints on

masses of the assigned pairs

Photon pairing

- - - EMC resolution — FIT1 resolution

Efit (MeV)

0 mass resolution parametrized as a function of the photon energy resolution after kinematic fit:

Fit function for energy resolution:

The photon combination that minimizes the following 2 is chosen:

21

21

2

1

EEMEEM

3.1000/21

PE

E

EPP

E

2

2

2

2

2 00

kl

lk

ij

ji

MM

MMMM

Photon pairing: dataMC comparison

Pairing 2

First kinematic fit

Distributions after all analysis cuts

1. e+e→ rejection using the two most energetic clusters of the event: E1+E2 > 900 MeV

2. accidentals background rejection: EFit2 > 7 MeV

3. Cut on 2nd kinematic fit: 2Fit2/ndf < 5

4. Cut on masses of the assigned pairs: |MM| < 5 M

Analysis cuts

Process ana S/B

e+e (53.120.05) % ─

S (50.30.1) % ─

a (23.20.1) % 18.9

(8.510.02) × 3.9

0.05)× 32.3

0.06)× 346.1

e+e 0.01)× 407.5

S= + S

ana(S) obtained using the 2000 data M shape

e+e rejection using the two most energetic clusters of the event:E1+E2 > 900 MeV

Cut 1: e+e rejection

DataData MC eventsMC events

Cut 3: 2Fit2 after sample selection

Analysis @ √s = 1019.75 MeV (Lint = 145 pb1)

Analysis efficiency and 2Fit2 cut

SS

This is related to the fact that our kinematic fit constrains the total energy of the event to the beam energy with an error of 300 keV

A 2/Ndof<5 cut reduces this effect while keeping the background to an acceptable level

S: efficiency almost flat, with a small constant drop when hardening the cut:efficiency not flat, with an increasing drop in the region M~750 MeV

ISR: →S vs e+e→

Very different ISR behaviour: The resonant S process has large (25%) radiative corrections with a ISR energy spectrum constrained by to be lower than 10 MeV The not-resonant behaviour makes instead small the overall radiative correction while the ISR energy spectrum shows large tails

SS

SS

─ GEANFI─ DAPHNE Handbook

Pairing efficiency

Pairing efficiency evaluted for events where all ’s are correctly matched

Overall efficiency: pair~ 85%

The non-flat behaviour is due to a similar energy distribution of the two pions in some particular MM region

The difference between S and processes is mainly due to their different ISR tails

Pairing efficiency: standard ISR vs EISR<10 MeV

All ISR tailsAll ISR tails

EISR < 10 MeVEISR < 10 MeV

Data-MC comparison after all analysis cuts

Analysis @ √s = 1019.75 MeV (Lint = 145 pb1)

Data-MC comparison after all analysis cuts

Analysis @ √s = 1019.75 MeV (Lint = 145 pb1)

Good agreement on M:reliable VMD descriptionin our simulation

Discrepancies on M:not precise description of the MC scalar mass spectrum orpossible interference between the two final states

Effect of Trigger, FILFO and ECL

1. Trigger and Cosmic Veto efficiency Calorimeter trigger fully efficient on the signal. Cosmic Veto losses evaluated with prescaled events: CV = (99.54 ± 0.08)%

2. MC evaluation of FILFO and ECL losses FLF = (99.95 ± 0.01)% ECL = (96.5 ± 0.1)%

3. DATA evaluation of FILFO and ECL losses The minimum bias sample streamed by C.DiDonato was used to evaluate with data FLF and ECL Only data with √s =1019.6 used.

FLF = (99.90 ± 0.05)% ECL = (99.2 ± 0.1)% !!! The large difference on ECL mainly due to the a wrong parametrization of time resolution in neurad code!

Total overall correction factor applied to (MC): Rpresel = 1.022 ± 0.004

Systematics on background evaluation (I)

(most relevant bckg contribution)

Background enriched

sample :

4 < 2/ndf < 20

In order to study the systematics connected to the background subtractionwe found for each category a distribution “background dominated” to be fitted with

two MC components: Hdata = 1 Hbckg + 2 Hothers

1(7) = 1.064 ±0.002

1(3) = 0.86 ± 0.02

1() = 2.35 ± 0.02

1() = 0.86 ± 0.02

For e+e , we fit the distribution for 2/ndf < 5 (and no rejection cut )

1() = 1.85 ± 0.03

For , , a0 we calculate a 2 in the mass hypothesis

Systematics on background evaluation (II)

Fit results are used to evaluate the systematic error on the background counting, defined as B = ( 1 1 )/2

Summary of relative systematic uncertainties on background estimate compared with the errors on the applied BRs (PDG+KLOE) and the S/B ratio after 2 cut:

Process BR/BR B/B S/B

e+e → ─ 1.6% 407.5

→→ 3.0% 3.2% 3.9

→→ 3.5% 7.0% 32.3

→ 10.0% 68.0% 346.1

→ 9.5% 7.5% 18.9

Systematics on background evaluation (III)

Systematics on cluster counting: signal

The counting of 5 photons in TW with Ecut and cut can be affected by:

1. MC energy scale 1.4% miscalibration in RAD04

2. MC cluster efficiency (old curves applied to RAD04 production) a. change of the opening cone when evaluating the MC correction b. new curves without residual Bhabha contamination

3. Angular acceptance NEGLIGIBLE

For each bin of the Dalitz plot thevariation of the efficiency (newold)/old (red) is compared

with the statistical error (black)

1.

2.a

2.b

Systematics on cluster counting: background

The change in the MC cluster efficiency also affects the quantity of residual background, especially for →→

The relative syst.error (red), defined as the difference of the background estimated with the two efficiency curves , is compared with the error in the Dalitz plot after background subtraction (blue)

Systematics on photon pairing: rate

To assign a systematics to the pairing procedure we studied thedifference between 2

SEL for the best and second best choise of

photons: 2SEL = 2

SEL (Best)- 2SEL (SecondBest)

We then fit the 2SEL

distribution in data with a linear combination of MC spectra for the right and wrong choise of paired photons (by MC truth)

Rpair = 1.08 ± 0.02Rpair = 1.08 ± 0.02

All events

M>700 MeV

M>700 MeV

Systematics on photon pairing: off-diagonal check

In the old exclusive analysis the regionwith M>700 MeV is dominated by events with wrong photon pairing

Good data-MC agreement

The 1.08 scale factor applied to events show a better data-MC agreement!!!!

VMD description reliable only at the peak

Only the √s bin with higher statistics around M considered

Fit to the Dalitz plot with the VDM and scalar term, including also interference

Two model considered: Kaon Loop (KL) and “No Structure” (NS)

Binning choice driven by the M, M mass resolutions after the second kinematic fit:

10.0 MeV in M

12.5 MeV in M

Dalitz plot @ √s=1019.75 MeV

Fit method

Dalitz plot density after background subtraction fitted using the expected number of events in the ith bin, Ni, built as the sum of contributions from all theoretical bins:

j

Vj

VIj

Sj

SSj

Vj

VVji jiAfjiAfjiAfLN ),(),(),(

V = VMD S = scalar I = interference

fj : integration of the differential cross section in the jth bin ;

correction for the radiator function applied

A(i,j) : smearing matrix

j : analysis efficiency

Fit function: the Achasov parametrization (I)

Scalar produced through a kaon loop [N.N.Achasov and V.N.Ivanchenko, Nucl. Phys. B 315 (1989) 465] one scalar [N.N.Achasov and V.V.Gubin, Phys. Rev. D 56 (1997) 4084] two scalars

f0/a0

Charged kaon loop final state

g(KK) from (K+K–) g(f0KK) g(a0KK) g(f0) g(a0)

} fit output

VDM contribution from the following diagrams :

1(2)

2(1)

e+

e─

1(2)

2(1)

e+

e─

All interferences considered

Fit function: the Achasov parametrization (II)

S

f0VP interf

[N.N.Achasov, A.V.Kiselev, private communication]

Model dependent

term

Improved Kaon Loop parametrization

Insertion of a KK phase:

Beyond to its contribution in the interference term, IT CHANGES THE SCALAR TERM AMPLITUDE IN THE M<2MK

+ REGION

New parametrization of the phase:

[N.N.Achasov, A.V.Kiselev, PRD73 (2006) 054029]

M (GeV)

00

Improved KL parametrization on OLD KLOE data

Combined fit to KLOE 2000 + scattering data

dBR/dM (KLOE 2000 data)dBR/dM (KLOE 2000 data)

dBR

/dM

×

108 (

MeV

)

M (MeV)M (GeV)

00

Theory advantages of the improved KL parametrization

Able to reproduce mass spectrum, 00 and inelasticity

Sum of overlapping resonances with the correct propagator matrix

A lot of theory restrictions applied:

- The scattering length a00 fixed to the recent

calculation of Colangelo - In the scattering amplitude the Adler zero in T() is granted in the region below the threshold (0 < m2

< 4M2)

Besides f0(980), a (600) meson is needed to obtain a good fit

Improved KL parametrization: the 10 “variants”

We cannot leave all f0(980) and (600) parameters free:

elastic background and the (600) parameters are closely related

We have used as free parameters some VMD parameters and the

f0(980) mass and couplings

The (600) and the parameters of and KK scattering are taken

from Achasov’s paper, where ten sets of different parameters are

reported, defined as K1…K10

KL fit results: the scalar term

We consider acceptable just the six variants with P(2)>1% We use the best fit results, adding the maximal variation with all the other accepted variants as the error associated to the theory When leaving the (600) mass free, the scattering phase does not reproduce data

Fit Mf0 (MeV) gfK+

K (GeV) gf+(GeV) 2/ndf P(2)

K1 976.8 ± 0.3 3.76 ± 0.04 2754/2676 0.145

K2 986.2 ± 0.3 3.87 ± 0.08 2792/2676 0.058

K3 ± 0.2 ± 0.06 2809/2676 0.036

K4 987.3 0.1 3.84 ± 0.11 2855/2676 0.008

987.0 0.2 2.61 ± 0.05 2970/2676 5 × 10

K6 983.5 0.4 2.52 ± 0.04 2981/2676 3 × 10

K7 981.6 0.2 4.53 0.05 2852/2676 0.009

982.3 0.4 4.02 ± 0.06 2787/2676 0.066

K9 983.3 ± 0.2 3.75 0.02 2823/2676 0.024

K10 986.9 ± 0.1 3.28 ± 0.05 2799/2676 0.048

KL fit results: the VMD term

Pretty stable results on the VMD side ≈ 0.6

C and unstable but determined with large errors

M = ( 782.5 0.3fit 0.4mod ) MeV

Fit C (GeV) C (GeV) b (deg) M (MeV)

K1 0.58 ± 0.11 0.850 ± 0.010

0.260 0.185

33.0

9.7782.52 0.29

K2 0.68 ± 0.03 0.832 ± 0.003

0.061 ± 0.211

K3 ± 0.17 ± 0.004

± 0.056

K40.72

0.04 0.826 ± 0.003

0.062 ± 0.003

0.71

0.050.814 ± 0.003

0.231 ± 0.054

K60.81

0.030.813 ± 0.003

0.060 ± 0.006

K70.74

0.060.825 0.002

0.065 0.006

0.64

0.050.836 ± 0.002

0.061 ± 0.005

K9 0.62 ± 0.01 0.838 0.006

0.298 0.126

K10 0.58 ± 0.04 0.843 ± 0.004

0.061 ± 0.003

Kaon Loop fit, variant K1: Dalitz plot slices

Data─ Fit result

Kaon Loop fit, variant K1: residuals

Kaon Loop fit, variant K1: VMD/S compositions

Scalar term

f0

Fit function: the No Structure model

Point-like S coupling

Scalar propagator described by a simple BW shape corrected by the Flatte’ condition on the and KK thresholds

Not resonant continuum background added as a expansion in M

SV

gVS

gSpp

Pe+

e-

[G.Isidori, L.Maiani, M.Nicolaci, S.Pacetti, hep-ph/0603241]

224

12

022

10

SM

Mvib

M

Mvib

SS

SSscal MMeM

ae

M

a

MiMMM

ggA

No Structure fit results

Parameter Value

1.43 ± 0.04

C (GeV) 0.953 ± 0.003

± 0.01

C (GeV) 0.270 0.039

3.11 0.14

b (deg) 73.1 1.6

M (MeV) 781.80 0.11

VMD termScalar term

Parameter Value

Mf0 (MeV) 984.7 ± 0.4

gf0(GeV) 0.40 ± 0.04

gf0(GeV) ± 0.01

Gf0(GeV) 2.61 0.02

a 4.19 0.01

a1 1.31 0.01

b1 (rad) 1.50 0.02

2/Ndof 2799/2672

P(2) 0.042

No Structure fit: Dalitz plot slices

Data─ Fit result

No Structure fit: residuals

No Structure fit: VMD/S compositions and phase

)Re(

)Im(arctan scal

scal

S A

A

Unexpected shape observed in S @ M ≈ 600 MeV

No Structure vs Kaon Loop: VMD/S comparison

─ Kaon Loop─ No Structure─ 2000 data

Fit systematics

Fit repeated by varying quantities related to the syst. described before:

1. Absolute normalization scale: Lint and ee varied by 1

2. Beam energy scale: 150 keV shift applied on √s

3. Cluster efficiency curve: new parametrization used to evaluate analysis efficiency, smearing matrix and background contribution

2Fit2 cut: tighter cut applied 2/Ndof <3

5. Smearing matrix: fraction of off-diagonal elements increased by 8%

6. Folding of interference term: S radiative correction, analysis efficiency and smearing matrix used for the interference term

7. Background scale factors applied to the background

Fit systematics: summary for Kaon Loop model

Syst. source Mf0 (MeV) gfK+

K (GeV) gf+(GeV)

Fit result 976.8 ± 0.3 3.76 ± 0.04 Lint +1 976.8 ± 0.3 3.74 ± 0.03 Lint ± 0.4 ± 0.05 ee +1 976.8 0.6 3.70 ± 0.06 ee 976.8 0.4 3.82 ± 0.04 √s scale shift 976.9 0.7 3.85 ± 0.07 Cluster eff. 976.5 0.3 3.68 0.03 cut 976.5 0.4 3.73 ± 0.04 Smearing matrix 976.2 ± 0.7 3.76 0.07 Interference 976.5 ± 0.7 3.72 ± 0.07 Background 977.7 0.7 3.91 0.07 0.01

Max. variation 0.6 / +0.9 0.08 / +0.15

Fit systematics: summary for No Structure model

Syst. source Mf0 (MeV) gfK+

K (GeV) gf+(GeV) gfGeV

Fit result 984.7 ± 0.4 0.40 ± 0.04 Lint +1 985.6 ± 0.3 1.02 ± 0.04 Lint ± 0.3 ± 0.07 ee +1 985.0 1.0 0.76 ± 0.15 ee 983.9 0.4 0.20 ± 0.07 √s scale shift 983.0 0.2 0.73 ± 0.03 Cluster eff. 987.1 0.3 0.11 0.02 cut 982.3 1.0 0.63 ± 0.12 Smearing matrix 982.3 ± 0.8 0.37 0.13 Interference 985.1 ± 1.3 0.73 ± 0.16 Background 981.0 0.7 0.77 0.09 0.01 Max. variation 3.7/+2.4 0.29/+0.62

Final results

BR obtained by taking into account both KL and NS results:

405.006.0

04.002.0

01.003.0

00 10(mod)(syst)(fit)07.1)(

SBR

Mf0 = ( 976.8 0.3fit syst + 10.1mod ) MeV

gf0K+K= ( 3.76 0.04fit +syst mod ) GeV

gf0= ( 1.43 0.01fit +0.010.06syst +0.03/0.60mod ) GeV

Rf0 = 6.9 0.1fit +0.2/0.1syst +0.3/3.9mod

gf0fitsystmodGeV

KL

Mf0 = ( 984.7 0.4fit syst ) MeV

gf0K+K= ( 0.40 0.04fit +syst ) GeV

gf0= ( 1.31 0.01fit +0.090.03syst ) GeV

Rf0 = 0.09 0.02fit +0.44/0.08syst

gf0fitsystGeV

NSFit resultsDerived

Conclusions

A lot of checks done on the experimental side

KL fit results: Comprehensive description of →S and scattering data f0(980) and (600) needed to describe data

f0(980) strongly coupled to K+K

NS fit results: Only f0(980) [+continuum background!] needed to describe data

f0(980) weakly coupled to K+K

scattering phase not well reproduced

Next step will be writing the paper

Comparison with results: Reasonable agreement for KL Contradictory results for NS for gf0 and gf0KK

Combined fit to and mass spectra needed for a final answer

Spare slides

The MC distribution of VDM events with an ISR photon >10 MeV is concentrated on the low-M tails of the omega peaks

ISR for events e+e→ in GEANFI ISR from DANE Handbook applied to our standalone VDM generator

Threshold cutoff at 4M2

Correct √s dependence on the x-sec

with a threshold behaviour around M+M

─ GEANFI─ DANE Handbook

The Handbook ISR tail applied to GEANFI with an HIT-OR-MISS procedure

Analysis efficiency and 2Fit2 cut for events

ISR as in GEANFIISR as in GEANFI ISR from DANE HandbookISR from DANE Handbook

The is introduced in the scalar term as in ref. PRD 56 (1997) 4084.• The two resonances are not described by the sum of two BW but wth the matrix of the inverse propagators GR1R2.• Non diagonal terms on GR1R2 are the transitions caused by the resonance mixing due to the final state interaction which occured in the same decay channels R1 → ab → R2

CR1R2= Cf0 takes into account the contributions of VV, 4 pseudoscalar mesons and other intermediate states. In the 4q, 2q models these are free parameters

The kaon loop parametrization with the meson

21

1)(

0

00

RkkRg

RRg

MD

gg Gf

fKKf

Where

GR1R2 = Df0 -f

-f0 DR1R2 = ab gR2ab PR1

ab (m) + CR1R2