F.Ambrosino Università e Sezione INFN, Napoli for the KLOE collaboration

F. Ambrosino Euridice Midterm Meeting LNF 11/02/05

1

F.AmbrosinoF.AmbrosinoUniversità e Sezione INFN, NapoliUniversità e Sezione INFN, Napoli

for the KLOE collaborationfor the KLOE collaboration

Study of Dalitz plot at KLOE

•Motivations•

•

•Conclusions and outlook


2

The decay occours primarily on account of the d-uquark mass differences and the result arising from lowest order chiral pertubation theory is well known:

222

2

2

2 33),,()(1),,(

FutsMmm

mm

QutsA K

K

With: 22

222 ˆ

ud

s

mmmm

Q

A good understanding of M(s,t,u) can in principle lead to a very accurate determination of Q:

42)3( QA

in chiral theory

22

243),,(

mmmsutsM

And, at l.o.


3

Still there are some intriguing questions for this decay :

•Why is it experimental width so large (270 eV) w.r.t theoretical calculation ? (Tree level: 66 eV (!!!); 1 loop : 160 eV ) Possible answers:

•Final state interaction•Scalar intermediate states •Violation of Dashen theorem

•Is the dynamics of the decay correctly described by theoretical calculations ?

…and its open questions


4

The usual expansion of square modulus of the decay amplitude about the center of the Dalitz plot is:

|A(s,t,u)|2 = 1 + aY + bY2 + cX + dX2 + eXY

Where: tu

QM

23

QTT3X -

12

313 200 smm

QmQTY

02 mmmQ

Dalitz plot expansion


5

Tabella sperimentale di Bijnens

Calculation a b dTreeOne-loop[1]Dispersive[2]Tree dispersiveAbsolute dispersive

-1.00 0.25 0.00-1.33 0.42 0.08-1.16 0.26 0.10-1.10 0.31 0.001-1.21 0.33 0.04

Measurement N a b dLayterGormley Crystal BarrelCrystal Barrel

808843000010773230

-1.08 0.14 0.034 0.027 0.046 0.031-1.17 0.02 0.21 0.03 0.06 0.04 -0.94 0.15 0.11 0.27-1.22 0.07 0.22 0.11 0.06 fixed

[1] Gasser,J. and Leutwyler, H., Nucl. Phys. B 250, 539 (1985) [2] Kambor, J., Wiesendanger, C. and Wyler, D., Nucl. Phys. B 465, 215 (1996)

Dalitz expansion: theory vs experiment


6

At KLOE is produced in the process .The final state for is thus , and the final state for is 7, both with almost no physical background.

at KLOE

Selection:• 2 track vertex+3 candidates• Kinematic fit


7

Resolutions and efficiency“core” X =

0.018

“core” Y =

0.027

Efficiency almost flat, and 36%


8

Comparison Data-MC:


9

Comparison Data-MC:


10

SignalB/S 0.8%


11

The analysis has been applied on 450 pb–1 corresponding to:

N(+-0) = 1,425,131

events in the Dalitz plot, fitted with function:

• fit is stable…• …but the model seems not to fit adeguately data (BAD P

2).We have added the cubic terms:

|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3+gX3+hX2Y+lXY2

|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY

Fitting function


12

Fit stability


13

ndf P2

%

a b c d e f

147 60 -1.072 0.006-0.007 +0.005

0.117 0.006-0.006 +0.004

0.0001 0.0029-0.0021 +0.0003

0.047 0.006-0.005 +0.004

-0.006 0.008

-0. +0.013

0.13 0.01-0.01 +0.02

150 63 -1.072 0.005-0.008 +0.005

0.117 0.006-0.006 +0.004 ---

0.047 0.006-0.005 +0.004

0.13 0.01-0.01 +0.02

150 0.02 -1.055 0.004-0.007 +0.006

0.100 0.005-0.002 +0.004

--- --- ---0.12 0.01

-0.02 +0.02

150 0 -1.013 0.003-0.007 +0.004

0.120 0.005-0.023 +0. ---

0.043 0.006-0.003 +0.004

--- ---

Results

150 63 -1.072 0.005-0.008 +0.005

0.117 0.006-0.006 +0.004 ---

0.047 0.006-0.005 +0.004

0.13 0.01-0.01 +0.02

|A(X,Y)|2 = 1+aY+bY2+cX+dX2+eXY+fY3


14

Results (II)

|A(X,Y)|2 = 1-1.072 Y+0.117 Y2+0.047 X2+0.13Y3

Using preliminary KLOE results shown at ICHEP 04 B.V. Martemyanov and V.S. Sopov (hep-ph\0502023) have extracted:

Q = 22.8 ± 0.4 against Qdashen= 24.2 (as already argued for example in J. Bijnens and J. Prades, Nucl. Phys. B490, 239 (1997)


15

The dynamics of the decay can be studied analysing the Dalitz plot distribution. The Dalitz plot density ( |A|2 ) is specified by a single parameter:

|A|2 1 + 2zwith:

2max

22

3

1

)3

3(

32

0

i

i

mmmE

z

Ei = Energy of the i-th pion in the rest frame. = Distance to the center of Dalitz plot.max = Maximun value of .

Z [ 0 , 1 ]

Dalitz plot expansion


16

Alde (1984) -0.022 0.023Crystal Barrel (1998) -0.052 0.020Crystal Ball (2001) -0.031 0.004

Dalitz expansion: theory vs experiment

Calculation TreeOne-loop[1]Dispersive[2]Tree dispersiveAbsolute dispersive

0.000.0015-0.007 - -0.014-0.006-0.007

[1] Gasser,J. and Leutwyler, H., Nucl. Phys. B 250, 539 (1985) [2] Kambor, J., Wiesendanger, C. and Wyler, D., Nucl. Phys. B 465, 215 (1996)


17

Recoil is the most energetic cluster.In order to match every couple of photon to the right 0 we build a 2-like variable for each of the 15 combinations:

23

1

2

0

00

ij

m

j

j

Mmi

With:j

oi

m is the invariant mass of i

0 for j-th combination0

M = 134.98 MeVj

m 0 is obtained as function of photon energies

Photons pairing


18

Cutting on: Minimum 2 value 2 between “best” and “second” combination

One can obtain samples with different purity-efficiencyPurity= Fraction of events with all photons correctly matched to ‘s

Combination selection

Pur 85 % Eff 22 %

Pur 92 % Eff

14 %

Pur 98 % Eff 4.5 %


19

The problem of resolution

Phase spaceMC reconstructed

Resolution Efficiency


20

Results on MC


21

Results on MC


22

Results on MC


23The agreement is good on all spectra

Comparison Data - MC


24

= -0.0ZZ 0.004̂

Low purity Medium purity High purity

= -0.0XX 0.002 ̂ = -0.0YY 0.002̂

Fitting Data

Systematics are at the same level of the statistical error


25

Conclusions

• KLOE is analyzing an unprecedented statistics of decays with negligible background

• For channel the analysis is almost completed and finds evidence for an unexpected large y3 term

• 3 analysis is much harder, we expect to provide soon a result at the same level of the Crystal Ball one.


26

SPARE SLIDES


27

Kinematic fit with no mass constrains


28

Tests of the fit procedure on MC

Generator slopes in MC rad-04:

a = -1.04b = 0.14c = 0.d = 0.06e = 0.

KLOE measure (100 pb-1)


29

Comparison Data-MC

data MC

A.U

.


30

Comparison Data-MC: Ych – Y0

Shift 1.33 MeV

Shift 0.03 MeV

NA48: 547.843 0.030st 0.041sys

Physica Scripta T99 140-142, 2002


31

• i is for each bin: the efficiency as a function of Dalitz-plot.• Ni is for each bin: the number of events of Dalitz-plot.• i is the statistical error on the ratio Ni / i •All the bins are included in the fit apart from the bins crossed by the Dalitz plot contour.

The fit is done using a binned 2 approach

21

22

2

)),((

i

Nbin

i bini

i dXdYYXAN

Fit procedure


32

Comparison Data-MC: X & Y


33

Comparison between efficiency corrected data and fitted function as function of the bin number.The structure observed is due to the Y distribution for X slices

P(2 02) 60%

Goodness of fit


34

A = (-0.009 0.093) 10-

2

NNNNA

4321

4231

NNNNNNNNAq

Aq = (-0.02 0.09) 10-2

654321

642531

NNNNNNNNNNNNAs

As = (0.07 0.09) 10-2

Asymmetries


35

We have tested the effect of radiative corrections to the Dalitz plot density.

The ratio of the two plots has been fitted with the usual expansion: corrections to parameters are compatible with zero


36

time stabilityTo check stability wrt data taking conditions we fit the integrated Dalitz plot in samples of 4 pb-1 each


37

Check on cubic term

No cubic dependence in |A(X,Y)|2

|A(X,Y)|2 = 1 + aY + bY2 + dX2 with a -1.

Can evaluate such as to mimic the cubic term.

Fitted function is actually :

Real (X,Y)MC(X,Y)

|A(X,Y)|2

Assume:

Real (X,Y)MC(X,Y)

1+Y+X2


38

MCMC weighted

MCMC weighted


39

The cuts used to select: are :

7 and only 7 prompt neutral clusters with 21° < < 159°

and E > 10 MeV opening angle between each couple of photons >

18° Kinematic Fit with no mass constraint 320 MeV < Erad < 400 MeV P(2) > 0.01

Sample selection


40


41

Once a combination has been selected, one can do a second kinematic fit imposing 0 mass for each couple of photons.

Second kinematic fit


42

i

iin log

But now:

ni = recostructed eventsi = from each single MC recostructed event weighted with the theoretical function

Still we minimize:

Doing it the hard way..


43

The center of Dalitz plot correspond to 3 pions with the same energy (Ei = M/3 = 182.4 MeV). A good check of the MC performance in evaluating the energy resolution of 0 comes from the distribution of E0 - Ei for z = 0

Comparison Data – MC (II)


44

E*1 - E*2

Vs.

E

Comparison Data – MC (II)

Documents

F.Ambrosino Università e Sezione INFN, Napoli for the KLOE collaboration