00 fit update fit update

P.Gauzzi

2

Outline

• Kaon Loop – Systematics on the fit parameters

– Fit with fixed VDM

• No Structure– systematics

– fit with free VDM

• KL and NS fits with Adler zeros

• New version of NS model

3

KLKL

Par. Fit uncert.

Ma0 (MeV) 982.5 1.5

gaK+K (GeV) 2.15 0.06

ga(GeV) 2.82 0.03

g a(GeV-1) 1.58 0.09(°) 222 12

Br(VDM) 0.92 0.40

R=Br( )/Br( 0) 1.70 0.04

Ra0=(ga0K+K─/ga0)2 0.58 0.03

2 157.6ndf 136

P(2) 9.9%

Ma0 1.000

ga0KK 0.931 1.000

ga0 0.584 0.550 1.000

0.277 0.236 0.156 1.000

Br(VDM) -0.252 -0.327 -0.513 0.130 1.000

R 0.004 -0.180 -0.111 0.008 -0.038 1.000

Correlation coefficients

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KL Systematics KL Systematics

• Sensitivity to fixed parameters– ga0' = -1.13 ga0KK (4q) vs ga0' = 1.2 ga0KK (qq)

– gK+K─ = 4.49 0.07

• Normalization (N 1)

• Data-MC discrepancy for the wrong pairing fraction

11.5% (data) vs 14%(MC)

• Sensitivity to the starting values of the parameters

( 10% variations < 0.1%)

3/222K

KK/M4M1M

)KK(48πg

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Systematics (KL)Systematics (KL)ga '= 1.2 gaK+K- N Wrong pairings g K+K─

Ma0 0.0% 0.0% 0.1% 0.0%

gaK+K 0.2% 1.5% 1.6% 0.2%

ga 0.3% 0.2% 1.2% 0.4%

g a -0.2% 0.5% 4.2% 0.7%

0.0% 0.1% -1.3% 0.3%

Br(VDM) 0.1% 2.4% -15.7% 0.0%

R=Br( )/Br( 0) 0.0% 0.2% 2.1% 0.0%

Ra0=(ga0K+K─/ga0)2 0.0% 2.4% 0.9% 0.4%

• Relative variations

Par. Fit uncert. systematic

Ma0 (MeV) 982.5 1.5 1.1

gaK+K (GeV) 2.15 0.06 0.08

ga(GeV) 2.82 0.03 0.04

g a(GeV-1) 1.58 0.09 0.16(°) 222 12 3

Br(VDM) 0.92 0.40 0.15

R=Br( )/Br( 0) 1.70 0.04 0.04

Ra0=(ga0K+K─/ga0)2 0.58 0.03 0.03

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KL with fixed VDMKL with fixed VDM

• Br(VDM) = 410-6 (same as NS fit)

Par. Fit uncert. VDM fixed Fit uncert. variations

Ma0 (MeV) 982.5 1.5 980.0 0.5 -0.2%

gaK+K (GeV) 2.15 0.06 2.05 0.02 -4.8%

ga(GeV) 2.82 0.03 2.70 0.02 -4.2%

g a(GeV-1) 1.58 0.09 1.45 0.09 -8.2%(°) 222 12 236 8 6.4%

Br(VDM) 0.92 0.40

R=Br( )/Br( 0) 1.70 0.04 1.74 0.04 2.4%

Ra0=(ga0K+K─/ga0)2 0.58 0.03 0.57 0.01 -2.5%

2 157.6 179.7ndf 136 137

P(2) 9.9% 0.8%

• Worse 2 probability

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NS Systematics NS Systematics

• Sensitivity to fixed parameters Ma0 = 982.5 MeV (KL fit) vs 985.1 MeV (PDG)

• Normalization (N 1)

• Data-MC discrepancy for the wrong pairing fraction

11.5% (data) vs 14%(MC)

• Sensitivity to the starting values of the parameters

(10% variations < 0.2%)

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NSNS

Par. Fit uncert.

Ma0 (MeV) 982.5 FIXED

gaK+K (GeV) 1.59 0.22

ga(GeV) 2.21 0.09

g a(GeV-1) 1.63 0.11

R=Br( )/Br( 0) 1.70

a0 14.8 1.10 (deg) 42.8 1.5

a1 25.5 1.81 (deg) 61.5 3.5

Ra0=(ga0K+K─/ga0)2 0.52 0.11

2 148.3ndf 134

P(2) 18.8%

ga0KK 1.000

ga0 0.849 1.000

ga0 0.885 0.971 1.000

R -0.226 -0.261 -0.309 1.000

a0 0.858 0.793 0.905 -0.275 1.000

0 0.584 0.787 0.805 -0.283 0.768 1.000

a1 0.684 0.707 0.813 -0.253 0.933 0.836 1.000

1 0.807 0.912 0.936 -0.294 0.868 0.931 0.816 1.000

Correlation coefficients

• Large correlations

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NSNS

Ma0=985.1 MeV N wrong pairings

gaK+K─ -20.7% -7.1% / -1% -3.2%

ga -3.9% -5.7% / -0.6% -4.5%

g a -3.5% -7.1% / +0.4% -3.9%

R=Br( )/Br( 0) -0.1% 0.3% 0.3%

a0 -0.2% -11.5% / -0.1% -7.9%0 1.0% 11.6% / 0.3% 11.4%

a1 -1.1% -14% / -0.3% -11.3%1 1.0% 19.5% / 0.3% 20.3%

Ra0=(ga0K+K─/ga0)2 -31.8% -3.1% / -0.8 % -1.3%

• Relative variations

• Large correlations also with the a0 mass

• Strange behaviour for N 1

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NS with free VDMNS with free VDM• Br(VDM) as free parameter (as for KL)

Par. Fit uncert. VDM free Fit uncert. Variations

Ma0 (MeV) 982.5 FIXED 982.5 FIXED

gaK+K─ (GeV) 1.59 0.22 2.01 0.07 26.4%

ga(GeV) 2.21 0.09 2.46 0.08 11.3%

g a(GeV-1) 1.63 0.11 1.83 0.03 12.3%

Br(VDM)106 0.05 4

R=Br( )/Br( 0) 1.70 1.7 0.04 0.0%

a0 14.8 1.1 14.9 0.6 0.7%0 (deg) 42.8 1.5 38.3 1.1 -10.5%

a1 25.5 1.8 21.3 1.4 -16.5%1 (deg) 61.5 3.5 57.3 1.4 -6.8%

Ra0=(ga0K+K─/ga0)2 0.52 0.11 0.67 0.07 28.8%

2 148.3 140.6ndf 134 134

P(2) 18.8% 33.1%

• No sensitivity to VDM

• Better fit quality

• Couplings more similar to KL results (ga0 still compatible)

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Fit with Adler zerosFit with Adler zeros

2KAA

22KKa

2π

2ηAA

22ηπa

M2

1s ; smg

M 2

1-M s ; smg

0

0

• According to some theoreticians the Adler zero is needed as a consequence

of Chiral Symmetry (however there is no general consensus)

It forces the PP interaction to vanish close to threshold:

2K

2

2K

2

2KK

2KK

2π

2η

2

2π

2η

2

2ηπ

2ηπ

M21

M

M21

mgg

M21

MM

M21

Mmgg

0

00

0

00

a

aa

a

aa

• I tried to include them into the fit functions: in order not to change the

meaning of the parameters I used:

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KL fit with Adler zerosKL fit with Adler zeros

Par. Uncert. Par. Uncert.

Ma0 (MeV) 982.5 1.5 1002 8

ga0KK (GeV) 2.15 0.06 3.09 0.02

ga0(GeV) 2.82 0.03 3.54 0.12

g a(GeV-1) 1.58 0.09 4.72 0.14(°) 222 12 165 13

Br(VDM) 0.92 0.40 1.44 0.61

Br( )/Br( 0) 1.70 0.04 1.70 0.04

R=(ga0KK/ga0)2 0.58 0.03 0.76 0.04

2 156.7 144.0ndf 136 136

P(2) 10.8% 30.3%

KL KL with Adler zero

— With A.z.

— Without A.z.

M (MeV)

• Fit quality improves

• All relevant parameters become larger

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NS with Adler zerosNS with Adler zeros• The fit convergence improves: no need to fix the a0 mass

Par. Fit uncert. with A.z. Fit uncert.

Ma0 (MeV) 982.5 FIXED 971.9 2.6

gaK+K─ (GeV) 1.59 0.22 2.70 0.06

ga(GeV) 2.21 0.09 2.60 0.04

g a(GeV-1) 1.63 0.11 1.97 0.02

R=Br( )/Br( 0) 1.70 0.04 1.69 0.04

a0 14.8 1.1 16.6 0.50 (deg) 42.8 1.5 35.2 1.0

a1 25.5 1.8 26.5 0.91 (deg) 61.5 3.5 59.0 1.8

Ra0=(ga0K+K─/ga0)2 0.52 0.11 0.58 0.03

2 148.3 146.3ndf 134 133

P(2) 18.8% 20.3%

• However according to Gino no Adler zeros should be put in the model, but…

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New modelNew model

• t’Hooft, Isidori, Maiani …. “A theory of Scalar Mesons” arXiv:0801.2288

• Scalars are “tetraquarks”

• “Instanton” induced transitions to explain decays like f0

• All couplings are written in terms of 2 parameters: cf and cI (|cI|<<| cf |)

• Pseudoscalars appear in the effective lagrangian with derivative couplings:

2

P22P1

2SP1P221SP1P2SP1P2 MMm

2

1g)p(pgg

• From the technical point of view of the fit, the effect is very similar

to the Adler zero

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New NS fitNew NS fit

2P

2P

2S

2P

2P

2

PSP(fit)

PSP MMM

MMmgg

Par. Fit uncert. new NS Fit uncert.

Ma0 (MeV) 982.5 FIXED 983.6 1.3

gaK+K─ (GeV) 1.59 0.22 1.40 0.05

ga(GeV) 2.21 0.09 1.94 0.04

g a(GeV-1) 1.63 0.11 1.38 0.02

R=Br( )/Br( 0) 1.70 0.04 1.70 0.03

a0 14.8 1.1 11.9 0.60 (deg) 42.8 1.5 37.6 0.9

a1 25.5 1.8 18.8 1.81 (deg) 61.5 3.5 60.4 0.6

Ra0=(ga0K+K─/ga0)2 0.52 0.11 0.52 0.02

2 148.3 148.9ndf 134 133

P(2) 18.8% 16.4%

The mass is in agreement with KL and with PDG cf=6.6 GeV-1 cI=1.6 GeV-1

(cf= 22 GeV-1 cI= -2.6 GeV-1 best fit by t’Hooft et al.)

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ConclusionsConclusions

• We should decide which fit show in the paper

• KL fit is stable

• NS has some problems; what systematics should we quote ?

• NS with VDM free goes in the same direction as KL– Very small VDM contribution

• Adler zeros improve the convergence; are they really needed ?

• New NS model: we should discuss the results with the authors (we are in contact with A.Polosa in Rome)

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Systematics from photon pairingSystematics from photon pairing

C(a0)

C(a0) is the difference between the

first and the second photon combination

for the a0 hypothesis

• Two component (right and wrong pairing)

fit to the C(a0) distribution of the data

(final sample)

• Right and wrong pairing shapes from MC

wrong pairings = (11.5 ± 0.70) %

(from MC 14 %)

• Data

─ Right p.

─ Wrong p.

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Mgen (MeV)

Mre

c (M

eV)

Systematics from photon pairing Systematics from photon pairing

• From C(a0) between the first and

the second best combination

Wrong pairings: data (11.5 ± 0.70) %

MC 14 %

• Check done by scaling the off-diagonal

part of the efficiency matrix by 0.115/0.14

and the diagonal region accordingly

to conserve normalization