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E831-FOCUSStato dell’analisi e prospettive

Sandra Malvezzi INFN-Milano

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Over 1 million reconstructed!!

Successor to E687. Designed to study charm particles produced by ~200 GeV photons using a fixed target spectrometer with upgraded Vertexing, Cerenkov, E+M Calorimetry, and Muon id capabilities. Includes groups from USA, Italy, Brazil, Mexico, Korea

1 million charm particles reconstructed into DK , K2 , K3

FOCUS Spectrometer

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LaLa collaborazione collaborazione FOCUSFOCUS

Univ. of California-Davis, CBPF-Rio de Janeiro, CINVESTAV Mexico City, Univ. Colorado-Boulder,

FERMILAB, Laboratori Nazionali di Frascati, Univ. of Illinois-Urbana-Champaign,

Indiana Univ.-Bloomington, Korea Univ.-Seoul, INFN and Univ.-Milano,

Univ. of North Carolina-Asheville, INFN and Univ.-Pavia, Univ. of Puerto Rico Mayaguez,

Univ. of South Carolina-Columbia, Univ. of Tennessee-Knoxville,

Vanderbilt Univ.-Nashville, Univ. of Wisconsin-Madison, Yonsei Univ.-Seoul

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Cronologia E831-FOCUS

•1996-1997 Presa dati•1998 Completata la ricostruzione di

piu`di 6 Miliardi di eventi•1999 ora

Sub-skimOttimizzazione MCAnalisiPresentazioni a conferenzePubblicazioni risultati di fisica

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Attività 2003

Analisi: - Presentazioni a conferenze - Articoli su riviste

Frascati – Spettroscopia degli stati eccitati (L=1) del mesone D

Milano – Studio dei mesoni con charm

Pavia – Studio dei barioni con charm

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Stato dell’analisi e prospettive•Nel periodo Giugno 2002-Giugno 2003 sono stati pubblicati 20 articoli su riviste internazionali (di cui 13su Physics Letters B)

•Entro la fine del 2004 sono previste altre 20 pubblicazioni

•Fondamentale contributo alla fisica del charm •Lifetimes

•Semileptonic decays

•Hadronic decays

•Rare decays

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An important lesson from

for the B physics and CP studies

“The advantages of high-statistics for the interpretation of Heavy-Flavour hadronic-decay dynamics

will vanish without a strategy for controlling strong effects among particles involved

in weak-decay processes ”

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Complication for Dalitz plot analysis

had to face the problem of dealing with light scalar particles populating charm meson

hadronic decays, such as D, D

Require understanding of light-quark hadronic physics including the riddle of and

(i.e, and states produced close to threshold), whose existence and nature is still controversial

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A bridge of language, knowledge and measurements between the two worlds

of Light Mesons and Heavy Flavoursis necessary

• S-matrix and its representations• Two-body unitarity • Analyticity • Limits of the Breit-Wigner approximation etc..

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Analysis techniques CAN and MUST be improved now in view of extensive application in high-statistics experiments (Cleo-c, Babar, Belle, BTeV, LHC-b etc...) for precision studies of CP and reliable New Physics measurements

Pioneering work performed by

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An instructive example from FOCUS

Milano group

D

analogy with operatively:

complete Dalitz plot analysis (time-dependent) to deal withall interference with other () intermediate channels

B

crucial for determination of the angle of the SM unitarity triangle

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For a well-defined wave with specific isospin and spin (IJ)characterized by narrow and well-isolated resonances, we knowhow.• the propagator is of the simple Breit-Wigner type and the amplitude is

How can we formulate the problem?

D r |

1 2

3

The problem is to write the propagator for the resonance r

rr

3

1

2

1 3 13 2 212

1(cos )

J Jr

D r Jr r r

A F F p p Pm m im

����������������������������traditionalisobar model

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when the specific IJ–wave is characterized by broad and heavily overlapping resonances (just like scalars!), the problem is not so simple.

1( )I iK where K is the matrix for the scattering of particles 1 and 2.

In this case it can be demonstrated on very general grounds that, in the context of the K-matrix approach, the propagator may be written as

Indeed, it is very easy to realize that propagation is no longer dominated by a single resonance, but is the result of complicated interplay among resonances.

i.e., to write down the propagator we need the scattering matrix

In contrast

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•Based on “first principles” of S-matrix scattering theory

The K-matrix formalism E.P.Wigner,Phys. Rev. 70 (1946) 15

S.U. Chung et al.Ann. Physik 4 (1995) 404

1 1K T i 1( )T I iK K

1/ 2 1/ 22S I i T S scattering matrix

= phase space

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•From T

to F

1( )T I iK K

From scattering to production: the P-vector approach

I.J.R. AitchisonNucl. Phys. A189 (1972) 514

1( )F I iK P

known from scattering data

describes coupling of resonances to D

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K-matrix advantages

• An elegant and direct way of incorporating the

two-body unitarity constraint • Proper handling of overlapping and wide resonances• Straightforward inclusion of already known physics

and disadvantages

requires translation into T-matrix to get the “physics”

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* p0n,n, ’n, |t|0.2 (GeV/c2)GAMSGAMS

* pn, 0.30|t|1.0 (GeV/c2)GAMSGAMS

* BNLBNL

*p- KKn

CERN-MunichCERN-Munich

::

* Crystal BarrelCrystal Barrel

* Crystal BarrelCrystal Barrel

* Crystal BarrelCrystal Barrel

* Crystal BarrelCrystal Barrel

pp

pp , ,

pp K+K-, KsKs, K+s

np -, KsK-, KsKs-

-p0n, 0|t|1.5 (GeV/c2)E852E852*

At rest, from liquid 2H

At rest, from gaseous

At rest, from liquid

At rest, from liquid

2H

2D2H

“K-matrix analysis of the 00++-wave in the mass region below 1900 MeV’’ V.V Anisovich and A.V.Sarantsev Eur.Phys.J.A16 (2003) 229

A description of the scattering ...

A global fit to all the available data has been performed!

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FOCUS D s +

++- analysis

Observe:

•f0(980)

•f2(1270)

•f0(1500) Sideband

Signal

Yield Ds+ = 1475 50

S/N Ds+ = 3.41

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First fits to charm Dalitz plots in the K-matrix approach!

C.L fit 3 %

sD

Low mass projection High mass projection

+

+20 +

(S - wave)π 87.04 ± 5.60 ± 4.17 0(fixed)

f (1275)π 9.74 4.49 2.63 168.0 18.7 2.5

ρ (1450)π 6.56 ± 3.43 ± 3.31 234.9 ±19.5 ±13.3

decay channel phase (deg)fit fractions (%)

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sD

•No significant direct three-body-decay component

•No significant (770) contribution

sD

Marginal role of annihilation in charm hadronic decays

But need more data!

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Yield DYield D++ = 1527 = 1527 5151

S/N DS/N D++ = 3.64 = 3.64

FOCUS D+ ++- analysis

Sideband Signal

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2lowm

2highm

D

C.L fit 6.8 %

K-matrix fit results

Low mass projection High mass projection

+

+2

0 +

(S - wave)π 56.46 ± 3.78 ±1.02 0(fixed)

f (1275)π 12.26 1.73 0.21 -38.6 20.9 4.2

ρ (770)π 26.89 ± 3.78 ±1.08 -128.9 ±18.5 ± 3.7

decay channel phase (deg)fit fractions (%)

No new ingredient (resonance) required not present in the scattering!

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With

Without

C.L. ~ 7.5%

Isobar analysis of D+ ++would instead require a new scalar meson:

C.L. ~ 10-6

m = 442.6± 27.0 MeV/c = 340.4 ± 65.5 MeV/c

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A.D. Polosa: “ Hadronic pollution in B”?

J.A. Oller: “On the resonant and non-resonant contributions to B”

CKM03 in B

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Conclusions•The K-matrix approach has been applied to charm decays for the first time

Such a result was not at all obvious! Such a result was not at all obvious!

•Full application to forthcoming high-statistics charm and beauty experiments for precision studies and search of New Physics !

•The same K-matrix description gives a coherent picture of

•Two-body scattering measurements•Light-quark spectroscopy experiments•Charm-decay data

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Slides for questions

• Slides for questions

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m = 1473.0 8.8 MeV/c= 109.5 16.3 MeV/c

20 0 1

2 2 2 20 12 0 0 1 1 2 2( )

m

m m im

K-matrix coupled-channel parametrization

FOCUS fit results

0 (980)f

0 (1475)S single channel Breit-Wigner

FOCUS fit results

0 0,m K-matrix mass and width

1 2γ , γ dimensionless normalizedcoupling constants

to and KK channels1 2ρ ,ρ

and KK phase space

Preliminary

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0m = 963.6 ± 5.4

0Γ = 284.2 ± 93.22

2

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γ= 2.04 ± 0.56

γ

MeV/c

MeV/c

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PDG does not help us!Large uncertainties in scalar-resonance paramenters

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f2(1270)f0(980)

f0(980)

f2(1270)S0(1475)

r

j

2iδ 2 2r r 12 13

r 2iδ 2 2j j 12 13j

a e A dm dmf =

a e A dm dm

Isobar approach results

Preliminary

+2

+0

+00

NR 24.85 ± 3.99 ± 5.67 246.8 ± 4.7 ± 4.8 0.516 ± 0.040 ± 0.055

f (1275)π 9.58 ±1.22 ±1.20 141.7 ± 6.8 ± 6.6 0.321 ± 0.021 ± 0.021

f (980)π 93.23 ± 2.39 ± 2.55 0(fixed) 1(fixed)

S (1475)π 17.18 ± 2.94 ± 3.00 248.9 ± 3.5 ± 5.7 0.429 ± 0.039 ± 0.041

ρ (1 +450)π 4.56 ± 0.79 ± 0.89 191.0 ±13.8 ±17.6 0.221 ± 0.020 ± 0.023

decay channel amplitude coefficientphase (deg)fit fractions (%)

C.L. Fit 7.2%

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f0(1500) PDG m = 1507 5 MeV = 109 7 MeV Preliminar

y

if

then0Γ (980) = 394.5 ±107.1

0 (980) (104.20 3.30)%

(43.53 4.88)%

f

NR

fit fractions:

C.L. 2%

Instability depending on the 1500 MeV region parametrization!

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2( )

( )ai aj

ij ija a

g gK c s

m s

Resonances in K-matrix formalism

where

2 ( )ai a aig m m

1( )T I iK K

S.U. Chung et al.Ann.Physik 4(1995) 404

E.P.Wigner,Phys.Rev.70 (1946) 15

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... from scattering to production:the P-vector approach

2( )i

i

gP

m s

(complex) carries the

production information i i iP P d

1( )F I iK P

I.J.R. AitchisonNucl.Phys. A189 (1972) 514

known from scattering data

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( ) ( ) 200 0

20 0 0

1 2( )

( )(1 )

scatti j scatt A

ij ij scattA A

g g s s s mK s f

m s s s s s s

( )ig

is the coupling constant of the bare state to the meson channelscatt

ijf0s describe a smooth part of the K-matrix elements

20 0( 2) ( )(1 )A A As s m s s s suppresses the false kinematical singularity

at s = 0 near the threshold

and

is a 5x5 matrix (i,j=1,2,3,4,5)

'

IJijK

K K1= 2= 3=4 4= 5=

A&S

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A&S K-matrix poles, couplings etc.

4 '

0.65100 0.24844 0.52523 0 0.38878 0.36397

1.20720 0.91779 0.55427 0 0.38705 0.29448

1.56122 0.37024 0.23591 0.62605 0.18409 0.18923

1.21257 0.34501 0.39642 0.97644 0.19746 0.00357

1.81746 0.15770 0.179

KKPoles g g g g g

0 11 12 13 14 15

0

15 0.90100 0.00931 0.20689

3.30564 0.26681 0.16583 0.19840 0.32808 0.31193

1.0 0.2

scatt scatt scatt scatt scatt scatt

A A

s f f f f f

s s

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A&S T-matrix poles and couplings

4 '13.1 96.5 80.9 98.6 102.1

116.8 100.2 61.9 140

( , / 2)

(1.019, 0.038) 0.415 0.580 0.1482 0.484 0.401

(1.306, 0.167) 0.406 0.105 0.8912 0.142

KKi i i i i

i i i i

m g g g g g

e e e e e

e e e e

.0 133.0

97.8 97.4 91.1 115.5 152.4

151.5 149.6 123.3 170.6

0.225

(1.470, 0.960) 0.758 0.844 1.681 0.431 0.175

(1.489, 0.058) 0.246 0.134 0.4867 0.100 0

i

i i i i i

i i i i

e

e e e e e

e e e e

133.9

.6 126.7 101.1

.115

(1.749, 0.165) 0.536 0.072 0.160 0.313

i

i i i i i

e

e e e e e

A&S fit does not need a as measured in the isobar fit