term θ cos V

Sandra Malvezzi - Charm Results from Focus and BaBar

1

Sandra Malvezzi I.N.F.N. Milano

Charm Review

(from FOCUS and BaBar)

IFAE 2003

Lecce

A new charm-physics era

The high statistics and excellent quality of data allow for unprecedented sensitivity & sophisticated studies

Lifetime measurements @ better than 1%

non-spectator processes Mixing

possible window on physics beyond SM

Investigation of decay dynamics both in the hadronic and semileptonic sector

Phases and Quantum Mechanics interference FSI role & CP studies

a lesson for the b physics!!!

Sandra Malvezzi - Charm Results from Focus and BaBar

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PWC

Over 1 million reconstructed!

Vertexing

Cerenkov

spectrometer

Muon id

Successor to E687. Designed to study charm particles produced by ~200 GeV photons using a fixed target spectrometer with updated Vertexing, Cerenkov, EM Calorimeters, and Muon id capabilities. Member

groups from USA, Italy, Brazil, Mexico, Korea.

Charm at BaBar B Factory

• Cross section is large

Present sample of 91 fb ^-1 sample contains

• Compare with earlier charm experiments:

– E791 - 35,400

– FOCUS - 120,000

– CDF - 56,320

• Approximately 1.12 x 10 ⁶ untagged

D

K

π

events

Brian Meadows: Moriond 2003

1. E791 Collaboration, Phys.Rev.Lett. 83 (1999) 32.

2. Focus Collaboration, Phys.Lett. B485 (2000) 62.

Sandra Malvezzi - Charm Results from Focus and BaBar

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Observation of a Narrow Meson decaying to at a Mass of 2.32 GeV/c in BaBar

hep-ex/0304021

0

D s π

2

Isospin-Violating Decay

2

mass=2316.8 ± 0.4 MeV/c

yield=1267 ± 53 evts

Meson lifetime

(Bigi Uraltsev):

1.00-1.07 (no WA/WX) ;

0.8-1.27(different process

Sandra Malvezzi - Charm Results from Focus and BaBar

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Baryon lifetime

0

1 15 1 3 ;

c

D

τ Ω ≈ τ

≈ τ Λ

need boost and precise vertexing

In the baryon sector the expected hierarchy: Γ Ξ < Γ Λ < Γ Ξ ⁽

^{) (}

^{) ( )}

∼ Γ Ω ⁽

⁾

Charm Mixing

; 2

x = ∆ M y = ∆Γ

Γ Γ

Mixing parameters:

Direct comparison of CP final state lifetime finds y _CP

0

( )

D → K K CP

+ → Γ

0

1 2

1 1

( & )

2 2

( ) 1 ( )

2

D K CP CP

K

π π

− +

− +

→ + −

→ Γ ≈ Γ + Γ

0 0

( )

( ) 1

CP

D K

y D KK

τ π

τ

= → −

→

Sandra Malvezzi - Charm Results from Focus and BaBar

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2 2

' ' 2 2

( ) ^t ( ' 2 )

WS DCS DCS

R t e R R t x y t

−Γ y + Γ

= + Γ +

' cos sin

' cos sin

x x y

y y x

δ δ

δ δ

≡ +

≡ − δ is the relative strong phase

Also

look for mixing in wrong sign semileptonic or hadronic decays

•Doubly Cabibbo Suppressed decays complicate hadronic decays

•With CP conservation, the wrong-sign to right-sign decay rate is

The three terms come from DCS decays, interference and mixing.

In semileptonic decays only the mixing term appears

FOCUS

CLEOII.V

E791

95% CL

BELLE

+

− +

→ − /

π π

0 K K

D

−

→K+

π

+

− +

→ − /

π π

0 K K

D

+

− +

→ − /

π π

0 K K

D

E791

ν FOCUS

FOCUS K+ µ-ν FOCUS K+ π−

D ⁰ -D ⁰ MIXING STATUS 2002

%

BaBar

FOCUS (2000)

y

= 3.42 ± 1.39 ± 0.74%

BELLE (2002)

y

= -0.5 ± 1.0

%

BABAR (2002)

y

= 1.4 ± 1.0±

%

Sandra Malvezzi - Charm Results from Focus and BaBar

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Published (23.4 fb

)

Moriond 2002

Moriond 2003

FOCUS, CLEO, BaBar, and Belle are all investigating mixing using semileptonics and various hadronic modes

BaBar: D

→ K

π

“No mixing No CP violation”

hep-ex 0304007

New results on D ⁺ → K πµν

Our Kπ spectrum looks like 100% K*(892)

This has been known for about 20 years

...but a funny thing happened when we tried to measure the form factor ratios

by fitting the angular distributions

Sandra Malvezzi - Charm Results from Focus and BaBar

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An unexpected asymmetry in the K* decay

forward-backward asymmetry in

cos below the K*

pole but almost none above the pole

θ

d

d ∝ 1 + α cos

θ Ω

Γ

Sounds like

QM interference

Simplest approach — Try an interfering spin-0 amplitude

B

B B

M

2

2 2

0

(1 cos ) sin

2 2

(1 cos ) sin

( )

2 2

sin (cos )

2

l V i

l V i

l

V

i

e

Ae H

t m e H

δ

H

χ

χ µ

θ θ

θ θ

θ θ

+

−

−

+

− −

∝ − +

+ − +

We simply add a new constant amplitude : A exp(iδ) in the place where the K* couples to an m=0 W

with amplitude H

. This assumes the q

dependence of the anomaly s-wave

coupling is the same as the K* (could be challenged)

2 2

0 0

B

where m

m m im

≡ Γ

− + Γ

+ muon mass terms

A exp(iδ) will produce 3 interference terms

A 4-body decay requires 5 kinematic variables:

• M

• M

≡ q

≡ t

Focus Semileptonic 15

Studies of the acoplanarity-averaged interference

(

)

2 2

8 cos

sin

Re

A e B

H

θ θ

+

Efficiency correction is small

Extract this interference term by weighting data by cosθ

Since all other χ-averaged terms in the decay intensity are constant or cos

θ

.

We begin with the mass dependence: ^Re ( ^{e B}

)

90

δ =

0

δ =

45

δ =

..looks just like the calculation ..

m − Γ

m

m + Γ

Our weighted mass distribution..

A=0

0.36 exp(iπ/4)

A constant 45

phase works great...

…other

options also

possible (next

slide).

-6000 -4000 -2000 0 2000 4000

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 FOCUS fit

LASS Scaled fit

Kappa Kappa

..but other options would work as well.

Asymmetry expected directly from LASS s-wave K π phase shift analysis.

And Kappa with no fsi phase shift and with a 100 degree phase shift.

cos θ

term

m K _π

cos θ

weighted M(Kπ), GeV/c

Sandra Malvezzi - Charm Results from Focus and BaBar

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Will there be similar effects (interference) in other charm semileptonic or

beauty semileptonic channels?Good question.

E691

E653

E791

FOCUS BEAT E687

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

E687

E791

FOCUS BEAT E691

E653

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Form Factor Measurements

1.66 0.060 ±

0.827 0.055 ±

The experimental R

value is getting smaller with the

passing years. The new Focus value is 2.9 σ below E791. We were consistent before charm background correction.

Apart from E691 the R

values have been pretty consistent.

Latest form factor calculation Damir Becirevic (ICHEP02) R

= 1.55 ± 0.11

which is remarkably close to R

= 1.504 ± 0.087(FOCUS)

time

R

R

New WA

New WA

New FOCUS Results:

R

= 1.504 ± 0.057 ± 0.039

R

= 0.875 ± 0.049 ± 0.064

Sandra Malvezzi - Charm Results from Focus and BaBar

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• Dynamics of hadronic decays

• substructures in the Dalitz plots

• interference & branching ratios

Over the last decade charm Dalitz-plot analysis has emerged as an excellent tool to study

• Role of non-spectator diagrams in charm decays e.g.

D s ^± → π π π ^{± ∓ ±}

• FSI effects in three-body decays

• phase shifts between different resonant amplitudes

• extension of the isospin analysis from the two-body system

The high statistics now available demands proper parametrization

Three -body hadronic decay dynamics

to face the problem of the light mesons

• certainly a complication for the interpretation of charm decay dynamics

• more difficult Dalitz plot analysis

Why the charm community had

to be educated in the general s-wave formalism

• two-body unitarity

• Breit-Wigner approx. limits, K-matrix approach etc...

and how it started

...a warning for beauty!

Sandra Malvezzi - Charm Results from Focus and BaBar

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For a well-defined wave with specific isospin and spin (IJ)

characterized by narrow and well-isolated resonances, we know how.

• the propagator is of the simple Breit-Wigner type and the amplitude is

How can we formulate the problem?

D → r r

| 1 2 3

The problem is to write the propagator for the resonance r r

3

1 2

1 3 13 2 2

(cos ) 1

J J r

D r J

r r r

A F F p p P

m m im ϑ

= × ×

− − Γ

when the specific IJ–wave is characterized by large and heavily overlapping resonances (just as the scalars!), the problem is not that simple.

( I iK − ⋅ ρ ) ⁻ 1

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 the propagator may be written in the context of the K-matrix approach as Indeed, it is very easy to realize that the 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

Sandra Malvezzi - Charm Results from Focus and BaBar

23 2

1 0

2 2

0 0 0

1 2

( )

( )(1 )

K j A

k kj j

A A

g s s s m

F I iK f

m m s s s s s

α α π

α α

ρ

^{ } β ^{−   −}

= − ⋅    ∑ − + −    × − −

We may summarize by saying that:

The decay amplitude may be written, in general, as a coherent sum of BW terms for waves with well-isolated resonances plus

K-matrix terms for waves with overlapping resonances.

0

1 1

( ) ^{i m} _i ⁱ

_i ^{BW n} _i ⁱ

_i ^K

i i m

A D a e ^δ a e F ^δ a e F ^δ

= = +

= + ∑ + ∑

Where the general form of for scalars is F _i ^K

In the light of this

But now the question arises:

Is this a meaningful description of the underlying physics or just a mirage?

if we try to fit a generic Dalitz plot with the simple isobar model, we have to let the masses and widths of overlapping resonances in the same waves float freely, in order to get a decent fit.

We shall see this problem in the FOCUS channels

s

,

D D

→ π π π

Sandra Malvezzi - Charm Results from Focus and BaBar

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FOCUS D _s ⁺ → π ⁺ π ⁺ π ^- analysis

Sideband

Yield D

= 1475 ±50 S/N D

= 3.41

Observe:

•f

(980)

•f

(1270)

•f

(1500)

Dominated by weird

resonances with simultaneous KK and ππ couplings

High mass

low mass

f

(1270) f

(980)

f

(980)

f

(1270) S

(1475)

r

j

2 2 2

r r 1 2 1 3

r 2

2 2

j j 1 2 1 3

j

A d m d m f

A d m d m

i i

a e a e

δ

= ∫

∫ ∑

^150%

r

f =

∑

Preliminary

m = 1475 ± 10 MeV Γ = 112 ± 24 MeV m = 975 ± 10 MeV

= 90 ± 30 MeV

= 36 ± 15 MeV

Isobar approach Coupled-channel BW

Γ

Γ

Sandra Malvezzi - Charm Results from Focus and BaBar

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S

(1475) (Focus) m = 1475 ± 10 MeV Γ = 112 ± 24 MeV

Preliminary

PDG Value for f0(1500)

m = 1507 ± 5 MeV

Γ = 109 ± 7 MeV

Yield D

Yield D

= 1527 = 1527 ± ± 51 51 S/N D

S/N D

= 3.64 = 3.64

FOCUS D ⁺ → π ⁺ π ⁺ π ^-

high mas s

low mass

Sandra Malvezzi - Charm Results from Focus and BaBar

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Single BW for f ₀ (400)

m = 443 ± 27 MeV Γ = 443 ± 80 MeV

E791 Results :

24 23 42 40

478 17 324 21

m MeV

MeV

+− +

−

= ±

Γ = ±

f

(400)

ρ

(770)

f

(980)

ρ

(770) f

(980)

S

(1475) f

(1275)

Prelim

inary

Isobar approach

Without f₀(400)

With f₀(400)

2

mlow 2

mhigh

2

mhigh

C.L. 10^-8

C.L. 0.8%

FOCUS D ⁺ → π ⁺ π ⁺ π ^-

Sandra Malvezzi - Charm Results from Focus and BaBar

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2

2 2

( ) ( )

( )

( )

ai aj

ij ij

a a

g m g m

K c m

m m

= +

∑ −

Resonances in K-matrix formalism

2 2

( ) ( )

( )

ai aj

ij

a a

g m g m

K = m m

∑ −

where

) ( )

2 ( m m m

g ^ai = _a Γ _ai Unitarity ...

( ) 1

T = − I iK ⋅ ρ ⁻ K

S.U. Chung et al.

Ann.Physik 4(1995) 404

... from scattering to production:

the P-vector approach

2 2

( )

( )

i i

g m

P m m

α α

α α

= β

∑ −

β (complex) carries the production information

i i i

P = + P d

( ) 1

F = I − i K ⋅ ρ ⁻ P

I.J.R. Aitchison

Nucl.Phys. A189 (1972) 514

known from scattering data

Sandra Malvezzi - Charm Results from Focus and BaBar

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“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

We need a description of the scattering ...

* GAMS GAMS

* GAMS GAMS

* ^{BNL BNL}

*

pp^-→ KKn

CERN CERN - - Munich Munich : :

p⁺p^-→ p⁺p^-

* Crystal Barrel Crystal Barrel

* Crystal Barrel Crystal Barrel

* Crystal Barrel Crystal Barrel

* Crystal Barrel Crystal Barrel

pp → p⁰p⁰p⁰, p⁰p⁰h

pp → p⁰p⁰p⁰, p⁰p⁰h , p⁰hh

pp → p⁺p^-p⁰, K⁺K^-p⁰, K_sK_sp⁰, K⁺K_sp^- np → p⁰p⁰p^-, p^-p^-p⁺, K_sK^-p⁰, K_sK_sp^- p^-p→p⁰p⁰n, 0<|t|<1.5 (GeV/c²)

E852 E852

*

( ) ( ) 2

00 0

2

0 0 0

1 2

( ) ( )(1 )

scatt

i j scatt A

ij ij scatt

A A

g g s s s m

K s f

m s s s s s s

α α

π

α α

 −  −

=    ∑ − + −    − −

( )

g

^α is the coupling constant of the bare state α to the meson channel

scatt

f

s 0 describe a smooth part of the K-matrix elements

2

0 0

( s s −

2 m

) ( s s −

)(1 − s

) suppresses the false kinematical singularity at s = 0 near the ππ threshold

and

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

IJ

K ij

1= ππ, 2= K K 3=4π 4= 5=

A&S

Sandra Malvezzi - Charm Results from Focus and BaBar

35

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

Poles 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

− −

− −

−

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

KK

i i i i i

i i i i

m g g g g g

e e e e e

e e e e

ππ π ηη ηη

−

Γ

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

− −

.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

−

101.6 134.2 − 123

0.7334

A&S T-matrix poles and couplings

A&S fit does not need the σ

Sandra Malvezzi - Charm Results from Focus and BaBar

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

preli min ary

D s → πππ

fit fractions phases

r

105%

r

∑ f ^∼

low proj high proj

m2 2

mhigh

fit fractions phases

preli min ary

D ⁺ → πππ

r

99%

r

∑ f ^∼

...parametrization of two-body resonances coming from light-

quark experiments works for charm decays too. Not obvious!

Sandra Malvezzi - Charm Results from Focus and BaBar

39

BaBar Three Body Decays of D Mesons

• Three body modes are also studied.

• The K

π

π

channel could contribute to mixing studies

– D

is tagged from D

so CF decay makes K

. DCS or mixing make K

. – These interfere and it may be possible to determine φ+δ from Dalitz plot.

• In any case, it contains much physics - a real challenge to fit well.

15,753 events 23 fb^-1

B.M Moriond 2003

ππ & Kπ interactions!

0

D → K s ππ

0

D → K KK s

Can we get a pure Κ _s φ CP odd from D ⁰ → K _s K ⁺ K ^- ?

Κ

φ is a CP odd state: Ks and φ are CP even Κ

φ is in a relative p-wave with parity -1

Κ

f

(980) is a CP even state: Ks and f

are CP even Κ

f

(980) is relative s-wave with parity +1 Two states interfere in same region in Dalitz plot:

Is there a pure CP odd eigenstate near the φ ?

No. A CP even eigenstate will be present with a non-negligible fraction.

Tagged sample

K⁺K^- K_s K

asymmetry in φ lobes indicates interference

Fraction of events in the φ region

due to φK

is:

62 3%

tota region

regio

l to al n

t

A A A A

φ

φ

φ φ

= ±

∫

∫

0

" "

is 62% CP odd and 3 8% CP even

D → φ K

Sandra Malvezzi - Charm Results from Focus and BaBar

41

• At 30 years from the discovery of the c quark the physics of the first heavy quark has reached a complete maturity

• With the high statistics now available in the charm sector, we start seeing strange effects which make the interpretation

of the decay processes more complicate

• Interplay between light hadrons and charm requires

a more proper formalism for Dalitz plot analysis (σ and κ puzzle)

• Lessons for the b sector?

•Many b particles decay to charm so branching ratios, lifetimes etc needed for accurate b results

•Experimental techniques, such as Dalitz plot, can be performed and tested in charm.

Conclusions