Sandra MalvezziI.N.F.N. Milano

Recent Results from FOCUS

QCD 2005Conversano 16 -20 June 2005

How charm can still be charming

• Charm physics is a paradigm of how – precise measurements have led to a revival of the sector

• New Physics search: Mixing, CPV, rare and forbidden decays

• Spectroscopy of high-mass states (“the renaissance of spectroscopy”)

– sophisticated investigations (typical of a mature field, under study over various decades)

• Dalitz plot analyses, Semileptonic Form-Factor measurements...

have revealed limits in the “standard” approach

precisely

• QCD effects in charm weak decays can complicate the analysis and the phenomenological interpretation of the results requiring a new direction/approach in the decay dynamics investigation

– What experimentalists have learnt so far

• Goals: – Proper tools for present/future precise high-statistics studies of charm

and beauty hadrons – coherent description of FSI in Beauty - Charm decays and & Light

hadron sector (hopefully)

– Synergy between experimentalists and theorists

• FOCUS has played a pioneering role in various analyses

• Lifetime hep-ex/0504056 A Measurement of the Ds+ Lifetime

• Mixing hep-ex/0501006 D0-D0 hadronic mixing and DCS decays (the best charm mixing limit from a fixed-target exp)

• Pentaquark hep-ex/0506013 Pentaquark search (Null)

• Rare & forbidden decays • Semileptonic • Hadronic decays (Dalitz plot)• Multi-body channels (4,5,6 bodies) • Charm Baryons• D* spectroscopy hep-ex/0406044- hep-ex/0312060

FOCUS role

0 (*)c D p

Charm lifetimes

(*) FOCUS (○) PDG 2002 0

( )2.54 0.02

( )

D

D

0 1 1( ) ( ) ( )

15 3c cD

Ds 5074 0.0055 0.0051

Bigi Uraltsev1.00-1.07 (no WA/WX) 0.8-1.27 (different process

interference)

0

( )1.239 0.014 0.009

( )sD

D

Charm mixing circa 2000

2 sigma hints of mixing at few percent level!

(K) = 409.4 1.34 ps

(KK) =395.4 5.5 ps

CP lifetime comparisons

Time evolution of wrong-sign D* decay

* 0D D

K

Some intriguing results.....not conclusive!

Mixing circa 2003

It will be interesting to see if mixing does occur at the percent level.

B-factories are leading the game

Things have come a long way since those heady days...

2004-2005: data continue....

Belle : hep-ex/0408125 Phys. Lett. B 618 - 23

The best mixing limit from a fixed-target experiment:

a valuable check

More and more stringent limits!

FOCUS has the world’s most accurate lifetime measurements and excellent lifetime-resolution.

hep-ex/0501006FOCUS

....agrees better with BaBar & Bellethan with the old CLEO contour

• .....The semileptonic sector

Decay dynamics investigation

New results on D K

Our K spectrum lookslike 100% K*(892)

This has been known for about20 years

...but a funny thing happened when we tried to measure the form factor ratios by fitting the angular distributions

Decay is very accessible to theoryAssuming the K spectrum contains nothing but K*, the decay rateis straight-foreward

An unexpected asymmetry in the K* decayA 4-body decay requires 5 kinematics variables: 3 angles and 2 masses

2

2

WM q t

KM

Vd

d 2cos1

forward-backwardasymmetry incos below the K*pole but almost noneabove the pole

V

Sounds like QM interference

-15 % F-B asymmetry

matches model

Try an interfering spin-0 amplitude

2

2 2

0

(1 cos )sin

2 2(1 cos )sin

( )2 2

sin (cos )

2

il V

il V

iδl V

e H

M t m e H

Ae H

B

B

B

will produce 3 interference terms

iAe

(plus mass terms)

02 2

0 0

mB

m m im

Phys.Lett.B535,43,2002

H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD...

•The S-wave amplitude is about 7% of the K* BW with a 45o relative phase

KM

F-B

asy

mm

etry

•D+ K is the natural place to study the K system in the absence of interactions with other hadrons. Due to Watson’s theorem the observed Kphase shift should be the same as those measured in elastic scattering

• K* interferes with S- wave K and creates a forward-backward asymmetry in the K* decay angle with a mass variation due to the varying BW phase

The S & P waves from LASS

892 MeV/c2

The phase difference between S & P wave at K*(892) pole from LASS is ~ 45 degrees!.

Most information on K-+ scattering comes from the

LASS experiment (SLAC, E135) Aston et al., Nucl. Phys. B296 (1988) 493

PWAby LASS

(900) with no fsi phase shift and with a 100 degree phase shift.

-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 fitLASS Scaled fitKappaKappa

Km

cos v weighted M(K), GeV/c2

A broad Breit-Wigner amplitude ( the controversial (900))?

hep-ex/0503043 Hadronic Mass Spectrum Analysis of D+ KDecay and Measurementof the K*(892)0 Mass and Width in FOCUS Additional checks: (900) is not required

Form Factors

The vector and axial form factors are generally parametrized by a pole dominance form

22 2

(0)( )

1i

iA

AA q

q M

2

2 2

(0)( )

1 V

VV q

q M

2.5

2.1A

V

M

M

2/GeV c2/GeV c

Nominal spectroscopicpole masses

v 1(0) (0)r V A

2 2 1(0) (0)r A A

D+

d

d

uu

s

5

02

2 2 2,0, 1,2,3

( , , )cos cos

( ) ( ), ( ))

tK V

t

df H H H

dm dq d d d

H q g A q V q

D K

Two numbers parameterize the decay

v 2

1.45 0.23 0.07 1.00 0.15 0.03

791( ) 1.90 0.11 0.09 0.71 0.08 0.09

791( ) 1.84 0.11 0.09 0.75 0.08 0.09

687 1.74 0.27 0.28 0.78 0.18 0.11

653 2.0

1.504 0.057 0.039 0.875 0.049 0.06

0 0 3

4

. 3

Group r rFOCUS

BEATRICE

E e

E

E

E

0.16 0.82 0.22 0.11

691 2.0 0.6 0.3 0.0 0.5 0.2E

•Our analysis is the first to include the effects on the acceptance due to changes in the angular distribution brought about by the S-wave interference

•The inclusion of the S-wave amplitude dramatically improved the quality of the Form-Factor Fit • Form -factor lattice calculation (Damir Becirevic ICHEP02) RV = 1.55 0.11 is remarkably close to the FOCUS result.

Phys.Lett.B 544(2002) 89

Decay dynamics investigation ..cont’d

• .....The hadronic sector– Dalitz-plot analysis of D decays

Dalitz Analysis of Heavy Flavour Decays

• Powerful tool!– It provides a “complete observation” of the decay– Everything could be in principle measured

• from the dynamical features of the HF decay mechanism

– Relative importance of non-spectator processes

• up to the CP-violating phases, mixing, etc

– Just recall from Bo and from B D(*)K

• We have already learnt a lot about charm

Recent articles (the Dalitz-plot revenge)

• hep-ex/0503052 Searches for CP violation and S-wave in the Dalitz Plot analysis of D0++0 (CLEO)

• hep-ex/0503045 Search for D0 - D0 Mixing in the Dalitz Plot Analysis of D0 KS

0 + - (CLEO)

• hep-ex/0504039 Measurement of in B D(*)K decays with a Dalitz analysis of D KS

0 + - (BaBar)  • hep-ex/0504013 Measurement of 3 with Dalitz Plot

Analysis of B D(*)K Decay (Belle)  • hep-ex/0408099 Measurement of CP-Violating Asymmetries

in B0 ()0 Using a Time-Dependent Dalitz Plot Analysis( BaBar)

Sophisticated studies both in charm & beauty

I will • Address key issues of the Heavy Flavour Dalitz analysis

– Formalization problems• Failure of the traditional “isobar” model

• Need for the K-matrix approach– Implications for the future Dalitz analyses in the B-sector

• Discuss these issues in the context of the recent Ds+, D++-

+ Dalitz analysis we performed in FOCUS

Formalization Problems

• The problem is to write the propagator for the resonance r– For a well-defined wave with specific isospin and

spin (IJ) characterized by narrow and well-isolated resonances, we know how.

rr3

1

2D r

|1 2

3

•the propagator is of the simple Breit-Wigner type

traditionalisobar modelj

j jj

Aia e M

Spin 0

Spin 1

Spin 2 )1cos3()(2

)2(

1

1322

13

13

ppP

ppP

P

J

J

J

21

21

)339(

)1(

1

4422

22

pRpRF

pRF

F

•the decay amplitude is

•the decay matrix element

1 3 13 2 212

1(cos )

J J rD r J

r r r

A F F p p Pm m im

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

i.e., to write down the propagator we need to know the related scattering K-matrix

In contrast

What is K-matrix?

• It follows from S-matrix and, because of S-matrix unitarity, it is real

• Viceversa, any real K-matrix would generate an unitary S-matrix

• This is the real advantage of the K-matrix approach:– It (heavily) simplifies the formalization of any scattering

problem since the unitarity of S is automatically respected.

1/ 2 1/ 22S I i T 1 1K T i 1( )T I iK K

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

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

From Scattering to Production

• Thanks to I.J.R. Aitchison (Nucl. Phys. A189 (1972) 514), the K-matrix approach can be extended to production processes

• In technical language,

– From

– To

• The P-vector describes the coupling at the production with each channel involved in the process– In our case the production is the D decay

1( )T I iK K

1( )F I iK P

K-Matrix Picture of D++-+

D

P

1

2

3 Multi body

4 =

5 '

K K

1(1 )iK

1( )F I iK P Describes couplingof resonances to D

Known from Scattering Data

Beside restoring the proper dynamical features of the resonances, it allows for the inclusion of all the knowledge coming from scattering experiments: enormous amount of results and science!

• For a single pole problem, far away of any threshold, K-matrix amplitude reduces to the standard BW formula

• The two descriptions are equivalent

• In all the other cases, the BW representation is not any more valid (limit of the traditional isobar model!!!)

• The most severe problem is that it does not respect unitarity

Add BW

Add K

Add BW Add K

The Unitarity circle

Adding BWs ala “traditional Isobar Model”

–Breaks the Unitarity

–Heavily modify the phase motion!

21 0 0

20 0

1 ( / 2)(1 )( )

( )jK A A

k kj jA

g s s s m sF I iK f

m s s s s s

The decay amplitude may be written, in general, as a coherent sumof BW terms for waves with well-isolated resonances plus K-matrix terms for waves with overlapping resonances.

00

1 1

( ) i i

m ni i iBW K

i i i ii i m

A D a e a e F a e F

Can safely say that in general K-matrix formalization is just required by scalars (J=0), whose general form is

KiF

Summarizing

Where can we get a reliable S-wave scattering parametrization from?

• In other words, we need to know K to proceed.• A global fit to (all) the available data has been performed

* 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

( ) ( ) 200 0 0

20 0

1 ( 2)(1 )( )

( )

scatti j scatt A A

ij ij scattA

g g s s s m sK s f

m s s s s s

( )ig is the coupling constant of the bare state to the meson channel

scattijf

0s 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

An impressive amount of data is well described in terms of 5 poles

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

•This set of poles and couplings coherently describes the scattering. a object is already included ....as very well known it is not a simple narrow BW

Can we fit our D data??

Yield DYield D++ = 1527 = 1527 5151

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

FOCUS D+ ++- analysis

Sideband Signal

PLB 585 (2004) 200

2lowm

2highm

D

C.L fit 7.7 %

K-matrix fit results

Low mass projection High mass projection

18 11.7

+

+2

0 +

(S - wave)π 56.00 ± 3.24 ± 2.08 0(fixed)

f (1275)π 11.74 1.90 0.23 -47.5 .7

ρ (770)π 30.82 ± 3.14 ± 2.29 -139.4 ±16.5 ± 9.9

decay channel phase (deg)fit fractions (%)

Reasonable fit with no retuning of the A&S K-matrix. No new ingredient (resonance) required not present in the scattering!

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

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

What about -meson then?

• Can conclude that – Do not need anything more than what is already in the S-wave

phase-shift to explain the main feature of D 3 Dalitz plot

Or, if you prefer,– Any -like object in the D decay should be consistent with the same -

like object measured in the scattering.

• Note: B D(*)K Dalitz plot analysis – The model used for the D0 Ks+- decay is one of the main sources of

systematics – Two “ad hoc” scalar states 1and 2 to describe excess of events not

reproduced by “established” resonances.

FOCUS D s+

++- analysis

Observe:

•f0(980)

•f2(1270)

•f0(1500) Sideband

Signal

Yield Ds+ = 1475 50

S/N Ds+ = 3.41

PLB 585 (2004) 200

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 (%)

No three-body non-resonant contribution

sD K-matrix fit results

• Just by a simple insertion of KK-1 in the decay amplitude F

• We can view the decay as consisting of an initial production of the five virtual states , KK,’and 4which then scatter via the physical T-matrix into the final state.

• The Q-vector contains the production amplitude of each virtual channel in the decay

1 1 1 1( ) ( )F I iK P I iK KK P TK P TQ

Even more: from P to Q-vector

Q-vector for Ds

• S-wave dominated by an initial production of and KK-bar states

The two peaks of the ratios correspond to the two dips of the normalizing modulus, while the two peaks due to the K-matrix singularities, visible in the normalization plot, cancel out in the ratios.

The normalizing modulus

Ratio of moduli of Q-vector amplitudes

Q-vector for D+

• The same!– s-wave dominated by an initial production of

and KK-bar states

The resulting picture

• The S-wave decay amplitude primarily arises from a ss-bar contribution such as that produced by– Cabibbo favored weak diagram for Ds

– One of the two possible singly Cabibbo suppressed diagram for D+. For the D+. the ss-bar contribution competes with a dd-bar contribution..

• The measured fit fractions seems to confirm this picture– S-wave decay fraction, 87% for Ds and only 56% for D+

– The dd-bar contribution in D+ case evidently prefers to couple to a vector state like (770), that alone accounts for about 30% of the decay.

Conclusions• Systematic investigation of charm decay dynamics is giving

interesting results in both semileptonic and hadronic sectors

• Dalitz plot analysis is and will be a crucial tool to extract physics from the HF decays

– Nevertheless, to fully exploit this unlimited potential a systematic revision of the amplitude formalization is required

• FOCUS has applied the K-matrix approach for the first time to the HF sector

– Its application has been decisive in clearing up a situation which recently became quite fuzzy and confusing: new “ad hoc” resonances were required to understand data

• K-matrix allows for a rigorous coupled-channel analysis

– This will be the further step in the Dalitz analysis of HF decays

• D+, D+s f0 amplitudes can feed both 3 and KK

Conclusions...cont’d

• Strong dynamics effects in D-decays now seem under control and

fully consistent with those measured by light-quark experiments.

• The new scenario is very promising for the future measurements of the CP violating phases in the B sector, where a proper description of the different amplitudes is essential.

• FOCUS is now sudying the D+K-++

– High statistics sample –Test of the model – Quasi two-body process or multi-body process ?

FOCUS D+K-

50000 events

Low momentum combination

Hig

h m

omen

tum

com

bina

tion

(GeV

2 )

(GeV2)

The first charm Dalitz analysis – MK1 (1977) D+K

“...consistent with a phase space Dalitz distribution.”

The future

*B D

*1 1 2, D ' and DD

1 node

B D

* *2 0 and DD

2 nodes!

We can learn even about D* states !!

BACKUP SLIDES

• My backup

What do you learn from Dalitz plots?D KK

*K K 2KKm

2KKm

2Km

sD KK

*K K

•Bands indicate resonance contributions

•For spinless parents, the number of nodes in the band give you the resonance spin

•Look at the band

•Interference pattern gives relative phases and amplitudes

•Look at the D+ K* band pattern of asymmetry

mm m

m

Aia e M 1 3 13

2 212

(cos )J J

rJ

r r r

p p PA

m m im

����������������������������Isobar model: Add up BW’s with angular factors

broad states

Nearly all charm analyses use the isobar model:

• For a two-body decay

CP violation on the Dalitz plot

AAtottot = g1M1ei1 + g2M2ei2

CP conjugate

AAtottot = g1M1ei1 + g2M2ei2** **

ii = strong phase

CP asymmetry:

aaCPCP==2Im(2Im(gg2 2 gg11**) sin() sin(11--22)M)M11MM22

|g|g11||22MM1122+|g+|g22||22MM22

22+2Re(+2Re(gg2 2 gg11**)cos()cos(11--22)M)M11MM22

|Atot|2- |Atot|2

|Atot|2+ |Atot|2==

2 different amplitudes strong phase-shift

Dalitz plot = FULL OBSERVATION FULL OBSERVATION of the decay

COEFFICIENTS and PHASES for each amplitude

Measured phase: =+CP conserving CP violating

CP conjugate =

=-=-

E831

aCP=0.006±0.011±0.005Measure of direct CP violation:asymmetrys in decay rates of DDKKK K

CP violation & Dalitz analysis

Ds , D+ KK

Ds+ K+ K+

D+ K+ K+

DsD

2Km

2KKm 2

KKm

2Km

KKm

+ -2

K Km

- +2

K πm

K+ Kprojection K projection

Yield D+ = 7106 92

S/N D+ = 8.62

Decay Fraction and phases

K*(892) = 20.7 1.0 % (0 fixed)

(1020) = 27.8 0.7 % (243.1 5.2)°

K*(1410) = 10.7 1.9 % (-47.4 4.9)°

K* (1430) = 66.5 6.0 % (61.8 3.8)°

f0(1370) = 7.0 1.1 % (60.0 5.3) °

a0(980) = 27.0 4.8 % (145.6 4.3)°

f2(1270) = 0.8 0.2 % (11.6 7.0) °

(1680) = 1.6 0.4 % (-74.3 7.5) °

Preliminary

phi(1020) K*(1430) a0(980) K1(1410) f2(1270) f0(1370) phi(1680)

K*(1430)phi(1020) a0(980) K1(1410) f2(1270) f0(1370) phi(1680)

Coefficients: D±,, DD++,, DD--

Phases: DD±±,, DD++,, DD--

Preliminary!

No evidence of CPV

K-matrix approach to improve the quality of the analysis

FSI effect

Watson’s theorem : weak amplitudes are relatively real; however complex phases can be introduced by

final state interaction

Interference term of and a nearly constant amplitude 0

* (892)K

cos senδi

Rare & forbidden decays

( ,

,

)sD D h

h K

FOCUS improved 8 results by a factor of 1.7 –14

CDF Br(D0+-)<2.4 x10-6 @ 90% C.L.is the best limit for this mode (65 pb-1 data)

CDF and D0 can trigger on dimuons promising

Cleo-c sensitivity 10-6

Phys.Lett. B572 (2003) 21

The best mixing limit from a fixed-target experiment, a valuable check on those results

Phys. Lett. B 618 - 23

....agrees better with BaBar & Bellethan with the old CLEO contour

(0.3810.017+0.008-0.016) %

(0.4290.063-0.061 0.027) % (FOCUS)

0

0

( )

( )D

D KR

D K

•FOCUS has the world’s most accurate lifetime measurements and excellent ifetime-resolution.

Additional more recent studies

• Search for other resonant contributions in the K spectrum– <1.6 % at 90 % C.L – <1.9 % at 90 % C.L

• Deeper investigation of the non-resonant amplitude– Non-resonant component fitted to an effective range model of the form

• cotLASS=1/ap*+ bp*/2 a=4.031.72 0.06 GeV-1

b=1.290.63 0.67 GeV-1

• NR contribution of 5.30 0.74 +0.99 – 0.51 %• angular distribution consistent with the effective-range scalar non-

resonant phase shift obtained by LASS (Watson)• excluded from further considerations.

• Hadronic decay D+K-++ will complete the K analysis ( see the end of this talk)

hep-ex/0503043

0( *(1680) )

( )

D K

D K

0( *(1680) )

( )

D K

D K

New measurement of the Ds+ ff

• According to flavor SU(3) symmetry the form factor ratios rv and r2 describing D+K0 should be close to Ds

+ since the only difference is a spectator quark d replaced with a s

• Lattice gauge calculations: max diff= 10%

• Experiment: – rv OK

– r2 inconsistent (3.3.

hep-ex/0401001

S-wave interference in

K*

dataccbar mc

even

ts

cos

V

even

ts

cos

V

090

00

045

0m - G 0

m + G0

m

even

ts

co

s V

data NO evidence for s-wave interference in Ds

v 2

791 2.27 0.35 0.22 1.570 0.250 0.190

0.9 0.6 0.3 1.400 0.500 0.300

653 2.3 1.0 0.4 2.

1.549 0.250 0.145 0.713 0.202 0

100 0.550 0.

.26

0

6

2 0

Group r r

E

CLE

FOC

O

US

E

Ds+ Form Factor results

1. Most precise measurement to date2. very consistent with D+K03. very consistent with theoretical expectation

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