Download ppt - Scalar Mesons in D and B Decays

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Scalar Mesons in

D and B Decays

Scalar Mesons in

D and B Decays

Stefan SpanierUniversity of Tennessee

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• Scalars are special

understand non-perturbative QCD (meson spectrum)

understanding of QCD vacuum (quantum numbers 3P0)

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• Scalars are special

f0 f0

K

K_

u,d

u,d_ _

s

s

_

easy transitions:

As states are mixtures:

ann + bss + cqqqq + dglue +

Decay obscures quark content need to study production and decay

_ _ _ _

Experimentally- broad states- often covered by tensors- featureless decay angle distributions

too many / heavily shifted !

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• Why Scalars in D, DS, and B Decays

• Initial state is single, isolated particle with well defined JB,D=0, JDs=1

• Operators for decay have simple lorentz- and flavor quantum numbers

• Short range QCD properties are known (better)

• Weak decay defines initial quark structure; and rules (e.g. I=1/2)

• Large variety of transitions to different flavor and spin states with large mass differences of the constituent quarks - combined/coupled channel analyses - isospin relations (simple BF measurements) - semileptonic decays (true spectator, form factors)

• Access to higher mass scalar states in B

• Input for B CP – physics - add penguin modes for New Physics Search, e.g. B0 f0 K0

- CP composition of 3-body modes, e.g. B0K0K+K-

- hadronic phase for CP angle in BDK from D-Dalitz plot

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c.c.

• Experiments

• E791 -(500 GeV) [Pt, C] charm

• Focus Brems [Be] charm

• BaBar 2008 • Belle > 2008

• CLEO-c e+e- (3S) DD 281pb-1

e+e- qq @ Y(4S)_

B-factories are also D-factories:

In each expect (2006)

> 1 Million of

– E791 - 35,400 1

– FOCUS - 120,000 2

– CLEO-c - D0K-+ : 51,200 3

BaBar

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

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

3. CLEO-c: hep-ex/0512063.

91fb-1

> 450 Million BB pairs

take more than 10BB / sec

__

D0 K-+

_

+

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• Formalism for X 3 body (Dalitz plot analysis)

a

b

c

d

ll

R

L

l

Spectator ?

d

R c

assuming dominance by 2-body interaction (isobar model) scalar resonances strongly overlap / decay channels open in vicinity

Dynamic amplitude not just a simple Breit Wigner

- Analytic- Unitary (2-body subsystem)- Lorentz-invariant

K-matrix formalism widely used:

2-body scattering

production / decay

R = (1-iK)-1

2-body PS

T = R K F = R P P-vector = Q T Q-vector

• Watson theorem: same phase motion in T and F in elastic range

• Adler zero: at m 0 for p=0: T = 0 near threshold; also/where for F ?

• Resonance: = pole in unphysical sheet of complex energy plane

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• Content

• I = 1 Scalars

• I = 1/2

• I = 0

• Charmless 3-body B Decays

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D*+ D0 +slow

K0 + - #92935

K0 K+K- #13536

K0 K0S +-

__

_

D-flavor tag

D =

6.1

MeV

/c2

D = 3.4 M

eV/c

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• I=1 Scalar a0(980) in D decays

In 91.5 fb-1 @ Y(4S) BaBar finds:

Ratio of branching fractions:

BaBar

BaBar

97.3% purity

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• I=1 Scalar a0(980) in D decays(1020)

f0(980)

(770)

K*(892)

a0(980)

f0(980)Efficiency:

Data:

BaBar BaBar

D0K0S+ - D0K0

SK+K-

a0(980)

BaBar

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• I=1 Scalar a0(980)

0 fixed by total BF

couplings gi (also tune lineshape)

e.g. F1 : X

F2 : X KK)

Pro

duct

ion

ampl

itude

2

Flatte formula:

Scattering amplitude

5 parameters

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we

igh

t/ 5

Me

V/c

2

• Extract S-wave and describe Flatte’ formula with Crystal Barrel parameters [Abele et al., PRD 57, 3860 (1998)]

• Moment analysis only S and P waves

Fix m0 and coupling g, but float gKK

Best description of S-wave from moments and floated in PWA inconsistent with CBAR: BaBar: gKK = 473 + 29 + 40 MeV1/2

CBAR: gKK = 329 + 27 MeV1/2

need coupled channel analysis with

D0 K0

• PWA needs ~3% contribution from higher mass resonance tail (outside PS) assume f0(1400) ; uniform distribution worse

what about a0(1450) ?

_

BaBar

DP projection

D0K0SK

+K-

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BaBar

I=0,1I=1

KK phase space corrected mass distributionnormalized to the same PS area

I=1 S-wave dominanceD0K0

S+ -

[BaBar: hep-ex/0408088][Belle : hep-ex/0411049]

~ 5.5 % f0(980) contribution

for f0(980) couplings need fix to better line-shape parameters

BaBar

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• I=1 Scalar a0(980) in B decays

In 9 fb-1 @ Y(4S) CLEO finds: [PRL 93 (2004) 111801]

Main contribution from a0K0S;

also a2(1320)K0S, K*(892), K0*(1430)

B(D0 K0 0 ) = (1.05 ± 0.16 ± 0.14 ± 0.10) %

fraction(a0(980)) = 1.19 ± 0.09 ± 0.20 ± 0.16

# (155 + 22) events

_

CLEO

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• I=1 Scalar a0(980) in B decays

K+

For scalar mesons with {u,d} quark content theory expects suppression

- all CKM suppressed (least a0K penguin Vts)

- G-parity (W does not couple to scalar) [Laplace,Shelkov, EPJ C 22, 431 (2001)]

- effective Hamiltonian decay amplitude 1 - G(mi,mb,mqi) (G1) ( + for 0- )

mi decay particle with quark content qi [Chernyak, PLB 509, 273 (2001)]

BaBar determines in 81.9 fb-1

B(B a0 X, a0

90% C.L. [10-6]

a0- + < 5.1

a0- K+ < 2.1

a0- K0 < 3.9

a00 + < 5.8

a00 K+ < 2.5

a00 K0 < 7.8

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• I=1 Scalar

a0(980) !

a0(1450) ?

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• I=1/2 Scalar Data from:

K-p K-+n

and

K-p K0-pNPB 296, 493 (1988)

No data below 825 MeV/c2

K Scattering LASS

0.7 0.9 1.1 1.3 1.5 MK (GeV)

150

100

50

0

-50

Ph

ase

(deg

rees

)

0.7 0.9 1.1 1.3 1.5MK (GeV)

• Most information on K-+ scattering comes from the

LASS experiment (SLAC, E135)

K’ threshold

• use directly in production if re-scattering is small• require unitarity approach …

LASS parameterization

• Disentangle I=1/2 and I=3/2 with K++ [NPB133, 490 (1978)]

PenningtonChPT compliant

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• I=1/2 Scalar

LASS experiment used an effective range expansion toparameterize the low energy behaviour: : scattering phase q cot = + a: scattering length b: effective range q: breakup momentumTurn into K-matrix: K-1 = cot

K = + and add a pole term (fits also pp annihilation data)

Both describe scattering on potential V(r) (a,b predicted by ChPT)

Take left hand cuts implicitly into account

Instead treat with meson exchange in t- () and u-channel (K* ) [JPA:Gen.Phys 4,883 (1971), PRD 67, 034025 (2003)]

only K0*(1430) appears as s-pole

(K*) exchange important for S-waves in general

1 b q2

a 2___ ______

a m g0

2 + a b q2 m02 – m2

___________ ___________

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• I=1/2 Scalar

D+ (K-+) +

• K system dominated by K*(892)• Observe ~15% forward-backward asymmetry in K rest frame• Hadronic phase of 45o corresponds to I=1/2 K wave measured by LASS required by Watson theorem in semileptonic decay below inelastic threshold

• S-wave is modeled as constant (~7% of K*(892) Breit-Wigner at pole). a phase of 90o would correspond to a kappa resonance, but …

Study semileptonic D decays down to threshold !

FOCUS

Reconstructed events: ~27,000D+

K-

+

csW+

[PLB 621, 72 (2005)][PLB 535, 43 (2002)]

I=1/2 ?

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• I=1/2 Scalar

BaBar

B J/ K* in 81.9 fb-1 study K mass from 0.8 – 1.5 GeV/c2

- weak process b ccs is a pure I=0 interaction isospin(K) = ½

- PVV 3 P-wave amplitudes (A0,A||,A) if no J/ – K* rescattering (Watson theorem) all P-waves are relatively real;

|| - - > 7 standard deviations !

- according to LASS finding consider K S wave and extract waves with moment analysis

- use change of S-P interference near K*(892) to resolve phase ambiguity S – 0 0 – S

- one solution does behave like

S(LASS) - P (LASS) +

BaBar

S –

0

LASS

_

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• I=1/2 Scalar E791

K*(892)

K*(1430)

D+ K-++

#15090

Fit with Breit-Wigner (isobar model):

~138 %

A

~89 %

C

2/d.o.f. = 0.73

2/d.o.f. = 2.7

M = (797 19 42) MeV/c2

eVc

D+K-

+

W++

[PRL 89, 121801 (2002)] unitarity

+

+

K-

W+

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• I=1/2 Scalar Fit with Breit-Wigner + energy-independent fit to K S-wave(P(K*(892), K*(1680)) and D-waves (K*2(1430))act as interferometer)

Model P- and D-wave (Beit-Wigner), S-wave A = ak eik bin-by-bin (40)

E791

Phase AmplitudeCompares well with BW Isobar fit

S w

ave

P w

ave

D w

ave

Mass projection2/NDF = 272/277 (48%)

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• I=1/2 Scalar E791

• Quasi-two body K interaction (isobar model ) broken ?

• Watson theorem does not apply ?

• Isospin composition I=1/2 % I=3/2 in D decay same as in K K?

if not

if not

K’ threshold

-75o

… but differs from LASS elastic scattering

|FI |

A(s) eis = F1/2(s) + F3/2(s) , s = mK2

FI(s) = QI(s) eiIT11

I(s)

s – s0I

Q-vector approach with Watson:

T11 from LASS ( same poles ?)

Constraint: Q smooth functions

Adler zero s0I removed

[Edera, Pennington: hep-ph/0506117]

big !

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• I=1/2 Scalar

(800) ?

K*(1430) !

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f0(980)

(770)

f 2(12

70)

0.1 0.8m13

2 (GeV2)

Extract S-wave phase (s)from left-right asymmetry inf2(1270)

F = a sin(s) ei((s)+)

Choose phasefrom 4 solutions

(o)

E791 fit ((500))

• E791: BW fit + (500)

m = (478 24 17) MeV

= (324 42 21) MeV

• FOCUS: use K-matrix A&S (no pole)

[PLB 633, 167 (2006)]

m() GeV

• I=0 Scalar Focus/E791D+ -++

E791~ 1680 events

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• I=0 Scalar

Au, Morgan, Pennington, Phys. Rev. D35, 1633 (1987)

Anisovich, Sarantsev, Eur. Phys. A16, 229 (2003)

4 pole, 2resonance 5 pole, 5 resonance

I=0 S-wave parameterization (several on market)

f0(980)

f0(1500)

… from fits to data from scattering, pp annihilation, …

• f0(980) : (988 – i 23) MeV (1024 – i 43) MeV describes (00)

• no (500) pole, but feature included

• also with t (u) channel (f2,..) exchange [Li,Zou,Li:PRD 63,074003(2001)] (also I=2 phase shift)

Coupled channel for pp-annihilation into 2 neutral PS, 3x3 K-matrixfinds pole at low mass

_

_

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• I=0 Scalar

FOCUS

f 0(98

0)

(1450)

DS + - +

FOCUS(#1475) E791 (#848)

S-wave 87% f0+f0(1370)+NR 90%K matrix,P vector* phase ~0,f MeV

f2(1270) 10% 20%(1450) 6% 6% (770) 6%

J/

FOCUS

* not sensitive to Adler zero

ss

flavor tag

_

c

s_

sDS

f2(1270)

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Mode Events(1/fb-1 )

D0→K+K- K0 ~140

B+→K+ BelleBABAR ~11

B+→K+K- K+ Belle ~8

B0→ K+ BABAR ~5

B0→K0 Belle2005 ~3

B0→K+K- K0 BABAR2005 ~2.5

B+→KSKS K+ ~0.9

B0→ K0S ~0.5

B0→KSKS KS ~0.4

- B→odd # of K : penguin-dominated decays- large phase-space, limited number of events- Dalitz plot analyses at feasibility limit

D0→K+K-K0

B0→K+K-K0

DalitzPlot

analysis

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• Charmless B Decay Reconstruction

Energy-substituted massEnergy-substituted mass Energy differenceEnergy difference Event shapeEvent shape

Main background from continuum events:

Some standard discrimination variables:

*2B

*2beamES pEm *

beam*B EEΔE

events

BB

events

qqee

cs,d,u, q ,qqee

* = e+e- CM frame Likelihood fit

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• B0K+K-K0S Dalitz Plot Results

D+,Ds+

reflections

X(1500)

non-res

[BABAR,hep-ex/0507094]

c0

Mode Fraction (%)

(1020)KS 15.43.40.6

X(1500)KS 5.22.20.9 (<8.3)38.97.30.9

Non-resonant

70.73.81.7

c0KS 3.11.60.8 (<5.5)

f0(980)KS 5.73.21.0 (<9.7)

Multiple solutions

• P-wave content consistent with isospin analysis Belle [hep-ex/0208030]

and moment analysis BaBar [PhysRevD71:091102(2005)]

(1020)

(1020)

no a0!

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• B+K+K-K+ Dalitz Plot Results

X(1500)

non-res

c0

Mode Fraction (%)

(1020)KS 15.01.3

X(1500)KS 8.21.9637

Non-resonant

705

Also penguin dominated ~ 4 times more events per fb-1:

1089 signal events, 140 fb-1

[Belle,PRD71:092003(2005)]

Multiple solutions

(1020)

(1020)

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Parameterization of non-resonant S-wave background? - large excess of events at lower (higher) masses (~70% of total yield) - flat (phase-space) model found inadequate by all analyses - try a set of ad hoc models:

Belle [PRD71,092003]

BABAR [hep-ex/0507094]

- little difference in fit quality with current statistics

12KK

2KK

2K

2KK

mαlogm4mm

2KK

mαexp flat

Contact termsKS

K+

K-

B0

0*SB

KS

K+

K-

B0

Resonance tails

[Cheng,Yang,Phys.Rev.D66:054015(2002)]

What is it ?

continuum

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• X(1500)

Is bump at 1.5GeV really f0(1500)?

- PDG: BF( f0(1500)→ )/BF( f0(1500)→KK ) ≈ 4

K+K-KSK+K-KS

Belle [PRD71]

[hep-ex/0507094]

K+K+K-K+K+K-- hard to assign a small excess of events in K to f0(1500)

-events assigned to f0(1370), f2(1270)

- f0(1500) interferes with S-wave background constructively for KKK,destructively for K ?

[Minkowski,Ochs,EPJC 39,71(2005)]

BABARKSKS

K+K+

Belle [hep-ex/0509001]

[hep-ex/0507094]

f0(980)

(77

0)

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• I=0 Scalars

(500) ?

f0(980) !

f0(1200-1500) ?

f0(1500) !

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• Summary / Outlook

• Since 40 years the scalar mesons are a puzzle !

• Charm production experiments, but particularly the B-factories will provide input.

• Missing states are found, existing ones can be studied in greater detail.

• BaBar and Belle are continuing sources, SuperB at Frascati may be a future source for scalar meson spectroscopy in D, DS, and B decays.

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HQET mc >> QCD

mc << QCD

D0*

D1

D1’decays in HQET

‘hydrogen’

‘positronium’

narrow

• Charmed Scalars

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2+

0+

2+/0+

M = ( 2308 ± 17 ± 15 ± 28 ) MeV/c2

= ( 276 ± 21 ± 18 ± 60 ) MeV/c2

B- D+ - -

K- + +

D0*0

Regions in pion helicity angle

Belle

virtual

Only pion S waveNo resonance in system

• Charmed Scalars

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• I=0 Scalar

K-matrix for coupled channel analysis- Adler zero (taken out for production – how P*Adler)- constant c=0.8 in K-matrix -> also propagator; allows 180o phase

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• I=1/2 Scalar

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B0→KKK0: Moments AnalysisB0→KKK0: Moments Analysis

6)%8(89 evenLf 6)%8(89 evenLf

[BABAR,PhysRevD71:091102(2005)]

L

HLL

2cosP PA

BABAR’s – analysis of angular moments:

0

2

P

P

4

51 evenLf

Piδ

S AeAA

Compute wave strengths using moments of Legendre polynomials:

Average moments computed using sPlot technique [Pivk, Le Diberder, physics/0402083]

Describe decay in terms of S and P-waves decaying into K+K-

Outside of KS region

Better errors with ½ statistics w.r.t. isospin analysisNot relying on any assumptions

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B0→KKK0: Isospin AnalysisB0→KKK0: Isospin Analysis

Belle’s – isospin analysis [hep-ex/0208030] - assume dominance of gluonic penguins- use SU(2)flav to relate rates for (K+ K-)K0 and (K0K0)K+

S

SSevenL KKKB

KKKBf

0

K+

K

B0

KSL

L’=LKS

KS

B0

K+ L

L’=L

Only L=even allowedAll L allowed

- fraction of L=even:

5)%9(93 evenLf 5)%9(93 evenLfOutside of KS region

Belle(386MBB)