Scalar Mesons in D and B Decays
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1
Scalar Mesons in
D and B Decays
Scalar Mesons in
D and B Decays
Stefan SpanierUniversity of Tennessee
2
• Scalars are special
understand non-perturbative QCD (meson spectrum)
understanding of QCD vacuum (quantum numbers 3P0)
3
• 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 !
4
• 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
5
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
2
• 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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• I=1 Scalar a0(980) in D decays
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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• I=1 Scalar a0(980) in D decays
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) !
24
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)
27
• Charmless 3-body B Decays
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
28
• 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
29
• 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!
30
• 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)
31
• Charmless 3-body B Decays
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
32
• 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)
33
• I=0 Scalars
(500) ?
f0(980) !
f0(1200-1500) ?
f0(1500) !
34
• 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.
35
HQET mc >> QCD
mc << QCD
D0*
D1
D1’decays in HQET
‘hydrogen’
‘positronium’
narrow
• Charmed Scalars
36
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
37
• 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
38
• I=1/2 Scalar
39
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
40
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)
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