Transcript Rescattering Z

Charged charmonium-like
states as rescattering effects
in B DsJ D(*)
P. Pakhlov
Phys. Lett. B702, 139 (2011)
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Z(4430)+
•
Belle’s observation vs BaBar non-observation
•
•
two spectra are in a good agreement: almost all (even minor) features matches!
Why so different conclusions?
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Real state or some other effect?

–
c
Molecular state

c– π u
u

u––cu
c

π
two loosely bound charm
mesons


quark/color exchange at short
distances
pion exchange at large
distance

Threshold effects: peak
influenced by nearby D(*(*))D(*(*))
threshold

J. Rosner (PRD, 76, 114002,
2007) paid attention to proximity
of M(Z) to M(D*(2010)) +
M(D1(2420))
BD* D1(2420) K
Tetraquark
tightly bound four-quark state
Hadro-charmonium

c c–

specific charmonium state
“coated” by excited lighthadron matter
π
Φ→Ψ, BINP, Novosibirsk.2011
rescattering to B'π K
Mass of the peak M=M(D*)+M(D1(2420))
Width of the peak  ~ (D1(2420))
P. Pakhlov
Rescattering
Consider decay B  DsJ D(*)
D
B
K

π
’

D*
Φ→Ψ, BINP, Novosibirsk.2011

DsJ decays to D(*)K at time scale << D* lifetime
velocity of c-quark in D(*) and -mesons is ~ (0.2-0.5)
c; comparable with D-meson velocities in DD* rest
frame at mass ~ 4.4GeV (0.5 c)
Overlapping of wave functions of (DD*) and ('π)
should not be negligible, although it is color
suppressed.
P. Pakhlov
Assumptions

Assume factorization of the decay B  DsJ D and (DD*)  ('π) rescattering

Assume the rescattering amplitude independent on M(DD*) ( = M('π))

Calculate only angular part of triangle graph
N. N. Achasov & A.A. Kozhevnikov, Z.Phys. C48, 121 (1990)
ON THE NATURE OF C(1480) RESONANCE

Φ→Ψ, BINP, Novosibirsk.2011
considered triangle graph to explain
anomalous cross-section pπ  nφπ0 found at
Serpukhov (has never confirmed by any other
experiment)
P. Pakhlov
Spin-parity constraints
DD*  (2S) π allowed with both sides of the reaction in s-wave

=> (2S) π system has JP=1+; B  1+ 0–(K) the final state with positive parity, therefore
only B  D(*)DsJ ( DD* K) decays with positive parity can contribute!
orbital
excitations
j=3/2
radial
excitations
• P-wave (j=1/2) are below D(*)K threshold;
• Two body B-decays to P-wave (j=3/2) are suppressed;
• Radial excitations are expected to be large
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Br(B  DD*K) ~ 1%
Search for DsJ candidates
Belle observation
of Ds* radial exct.
M=27151114 GeV
=1152014 GeV
■B+→D0DsJ(2700) ■B+→ψ(3770)K+
■B+→ψ(4160)K+ ■B+→D0D0K+NR ■threshold comp
N=182±30
new DsJ
(4160)
(3770)
Angular analysis –
DsJ(2700) polarization:
J=0 2/ndf = 185/5
J=1 2/ndf = 7/5
J=2 2/ndf = 250/5
New Ds vector state produced with a
huge rate (>0.1%) in two-body B decay;
this state is a good candidate for the
first radial excitation of Ds*.
The first radial excitation of Ds should be 60-100 MeV lighter;
two-body B decay into Ds' are also expected to be large.
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Calculate B  DDs'  DD*K  ZK
Angular part for B  DDs' DD* K  Z K
Ds' decay (0–  1– 0– ):
ADs ~ 1;
D* helicity (in Ds' frame)= 0
D*
K
θ
Z formation (1– 0–  1+):
AZ ~ d100(θ'') = cos(θ'');
D* helicity (in Z frame)= 0
D*
θ''
D
D
Z
Ds
K
D* spin rotation between different frames
AD* ~ d100(θ') = cos(θ'); θ' – angle between Ds'and Z in D* rest frame
Full amplitude:
ABW (MD*K) × ADs × AD* × AZ
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Why rescattering results in a peak?
cos(angle rotation D* spin )
correlates with M(DD*)
M(DD*) distribution from
B  Scalar Scalar is flat
M(DD*) ~ 4.6 GeV
suppressed
M(DD*) ~ 4.8 GeV
suppressed
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Comments on Ds' mass
• Ds' is not observed yet, expected mass 2600-2660
MeV (2S1 -2S3 splitting 60-100 MeV)
• tune mass and width to agree with Belle Z
parameters
dependence
on Ds' mass
2.60 GeV
2.61 GeV
2.62 GeV
2.63 GeV
toy MC with
M =2610 MeV
 = 50MeV
dependence
on Ds' width
10 MeV
50 MeV
100 MeV
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Calculate B  D*Ds*'  DD* K  ZK
Angular part for B  D*Ds*' DD* K  Z K
Three amplitudes (D* helicity (in B frame) = ±1, 0)
Ds*' decay (1–  0– 0– ):
– 0–  1+):
Z
formation
(1
1
ADs ~ d 0λ(θ) = cos(θ) or ±sin(θ)/√2
AZ ~ d100(θ'') = cos(θ'');
D* helicity (in Z frame)= 0
D
D θ
D
*
*
θ
''
D
K
Z
Ds
K
D* spin rotation between different frames
AD* ~ d1λ0(θ') = cos(θ') or ±sin(θ') /√2;
θ' – angle between B and Z in D* rest frames
Full amplitude:
 aλ ABW (MDK) × ADs × AD* × AZ ,
assuming only s-wave a0=1/√3, a±1= –1 /√3
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Calculate B  D*Ds*'  DD* K  ZK
λ=1
• Only two amplitudes match parity constraint
(S and D-waves)
• assuming S-wave dominates
a0= –1/√3, a±1= 1 /√3
S-wave
(1/√3 a1 –1/√3 a0 )
λ=0
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Compare with Belle/BaBar data
Sum B  DDs'  DD* K and B  D*Ds*'  DD* K (S-wave). Not a perfect description.
• should sum complex amplitudes (interference).
• also need to take into account interference with remaining (after veto) K*(*)
background
• efficiency is also important issue: sharp drop around high mass limit due to soft kaon.
This is just very naive illustration: correct procedure is fit!
+
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Peaks in χc1π mass spectrum
Any D(*)D(*)  χc1 π requires at least one p-wave to conserve parity.




Only B  D(*)DsJ  D(*)D(*)K chains with negative parity is allowed for rescattering
(D(*)D(*))P (χc1 π)S
Note χc1 is a p-wave orbital excitation, therefore p-wave D(*)D(*) rescattering can be not
suppressed (and even favored)!
The simplest one is (DD)P (χc1 π)S: JP(Z)= 1–
Other are also possible. Can be useful to describe the double peak structure in M(χc1 π)).
Known decay chain B  DDs*' D DK ( Z K)
Ds*' decay (1–  0– 0– ):
ADs ~ d100(θ) = cos(θ)
No spin rotation
AD* ~ d000(θ') = 1
Full amplitude:
ABW (MDK) × ADs × AD* × AZ
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Z formation (0– 0–  1–):
AZ ~ d100(θ'') = cos(θ'')
Calculate B  DDs*' DDK  ZK
B  DDs*' DD K roughly reproduces the broad bump near 4.2GeV; the second
peak at high mass limit expected from this chain is hidden in the data by sharp drop
of reconstruction efficiency.
Other DsJ D(*) (only with negative parity!) can contribute
e.g. B  D*Ds*'  D*D* K (P-wave only)
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Summary

A peak (and nearby structure) in M(' π) in B  ' π K decay
can be explained by B  DDs' and B  D*Ds*' decays followed
by rescattering DD*  ' π



both decays are not observed so far, but both are expected to be large
even Ds' is not observed so far, but its mass/width are in agreement with
expectations
A chain with opposite parity is required to explain peak(s) in
χc1 π. The simplest (and probably the largest) one is the known
B  DDs*'  DDK can describe the general features of the
data spectrum.
While within the proposed explanation the peaks in
charmonium-π system are results of the kinematics, these
peaks reveal a very interesting effect: large rescattering, not
expected by theory
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov
Summary
•
If the proposed explanation is true there are many ways to check
it with the BaBar/Belle data.
•
Direct search for Ds' in two body B decays:
M ~ 2610 GeV;  ~ 50 MeV; Br(BDs' D) × Br(Ds'  D*K) ≥ 10–3
• Dalitz (Dalitz+polarization fit) of B  ' π K: check Z+ vs rescattering
hypothesis
•
If rescattering D*D ' π is large in B decays it should also reveal
itself in all process where DD* (JP=1+) are produced at one point
THAN K YOU !
Φ→Ψ, BINP, Novosibirsk.2011
P. Pakhlov