Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Phys. Lett. B702, 139 (2011)

Charged charmonium-like states as rescattering effects

in B DsJ D(*)

P. Pakhlov

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? Molecular state

two loosely bound charm mesons

quark/color exchange at short distances

pion exchange at large distance

Tetraquark tightly bound four-quark state

Hadro-charmonium specific charmonium state

“coated” by excited light-hadron matter

u– cuc–

c c–π

π

πc c–uu–

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))

BD* D1(2420) K

rescattering to B'π K

Mass of the peak M=M(D*)+M(D1(2420))Width of the peak ~ (D1(2420))

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Rescattering

B

D

D*

’ π

K

Consider decay B DsJ D(*)

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.

Φ→Ψ, BINP, Novosibirsk.2011 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

considered triangle graph to explain anomalous cross-section pπ nφπ0 found at Serpukhov (has never confirmed by any other experiment)

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Spin-parity constraintsDD* (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!

orbitalexcitationsj=3/2

radialexcitations

• 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 Br(B DD*K) ~ 1%

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Search for DsJ candidates

new DsJ

(4160)(3770)

J=0 2/ndf = 185/5J=1 2/ndf = 7/5 J=2 2/ndf = 250/5

N=182±30

■B+→D0DsJ(2700) ■B+→ψ(3770)K+ ■B+→ψ(4160)K+ ■B+→D0D0K+

NR ■threshold compM=27151114 GeV=1152014 GeV

Angular analysis – DsJ(2700) polarization:

The first radial excitation of Ds should be 60-100 MeV lighter;two-body B decay into Ds' are also expected to be large.

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

*.

Belle observation of Ds

* radial exct.

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Calculate B DDs' DD*K ZK

DDs

KD* θ D

ZK

D*

θ''

Angular part for B DDs' DD* K Z K

Ds' decay (0– 1– 0– ): ADs ~ 1; D* helicity (in Ds' frame)= 0

Z formation (1– 0– 1+): AZ ~ d1

00(θ'') = cos(θ''); D* helicity (in Z frame)= 0

D* spin rotation between different frames AD* ~ d1

00(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?M(DD*) distribution from B Scalar Scalar is flat

cos(angle rotation D* spin ) correlates with M(DD*)

M(DD*) ~ 4.6 GeVsuppressed

M(DD*) ~ 4.8 GeVsuppressed

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Comments on Ds' mass

toy MC with M =2610 MeV = 50MeV

• 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' width

dependence on Ds' mass

10 MeV50 MeV100 MeV

2.60 GeV2.61 GeV2.62 GeV2.63 GeV

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Calculate B D*Ds*' DD* K ZK

D

DsK

D*θD

ZK

D*

θ''

Angular part for B D*Ds*' DD* K Z K

Three amplitudes (D* helicity (in B frame) = ±1, 0) Ds

*' decay (1– 0– 0– ): ADs ~ d1

0λ(θ) = cos(θ) or ±sin(θ)/√2 Z formation (1– 0– 1+): AZ ~ d1

00(θ'') = cos(θ''); D* helicity (in Z frame)= 0

D* spin rotation between different frames AD* ~ d1

λ0(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

• Only two amplitudes match parity constraint (S and D-waves)• assuming S-wave dominates a0= –1/√3, a±1= 1 /√3

λ=1

λ=0

S-wave(1/√3 a1 –1/√3 a0 )

Calculate B D*Ds*' DD* K ZK

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Compare with Belle/BaBar dataSum 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!

+

soft

kaon

– low

effic

ieny

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

Peaks in χc1π mass spectrumAny 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)).

Ds*' decay (1– 0– 0– ):

ADs ~ d100(θ) = cos(θ)

Z formation (0– 0– 1–): AZ ~ d1

00(θ'') = cos(θ'')No spin rotation AD* ~ d0

00(θ') = 1

Known decay chain B DDs*' D DK ( Z K)

Full amplitude: ABW (MDK) × ADs × AD* × AZ

Φ→Ψ, BINP, Novosibirsk.2011 P. Pakhlov

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(BDs' 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

T H A N K Y O U !