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Charged charmonium-like states as rescattering effects in B  D sJ D (*). P. Pakhlov. Phys. Lett. B702 , 139 ( 2011 ). 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?.

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charged charmonium like states as rescattering effects in b d sj d

Charged charmonium-like states as rescattering effects in B DsJ D(*)

P. Pakhlov

Phys.Lett.B702, 139 (2011)

P. Pakhlov

z 4430
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?

P. Pakhlov

real state or some other effect
Real state or some other effect?

c

u

c

c

c

π

c

π

u

u

c

π

u

  • 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
  • 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

rescattering to B\'π K

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

Width of the peak  ~ (D1(2420))

P. Pakhlov

rescattering
Rescattering

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.

D

π

’

B

D*

K

P. Pakhlov

assumptions
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)

P. Pakhlov

spin parity constraints
Spin-parity constraints

DD* (2S)π allowed with both sides of the reaction in s-wave

  • => (2S)πsystem 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

Br(B  DD*K) ~ 1%

P. Pakhlov

search for d sj candidates
Search for DsJ candidates

new DsJ

(4160)

(3770)

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 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*.

Angular analysis –

DsJ(2700) polarization:

J=02/ndf= 185/5

J=12/ndf= 7/5

J=22/ndf= 250/5

The first radial excitation of Ds should be 60-100 MeV lighter;

two-body B decay into Ds\' are also expected to be large.

P. Pakhlov

calculate b dd s dd k zk
Calculate B  DDs\'  DD*K  ZK

D*

θ

D

K

Ds

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 ~ d100(θ\'\') = cos(θ\'\');

D* helicity (in Z frame)= 0

D*

D

θ\'\'

Z

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

P. Pakhlov

why rescattering results in a peak
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

P. Pakhlov

comments on d s mass
Comments on Ds\' mass

dependence 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

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

P. Pakhlov

calculate b d d s dd k zk
Calculate B  D*Ds*\'  DD* K  ZK

D

D

D*

θ

θ\'\'

D*

K

Z

Ds

K

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 ~ d10λ(θ) = cos(θ) or ±sin(θ)/√2

Z formation (1– 0–  1+):

AZ ~ d100(θ\'\') = cos(θ\'\');

D* helicity (in Z frame)= 0

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

P. Pakhlov

calculate b d d s dd k zk1
Calculate B  D*Ds*\'  DD* K  ZK

S-wave

(1/√3 a1 –1/√3 a0 )

λ=1

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

λ=0

P. Pakhlov

compare with belle babar data
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!

+

soft kaon – low efficieny

P. Pakhlov

peaks in c1 mass spectrum
Peaks in χc1π mass spectrum

Any D(*)D(*) χc1π 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 (χc1π)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 (χc1π)S: JP(Z)= 1–
  • Other are also possible. Can be useful to describe the double peak structure in M(χc1π)).

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

Ds*\' decay (1–  0– 0– ):

ADs ~ d100(θ) = cos(θ)

Z formation (0– 0–  1–):

AZ ~ d100(θ\'\') = cos(θ\'\')

No spin rotation

AD* ~ d000(θ\') = 1

Full amplitude:

ABW (MDK) × ADs× AD*× AZ

P. Pakhlov

calculate b dd s ddk zk
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)

P. Pakhlov

summary
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 χc1π. 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

P. Pakhlov

summary1
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

T H A N K Y O U !

P. Pakhlov

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