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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  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 (*)

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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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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