Mixing of Ds1(2460) and Ds1(2536)Mixing of Ds1(2460) and Ds1(2536)

Institute of High Energy Physics, CASInstitute of High Energy Physics, CAS

Xiao-Gang WuInstitute of High Energy Physics, CAS

wuxiaogang@ihep.ac.cn

In collaboration with Qiang Zhao

QNP2012, April 16-20, Palaiseau, France

Outline

Introduction Mixing through hadron loop Coupling form factors in the chiral quark

model Result and discussion Summary

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1. Introduction Phys. Rev. D83, 072003 (2011). (BABAR) PDG2010 Constraints on the property and internal structure of

Ds1(2536) and Ds1(2460)?

Mass, width and mixing angle

Meson Tetraquark Hadronic molecule

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Ds spectrum

Low mass: Ds0(2317) DK threshold Ds1(2460) D*K threshold

Narrow width : isospin violation Ds0(2317)-> Ds π Ds1(2460)-> Ds

* π 4

The mixing between 3P1 and 1P1 can shed light on our understanding of Ds1(2460) and Ds1(2536) .

3P1 and 1P1cs states are not charge conjugation eigenstates3P1 and 1P1 have strong couplings to D*K through S wave

Heavy quark limit: Ds1(2460) pure j=1/2 , couple to D*K through S wave Ds1(2536) pure j=3/2 , couple to D*K through D wave

masswidth mixing angle

3P11P1

D*

K

5

a0 -f0 mixing, J.-J. Wu, Q. Zhao, and B. S. Zou, Phys. Rev. D 75, 114012(2007)

Hadron loop model

The mass shift of charmonium

E.Eichten etc., Phys.Rev., D17(1987)30900

。。。

Qian Wang etc, hep-ph/ 1202.3026

Xiao-Hai Liu etc,

Phys. Rev., D81(2010)014017

Yuan-Jiang Zhang etc,

Phys.Rev.Lett., 17(2009)172001。。。

Gang Li and Qiang Zhao, Phys.Rev.D84(2011)074005

Feng-Kun Guo and Ulf-G Meissner, Phys.Rev.Lett., 108(2012)112002

Feng-Kun Guo etc., Phys.Rev., D83(2011)034013

。。。

See talk by Qian Wang6

2. Mixing through hadron loop

Propagator matrix Gab

Diagonalization

Mass and width: pole in complex s planeMixing angle and relative phase

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Propagator matrix of two-state systemScalar or pseudo-scalar e.g., a0-f0 mixing

Vector or axial-vector e.g., and (3770)

a b

a,μ b,ν

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Ds1(2460) and Ds1(2536)Mixing scheme

Mixing term: D*K, Ds*η, DK*

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Couplings and divergence?

3. Couplings in the chiral quark model

Effective vertex in the hadron level

Couplings in the chiral quark model

e.g., heavy-light meson decays by X.-h. Zhong and Q. Zhao, Phys. Rev. D 78, 014029(2008), Phys. Rev. D 81, 014031(2010)

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Exponential Form Factor from the NR chiral quark model

Can remove UV divergence.Cutoff Λ is fixed and it characterizes the size of meson.No pole in the form factor and do not introduce unphysical

freedom.

Couplings gs

•insensitive to the initial meson mass•Strong coupling to D*K •Couplings to DK* are vanishing in LO•Isospin symmetry

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4. Result and discussion The mixing term

Real part and imaginary partTwo kinks for charged and neutral D*K thresholdsDs*η loop 1%Contribution from gμν is dominantContribution from Kμkν suffers an O(1/m2) suppression… …

12Xiao-Gang Wu and Qiang Zhao, Phys.Rev. D85 (2012) 034040

1P13P1

Mass and widthBare masses are taken from GI model.Two poles in the propagator matrix.Ds1(2460) large mass shift, Ds1(2536) small mass shift. The higher pole is insensitive to cutoff Λ, while the lower pole is sensitive.width

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Mass shift procedure

On shell state and virtual stateDiagonal shift and off-diagonal shiftD*K thresholds lower the mass spectrumBoth have a larger 1P1 component

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Mixing parameters

Heavy quark limit ma=mb

Ds1(2460) deviate from pure j=1/2 state by Ds1(2536) deviate from pure j=3/2 state by relative phase

Mixing angles are different for the two physical states!

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Experimental constraints

Width puts the strongest constraint.Two solutions symmetric respect to the heavy quark limit Our analysis favors the bigger one.

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5. summary When taking into the D*K loop corrections , we can explain the

masses, widths and extract mixing angles of Ds1(2460) and Ds1(2536) with no additional free parameter.

Loop corrections can cause both large mass shifts from quark model and significant mixing angle shifts from the heavy quark limit.

The exponential form factor from the quark model can give a good estimate of the real part of the meson loop.

Mass shift Mixing angle shift D*K coupling

Ds1(2460) 115MeV 12.3⁰ S wave

Ds1(2536) 15MeV 4.4⁰ D wave

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