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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
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
2
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
3
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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