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Mixing of D s1 (2460) and D s1 (2536)

Institute of High Energy Physics, CAS. Mixing of D s1 (2460) and D s1 (2536). Xiao-Gang Wu Institute 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

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Mixing of D s1 (2460) and D s1 (2536)

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  1. Institute of High Energy Physics, CAS Mixing of Ds1(2460) and Ds1(2536) Xiao-Gang Wu Institute of High Energy Physics, CAS wuxiaogang@ihep.ac.cn In collaboration with Qiang Zhao QNP2012, April 16-20, Palaiseau, France

  2. Outline • Introduction • Mixing through hadron loop • Coupling form factors in the chiral quark model • Result and discussion • Summary

  3. 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

  4. Ds spectrum • Low mass: • Ds0(2317) DK threshold • Ds1(2460) D*K threshold • Narrow width : isospin violation • Ds0(2317)-> Dsπ • Ds1(2460)-> Ds*π

  5. The mixing between 3P1 and 1P1 can shed light on our understanding of Ds1(2460) and Ds1(2536) . • 3P1 and 1P1cs states are not charge conjugation eigenstates • 3P1 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 mass width mixing angle D* 3P1 1P1 K a0 -f0 mixing, J.-J. Wu, Q. Zhao, and B. S. Zou, Phys. Rev. D 75, 114012(2007)

  6. 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 。。。 Feng-Kun Guo etc., Phys.Rev., D83(2011)034013 Gang Li and Qiang Zhao, Phys.Rev.D84(2011)074005 Feng-Kun Guo and Ulf-G Meissner, Phys.Rev.Lett., 108(2012)112002 See talk by Qian Wang 。。。

  7. Mixing through hadron loop • Mass and width: • pole in complex s plane • Mixing angle and • relative phase Propagator matrix Gab Diagonalization

  8. Propagator matrix of two-state system • Scalar or pseudo-scalar • e.g., a0-f0 mixing • Vector or axial-vector • e.g.,and (3770) b,ν b a,μ a

  9. Ds1(2460) and Ds1(2536) • Mixing scheme • Mixing term: D*K, Ds*η, DK* • Couplings and divergence?

  10. 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)

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

  12. Result and discussion • The mixing term • Real part and imaginary part • Two kinks for charged and neutral D*K thresholds • Ds*η loop 1% • Contribution from gμν is dominant • Contribution from • Kμkνsuffers an O(1/m2) suppression • … … Xiao-Gang Wu and Qiang Zhao, Phys.Rev. D85 (2012) 034040

  13. Bare 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 • Mass and width 1P1 3P1

  14. Mass shift procedure • On shell state and virtual state • Diagonal shift and • off-diagonal shift • D*K thresholds lower the mass spectrum • Both have a larger 1P1 component

  15. 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!

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

  17. 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. Thanks for your attention!

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