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Study on the Mass Difference btw p and r using a Rel. 2B Model

Study on the Mass Difference btw p and r using a Rel. 2B Model. 2011. 08. 25 Jin-Hee Yoon ( ) Dept. of Physics, Inha University collaboration with C.Y.Wong and H. Crater. Introduction. m p = 0.140 GeV, m r = 0.775 GeV Why is the pion mass so small?

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Study on the Mass Difference btw p and r using a Rel. 2B Model

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  1. Study on the Mass Difference btw p and r using a Rel. 2B Model 2011. 08. 25 Jin-Hee Yoon ( ) Dept. of Physics, Inha University collaborationwith C.Y.Wong and H. Crater

  2. Introduction • mp = 0.140 GeV, mr = 0.775 GeV • Why is the pion mass so small? • Why is the pion mass not zero? • Chiral symmetry breaking • What we will do? • Trace the origin of the mass of p / r using the 2B relativistic potential model.

  3. 2-Body Constraint Dynamics P. van Alstine et al., J. Math. Phys.23, 1997 (1982) • Two free spinless particles with the mass-shell constraint → removes relative energy & time • Two free spin-half particles with the generalized mass-shell constraint • → potential depends on the space- like separation only & P ⊥ p

  4. 2-Body Constraint Dynamics P. van Alstine et al., J. Math. Phys.23, 1997 (1982) • Pauli reduction + scale transformation 16-comp. Dirac Eq. → 4-comp. rel. Schrodinger Eq.

  5. Why Rel.? • Even within the boundary, their kinetic energy can be larger than the quark masses. • Already tested in e+e- binding system (QED) [Todorov, PRD3(1971)] • can be applied to two quark system( p and r ) (QCD) • Can treat spin-dep. terms naturally

  6. What's Good? • TBDE : 2 fermion basis 16-component dynamics 4-component • Particles interacts through scalar and vector interactions. • Leads to simple Schrodinger-type equation. • Spin-dependence is determined naturally.

  7. QCD Potentials • Common non-relativistic static quark potential • Dominant Coulomb-like + confinement • But asymptotic freedom is missing • Richardson[Phys. Lett. 82B,272(1979)] FT [Eichten et al., PRD 21 (1980)]

  8. QCD Potentials • Richardson potential in coord. space • For : asymptotic freedom • For : confinement • We will use fitting param.

  9. QCD Potentials • Scalar Pot. • Vector Pot.

  10. What's Good again? • TBDE : 2 fermion basis 16-component dynamics 4-component • Particles interacts through scalar and vector interactions. • Yields simple Schrodinger-type equation. • Spin-dependence is determined naturally. • No cutoff parameter • No singularity

  11. Formulation • central potentials + darwin + SO + SS + Tensor + etc. FSOD & FSOX=0 when m1=m2

  12. Formulation

  13. FSOD=0 and FSOX=0 when m1=m2 For singlet state with the same mass, no SO, SOT contribution ← Terms of ( FD, FSS, FT ) altogether vanishes. H=p2 + 2mwS + S2 + 2ewA - A2 Formulation

  14. For p (S-state), For r (mixture of S & D-state), Formulation

  15. Once we find b2, Invariant mass Formulation

  16. MESON Spectra 32 mesons

  17. MESON Spectra All 32 mesons

  18. Wave Functions(p & r) 3 X r

  19. Individual Contribution(p) W = 0.159 GeV-1

  20. Individual Contribution(r) W = 0.792 GeV-1

  21. Summary • Using Dirac’s rel. constraints, TBDE successfully leads to the SR-type Eq. • With Coulomb-type + linear potential, • By fitting to 32 meson mass spectra, determine 3 potential parameters and 6 quark masses • Small quark masses : mu=0.0557 GeV, md=0.0553 GeV • Non-singular(well-beaved) rel. WF is obtained. • At small r, S-wave is proportional to D-wave.

  22. Summary • Can reproduce the huge mass split of p-r • In pion mass • Still large contributions from Darwin and Spin-Spin terms (3~4 GeV compared to 0.16 GeV) • But cancelled each other, remained ~20% • Balanced with kinetic term • resulting small pion mass • This Model inherits Chiral Symmetry Braking.

  23. Thank you for your attention!

  24. Backup slides

  25. Pure Coulomb : BE=-0.0148 GeV for color-singlet =-0.0129 GeV for color-triplet(no convergence) + Log factor : BE=-0.0124 GeV for color-singlet =-0.0122 GeV for color-triplet + Screening : BE=-0.0124 GeV for color-singlet No bound state for color-triplet Overview of QQ Potential(1)

  26. Overview of QQ Potential(2) • + String tension(with no spin-spin interaction) When b=0.17 BE=-0.3547 GeV When b=0.2 BE=-0.5257 GeV Too much sensitive to parameters!

  27. and QQ Potential • Modified Richardson Potential Parameters : m, L And mass=m(T) A : color-Coulomb interaction with the screening S : linear interaction for confinement

  28. Work on process • To solve the S-eq. numerically, • We introduce basis functions fn(r)=Nnrlexp(-nb2r2/2) Ylm fn(r)=Nnrlexp(-br/n) Ylm fn(r)=Nnrlexp(-br/√n) Ylm … • None of the above is orthogonal. • We can calculate <p2> analytically, but all the other terms has to be done numerically. • The solution is used as an input again → need an iteration • Basis ftns. depend on the choice of b quite sensitively and therefore on the choice of the range of r.

  29. Future Work • Extends this potential to non-zero temperature. • Find the dissociation temperature and cross section of a heavy quarkonium in QGP. • Especially on J/y to explain its suppression OR enhancement. • And more…

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