1. Masses & Magnetic Moment of Charmed Baryons in Hyper Central Modelq c
Masses & Magnetic Moment of Charmed Baryons in Hyper Central Model
Bhavin Patel
Department of Physics, Sardar Patel University,
Vallabh Vidyanagar , Gujarat, INDIA
XII International conference on Hadron Spectroscopy: Hadron

2. Plan of the talk Introduction
Frame work of hyper central potential model
Result and comparisons
Conclusion

3. Introduction
There is a flood of experimental data from high energy experiments from different hadron colliders [LHC, BaBar, CDF, CLEO, DELPHI, BELLE etc] in the spectroscopy of heavy flavour hadrons.
Though much of the data are related to mesons, there exists interesting observations related to the heavy flavour baryons.
Baryons themselves are interesting as they represent simple three body systems. Its treatment is complicated compared to the two body meson systems.
Due to disparities among the model predictions of the static properties of baryons and their magnetic moments at the heavy flavour sector [P. Avery et.al(1995)], alternate schemes to describe the properties of baryons particularly in the heavy flavour sector are of recent interest [D. Ebert et .al, (2005)] .
For the present study, we employ the hyper central description of the three-body problem [M. M. Giannini et. al (2001), E. Santopinto et. al , (1998)] for the baryons constituting one or more charm quarks.

4. Hyper Central Model 1 2 3
We consider baryons as a bound state of three constituent quarks and their coordinates are described by the Jacobi Vectors [Yu. A. Simonov, (1966)],
(1)
(2)

5. Reduced mass of the system
Introducing the hyper spherical coordinates which are given by the angles [Yu. A. Simonov, (1966)],
Hyper radius
Hyper angle
The Hamiltonian for the three body system is written as [E. Santopinto et al.,1998]
(3)
Reduced mass of the system

6. Some of examples of hyper central potential
[M. M. Giannini et al. (2001)]
Besides these two analytical solutions, we have studied three-body potentials of the form which is known as the power plus hyper coulomb potential and it is given by [J.N.Pandya et. al, (2001), Ajay K Rai et. al, (2005)]

7. Our model Potential [Ajay Rai et al., 2005]:
(4)
We employ the variational approach with a trial wave function
(5)
The baryon masses are calculated using,
(6)

8. Effective quarks mass and Magnetic moments
of heavy baryons
The magnetic moment of heavy baryons is given by
(7)
Spin flavour wave function of respective baryonic state,
Charge of the quark,
Spin structure of the quarks within the baryon.
Where,
And the effective quark mass is defined as
(8)

9. Spin-flavour wave functions & magnetic moments of charm baryons with JP=

10. Spin-flavour wave functions & magnetic moments of charm baryons with JP=

11. JP=
JP=

12. Variation of spin average masses with potential index for single charm baryons
Variation of spin average masses with potential index for doubly charm baryons

13. Single Charm Baryon Masses (Masses are in MeV)

15. Double Charm Baryon Masses (Masses are in MeV)

16. Magnetic Moments of Single Charm Baryons in terms of Nuclear Magnetron

17. Magnetic Moments of Doubly Charm Baryons in terms of Nuclear Magnetron
[8] C. Albertus 2006

18. Conclusion
Present study suggests the potential scheme for the description of heavy flavour baryons as hyper Coulomb plus power potential with power index ν≥ 1.5.
Our model contains few parameters compared to many other models.
The study demonstrates the success of a simple hyper central potential model in the description of the masses and magnetic moments of single heavy (qqQ) and double heavy (QQq) baryons.
We look forward the future experiments in conformation of our predicted states.

19. References W. M. Yao et al. (Particle Data Group), J. Phy. G 33 (2006)
M. M. Giannini, E. Santopinto and A. Vassallo, Eur. Phys. J. A 12, 447 (2001).
E. Santopinto, F. lachello and M. M. Giannini, Eur. Phys. J. A 1, (1998).
Amand Faessler et al., Phys. Rev. D 73, (2006).
K.C.Bowler et al. (UKQCD Collobration), Phys. Rev D 54, 3619 (1996).
A. Ali Khan et al., Phys. Rev D 62, (2000).
D. Ebert, R. N. Faustov and V. O. Galkin, Phys. Rev. D 72, (2005).
R. Roncaglia, D. B. Lichtenberg and E. Predazzi, Phys. Rev. D 52, 1722 (1995).
S. P. Tong et al., Phys. Rev. D 62, (2000).
D. Ebert, et al., Phys. Rev. D 66, (2002).
N. Mathur, R. Lewis and R. M. Woloshyn, Phys. Rev. D 66, (2002).
V. Gorelov (CDF Collaboration), arXiv:hep-ex/ (2007).
H Garcilazo et al., J. Phys. G 34, (2007).
C. Albertus et al., arXiv:hep-ph/ v1(2006), hep-ph/ v2 (2007).
V.V.Kiselev and A. K. Likhoded, Phys. Usp. 45, 455 (2002).
S.S.Gershtein et al., Phys. Rev. D 62, (2000).
R. Lewis et al., Phys. Rev D 64, (2001).
P.Avery et. al., CLEO collab. Phys.Rev. Lett. 75, 4364 (1995).
Yu. A. Simonov, Sov J. Nucl. Phys. 3,461(1966)
Ajay k Rai et. al, J. Phy.G.31, 1453 (2005)