1. University of Salamanca
Excited bottom mesons in constituent quark model
Excited bottom mesons in constituent quark model
Francisco Fernández
University of Salamanca

2. Light – Heavy Quark Mesons
Light – Heavy quark mesons are hydrogenic atoms of QCD
Heavy Quark limit  static colour field & decoupling of light degrees of freedom
Light quarks characterized by their total angular momentum jq = sq + L
jq is combined with SQ to give total angular momentum
SQ and jq are separately conserved
In Heavy Quark Limit, each energy level has pair of degenerate states :
L=1 states, also known as B*
L=0
jq=1/2
J=0,1
B0*, B1*
jq=3/2
J=1,2
B1, B2*
jq=1/2
J=0 B
J=1 B*

3. B** Spectroscopy
B1 and B2* decay through D-wave  narrow resonances
B0* and B1* decay through S-wave  wide resonances, difficult to distinguish from phase space

4. B** Spectroscopy jq JP
Bs*
Decay
Width
1/2 0+
Bs0 BK
Broad (S-wave) 1+
Bs1*
B*K
3/2
Bs1
Narrow (D-wave) 2+
Bs2*
BK, B*K

6. Excited B Mesons (B1, B2*)

7. Excited B Mesons (B1, B2*)
CDF Run II
B1 g B*+p, B2* g B*+p, B2* g B+p

8. Excited B Mesons (B1, B2*)
DØ Run II
DØ 1 fb-1

9. Orbitally Excited Bs-mesons

10. Constituent Quark Model
Generalization to heavy flavours of the original SU(2)F model developed in J. Phys. G (1993)
Basic ingredients
Chiral symmetry is spontaneously broken at some momentum scale provinding a constituent quark mass M(q2) for the ligth quarks
As a consecuence light constituent quarks exchange Goldstone bosons
Both light and heavy quarks interacts besides by gluon exchange
Finally both type of quarks are confined by a two body linear potential screened at large distancies due to pair creation
Diapositiva 4.
SIMULTANEIDAD
This model has been able to describe the NN interaction (NN phase shifts and deuteron phenomenology), the triton binding energy, baryon spectroscopy and meson spectroscopy and decays.
Details can be found in J. of Phys. G: Nucl. Part Phys

11. N-N interaction Baryon spectrum Meson spectrum.
Constituent Quark Model
N-N interaction
F. Fernández, A. Valcarce, U. Straub, A. Faessler. J. Phys. G19, 2013 (1993)
A. Valcarce, A. Faessler, F. Fernández. Physics Letters B345, 367 (1995)
D.R. Entem, F. Fernández, A. Valcarce. Phys. Rev. C (2000)
B. Juliá-Diaz, J. Haidenbauer, A. Valcarce, and F. Fernández. Physical Review C 65, , (2002)
Baryon spectrum
H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 64, , (2001)
H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 63, (2001)
Meson spectrum.
L.A. Blanco, F. Fernández, A. Valcarce. Phys. Rev. C59, 428 (1999)
J. Vijande, F. Fernández, A. Valcarce. J. Phys. G31, (2005)
Diapositiva 4.
SIMULTANEIDAD
This model has been able to describe the NN interaction (NN phase shifts and deuteron phenomenology), the triton binding energy, baryon spectroscopy and meson spectroscopy and decays.

12. Constituent Quark Model
Deuteron
NN phase shifts
Triton

13. Meson spectra (I)
Light I=1

14. Meson spectra (VI)
Bottomonium

15. Quark model predictions

16. Quark model predictions

17. END
what have we learned from the open charm sector?

18. DSJ*(2317) Narrow peak in DS0. JP=0+ I=0 favored.
Width consistent with the detector resolution, less than 10 MeV.
Mass near 2317 MeV, 40 MeV below DK threshold.
BaBar: PRL 90, (2003)

19. DSJ (2460)
Narrow peak in D*S0, and also observed in DS. JP=1+ favored.
Width consistent with the detector resolution, less than 8 MeV.
Mass close to 2460 MeV, below D*K threshold.
CLEO: PRD 68, (2003)

21. ←

22. qqqq cs  L=1 L=0 − → Jπ=0+,1+ P( s )=-1 P(qq)=+1
Why four quarks configuration?
qqqq  cs
Jπ=0+,1+
L=0
P( s )=-1 − →
P(qq)=+1
L=1

23. + Numerical techniques z y r x Two- and four-body mixing.
The two-body problem is solved using the Numerov algorithm.
The four-body problem (two particles and two antiparticles) is solved by means of a variational method.
Three main difficulties:
Non-trivial color structure.
Symmetry properties in the radial wave function (Pauli Principle)
Two- and four-body mixing.

24. Four-Body formalism 1 2! Non-trivial color structure.
Symmetry properties in the radial wave function (Pauli Principle)
We expand the radial wave function in terms of generalized gaussians with
Well defined permutation properties
(SS, AA, AS, SA).
L= 0 (relative angular momenta li 0)
Positive parity

25. Four-Body configurations. Tetraquarks structuresx y z
Two color singlets with different symmetry.

26. We solve the tetraquark system using a variational method
expanding the radial part of the wave function in terms of generalized gaussian (GG) defined as:
The radial wave function defined in this way has L=0
But each generalized gaussian contains an infinite number
of relative angular momentum.

27. Four-Body configurations.
Two- and four-body mixing

29. B meson sector → → →
Below BK and B*K thresholds
Above Bπ threshold

30. Back to the L3 Collaboration
M(B0*)=5658 MeV
M(B1) =5756 MeV

31. → →

32. Conclusions We have performed a study of the L=1 excited B mesons
in terms of two and four quark components
Our results agree with the recently measured B meson
states by CDF and D0 collaborations
We predict the existence of two resonances Bs0* and Bs1’
below the BK and BK* thresholds

33. BC
M(PDG) = 6400 390 130 MeV
M(D0) = 5950 140 340 MeV
M(CDF) = 6287 4.8 1.1 MeV
M(CQM) = 6277 MeV