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

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*

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

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

Excited B Mesons (B1, B2*)

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

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

Orbitally Excited Bs-mesons

Constituent Quark Model Generalization to heavy flavours of the original SU(2)F model developed in J. Phys. G19 2013 (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. 31 1-26

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. C62 034002 (2000) B. Juliá-Diaz, J. Haidenbauer, A. Valcarce, and F. Fernández. Physical Review C 65, 034001, (2002) Baryon spectrum H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 64, 058201, (2001) H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 63, 035207 (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. http://web.usal.es/~gfn

Constituent Quark Model Deuteron NN phase shifts Triton

Meson spectra (I) Light I=1

Meson spectra (VI) Bottomonium

Quark model predictions

Quark model predictions

END what have we learned from the open charm sector?

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, 242001 (2003)

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, 032002 (2003)

←

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

+ 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.

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

Four-Body configurations. Tetraquarks structures x y z Two color singlets with different symmetry.

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.

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

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

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

→ →

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

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