Excited bottom mesons in constituent quark model Francisco

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 u u 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 2 J=0 J=1 B B* jq=1/2 J=0, 1 B 0*, B 1* jq=3/2 J=1, 2 B 1, B 2* Andrei Nomerotski (Oxford)

B** Spectroscopy B 1 and B 2* decay through D-wave narrow resonances B 0* and B 1* decay through S-wave wide resonances, difficult to distinguish from phase space

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

Excited B Mesons (B 1, B 2*)

Excited B Mesons (B 1, B 2*) CDF Run II B 1 g B*+ , B 2* g B+

Excited B Mesons (B 1, B 2*) DØ Run II DØ 1 fb-1

Orbitally Excited Bs-mesons Bs 2* Bs 1

Constituent Quark Model Generalization to heavy flavours of the original SU(2)F model developed in J. Phys. G 19 2013 (1993) Basic ingredients • Chiral symmetry is spontaneously broken at some momentum scale provinding a constituent quark mass M(q 2) 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 Details can be found in J. of Phys. G: Nucl. Part Phys. 31 1 -26

Constituent Quark Model • N-N interaction – F. Fernández, A. Valcarce, U. Straub, A. Faessler. J. Phys. G 19, 2013 (1993) – A. Valcarce, A. Faessler, F. Fernández. Physics Letters B 345, 367 (1995) – D. R. Entem, F. Fernández, A. Valcarce. Phys. Rev. C 62 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. C 59, 428 (1999) – J. Vijande, F. Fernández, A. Valcarce. J. Phys. G 31, (2005) http: //web. usal. es/~gfn

Constituent Quark Model Deuteron Triton NN phase shifts

Meson spectra (I) Light I=1

Meson spectra (VI) Bottomonium

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 Me. V. • Mass near 2317 Me. V, 40 Me. V below DK threshold. Ba. Bar: 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 Me. V. • Mass close to 2460 Me. V, below D*K threshold. CLEO: PRD 68, 032002 (2003)

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

Numerical techniques r + z x y 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 • Non-trivial color structure. 1 2! • 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. • Two- and four-body mixing

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

Back to the L 3 Collaboration M(B 0*)=5658 Me. V M(B 1) =5756 Me. V

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 D 0 collaborations -We predict the existence of two resonances Bs 0* and Bs 1’ below the BK and BK* thresholds

BC M(PDG) = 6400 390 130 Me. V M(D 0) = 5950 140 340 Me. V M(CDF) = 6287 4. 8 1. 1 Me. V M(CQM) = 6277 Me. V