Workshop honoring the 70th birthday of SCADRON 70 Workshop on "Scalar Mesons and Related Topics" February 11-16, 2008, at IST in Lisbon, Portugal RECENT ISSUES IN HEAVY-LIGHT MESON SPECTROSCOPY RECENT ISSUES IN HEAVY-LIGHT MESON SPECTROSCOPY Francisco Fernández University of Salamanca

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 j q = s q + L –j q is combined with S Q to give total angular momentum –S Q and j q are separately conserved In Heavy Quark Limit, each energy level has pair of degenerate states : j q =1/2J=0D/B J=1D*/ B * L=0 j q =1/2J=0,1 B 0 *, B 1 * j q =3/2J=1,2 B 1, B 2 * L=1 states, also known as B* D 1, D 2 * D 0 *, D 1 *

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

jqjq JPJP Bs*Bs* DecayWidth 1/20+0+ B s0 BKBroad (S-wave) 1/21+1+ Bs 1 * B*KB*KBroad (S-wave) 3/21+1+ B s1 B*KB*KNarrow (D-wave) 3/22+2+ Bs 2 * BK, B * KNarrow (D-wave) B** Spectroscopy

Recent experimental results

New States - D sJ (2860) +, X(2690) + (?) New resonance at 2.86 GeV/c 2 Broad state at 2.69 GeV/c 2 D sJ (2860) + invariant mass (GeV/c 2 ) Combined modes bkgd subtracted D s 2573) + D 0  K -  + D 0  K -  +  0 D +  K -  +  + BaBar data PRL 97 (2006) No structures seen in D*K

B+→D0D0K+B+→D0D0K+B+→D0D0K+B+→D0D0K+ J=0  2 /ndf = 185/5 J=1  2 /ndf = 7/5 J=2  2 /ndf = 250/5 J P = 1 - ■ ψ(4160) reflection Spin Analysis BELLE data arXiv

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

D SJ (2460) Narrow peak in D * S  0, and also observed in D S . J P =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)

MesonMassJPJP D sJ *(2317) m=( ± 0.2 ± 1.4) MeV/c 2 0+ D sJ *(2460) m=(2460.1± 0.2 ± 0.8) MeV/c 2 1+ D s1 *(2535) m=(2535.3± 0.6 ± 1.4) MeV/c 2 1+ D s2 *(2572) m=(2572.2± 0.3 ± 1.0) MeV/c 2 2+ D sJ *(2860) m=(2856.6± 1.5 ± 5.0) MeV/c 2 ? D sJ *(2700) m=(2715± ) MeV/c Summary

Excited B Mesons (B1, B2*)

CDF Run II B 1  B* + , B 2 *  B* + , B 2 *  B + 

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

Orbitally Excited B s -mesons B s2 * B s1

MODELS

QUARK MODELS MOST OF THESE STATES PRESENT UNEXPECTED PROPERTIES QUITE DIFFERENT FROM THOSE PREDICTED BY THE STANDARD QUARK POTENTIAL MODELS IF A PURE CONFIGURATION IS CONSIDER cq _ Modification are needed Matsuki: Semirelativistic potential model Talk on Friday

One loop corrections to the Fermi-Breit interaction → → → J P =0 + CONFIGURATION cq _

Strong coupling with the nearby S wave DK channel J P =0 +

J P =3 -

Salamanca model Vijande, Valcarce

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(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

N-N interaction –F. Fern á ndez, A. Valcarce, U. Straub, A. Faessler. J. Phys. G19, 2013 (1993) –A. Valcarce, A. Faessler, F. Fern á ndez. Physics Letters B345, 367 (1995) –D.R. Entem, F. Fern á ndez, A. Valcarce. Phys. Rev. C (2000) –B. Juli á -Diaz, J. Haidenbauer, A. Valcarce, and F. Fern á ndez. 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) Constituent Quark Model

Deuteron NN phase shifts Triton Constituent Quark Model

Meson spectra (I) Light I=1

Meson spectra (VI) Bottomonium

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

Numerical techniques x y z 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. r +

Non-trivial color structure. Four-Body formalism 1 2! 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 l i  0) - Positive parity Symmetry properties in the radial wave function (Pauli Principle)

x y z Four-Body configurations. 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

Quark model predictions → →

←

DECAY WIDTHS Γ[D sJ (2860)0 + → D s *γ] = keV Γ[D sJ (2860)0 + → D s *γ] = 1.8 eV multiquark 2P radial excitation

B meson sector

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

M(B 0 * )=5658 MeV M(B 1 ) =5756 MeV Back to the L3 Collaboration

→ →

Thank you