Workshop honoring the 70th birthday of SCADRON 70 Workshop on "Scalar Mesons and Related Topics"...
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Transcript of Workshop honoring the 70th birthday of SCADRON 70 Workshop on "Scalar Mesons and Related Topics"...
Workshop honoring the 70th birthday of
SCADRON 70Workshop 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 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 :
Qs
Lsj qq
Q qJ s j
jq=1/2 J=0 D/B
J=1 D*/ B*
L=0jq=1/2 J=0,1 B0
*, B1*
jq=3/2 J=1,2 B1, B2*
L=1 states, also known as B*
D1, D2*
D0*, D1
*
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
jq JP Bs* Decay Width
1/2 0+Bs
0
BK Broad (S-wave)
1/2 1+ Bs1* B*K Broad (S-wave)
3/2 1+ Bs1 B*KNarrow (D-
wave)
3/2 2+ Bs2* BK, B*K
Narrow (D-wave)
B** Spectroscopy
New States - DsJ(2860)+, X(2690)+ (?)
• New resonance at 2.86 GeV/c2 • Broad state at 2.69 GeV/c2
DsJ(2860)+
invariant mass (GeV/c2)
Combined modes bkgd subtracted
Ds2573)+
D0 K-+D0 K-+ 0 D+ K-++
BaBar data PRL 97 (2006)
No structures seen in D*K
BB++→→DD00DD00KK++
J=0 2/ndf = 185/5J=1 2/ndf = 7/5 J=2 2/ndf = 250/5
JP = 1-
■ ψ(4160) reflection
Spin Analysis
BELLE data arXiv 0707.3941
DSJ*(2317)
BaBar: PRL 90, 242001 (2003)
•Narrow peak in DS0. JP=0+ I=0 favored.
•Width consistent with the detector resolution, less than 10 MeV.
•Mass near 2317 MeV, 40 MeV below DK threshold.
DSJ (2460)
•Narrow peak in D*S0,
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)
Meson Mass JP
DsJ*(2317) m=(2319.6 ± 0.2 ± 1.4) MeV/c2
0+
DsJ*(2460) m=(2460.1± 0.2 ± 0.8) MeV/c2
1+
Ds1*(2535) m=(2535.3± 0.6 ± 1.4) MeV/c2
1+
Ds2*(2572) m=(2572.2± 0.3 ± 1.0) MeV/c2
2+
DsJ*(2860) m=(2856.6± 1.5 ± 5.0) MeV/c2
?
DsJ*(2700) m=(2715± 11 +11-14 ) MeV/c2 1-
Summary
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 CONSIDERcq
_
Modification are needed
Matsuki: Semirelativistic potential model
Talk on Friday
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
Details can be found in J. of Phys. G: Nucl. Part Phys. 31 1-26
• 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)
Constituent Quark Model
Meson spectra (I)
0
2 0 0
4 0 0
6 0 0
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0
1 6 0 0
1 8 0 0
2 0 0 0
E (
MeV
)
0 -+ 2 -+ (1 --) 3 -- b 1(1 + -) a 2(2 + +) a 1(1 + +)
Light I=1
Meson spectra (VI)
9 2 0 0
9 4 0 0
9 6 0 0
9 8 0 0
1 0 0 0 0
1 0 2 0 0
1 0 4 0 0
1 0 6 0 0
1 0 8 0 0
11 0 0 0
11 2 0 0
E (
MeV
)
b(0 -+ ) (1 --) b 0(0 + + ) b 1(1 + +) b 2(2 + + ) (2 --)
Bottomonium
Numerical techniques
4q
3q1q
2qx 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.
2q
1q
r +
3 3 3 8 8 101Baryon
6 6 8 27
6
1
3 8 10
3 6 8 103 3 3 3
3 3 1 8
Tetraquark
3 3 81Meson
•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 li 0)- Positive parity
•Symmetry properties in the radial wave function (Pauli Principle)
Four-Body configurations.
1 2| 0 | |B qq qqqq
q
q
q
q
q
q s
s
q
q
s
s
qC
• Two- and four-body mixing
nncnncD
nscnscD
nscnscD
J
SJ
SJ
33*
22
11*
)2308(
)2460(
)2317(
DECAY WIDTHS
Γ[DsJ(2860)0+ → Ds*γ] = 13.67 keV
Γ[DsJ(2860)0+ → Ds*γ] = 1.8 eV
multiquark
2P radial excitation