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Meson spectroscopy
Hybrid mesons
and
Multiquark states
Samuel Hoekman
Zorione Herrasti
1
Introduction
• To understand the dynamics on quark scale one
relies on lattice QCD and phenomological
methods
• Last time glueball spectroscopy was discussed
as a way to confirm QCD by searching for exotic
JPC quantum numbers
• Another way is using hybrid mesons, since
hybrid mesons are richer in number
(theoretically…)
• One can also search for exotic flavors:
multi quarks
2
Overview
• Hybrid meson (Zorione)
• QCD (Zorione)
• Flux Tube model (Zorione)
– 3P0 pair creation
• Phenomenological methods (Samuel)
– Simulation
• Monte Carlo Methods
• Partial Wave Analysis
•
•
•
•
•
Conclusions (Samuel)
Multi quarks (Samuel)
MIT-bag model (Samuel)
BES-II experiment (Zorione)
Conclusions (Zorione)
3
Mesons
•
Formed by a quark antiquark pair.
•
Quantum numbers.
- Parity (-1)l+1
- Charge conjugation (-1)l+s
4
Hybrid mesons
• Quantum numbers for hybrid mesons
- Quantum numbers that cannot be explained by
the quark model. (JPC)
- Formed by a q q pair plus one explicit gluon.
- If kinematics and other conservation laws allow,
the production cross section for hybrids, is
expected to be the same as that for ordinary
mesons.
- Hybrid mesons and ordinary mesons with the
same quantum numbers can mix freely.
- Identification of hybrid mesons difficult unless
they have exotic quantum numbers.
5
Quantum chromodynamics (QCD)
• Seems to be the correct theory of the strong
interactions.
• The spectrum of QCD is probably richer than
that of the naive quark model.
• If we remove the quarks from QCD, there
should remain a nontrivial color SU(3) which
must have its own spectrum of states.
• Constituent quark, constituent
gluon.(q q g)
• Gluonic degrees of freedom condensed
into collective string like flux tube.
6
A QCD FLUX TUBE BETWEEN TWO QUARKS (sapac)
A quark-antiquark pair, linked by a strong color field. The arrows point the
direction of the color field.
This system can have excitations with a vibration perpendicular to the axis.
7
Theoretical foundation of the flux tube
model
• In the Hamiltonian formulation of QCD on a cubic spatial lattice,
– Quark degrees of freedom “live” on the lattice sites
– Gluonic degrees of freedom “live” on the links between this sites.
HQCDlattice = Hglue + Hquark
• We define QCD field operators (Ul), on this lattice, the points are
linked with Gauge transformations.
• We can define: pure gluon states, or quark gluon states.
a
8
The pure glue sector, the simplest
states are “glue loops”.
Energy: (2g2 /3a2)L
g= coupling constant
a=lattice spacing
L=Length of the path
The simplest quark containing
state consits of a quark antiquark
on the lattice joined by a path of
flux links.
Energy: mq+ mq +(2g2/3a2)L
9
The Flux tube model
•The quarks move adiabatically in an effective
potential generated by the dynamics of the flux
tube.
•The flux tube can rotate along its axis, but the
orbital angular momentum along the flux tube is 0.
•The ground state, well approximated by a pair q q
with a string in its quantum-mechanical ground
state. (Quark model, low frequency limit)
• Hybrid mesons: Excitations of the color flux
tube.
10
11
Hybrid mesons
• There are two transverse polarization states of
the string, clockwise (+) or anticlockwise (-)
about the quark-antiquark axis.
• We define an angular component momentum
about the axis (Λ)
– The dependence of the string wave function on
the angle γ about the axis is eiγΛ
• Λ= Σ (n m+ - n m- ) ,
nm+- mode occupation numbers
• η p= (-1)L+Λ+1
• ηC= (-1)L+S+ΛΠm[(-1)m]n(m-) + n(m+)
12
- Lowest hybrids with one m=1 phonon, leading to
among other possibilities, the exotic quantum
numbers:
JPC= 0+-, 1-+, 2+The complete set of quantum numbers to one
phonon m=1:
S=1, JPC= 2+-, 2-+, 1+-, 1-+, 0+-, 0-+
S=0, JPC= 1++, 1-Prediction of mass for different flavor hybrid mesons
Flavor
Mass (GeV)
u,d
1.7- 1.8
s
1.9
c
4.2
b
10.8
13
EXAMPLE (1-+)
L=1, S=1 J= 0, 1, 2
Λ= Σ (n m+ - n m- ) ,
η p= (-1)L+Λ+1
n(m+)
ηC= (-1)L+S+ΛΠm[(-1)m]n(m-) +
J=1
m=1 mode, nm+ =1, Λ=1
P= (-1)1+1+1= -1
C= (-1)1+1+1 (-1) = +1
14
3P
0
quark pair creation
• The hybrid meson (A) can decay into two B, C
mesons.
• In the breaking process there´s no introduction of
extra angular momentum
• The relative angular momentum during the
breaking process has (S=1, L=1, J=0).
A
B+C
A
B + C
15
• The angular momentum Λ, has to be absorbed.
• Cannot decay into a pair of ground state mesons, as ππ,
πη, πρ...
• The preferential decay modes, those with one excited
meson: b1π, f1π...
16
Isgur and
Paton ’85
• Many decay channels are predicted from the FTM!
17
“Practical” part of hybrids
• Easiest to search for lower lying states
• For instance states with JPC=1-+
• Crystal Barrel Collaboration experiment ‘98
• Resonant behavior of  P-wave @ 1.4 GeV
• Experiment is ongoing @ BES-III
• BESIII/GEANT4 sensitivity simulation
• Monte Carlo simulation of J/  0
18
Reaction: J/  0
Energy diagram for the reaction:
Kinematics of the reaction:
19
Simulation
• Monte Carlo method
• Define input domain, i.e. the decay channels
• Generate the inputs using a prob. density
• Compute a result
• Generated input
•
•
•
•
•
1(1400) ~ 14.57%
a0(980) ~ 4.38%
a1(1320) ~ 21.39%
a2(1700) ~ 41.64%
Background
20
Criteria for 1-+ candidates
• Require two ‘good’ tracks with zero net
charge (i.e. being a -+-pair for sure)…
• Within polar angle region
• 5 cm within interaction region
• …and at least four ‘good’ photons
• Energy deposit > 50 MeV in the EM
calorimeter
• Angles correspond to kinematics
21
Selection from data
• Kinematic fit with criteria used as input
Allow values to vary within uncertainty
• Points with 2 < 15 were chosen
• Constraint on the photons from 0 and 
decay:
  (M  M  1 2 ) 2  (M   M  3 4 ) 2
0
22
Results
• Use invariant mass for products:
M 2  ( Ei )2  ( pi )2
• The MCS shows three “resonances”
23
Partial Wave Analysis
• Today: simplified PWA of elastic scattering
in terms of plane waves interacting with a
centre and spins 0
• Plane waves in spherical harmonics
24
Partial wave analysis
• A result is the formula for the DCS:
i

d
1
e
1
2
| f ( ) | |  (2l  1)
Pl (cos  ) |2
l
d
k
l 0
2i
• How about the resonances? Take the
partial wave amplitude and let’s see:
ei l  1
1
/2


2i
cot  l  i ( ER  E )  i / 2
d cot  l ( E )
cot  l ( E )  cot[ l ( ER )]  ( ER  E )
 H .O.
dE
 0  ( ER  E)2 / 
25
Breit-Wigner fit
• What follows is the Breit-Wigner formula
for the cross section (here most general
form):
4
2J 1
2 / 4
 (J )  2
2
2
k (2s1  1)( 2s2  1) ( ER  E )   / 4
26
Results
• Four fits appear for the different
resonances:
a2*
a2
a0
1
27
Results
• The simulation was good, the angular
distributions shows no irregularities
28
Conclusions
• The results from PWA correspond to the
input values from MC
• So with the setup at BES-III these
resonances can be identified (if they exist)
29
Multi quarks: confinement
• A multiquark state is formed if there are more than four
quarks confined in a so called MIT-bag
• The Dirac eqn. gives with appropriate boundary
conditions a zero normal quark flow
• To conserve energy and momentum at the boundary,
the external pressure is balanced by internal pressure
30
Multiquarks: measurement
• Above a threshold value, the multiquark
decays into mesons & baryons
• So, such a state has a broad width (makes
experiments difficult)
• However, a number of new structures
were seen in J/ decays
31
BES II Experiment
•
An anomalous enhancement near the mass
threshold in the pp invariant mass-spectrum
J/ψ
γ pp
•
Theoretical interpretation of the pp mass
threshold enhancement:
pp bound state= baryonium
•
Baryonium interpretation of the pp mass
enhancement requires a new resonance with
a mass around 1.85 Gev/c2
32
Observation of X(1835) in J/Ψ
J/ψ
γπ+π-η’
γ
Χ(1835)
π+π-
pp
η’
π+
γ
ρ
ππ+π-η
π+π-
γγ
33
π0
π0
η
η
ω
η’
η’
34
Selection of candidates
•
•
•
•
•
Reject events Mγγ < 0.22 GeV/c2 and
0.72 GeV/c2< Mγγ < 0.82 GeV/c2
[Mγγ – mη] < 0.05 GeV/c2
[Mπ+π-η – mη´] < 0.015 GeV/c2
[Mπ+π- - mρ] < 0.2 GeV/c2
[Mγπ+π- - mη´] < 0.025 Gev/c2
Conclusion
•
To ensure that the peak near 1835 MeV/c2 is not
due to background, extensive studies of potential
background processes, using both data and MC
have been made.
•
The main background channel
J/ψ π0π-π+η´, and other background processes
with multiphotons and /or kaons are reconstructed
with data.
•
None of these background processes
produce a peak around 1835 MeV/c2 in the
π-π+η´ invariant-mass spectrum.
Baryonium is a candidate for a 6 quark
system.
Summary
• There is a wide field within QCD theory
describing exotic mesons
• Good tools to analyse meson
spectroscopy are on the market
• Measured decay channels at BES-III can
be identified pretty well
• There may be a 6 quark state which is a
multi quark
37
Bibliography
• IHEP-Physics-Report-BES-III-2008-001v1(chapters 9.4-9.5)
• N.Isgur, R.Kokoski and J.Paton, Phys. Rev.Lett
54 (1985) 869
• N.Isgur and J.Paton, Phys.Rev. D31 (1985)
2910
• BES collaboration, M.Ablikim et al.,
Phys.Rev.Lett.95, 262001 (2005)
• R. Jaffe, Phys. Rev. D17 (’78) 1444
• Any readable QM book
• B. Muller, Gluon Quark Physics, Ch. 2