The theory of confinement based on the stochastic field mechanism, known as the field correlator method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of ...material on the properties of confinement in QCD. We enumerate all these properties as (1)–(7), and discuss beyond FCM two existing approaches: monopole based dual Ginzburg-Landau (DGL) theory, and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its self-consistency; in particular, it is shown that the string tension σ is the only scaleful parameter in the theory beyond fermion masses, and ΛQCD is calculated explicitly to the lowest order in terms of σ. We also formulate physical consequences of confinement, such as string breaking, Regge trajectories, role of confinement in the perturbation theory, chiral symmetry breaking, confinement in the boosted systems etc. It is demonstrated that the FCM is a suitable tool for the solution of these problems.
A
bstract
The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions ...inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at
E
= 4.12 GeV for the transitions
J
/
ψ
+
ϕ
↔
D
s
∗
+
D
¯
s
∗
, which can be associated with
χ
c
1
(4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions
D
s
−
+
D
0
∗
↔
J
/
ψ
+
K
∗
−
, which can be associated with th recently discovered
Z
cs
(3985).
The standard chiral perturbation theory is known to predict much weaker effects in magnetic field, than found in numerical lattice data. To overcome this disagreement we are using the effective ...chiral confinement Lagrangian,
L
ECCL
, containing both chiral and quark degrees of freedom, in the presence of external magnetic field. Without magnetic fields
L
ECCL
reduces to the ordinary chiral Lagrangian
L
ECL
, yielding in the lowest order
O
(
∂
μ
φ
)
2
all known relations, and providing explicit numerical coefficients in the higher
O
(
p
4
,
p
6
)
orders. The inclusion of the magnetic field in
L
ECCL
strongly modifies ECL results for chiral condensates, coupling constants
f
π
,
f
K
and masses of chiral mesons. The resulting behavior contains the only parameter – the string tension
σ
, is roughly proportional to
O
eB
σ
and agrees very well with lattice data. These results show that the magnetic field acts not only on the chiral degrees of freedom
(
φ
π
)
, but also on quarks in the quark-chiral Lagrangian, which produce much stronger effect.
The relativistic formalism of Green's functions is discussed in QCD and QED, where the relativistic Green's functions are constructed using the Schwinger proper time formalism and analyzed using the ...Fock–Feynman–Schwinger method. As a result, a simple and exact method is found for the relativistic systems, where the interaction can be written in a time-independent form. In this case one can write the relativistic Green's function as a one-dimensional integral of the corresponding nonrelativistic Green's function. The explicit example for the problem of a charge in the constant magnetic field is discussed in detail, and the exact agreement with the Schwinger relativistic form is demonstrated. A similar analysis is performed in the relativistic Coulomb problem, supporting the accuracy of the proposed relativistic formalism.
Numerous resonances in the
c
c
¯
and 4
q
systems, containing
c
c
¯
plus
s
s
¯
quarks (or light
q
q
¯
) were observed during last decades and recently the LHCb has found a remarkable narrow peak
T
cc
...(
3875
)
in the
D
D
∗
system. Besides there are several highly excited charmonium-like resonances, which can be treated as the shifted standard charmonium states. We analyze all these groups of the resonances in the mass region (3900–4700) MeV, using relativistic strong coupling theory with possible channel coupling phenomena. For the shifted charmonium states conventional charmonium spectrum is presented, being calculated with the relativistic string Hamiltonian, which does not contain fitting parameters, while for high excitations the universal flattened confining potential is used. It is shown that
X
(4274),
X
(4500),
X
(4700) can be identified as
3
3
P
1
,
4
3
P
0
,
5
3
P
0
states. The group of exotic states are considered using the Extended Recoupling Model, where two mesons
m
1
,
m
2
transfer into another pair of mesons
m
3
,
m
4
and back (infinite number of times), creating the four-quark resonance. Within this approach the resonances –
T
cc
(
3875
)
,
Z
c
(
3900
)
,
X
(
3915
)
,
Z
cs
(
3985
)
,
X
(
4014
)
, and
X
(4140) – can be explained as the exotic four-quark states in the
S
-wave decay channels.
Colormagnetic confinement as a natural component of the QCD confinement is explained and treated in the framework of the Field Correlator Method (FCM). For quarks and gluons in hadrons the effects of ...the colormagnetic confinement are discussed at zero temperature,where it contributes to the spectrum properties and can create its ownbound states, while at nonzero temperature in the EoS of the quark gluon plasma the colormagnetic confinement plays a dominating role.Its properties in the QCD thermodynamics are discussed in detail.In particular the CM string tension and the Debye screening mass calculated in FCM are compared with lattice data.
The phenomenon of narrow peak
(3875), discovered recently by the LHCb in the
system, and the absence of resonances in the
and
systems is discussed within the new extended version of the Recoupling ...Model, where the resonance is the result of infinite recoupling transitions of confining strings between quarks and antiquarks. We show that existence of the resonance in the
and its absence in
and
systems are the natural results of the Recoupling Mechanism. The application of this mechanism to the
system allows to obtain the resonance
(3900) with a larger width in agreement with experimental data.
The thermodynamics of quarks and gluons strongly depends on the vacuum colormagnetic field, which grows with the temperature
T
, so that spatial string tension
σ
s
=
const
g
4
(
T
)
T
2
. We ...investigate below what happens when one imposes in addition constant magnetic field and discover remarkable structure of the resulting thermodynamic potential.
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