在瞬子真空模型的框架下，我们对当前质量m和色数N_c作了展开，并计算了对动力学夸克质量M、夸克凝聚$<\bar qq>$、π介子质量M_π和衰变常数F_π的${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$ -修正。这些修正有几个来源：介子环，有限大小的瞬子分布和夸克-夸克“张量”相互作用项。与预期相反，我们发现在数值上对动力学质量的1/N_c修正很大，而且主要来自介子环。因此，我们对所有其他量都有很大的1/N_c-修正。为了提供与\chiPT一致的$F_π(m=0), \ave{\bar qq(m=0)}$的值，我们提供了一组新的参数ρ，R。最后，我们发现低能SU（2）_f手征拉格朗日常数$\bar l_3, \bar l_4$与唯象理论有较好的对应.
英文摘要：
In the framework of the instanton vacuum model we make expansion over the current mass m and number of colors N_c and evaluate ${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$-corrections to the dynamical quark mass M, the quark condensate $<\bar qq>$, the pion mass M_πand decay constant F_π. There are several sources of these corrections: meson loops, finite size of the instanton distribution and the quark-quark "tensor" interaction terms. In contrast to the expectations, we found that numerically the 1/N_c-corrections to dynamical mass are large and mostly come from meson loops. As a consequence, we have large 1/N_c-corrections to all the other quantities. To provide the values of $F_π(m=0), \ave{\bar qq(m=0)}$ in agreement with \chiPT, we offer a new set of parameters ρ, R. Finally, we find the low-energy SU(2)_f chiral lagrangian constants $\bar l_3, \bar l_4$ in a rather good correspondence with the phenomenology.
In the framework of the instanton vacuum model we evaluate the Chiral Perturbation Theory (ChPT) low-energy constants h_3,l_7. We found that in the instanton vacuum model the constant l_7 is very sensitive to the shape of the instanton and the instanton vacuum parameters. We evaluated the constant l_7 for two different zero-mode profiles and as a function of the average instanton size ρand inter-instanton distance R. Our result agrees with an old "order of magnitude" estimate of this constant from [1]. The obtained value of l_7 implies that the pure QCD contribution to the pion mass difference…
We study the contribution of instantons to the binding and the mass of the lightest scalar glueball, in gluondynamics. We show that the short-range correlations introduced by such non-perturbative vacuum fluctuations are sufficient to give raise to a scalar glueball bound-state, with mass in good agreement with the results of recent lattice calculations.
We discuss the pion and kaon distribution amplitudes up to twist-3 in the context of the random instanton vacuum (RIV). We construct explicitly the pertinent quasi-pion and quasi-kaon distributions in the RIV, and analyze them in leading order in the diluteness factor, at a resolution fixed by the inverse instanton size. The distribution amplitudes (DA) follow from the large momentum limit. The results at higher resolution are discussed using QCD evolution, and compared to their asymptotic limits and some lattice results.
We are considering the modifications of gluon properties in Instanton Liquid Model (ILM) for the QCD vacuum. Re-scattering of a gluons on an instantons leads to the dynamical momentum-dependent gluon mass $M_g(q).$ First, we considered scalar "gluon", since there are no zero-modes problem and found its dynamical mass $M_s(q)$. At the typical phenomenological values of the average instanton size $ρ=1/3\,\,fm$ and average inter-instanton distance $R=1\,\, fm$ we got $M_s(0)=256\,\,MeV$. Further, we extended this approach to the real vector gluon with careful consideration of zero-modes and got $…
We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the instantons of large and small sizes. The former are described in terms of the local scalar condensate, while the latter can be interpreted as the nonlocal scalar condensate. We solve the corresponding QCD sum rules equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small size instantons w_s \approx 2/3.
Assuming the gluon field is well approximated by instanton configurations we derive a partition function and calculate the specific correlators. Namely, the heavy quark propagator and heavy quark-aniquark correlator with the account of the light quark determinant and QCD instanton vacuum properties. With these knowledge we calculate the light quark contribution to the interaction between heavy quarks, which might be essential for the properties of a few heavy quarks systems like oniums and double-heavy baryons.
We discuss the quark and gluon condensates in the presence of a rectangular Wilson loop using the QCD instanton vacuum with three light dynamical quarks. The scalar quark condensate is found to decrease while the gluon condensate to increase. We also derive the static potential between two QCD dipoles and show that it is attractive but short ranged at large distances. Its relevance to static QCD string interactions is discussed.
We calculate the nucleon matrix element of Weinberg's dimension-6 CP-odd gluon operator $f^{abc} (\tilde F_{μν})^a (F^{μρ})^b (F^ν_{\;\;ρ})^c$ in the instanton vacuum. In leading order of the instanton packing fraction, the dimension-6 operator is effectively proportional to the topological charge density $(\tilde F_{μν})^a (F^{μν})^a$, whose nucleon matrix element is given by the flavor-singlet axial charge and constrained by the $U(1)_A$ anomaly. The nucleon matrix element of the dimension-6 operator is obtained substantially larger than in other estimates, because of the strong localization…
In this talk, we report our present work on the chiral magnetic effect (CME) under a strong magnetic field at low temperature. To this end, we use the instanton vacuum with the finite instanton-number fluctuation Delta, which relates to the nontrivial topological charge Q_t. We compute the vacuum expectation values of the local chiral density <rho_chi>, chiral charge density <n_chi> and induced electromagnetic current <j_mu>. We observed that the longitudinal EM current is much larger than the transverse one, |j_perp/j_parallel| ~ Q_t, and the <n_chi> equals to the |<j_(3,4)>|. It also turns o…
单重态耦合到瞬子真空中的拓扑电荷密度，导致瞬子和反瞬子在1/2 fm量级的距离上被屏蔽。稀瞬子系统表现为自由气体，而致密瞬子系统表现为等离子体。1 fm $^{-4}$的密度有利于自由气体行为。由于希格斯机制，$η$的质量很重（1100 MeV）。真空拓扑磁化率很小（0.07 fm $^{-4}$），与QCD沃德恒等式一致。在手征极限下，单重屏蔽消失，导致四维等离子体状态，其温度由九重衰变常数$f$（90 MeV）给出。相位是德拜屏蔽的。在物质的存在下，屏蔽被淬灭，并且可能发生Kosterlitz-numerless跃迁，这表明$U_A(1)$对称性的恢复。我们建议利用静态拓扑电荷相关器的空间渐近性和拓扑磁化率来研究有限温度QCD中$U_A(1)$恢复和手征恢复之间的相互作用。这些结果的相关性，在瞬子真空体热力学进行了讨论。
In the framework of the Instanton Liquid Model we evaluate the heavy quark $\bar{Q}Q$ potential at nonzero temperature $T$. The potential has two components: contribution due to direct interaction with instantons, and the modification of the one-gluon exchange contribution via instanton-generated dynamical \char`\"{}electric\char`\"{} gluon mass $M_{el}(q,T)$. We conclude that the nonperturbative ILM contributions to the $Q\bar{Q}$ potential have pronounced temperature dependence, which might be tested in phenomenological analyses of charmonia production data.
The QCD vacuum is populated by instantons that correspond to the tunneling processes in the vacuum. This mechanism creates the strong vacuum gluon fields. As result, the QCD vacuum instantons induce very strong interactions between light quarks, initially almost massless. Such a strong interactions bring a large dynamical mass M of the light quarks and bound them to produce almost massless pions in accordance with the spontaneous breaking of the chiral symmetry (SBCS). On the other hand, the QCD vacuum instantons also interact with heavy quarks and responsible for the generation of the heavy-h…
Assuming the gluon field is well approximated by instanton configurations we derive a light quarks determinant and calculate its contribution to the specific heavy quarks correlators -- namely, the heavy quark propagator and heavy quark-aniquark correlator, receiving the instanton generated light-heavy quarks interaction terms contributions. With these knowledge we calculate the light quark contribution to the interaction between heavy quarks, which might be essential for the properties of a few heavy quarks systems.
In the framework of the instanton liquid model (ILM), we consider thermal modifications of the gluon properties in different scenarios of temperature $T$ dependence of the average instanton size $\barρ(T)$ and the instanton density $n(T)$ known from the literature. Due to interactions with instantons, the gluons acquire the dynamical temperature dependent "electric" gluon mass $M_{el}(q,T).$ We found that at small momenta and zero temperature $M_{el}(0,0)\approx362\,{\rm MeV}$ at the phenomenological values of $\barρ(0)=1/3\,{\rm fm}$ and $n(0)=1\,{\rm fm}^{-4}$, however the $T$-dependence of …
In this review we will concentrate on the nonperturbative effects in the properties of hadrons made from the light-heavy and heavy-heavy quarks in the framework of Instanton Liquid Model (ILM) of QCD vacuum. We briefly discuss the main features of ILM and its applicability in the heavy quark sector. The properties of gluonic systems, light and heavy quark correlators in the instanton background are also analyzed. Consideration of the both, perturbative and nonperturbative, gluon effects in the instanton background for the single heavy quark will lead to the mass shift due to the direct-instant…
We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.
