arXiv subjects

M. M. Musakhanov

Publications and source records attributed to M. M. Musakhanov.

At least 19 recordsLinked to original sources

arXiv2025

Dark energy and QCD instanton vacuum in Friedmann-Lemaitre-Robertson-Walker universe

The standard model of the universe, $λ$CDM, is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations~\cite{ParticleDataGroup:2024cfk}. The cosmological constant $λ$ provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model (ILM) of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters $w_0=-1,\,\,\,w_a=0$ in accordance with $λ$CDM, while the newest data, analyzed at~\cite{Shajib:2025tpd}, give them at least in the range $-0.91 <w_0< -0.73,\,\,\,\,-1.05< w_a <- 0.65$. They are requesting a contribution from an ultralight scalars such an axions, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state ~\cite{VanWaerbeke:2025shm}.

hep-ph↗

arXiv2025

Heavy-light quark systems from the QCD instanton vacuum: $N_f=1$ light flavor case

We investigate heavy-light quark systems within the framework of the QCD instanton vacuum, focusing on the $N_f = 1$ light flavor case. We derive an effective heavy-light quark interaction from the low-energy QCD partition function and construct a heavy-meson effective Lagrangian. The physical residual mass of heavy mesons, $Λ$, is determined by employing compositeness and normalization conditions. We calculate the masses of $D$ and $B$ mesons and their weak decay constants to the leading order and next-to-leading order in the $1/m_Q$ expansion. The current results for $f_D$ and $f_B$ are in good agreement with recent lattice QCD data and PDG average values.

hep-ph↗

arXiv2017

Instanton effects on the heavy-quark static potential

We investigate the instanton effects on the heavy-quark potential,including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. We finally solve the nonrelativistic two-body problem, associating with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra.

hep-ph↗

arXiv2017

Normal state pair nematicity and hidden magnetic order and metal-insulator (fermion-boson)- crossover origin of pseudogap phase of cuprates II

In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to the PG pair intra charge and spin fluctuations. We will try to obtain an answer on the question: why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Laliberté et al. [2] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependence $n\sim T^3n_2$ for $T\rightarrow 0$, where $n_2$ is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within the PG pair physics.

cond-mat.supr-con↗

arXiv2016

Intra pseudogap- and superconductivity-pair spin and charge fluctuations and underdome metal-insulator (fermion-boson)-crossover phenomena as keystones of cuprate physics

The most intriguing observation of cuprate experiments is most likely the metal-insulator-crossover (MIC), seen in the underdome region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed. This MIC, which results in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, nonlinear entropy, insulating ground state, nematicity- and stripe-phases and Fermi pockets, reveals the nonconventional dielectric property of the pseudogap-normal phase. Since conventional superconductivity appears from a conducting normal phase, the understanding of how superconductivity arises from an insulating state becomes a fundamental problem and thus the keystone for all of cuprate physics. Recently, in interpreting the physics of visualization in scanning tunneling microscopy (STM) real space nanoregions (NRs), which exhibit an energy gap, we have succeeded in understanding that the minimum size for these NRs provides pseudogap and superconductivity pairs, which are single bosons. In this work, we discuss the intra-particle magnetic spin and charge fluctuations of these bosons, observed recently in hidden magnetic order and STM experiments. We find that all the mentioned MIC phenomena can be obtained in the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of sample percolating NRs of single fermions into those of single bosons.

cond-mat.supr-con↗

arXiv2012

Nanoscale Phenomenology from Visualizing Pair Formation Experiment

Recently, Gomes et al. [1] have visualized the gap formation in nanoscale regions (NRs) above the critical temperature T_c in the high-T_c superconductor Bi_2Sr_2CaCu_2O_{8+δ}. It has been found that, as the temperature lowers, the NRs expand in the bulk superconducting state consisted of inhomogeneities. The fact that the size of the inhomogeneity [2] is close to the minimal size of the NR [1] leads to a conclusion that the superconducting phase is a result of these overlapped NRs. In the present paper we perform the charge and percolation regime analysis of NRs and show that at the first critical doping x_{c1}, when the superconductivity starts on, each NR carries the positive electric charge one in units of electron charge, thus we attribute the NR to a single hole boson, and the percolation lines connecting these bosons emerge. At the second critical doping x_{c2}, when the superconductivity disappears, our analysis demonstrates that the charge of each NR equals two. The origin of x_{c2} can be understood by introducing additional normal phase hole fermions in NRs, whose concentration appearing above x_{c1} increases smoothly with the doping and breaks the percolation lines of bosons at x_{c2}. The last one results in disappearing the bulk bosonic property of the pseudogap (PG) region, which explains the upper bound for existence of vortices in Nernst effect [3]. Since [1] has demonstrated the absence of NRs at the PG boundary one can conclude that along this boundary, as well as in x_{c2}, all bosons disappear.

cond-mat.supr-con↗

arXiv2009

Magnetic susceptibility of the QCD vacuum at finite quark-chemical potential

We investigate the QCD magnetic susceptibility chi at the finite quark-chemical potential (mu>0) and at zero temperature (T=0) to explore the pattern of the magnetic phase transition of the QCD vacuum. For this purpose, we employ the nonlocal chiral quark model derived from the instanton vacuum in the presence of the chemical potential in the chiral limit. Focusing on the Nambu-Goldstone phase, we find that the magnetic susceptibility remains almost stable to mu~200 MeV, and falls down drastically until the the quark-chemical potential reaches the critical point mu_c~320 MeV. Then, the strength of the chi is reduced to be about a half of that at mu=0, and the first-order magnetic phase transition takes place, corresponding to the chiral restoration. From these observations, we conclude that the response of the QCD vacuum becomes weak and unstable to the external electromagnetic field near the critical point, in comparison to that for vacuum. It is also shown that the breakdown of Lorentz invariance for the magnetic susceptibility, caused by the finite chemical potential, turns out to be small.

hep-ph↗

arXiv2007

1/N_c corrections to the magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum with the $1/N_c$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/N_c$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\mathcal{O}(1/N_c)$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $χ< iψ^\dagger ψ>_0 \simeq 35-40 \mathrm{MeV}$ with the quark condensate $ _0$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.

hep-ph↗

arXiv2007

Low energy constants of \chiPT from the instanton vacuum model

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.

hep-ph↗

arXiv2006

The leading-twist pion and kaon distribution amplitudes from the QCD instanton vacuum

We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon, based on the nonlocal chiral quark model from the instanton vacuum. Effects of explicit flavor SU(3)-symmetry breaking are taken into account. The Gegenbauer moments are computed, analyzed and compared with those of other models. The one-loop QCD evolution of the moments is briefly discussed. The transverse momentum distributions are also discussed for the pion and kaon light-cone wave functions.

hep-ph↗

arXiv2005

Meson-loop contributions to the quark condensate from the instanton vacuum

We investigate the quark condensate of the QCD vacuum within the instanton vacuum model. We calculate the meson-loop contributions to the dynamical quark mass and quark condensate to ${\cal O}(1/N_c)$-, ${\cal O}(m/N_c)$-, and ${\cal O}((m\ln m) /N_c)$-order corrections. We find that the meson (especially pion) loops provide substantial contributions to the dynamical quark mass and as a result to the quark condensate. The results indicate that the $1/N_c$ corrections should be reconsidered in the systematical way. The present results are consistent with those from chiral perturbation theory.

hep-ph↗

arXiv2005

Is there a crystalline state of nuclear matter?

A possibility of the crystalline state of nuclear matter is discussed in a medium--modified Skyrme model. The interaction energy per nucleon in nuclear matter is evaluated by taking into account the medium influence on single nucleon--skyrmion properties and the tensor part of the nucleon--nucleon potential, and by using a variational method of Hartree--Fock type including zero--point quantum fluctuations. It is shown that in this approach the ground state of nuclear matter has no crystalline structure due to quantum fluctuations as well as medium modifications of hadron properties.

nucl-th↗

arXiv2005

Knot soliton in Weinberg-Salam model

We study numerically the topological knot solution suggested recently in the Weinberg-Salam model. Applying the SU(2) gauge invariant Abelian projection we demonstrate that the restricted part of the Weinberg-Salam Lagrangian containing the interaction of the neutral boson with the Higgs scalar can be reduced to the Ginzburg-Landau model with the hidden SU(2) symmetry. The energy of the knot composed from the neutral boson and Higgs field has been evaluated by using the variational method with a modified Ward ansatz. The obtained numerical value is 39 Tev which provides the upper bound on the electroweak knot energy.

hep-th↗

arXiv2004

Nucleon-nucleon potential in finite nuclei

We consider the spin-isospin-independent central part of the residual nucleon-nucleon potential in finite spherical nuclei taking into account the deformation effects of the nucleons within the surrounding nuclear environment. It is shown that inside the nucleus the short-range repulsive contribution of the potential is increased and the intermediate attraction is decreased. We identify the growth of the radial component of the spin-isospin independent short-range part of the in-medium nucleon-nucleon interaction as the responsible agent that prevents the radial collapse of the nucleus.

nucl-th↗

arXiv2003

A test of the instanton vacuum with low-energy theorems of the axial anomaly

We revisit the QCD+QED axial anomaly low-energy theorems which give an exact relation between the matrix elements of the gluon and photon parts of the axial anomaly operator equation within the framework of the {\em effective action} derived from the instanton vacuum. The matrix elements between the vacuum and two photon states and between the vacuum and two gluon states are investigated for arbitrary $N_f $ in the chiral limit. Having gauged the effective action properly, we show that the model does exactly satisfy the low-energy theorems.

hep-ph↗

arXiv2001

Nucleon deformation in finite nuclei

The deformation of a nucleon embedded in various finite nuclei is considered by taking into account the distortion of the chiral profile functions under the action of an external field representing the nuclear density. The baryon charge distribution of the nucleon inside light, medium-heavy and heavy nuclei is discussed. The mass of the nucleon decreases as it is placed deeper inside the nucleus and reaches its minimum at the center of the nucleus. We discuss the quantization of non-spherical solitons and its consequences for the mass splitting of the delta states. We show that bound nucleons acquire an intrinsic quadrupole moment due to the deformation effects. These effects are maximal for densities of nuclei about ρ(R)\sim 0.3...0.35 ρ(0). We also point out that scale changes of the electromagnetic radii can not simply be described by an overall swelling factor.

nucl-th↗

arXiv2001

The simulation of the spin ground states of the coulomb clusters in a broad 2D parabolic well

By variational Monte-Carlo method developed Ceperley et al. for the simulation of fermi systems in macroscopic confining potential well we simulate various spin ground states of the coulomb clusters with 2,3 and 4 particles in a broad two-dimensional (2D) parabolic well. In this method quantum state numbers determining the variational wave function are not the numbers of well quantum states but numbers of the equilibrium spatial positions of particles that give a minimum of the system potential energy. The ground states with parallel, antiparallel spins and as well, as bose state are simulated. For the cluster with three particles it is also simulated the state when two particles have one direction of spin and third opposite. The simulation shows that clusters with parallel spins have lower ground state energy than clusters with other spin configurations and bose state. That reminds a Hund's rule in atomic physics when in not full filled atomic shells electrons prefer to have a state with parallel spins.

cond-mat↗

arXiv2000

Spectra of Doubly Heavy Quark Baryons

Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schrödinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.

hep-ph↗