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M. A. Zubkov

Publications and source records attributed to M. A. Zubkov.

At least 109 records · Page 6Linked to original sources
arXiv2012

Green functions in graphene monolayer with Coulomb interactions taken into account

We consider the low energy effective field model of graphene monolayer. Coulomb interactions are taken into account. The model is simulated numerically using the lattice discretization with staggered fermions. The two point fermionic Green functions are calculated. We find that in the insulator phase these Green functions almost do not depend on energy. This indicates that the effective field model (in its insulator phase) does not correspond to the real graphene.

hep-lat↗
arXiv2012

Momentum space topology in the lattice gauge theory

Momentum space topology of relativistic gauge theory is considered. The topological invariants in momentum space are introduced for the case, when there is the mass gap while the fermion Green functions admit zeros. The index theorem is formulated that relates the number of massless particles and generalized unparticles at the phase transitions to the jumps of the topological invariants. The pattern is illustrated by the lattice model with overlap fermions.

hep-lat↗
arXiv2012

Generalized unparticles, zeros of the Green function, and momentum space topology of the lattice model with overlap fermions

The definition of topological invariants $\tilde{\cal N}_4, \tilde{\cal N}_5$ suggested in \cite{VZ2012} is extended to the case, when there are zeros and poles of the Green function in momentum space. It is shown how to extend the index theorem suggested in \cite{VZ2012} to this case. The non - analytical exceptional points of the Green function appear in the intermediate vacuum, which exists at the transition line between the massive vacua with different values of topological invariants. Their number is related to the jump $Δ\tilde{\cal N}_4$ across the transition. The given construction is illustrated by momentum space topology of the lattice model with overlap fermions. In the vicinities of the given points the fermion excitations appear that cannot be considered as usual fermion particles. We, therefore, feel this appropriate to call them generalized unparticles. This notion is, in general case different from the Georgi's unparticle. However, in the case of lattice overlap fermions the propagator of such excitations is indeed that of the fermionic unparticle suggested in \cite{fermion_unparticle}.

hep-lat↗
arXiv2012

Schwinger pair creation in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) in external Electric field is considered. The Schwinger pair creation rate and the vacuum persistence probability are calculated using the semi - classical approach.

hep-ph↗
arXiv2012

Zero temperature lattice Weinberg - Salam model for the values of the cutoff $Λ\sim 1$ TeV

The lattice Weinberg - Salam model at zero temperature is investigated numerically. We consider the model for the following values of the coupling constants: the Weinberg angle $θ_W \sim 30^o$, the fine structure constant $α\sim 1/150$, the Higgs mass $M_H \sim 150$ GeV. We find that the fluctuational region begins at the values of the cutoff $Λ$ above about 0.8 TeV. In this region the average distance between Nambu monopoles is close to their sizes. At $Λ> 1$ TeV the Nambu monopole currents percolate. Within the fluctuational region the considered definitions of the scalar field condensate give values that differ from the expected one $2 M_Z/g_z$. We consider the given results as an indication that the nonperturbative effects may be present in the Weinberg - Salam model at the large values of the cutoff. Our numerical results were obtained on the lattices of sizes up to $16^3\times 32$.

hep-lat↗
arXiv2012

Momentum space topological invariants for the 4D relativistic vacua with mass gap

Topological invariants for the 4D gapped system are discussed with application to the quantum vacua of relativistic quantum fields. Expression $\tilde{\cal N}_3$ for the 4D systems with mass gap defined in \cite{Volovik2010} is considered. It is demonstrated that $\tilde{\cal N}_3$ remains the topological invariant when the interacting theory in deep ultraviolet is effectively massless. We also consider the 5D systems and demonstrate how 4D invariants emerge as a result of the dimensional reduction. In particular, the new 4D invariant $\tilde{\cal N}_5$ is suggested. The index theorem is proved that defines the number of massless fermions $n_F$ in the intermediate vacuum, which exists at the transition line between the massive vacua with different values of $\tilde{\cal N}_5$. Namely, $ 2 n_F$ is equal to the jump $Δ\tilde{\cal N}_5$ across the transition. The jump $Δ\tilde{\cal N}_3$ at the transition determines the number of only those massless fermions, which live near the hypersurface $ω=0$. The considered invariants are calculated for the lattice model with Wilson fermions.

hep-ph↗
arXiv2011

Numerical investigation of lattice Weinberg - Salam model

Lattice Weinberg - Salam model without fermions for the value of the Weinberg angle $θ_W \sim 30^o$, and bare fine structure constant around $α\sim 1/150$ is investigated numerically. We consider the value of the scalar self coupling corresponding to bare Higgs mass around 150 GeV. We investigate phenomena existing in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model. This is the region of the phase diagram, where the continuum physics is to be approached. We find the indications that at the energies above 1 TeV nonperturbative phenomena become important in the Weinberg - Salam model.

hep-lat↗
arXiv2011

Effective constraint potential in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions for the value of the Weinberg angle $θ_W \sim 30^o$, and bare fine structure constant around $α\sim 1/150$. We consider the value of the scalar self coupling corresponding to bare Higgs mass around 150 GeV. The effective constraint potential for the zero momentum scalar field is used in order to investigate phenomena existing in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model. This is the region of the phase diagram, where the continuum physics is to be approached. We compare the above mentioned effective potential (calculated in selected gauges) with the effective potential for the value of the scalar field at a fixed space - time point. We also calculate the renormalized fine structure constant using the correlator of Polyakov lines and compare it with the one - loop perturbative estimate.

hep-lat↗
arXiv2010

How to approach continuum physics in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions numerically for the realistic choice of coupling constants correspondent to the value of the Weinberg angle $θ_W \sim 30^o$, and bare fine structure constant around $α\sim 1/150$. We consider the values of the scalar self coupling corresponding to Higgs mass $M_H \sim 100, 150, 270$ GeV. It has been found that nonperturbative effects become important while approaching continuum physics within the lattice model. When the ultraviolet cutoff $Λ= \fracπ{a}$ (where $a$ is the lattice spacing) is increased and achieves the value around 1 TeV one encounters the fluctuational region (on the phase diagram of the lattice model), where the fluctuations of the scalar field become strong. The classical Nambu monopole can be considered as an embryo of the unphysical symmetric phase within the physical phase. In the fluctuational region quantum Nambu monopoles are dense and, therefore, the use of the perturbation expansion around trivial vacuum in this region is limited. Further increase of the cutoff is accompanied by a transition to the region of the phase diagram, where the scalar field is not condensed (this happens at the value of $Λ$ around 1.4 TeV for the considered lattice sizes). Within this region further increase of the cutoff is possible although we do not observe this in details due to the strong fluctuations of the gauge boson correlator. Both mentioned above regions look unphysical. Therefore we come to the conclusion that the maximal value of the cutoff admitted within lattice Electroweak theory cannot exceed the value of the order of 1 TeV.

hep-lat↗
arXiv2010

Holst action and Dynamical Electroweak symmetry breaking

We consider Poincare gravity coupled in a nonminimal way to spinors. The gravitational action is considered that contains both Palatini and Holst terms. Due to torsion the effective four - fermion interactions appear that may lead to the left - right asymmetry and the condensation of fermions. When the mass parameter entering the mentioned terms of the gravitational action is at a Tev scale the given construction may provide the dynamical Electroweak symmetry breaking. This is achieved via an arrangement of all Standard Model fermions in the left - handed Dirac spinors while the right - handed spinors are reserved for the technifermions. Due to the gravitational action the technifermions are condensed and, therefore, cause the appearance of gauge boson masses.

gr-qc↗
arXiv2010

The vicinity of the phase transition in the lattice Weinberg - Salam Model

We investigated the lattice Weinberg - Salam model without fermions for the Higgs mass around $300$ GeV. On the phase diagram there exists the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase, where the fluctuations of the scalar field become strong while Nambu monopoles are dense. According to our numerical results (obtained on the lattices of sizes up to $20^3\times 24$) the maximal value of the ultraviolet cutoff in the model cannot exceed the value around $1.4$ TeV.

hep-lat↗
arXiv2010

Torsion instead of Technicolor

We consider the model, which contains a nonminimal coupling of Dirac spinors to torsion. Due to the action for torsion that breaks parity the left - right asymmetry of the spinors appears. This construction is used in order to provide dynamical Electroweak symmetry breaking. Namely, we arrange all Standard Model fermions in the left - handed spinors. The additional technifermions are arranged in right - handed spinors. Due to interaction with torsion technifermions are condensed and, therefore, cause appearance of gauge boson masses. In order to provide all fermions with masses we consider two possibilities. The first one is related to an additional coupling of a real massive scalar field to considered spinors. The second possibility is to introduce the mass term for the mentioned Dirac spinors composed of the Standard Model fermions and the technifermions.

hep-ph↗
arXiv2010

A model for fermion mass generation in Technicolor theory

We consider the $SU(N_{TC})$ Farhi - Susskind Technicolor model, in which SU(2) doublets of technifermions are right-handed while SU(2) singlets of technifermions are left-handed. We add coupling of fermions and technifermions to $SU(N_{TC})$ fundamental massive scalar fields. Due to this coupling the transitions between both types of fermions occur. Therefore the Standard Model fermions acquire masses.

hep-ph↗
arXiv2010

A superstructure over the Farhi - Susskind Technicolor model

We suggest the model with the gauge group $ ... \otimes SU(6) \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. This group is the infinite continuation of the gauge group $SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$ of Farhi - Susskind model. The constructed model contains fermions from the fundamental representations of any SU(N) subgroups of the gauge group. In the construction of the model we use essentially the requirement that it posseses an additional discrete symmetry $\cal Z$ that is the continuation of the $Z_6$ symmetry of the Standard Model. It has been found that there exists such a choice of the hypercharges of the fermions that the chiral anomaly is absent while the symmetry $\cal Z$ is preserved.

hep-ph↗
arXiv2010

The fluctuational region on the phase diagram of lattice Weinberg - Salam model

The lattice Weinberg - Salam model without fermions is investigated numerically for the realistic choice of bare coupling constants correspondent to the value of the Weinberg angle $θ_W \sim 30^o$, and the fine structure constant $α\sim {1/100}$. On the phase diagram there exists the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase, where the fluctuations of the scalar field become strong. The classical Nambu monopole can be considered as an embryo of the unphysical symmetric phase within the physical phase. In the fluctuational region quantum Nambu monopoles are dense and, therefore, the perturbation expansion around trivial vacuum cannot be applied. The maximal value of the cutoff at the given values of coupling constants calculated using the lattices of sizes $8^3\times 16$, $12^3\times 16$, and $16^4$ is $Λ_c \sim 1.4 \pm 0.2$ Tev. As the lattice sizes used are rather small we consider this result as preliminary.

hep-lat↗
arXiv2009

Upper bound on the cutoff in the Standard Model

The main objective of this presentation is to point out that the Upper bound on the cutoff in lattice Electroweak theory is still unknown. The consideration of the continuum theory is based on the perturbation expansion around trivial vacuum. The internal structure of the lattice Weinberg - Salam model may appear to be more complicated especially in the region of the phase diagram close to the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model, where the continuum physics is to be approached. We represent the results of our numerical investigation of the quenched model at infinite bare scalar self coupling $λ$. These results demonstrate that at $λ= \infty$ the upper bound on the cutoff is around $\fracπ{a} = 1.4$ Tev. The preliminary results for finite $λ$ are also presented. Basing on these results we cannot yet make a definite conclusion on the maximal value of the cutoff admitted in the lattice model, although we have found that the cutoff cannot exceed the value around $1.4 \pm 0.2$ Tev for a certain particular choice of the couplings ($λ= 0.009$, $β= 12$, $θ_W = 30^o$) for the lattices of sizes up to $12^3\times16$. We also observe that the topological defects, which are to be identified with quantum Nambu monopoles, dominate in vacuum in the vicinity of the transition. This indicates that the vacuum of the model is different from the trivial one. In addition we remind the results of the previous numerical investigations of the SU(2) gauge - Higgs model, where the maximal reported value of the cutoff was around 1.5 Tev.

hep-lat↗
arXiv2009

Hypercolor tower

We construct the ultraviolet completion of the Standard Model that contains an infinite sequence of Hypercolor gauge groups. So, the whole gauge group of the theory is $... \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. Here SU(4) is the Technicolor group of Farhi - Susskind model. The breakdown of chiral symmetry due to the the Technicolor gives rise to finite $W$ and $Z$ boson masses in a usual way. The other Hypercolor groups are not confining. We suggest the hypothesis that the fermion masses are not related in any way to technicolor gauge group. We suppose that the fermion mass formation mechanism is related to the energies much higher than the technicolor scale. Formally the fermion masses appear in our model as an external input. In the construction of the theory we use essentially the requirement that it posseses an additional discrete symmetry $\cal Z$ that is the continuation of the $Z_6$ symmetry of the Standard Model. It has been found that there exists such a choice of the hypercharges of the fermions that the chiral anomaly is absent while the symmetry $\cal Z$ is preserved.

hep-ph↗