arXiv subjects

M. A. Zubkov

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

At least 91 records · Page 5Linked to original sources

arXiv2014

Modified model of top quark condensation

We develop the modification of the top - quark condensation scenario, in which the Higgs boson is composed of all Standard Model fermions. Within this scenario we suggest the phenomenological model with non - local four - fermion interactions in which at the distances of the order of $\sim 1/100$ GeV the theory is represented in terms of only one Majorana spinor that carries the $U(12)$ index and, in addition, belongs to the spinor representation of $O(4)$. The Standard Model fermions are the components of this spinor. The symmetry $U(12)\otimes O(4)$ is responsible for the one - loop relation between the Higgs boson mass and the top quark mass $M_H^2 = m_t^2/2$. At the distances $\gg 1/100$ GeV the mentioned symmetry is broken, and the interaction term dominates that provides the nonzero mass of the top quark. Our phenomenological model should be considered in zeta or dimensional regularization. In conventional cutoff regularization this is equivalent to the existence of the additional counter - terms that cancel all quadratic divergences. As a result the $1/N$ expansion may be applied.

hep-ph↗

arXiv2014

Mirror as polaron with internal degrees of freedom

We consider the model suggested by Wang and Unruh \cite{WangUnruh2013} for the $1+1$ D mirror moving in the quantum vacuum. We consider the relation of this model to the problem of polaron -- the electron moving in the vacuum of the quantum field of phonons. We introduce the field - theoretical model of such a mirror. It contains the multi - component spinor field interacting with the scalar field. We discuss the source of the logarithmic divergence in the mirror mass and its relation to the problem of the divergencies in vacuum energy.

gr-qc↗

arXiv2014

Dynamical torsion as the microscopic origin of the neutrino seesaw

It is assumed, that there are two scales in quantum gravity. Metric fluctuates at the scales of the order of the Plank mass. The second scale $M_T$ is related to the fluctuations of torsion. We suppose, that it may be as low as $M_T \sim 1$ TeV. Due to the non - minimal coupling to torsion the attractive interaction between the fermions appears. The non - minimal coupling admits the appearance of different coupling constants for different fermions. This opens the possibility that the interaction with torsion gives the Majorana masses for the right - handed neutrinos (that are assumed to be of the order of $M_T$). We suppose, that the Dirac masses for the neutrino are all close to the mass of electron. This gives the light neutrino masses $\le 0.25$ eV. In addition, the model predicts the appearance of Majorons that may contribute to the dark matter as well as to the invisible decay of the $125$ GeV Higgs boson.

hep-ph↗

arXiv2014

Emergent Weyl fermions and the origin of $i=\sqrt{-1}$ in quantum mechanics

Conventional quantum mechanics is described in terms of complex numbers. However, all physical quantities are real. This indicates, that the appearance of complex numbers in quantum mechanics may be the emergent phenomenon, i.e. complex numbers appear in the low energy description of the underlined high energy theory. We suggest a possible explanation of how this may occur. Namely, we consider the system of multi - component Majorana fermions. There is a natural description of this system in terms of real numbers only. In the vicinity of the topologically protected Fermi point this system is described by the effective low energy theory with Weyl fermions. These Weyl fermions interact with the emergent gauge field and the emergent gravitational field.

hep-ph↗

arXiv2014

Strong dynamics behind the formation of the $125$ GeV Higgs boson

We consider the scenario, in which the new strong dynamics is responsible for the formation of the $125$ GeV Higgs boson. The Higgs boson appears as composed of all known quarks and leptons of the Standard Model. The description of the mentioned strong dynamics is given using the $ζ$ - regularization. It allows to construct the effective theory without ultraviolet divergences, in which the $1/N_c$ expansion works naturally. It is shown, that in the leading order of the $1/N_c$ expansion the mass of the composite $h$ - boson is given by $M_h = m_t/\sqrt{2} \approx 125$ GeV, where $m_t$ is the top - quark mass.

hep-ph↗

arXiv2014

Emergent Weyl spinors in multi-fermion systems

In Ref. \cite{Horava2005} Hořava suggested, that the multi - fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the $3+1$ D system and concentrate on the particular case when the Fermi surface has co-dimension $p=3$, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the vicinity of the Fermi point the original system is reduced to the model with two - component Weyl spinors. Next, we generalize the construction of Hořava to the situation, when the original $3+1$ D theory contains multi - component Majorana spinors. In this case the system is also reduced to the model of the two - component Weyl fermions in the vicinity of the topologically stable Fermi point. Those fermions experience the emergent gauge field and the gravitational field given by the emergent veirbein. Both these fields (the emergent gauge field and the emergent gravitational field) originate from certain collective excitations of the original system. We speculate, that the given construction may be relevant for the high energy physics in the paradigm, in which the Lorentz symmetry as well as the gravitational and gauge fields are the emergent phenomena, i.e. they appear dynamically in the low energy approximation of the underlined high energy theory.

cond-mat.mes-hall↗

arXiv2013

In memory of M. I. Polikarpov

This obituary is devoted to M. I. Polikarpov (28.12.1952 - 18.07.2013), our teacher, our colleague, our friend. We recollect some facts of his biography and stages of his scientific career, and make a brief review of some of his most known scientific works. We conclude with some messages of condolence which were received from his colleagues and friends after his sudden death.

physics.hist-ph↗

arXiv2013

On symmetry and topological origin of Weyl particles

We suggest that the Weil spinors originate from the multi - component fermion fields. Those fields belong to the unusual theory that, presumably, exists at extremely high energies. In this theory there is no Lorentz symmetry. Moreover, complex numbers are not used in the description of its dynamics. Namely, the one - particle wave functions are real - valued, the functional integral that describes the second - quantised theory does not contain the imaginary unit as well. In the low energy effective theory the two - component Weil spinors appear. Their appearance is related to the Atiyah-Bott-Shapiro construction and to the expansion of the real matrix near the topologically protected nodes in three dimensional momentum space. The complex numbers entering ordinary quantum mechanics emerge together with the Weil fermions. In this pattern gauge fields and gravitational fields appear as certain collective excitations (of the original theory) experienced by the low - energy Weil fermions.

physics.gen-ph↗

arXiv2013

Polarons as stable solitary wave solutions to the Dirac-Coulomb system

We consider solitary wave solutions to the Dirac--Coulomb system both from physical and mathematical points of view. Fermions interacting with gravity in the Newtonian limit are described by the model of Dirac fermions with the Coulomb attraction. This model also appears in certain condensed matter systems with emergent Dirac fermions interacting via optical phonons. In this model, the classical soliton solutions of equations of motion describe the physical objects that may be called polarons, in analogy to the solutions of the Choquard equation. We develop analytical methods for the Dirac--Coulomb system, showing that the no-node gap solitons for sufficiently small values of charge are linearly (spectrally) stable.

math-ph↗

arXiv2013

Gauge theory of Lorentz group on the lattice

The model with the fermions coupled in the non - minimal way to the gauge theory of Lorentz group is considered. The lattice regularization is suggested. It is argued that this model may exist in the phase with broken chiral symmetry and without confinement. We speculate about the possibility that this construction may serve as an origin of the dynamical electroweak symmetry breaking.

hep-lat↗

arXiv2013

Gauge theory of Lorentz group as a source of the dynamical electroweak symmetry breaking

We consider the gauge theory of Lorentz group coupled in a nonminimal way to fermions. We suggest the hypothesis that the given theory may exist in the phase with broken chiral symmetry and without confinement. The lattice discretization of the model is described. This unusual strongly coupled theory may appear to be the source of the dynamical electroweak symmetry breaking. Namely, in this theory all existing fermions interact with the SO(3,1) gauge field. In the absence of the other interactions the chiral condensate may appear and all fermionic excitations may acquire equal masses. Small corrections to the gap equations due to the other interactions may cause the appearance of the observed hierarchy of masses.

hep-lat↗

arXiv2013

Emergent gravity in graphene

We reconsider monolayer graphene in the presence of elastic deformations. It is described by the tight - binding model with varying hopping parameters. We demonstrate, that the fermionic quasiparticles propagate in the emergent 2D Weitzenbock geometry and in the presence of the emergent U(1) gauge field. Both emergent geometry and the gauge field are defined by the elastic deformation of graphene.

cond-mat.str-el↗

arXiv2013

Higgs bosons in particle physics and in condensed matter

Higgs bosons - the amplitude modes - have been experimentally investigated in condensed matter for many years. An example is superfluid $^3$He-B, where the broken symmetry leads to 4 Goldstone modes and at least 14 Higgs modes, which are characterized by angular momentum quantum number $J$ and parity. Based on the relation $E_{J+}^2+E_{J-}^2=4Δ^2$ for the energy spectrum of these modes, Yoichiro Nambu proposed the general sum rule, which relates masses of Higgs bosons and masses of fermions. If this rule is applicable to Standard Model, one may expect that the observed Higgs boson with mass $M_{{\rm H}1}=125$ GeV has a Nambu partner -- the second Higgs boson with mass $M_{{\rm H}2}=325$ GeV. Together they satisfy the Nambu relation $M_{{\rm H}1}^2 + M_{{\rm H}2}^2 = 4 M_{\rm top}^2$, where $M_{\rm top}$ is the top quark mass. Also the properties of the Higgs modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of the Standard Model, suggest the possible existence of two electrically charged Higgs particles with masses $M_{{\rm H}+}=M_{{\rm H}-}\sim 245$ GeV, which together obey the Nambu rule $M_{{\rm H}+}^2 + M_{{\rm H}-}^2 = 4 M_{\rm top}^2$. A certain excess of events at 325 GeV and at 245 GeV has been reported in 2011, though not confirmed in 2012 experiments. Besides, we consider the particular relativistic model of top - quark condensation that suggests the possibility that two twice degenerated Higgs bosons contribute to the Nambu sum rule. This gives the mass around 210 GeV for the Nambu partner of the 125 GeV Higgs boson. We also discuss the other possible lessons from the condensed matter to Standard Model, such as hidden symmetry, where light Higgs emerges as quasi Nambu-Goldstone mode, and the role of broken time reversal symmetry.

hep-ph↗

arXiv2013

Emergent Horava gravity in graphene

First of all, we reconsider the tight - binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1 D teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations with the emergent zweibein. Next, we investigate the tight - binding model with the varying intralayer hopping parameters for the multilayer graphene with the ABC stacking. In this case the emergent 2D Weitzenbock geometry and the emergent U(1) gauge field appear as well, the emergent low energy effective field theory has the anisotropic scaling.

cond-mat.mes-hall↗

arXiv2013

Unruh effect in vacua with anisotropic scaling: Applications to multilayer graphene

We extend the calculation of the Unruh effect to the universality classes of quantum vacua obeying topologically protected invariance under anisotropic scaling ${\bf r} \rightarrow b {\bf r}$, $t \rightarrow b^z t$. Two situations are considered. The first one is related to the accelerated detector which detects the electron - hole pairs. The second one is related to the system in external electric field, when the electron - hole pairs are created due to the Schwinger process. As distinct from the Unruh effect in relativistic systems (where $z=1$) the calculated radiation is not thermal, but has properties of systems in the vicinity of quantum criticality. The vacuum obeying anisotropic scaling can be realized, in particular, in multilayer graphene with the rhombohedral stacking. Opportunities of the experimental realization of Unruh effect in this situation are discussed.

cond-mat.mes-hall↗

arXiv2013

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.

hep-ph↗

arXiv2013

Nambu sum rule in the NJL models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models \cite{Nambu}. This rule was originally considered by Nambu for superfluid $^3$He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is $\sim$ 325 GeV. They together satisfy the Nambu sum rule $M_1^2 + M_2^2 = 4 M_t^2$, where $M_t \sim $174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is $\sim$ 210 GeV. In this case the Nambu sum rule is $2 M_1^2 + 2 M_2^2 = 4 M_t^2$. In addition, the properties of the Higgs modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule $M_+^2 + M_-^2 = 4 M_t^2$.

hep-ph↗

arXiv2013

Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field $E$ at $E/B \ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E \ll 1$).

cond-mat.mes-hall↗