arXiv subjects

Piotr H. Chankowski

Publications and source records attributed to Piotr H. Chankowski.

At least 19 recordsLinked to original sources

arXiv2026

Free energy of the gas of spin 1/2 fermions beyond the second order and the Stoner phase transition

Applying the previously developed systematic thermal (imaginary time) perturbative expansion to the relevant effective field theory we compute the free energy $F$ of the diluted gas of (nonrelativistic) spin $1/2$ fermions interacting through a spin-independent repulsive two-body potential as a function of the numbers $N_+$ and $N_-$ of spin up and spin down fermions (i.e. as a function of the system's polarization) and the temperature $T$. We give the complete order $(k_{\rm F}a_0)^3$ ($k_{\rm F}$ is the Fermi wave vector and $a_0$ is the $s$-wave scattering length characterizing the interaction potential) contribution to $F$. We also extend the computation beyond a fixed order by resumming to all orders in the parameter $k_{\rm F}a_0$ the contributions to $F$ of two infinite sets of Feynman diagrams: the so-called particle-particle rings and the particle-hole rings. We find that including the second one of these two contributions has a dramatic consequence for the transition of the system from the paramagnetic to the ferromagnetic phase (the so called Stoner phase transition): in this approximation the phase transition simply disappears. This result does not contradict the expectation that a transition to the magnetically ordered state should occur in truly repulsive systems. The $p$-wave and higher scattering lengths, as well as other parameters chacterizing the interaction potential, are in such systems generally of the same order of magnitude as $a_0$ and contributions depending on them should be, therefore, also included in $F$. Our results may, however, have implications for the search of the itinerant ferromagnetism of cold atomic gases in which large $a_0$, much larger than all other parameters, is artificially created by exploiting the physics of the Feshbach resonance.

cond-mat.quant-gas↗

arXiv2023

Perturbative computation of thermal characteristics of the Stoner phase transition

We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic) spin 1/2 fermions interacting through a short-range spin independent repulsive binary interaction potential. We show how to obtain a systematic expansion of the system's free energy depending on the densities $n_+$ and $n_-$ of spin-up and spin-down fermions. In this paper we truncate this expansion at the second order and determine, by numerically minimizing the free energy, the equilibrium proportions of $n_+$ and $n_-$ (that is, the system's polarization) as functions of the temperature, the system's overall density $n = n_+ + n_-$ and the strength of the interaction.

cond-mat.quant-gas↗

arXiv2023

Third order corrections to the ground state energy of the gas of spin $s$ fermions with arbitrary densities of different spin projections

Recently we have computed the third order corrections to the ground state energy of the arbitrarily polarized diluted gas of spin 1/2 fermions interacting through a spin-independent repulsive two-body potential. Here we extend this result to the gas of spin $s$ fermions - a system the Hamiltonian of which has an accidental $SU(2s+1)$ symmetry - with arbitrary densities of fermions having different spin projections. The corrections are computed semi-analytically using the effective field theory approach and are parametrized by the $s$- and $p$- wave scattering lengths $a_0$ and $a_1$ and the $s$-wave effective radius $r_0$, measurable in the low energy fermion-fermion elastic scattering. The result is used to study the impact the higher order corrections can have on the characteristics of the phase transition (at zero temperature) to the ordered phase (on the emergence of the itinerant ferromagnetism).

cond-mat.quant-gas↗

arXiv2022

Ground state energies of the Hubbard models and the Hartree Fock approximation

According to the `folk knowledge', the Hartree-Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling $U$ (the smaller $|U|$, the better is the H-F approximation). In \cite{BP} Bach and Poelchau have substantiated a certain version of this assertion by providing a rigorous estimate of the difference between the true ground-state energy of the simplest version of the Hubbard model and the H-F approximation to this quantity. In this paper we extend their result in two directions: i) we relax the assumption about the strict translational invariance of the hopping matrix, ii) we prove an analogous estimate for a class of multiband Hubbard models.

math-ph↗

arXiv2022

Third order corrections to the ground state energy of the polarized diluted gas of spin $1/2$ fermions

We present the results of the computation of the third order corrections to the ground state energy of the diluted polarized gas of nonrelativistic spin $1/2$ fermions interacting through a spin-independent repulsive two-body potential. The corrections are computed within the effective field theory approach which does not require specifying the interaction potential explicitly but only to characterize it by only a few parameters - the scattering lengths $a_0$, $a_1,\dots$ and effective radii $r_0,\dots$ - measurable in low energy fermion-fermion elastic scattering. The corrections are computed semi-analytically, that is are expressed in terms of two functions of the system's polarization. The functions are given by the integrals which can be easily evaluated using the Mathematica built-in routines for numerical integration.

cond-mat.quant-gas↗

arXiv2016

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $Λ$ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\overline{\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\overline{\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating $Λ$ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

hep-ph↗

arXiv2016

Ultraviolet cutoffs and the photon mass

The momentum UV cutoff in Quantum Field Theory is usually treated as an auxiliary device allowing to obtain finite amplitudes satisfying all physical requirements. It is even absent (not explicit) in the most popular approach - the dimensional regularization. We point out that the momentum cutoff treated as a bona fide physical scale, presumably equal or related to the Planck scale, would lead to unacceptable predictions. One of the dangers is a non-zero mass of the photon. In the naive approach, even with the cutoff equal to the Planck scale, this mass would grossly exceed the existing experimental bounds. We present the actual calculation using a concrete realization of the physical cutoff and speculate about the way to restore gauge symmetry order by order in the inverse powers of the cutoff scale.

hep-th↗

arXiv2014

Softly broken conformal symmetry and the stability of the electroweak scale

We point out a novel possible mechanism by which the electroweak hierarchy problem can be avoided in the (effective) quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale $Λ$ of the effective field theory as a real physical scale we argue that the hierarchy problem would be solved if the coefficient in front of quadratic divergences vanished for some choice of $Λ$, and if the effective theory mass parameters fixed at $Λ$ by the fundamental theory were hierarchically smaller than $Λ$ itself. While this mechanism most probably cannot work in the Standard Model if the scale $Λ$ is to be close to the Planck scale, we show that it can work in a minimal extension (Conformal Standard Model) proposed recently for a different implementation of soft conformal symmetry breaking.

hep-ph↗

arXiv2007

Violation of the Appelquist-Carazzone decoupling in non-SUSY GUT

We point out that in non supersymmetric GUTs, in which the SU(5) gauge symmetry is broken down to the Standard Model gauge group by a $\mathbf{24}$ Higgs multiplet the Appelquist-Carazzone decoupling is violated. This is because the $SU(2)_L$ Higgs triplet contained in the $\mathbf{24}$ acquires a dimensionfull coupling to the $SU(2)_L$ Higgs doublets which is proportional to the GUT breaking vacuum expectation value (VEV) $V$. As a result, at one loop heavy gauge and Higgs fields contribution to tadpoles generate a VEV of the triplet which is not suppressed for $V\to\infty$ and violates the custodial symmetry.

hep-ph↗

arXiv2005

Double protection of the Higgs potential

A mechanism of double protection of the Higgs potential, by supersymmetry and by a global symmetry, is investigated in a class of supersymmetric models with the SU(3)xSU(3)xU(1) gauge symmetry. In such models the electroweak symmetry can be broken with no fine-tuning at all.

hep-ph↗

arXiv2005

Flavour violation in general supergravity

We reappraise the flavour changing neutral currents (FCNC) problem in string--derived supergravity models. We overview and classify possible sources of flavour violation and find that the problem often does not arise in classes of models which generate hierarchical Yukawa matrices. In such models, constraints from the K- and D-meson systems leave room for substantial flavour non-universality of the soft terms. The current B-physics experiments only begin to probe its natural range. Correlations among different observables can allow one to read off the chirality structure of flavour violating sources. We briefly discuss the lepton sector where the problem of FCNC is indeed serious and perhaps points at an additional symmetry or flavour universality.

hep-ph↗

arXiv2004

CP violation in B0_d --> tau+ tau- decays

Establishing CP violation in B0 (bar{B0}) --> l+ l- decays requires a measurement of polarization of the final lepton pair, or a precise determination of the B0 --> l+ l- and bar{B0} --> l+ l- rates. We first argue that if the amplitudes of these decays are dominated by the scalar and pseudoscalar Higgs penguin diagrams, as happens e.g. in supersymmetry with large tan(beta), the CP asymmetries depend practically on only one CP violating phase. This phase can be large, of the order of the CKM phase, leading to large CP asymmetries in the tau+ tau- decay channel of B0_d (bar{B0}_d) mesons, potentially measurable in BELLE or BABAR experiments. Secondly, we show that the existing TAUOLA tau-lepton decay library supplemented by its universal interface can efficiently be used to search for B0 (bar{B0}) --> tau+ tau- decays, and to investigate how the CP asymmetry is reflected in realistic experimental observables.

hep-ph↗

arXiv2004

Electroweak symmetry breaking in supersymmetric models with heavy scalar superpartners

We propose a novel mechanism of electroweak symmetry breaking in supersymmetric models, as the one recently discussed by Birkedal, Chacko and Gaillard, in which the Standard Model Higgs doublet is a pseudo-Goldstone boson of some global symmetry. The Higgs mass parameter is generated at one loop level by two different, moderately fine-tuned sources of the global symmetry breaking. The mechanism works for scalar superpartner masses of order 10 TeV, but gauginos can be light. The scale at which supersymmetry breaking is mediated to the visible sector has to be low, of order 100 TeV. Fine-tuning in the scalar potential is at least two orders of magnitude smaller than in the MSSM with similar soft scalar masses. The physical Higgs boson mass is (for $\tanβ\gg1$) in the range 120-135 GeV.

hep-ph↗

arXiv2004

Patterns of Lepton-Flavour Violation Motivated by Decoupling and Sneutrino Inflation

We present predictions for flavour-violating charged-lepton decays induced by the seesaw mechanism implemented within the constrained minimal supersymmetric standard model (CMSSM) with universal input soft supersymmetry breaking terms. We assume that one heavy singlet neutrino almost decouples from the see-saw mechanism, as suggested by the pattern of light neutrino masses and mixing angles. This is suggested independently by sneutrino inflation with a low reheating temperature, T(RH)<10^7 GeV, so as to avoid overproducing gravitinos. This requirement further fixes the mass of the weakly-coupled sneutrino, whose decays may lead to leptogenesis. We find that BR(mu->e gamma)>10^(-13) but BR(tau->mu gamma)<10^(-9) in the bulk of the acceptable parameter space, apart from a few isolated points. The ratio BR(mu->e gamma)/BR(tau->mu gamma) depends on only one complex parameter, and is particularly interesting to compare with experiment.

hep-ph↗

arXiv2001

$ΔM_s/ΔM_d$, $\sin 2β$ and the angle $γ$ in the Presence of New $ΔF=2$ Operators

We present formulae for the mass differences $ΔM_d$ and $ΔM_s$ in the \BBds systems and for the CP violation parameter $ε$ which are valid in minimal flavour violation models giving rise to new four-fermion $ΔF=2$ operators. Short distance contributions to $ΔM_s$, $ΔM_d$ and $ε$ are parameterized by three {\it real} functions $F^s_{tt}$, $F^d_{tt}$ and $F^ε_{tt}$, respectively ($F^s_{tt} = F^d_{tt} = F^ε_{tt}$ holds only if the Standard Model $(V-A) \otimes (V-A)$ operators dominate). We present simple strategies involving the ratio $ΔM_s/ΔM_d$, $\sin2β$ and $γ$ that allow to search for the effects of the new operators. We point out that their sizable contributions to the ratio $ΔM_s/ΔM_d$ would in principle allow $γ$ to be larger than $90^\circ$. Constraints on the functions $F^i_{tt}$ imposed by the present (and future) experimental data are also discussed. As an example we show that for large $\tan\barβ\equiv v_2/v_1$ and $H^+$ not too heavy, $F^s_{tt}$ in the MSSM with heavy sparticles can be substantially smaller than in the SM due the charged Higgs box contributions and in particular due to the growing like $\tan^4\barβ$ contribution of the double penguin diagrams involving neutral Higgs boson exchanges. As a result the bounds on the function $F^s_{tt}$ can be violated which allows to exclude large mixing of stops. In this scenario the range of $\sin2β$ following from $ε$ and $ΔM_d$ is identical to the SM ones ($0.5<\sin 2β<0.8$). On the other hand $γ$ following from $ΔM_s/ΔM_d$ is lower.

hep-ph↗

arXiv2001

Unification in models with replicated gauge groups

We examine unification of gauge couplings in four dimensional renormalizable gauge theories inspired by the latticized (deconstructed) SM or MSSM in five dimensions. The models are based on replicated gauge groups, spontaneously broken to the diagonal subgroup. The analysis is performed at one-loop level, with the contribution from the heavy vector bosons included, and compared with the analogous results in the SM or MSSM. Unification at or above the diagonal breaking scale is discussed. We find that in the considered class of extensions of the SM(MSSM) unification is possible for a wide range of unification scales and with the similar accuracy as in the SM(MSSM). Unification above the diagonal breaking scale is particularly attractive: it is a consequence of the SM(MSSM) unification, but with the unification scale depending on the number of replications of the gauge group.

hep-ph↗

arXiv1998

Cosmological Fine Tuning, Supersymmetry, and the Gauge Heirarchy Problem

We study the extent to which the cosmological fine-tuning problem - why the relic density of neutralino cold dark matter particles $χ$ is similar to that of baryons - is related to the fine-tuning aspect of the gauge hierarchy problem - how one arranges that M_W << M_P without unnatural choices of MSSM parameters. Working in the minimal supergravity framework with universal soft supersymmetry-breaking parameters as inputs, we find that the hierarchical fine tuning is minimized for Ω_χ h^2 \sim 0.1. Conversely, imposing Ω_χ h^2 < 1 does not require small hierarchical fine tuning, but the exceptions to this rule are rather special, with parameters chosen such that m_χ\sim M_Z/2 or M_h/2, or else m_χ \simgt m_t. In the first two cases, neutralino annihilation receives a large contribution from a direct-channel pole, whereas in the third case it is enhanced by the large top Yukawa coupling.

hep-ph↗

arXiv1994

Combined constraints on the SUSY parameter space from $Δr$ ~and Higgs boson search

Combining the constraints coming from the ~$M_W$ ~measurements and the unsuccesful search for the Higgs boson at LEP we determine in the framework of MSSM the allowed mass regions for the lighter scalar partner of the top quark. For a heavy top quark particularily strong bounds are obtained for low values of ~$\tanβ\equiv v_2/v_1$ ~and light bottom squark.

hep-ph↗