Petr Beneš

We discuss a class of effective extensions of the $SU(2)$ Georgi-Glashow model and discuss its Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We identify a specific subclass of these models that admit analytical solutions of the monopole type. We present some concrete examples and find that the resulting monopoles tend to have their energy concentrated not in their center, but rather in a spherical shell around it.

We present a systematic exploration of a general family of effective $SU(2)$ models with an adjoint scalar. First, we discuss a redundancy in this class of models and use it to identify seemingly different, yet physically equivalent models. Next, we construct the Bogomol’nyi-Prasad-Sommerfield limit and derive analytic monopole solutions. In contrast to the ’t Hooft-Polyakov monopole, included here as a special case, these solutions tend to exhibit more complex energy density profiles. Typically, we obtain monopoles with a hollow cavity at their core where virtually no energy is concentrated; accordingly, most of the monopole’s energy is stored in a spherical shell around its core. Moreover, the shell itself can be structured, with several “subshells.” A recipe for the construction of these analytic solutions is presented.

We present a "primitive" way of realizing finite-mass Dirac monopoles in $U(1)$ gauge theories involving a single non-minimally interacting scalar field. Typically, the energy density of this type of monopole is not concentrated at its core, but it is distributed in a spherical shell, as we illustrate on several exact solutions in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We show that our construction can be interpreted as a limit of infinitely massive $W$ bosons coupled to electromagnetic field-strength via a dipole moment. Combining our approach with ideas of Weinberg and Lee, we present a general landscape of $U(1)$ gauge models that support a finite-mass Dirac monopole. In fact, all classical monopoles, i.e., Wu-Yang, 't Hooft-Polyakov, Cho-Maison, etc., are special points on this landscape.

We present a “primitive” way of realizing finite-mass Dirac monopoles in $U(1)$ gauge theories involving a single nonminimally interacting scalar field. Typically, the energy density of this type of monopole is not concentrated at its core, but it is distributed in a spherical shell, as we illustrate on several exact solutions in the Bogomol’nyi-Prasad-Sommerfield limit. We show that our construction can be interpreted as a limit of infinitely massive $W$ bosons coupled to electromagnetic field strength via a dipole moment. Combining our approach with ideas of Weinberg and Lee, we present a general landscape of $U(1)$ gauge models that support a finite-mass Dirac monopole. In fact, all classical monopoles, i.e., Wu-Yang, ’t Hooft-Polyakov, Cho-Maison, etc., are special points on this landscape.

We study quark and lepton masses and mixings in a double covering of modular $A_4$ flavor symmetry in which we search for common solution of a single modulus $\tau$, applying chi-square numerical analysis under the as minimum framework as possible. We have found the common region of $\tau$ within $5\sigma$ interval that is narrow in case of normal hierarchy, but not found in case of inverted hierarchy.

The MoEDAL trapping detector consists of approximately 800 kg of aluminum volumes. It was exposed during run 2 of the LHC program to $6.46{\mathrm{fb}}^{-1}$ of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminum volumes comprising the detector through a superconducting quantum interference device (SQUID) magnetometer. The presence of a trapped dyon would be signaled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to five Dirac charges ($5g_D$) and an electric charge up to 200 times the fundamental electric charge for mass limits in the range 870–3120 GeV and also monopoles with magnetic charge up to and including 5$g_D$ with mass limits in the range 870–2040 GeV.

Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor $SU(3)_f$ symmetry with scale $\Lambda$. Anomaly freedom requires addition of three $\nu_R$. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies $\Sigma_f(p^2)$ has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) $\Sigma_f(p^2)=M_{fR}^2/p$ where three Majorana masses $M_{fR}$ of $\nu_{fR}$ are of order $\Lambda$. (2) $\Sigma_f(p^2)=m_f^2/p$ where three Dirac masses $m_f=m_{(0)}1+m_{(3)}\lambda_3+m_{(8)}\lambda_8$ of SM fermions are {\it exponentially suppressed w.r.t. $\Lambda$}, and {\it degenerate for all SM fermions in $f$}. (1) $M_{fR}$ break $SU(3)_f$ symmetry completely; $m_{(3)},m_{(8)}$ superimpose the tiny breaking to $U(1) \times U(1)$. All flavor gluons thus acquire self-consistently the masses $\sim \Lambda$. (2) All $m_f$ break the electroweak $SU(2)_L \times U(1)_Y$ to $U(1)_{em}$. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) Three $\nu_{R}$-composed Higgses $\chi_i$ with masses $\sim \Lambda$. (2) Two new SM-fermion-composed Higgses $h_3, h_8$ with masses $\sim m_{(3)}, m_{(8)}$, respectively. (3) The SM-like SM-fermion-composed Higgs $h$ with mass $\sim m_{(0)}$, the effective Fermi scale. $\Sigma_f(p^2)$-dependent vertices in the electroweak Ward-Takahashi identities imply: The axial-vector ones give rise to the $W$ and $Z$ masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in $f$. At the present exploratory stage the splitting comes out unrealistic.

We construct a class of effective extensions of the Standard Model that support finite-mass Cho-Maison magnetic monopole in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We present an example of exact analytic monopole solution and derive a universal lower mass bound $M \geq 2\pi v/ g \approx 2.37\,\,\mathrm{TeV}$ of the Cho-Maison magnetic monopole.