Breaking Terms Research Articles

Explicit Renormalization of Nuclear Chiral EFT and Nonperturbative Effects

Nucleon-nucleon interaction is studied within chiral effective field theory at next-to-leading order in the chiral expansion. The leading order interaction is resummed nonperturbatively, whereas the next-to-leading-order terms are taken into account in a perturbative manner. Explicit renormalizability of such a scheme is analyzed in several important cases. The possibility to absorb the power-counting breaking terms originating from the integration regions with large momenta is studied for both perturbative and nonperturbative regimes. A comparison of the schemes with a finite and an infinite cutoff is performed.

Hydrodynamics, spin currents and torsion

We construct the canonical constitutive relations for a fluid description of a system with a spin current, valid in an arbitrary number of dimensions in the absence of parity breaking or time reversal breaking terms. Our study encompasses the hydrostatic partition function, the entropy current, Kubo formula, conformal invariance, and the effect of charge. At some stages of the computation we turn on a background torsion tensor which naturally couples to the spin current.

Numerical Simulation of Nonlinear Wave Propagation from Deep to Shallow Water

Herein, a numerical model is proposed to simulate the nonlinear wave propagation from deep to shallow water and wave breaking phenomena. In the numerical model, the governing equations selected, in which the momentum equations were added to the eddy-viscous breaking and bottom friction terms to simulate the wave breaking phenomenon, are suitable for the wave propagation from deep to shallow water. The spatial derivations of the governing equations are discretized with the hybrid scheme, combining the finite-difference and finite-volume methods. To numerically simulate the nonlinear wave propagation in waters with various depths accurately, the non-conservative governing equations are reorganized as conservative to facilitate a total variation diminishing (TVD) type scheme using a Riemann solver. Extensive numerical tests of nonlinear wave propagation have been realized in waters with large relative water depths and varying water depths. The comparisons between numerical and analytical or experimental results indicated that the numerical results are reasonable and reliable, and the present numerical model can effectively simulate the wave-breaking phenomenon.

Higher-order topological insulators in hyperbolic lattices

To explore the non-Euclidean generalization of higher-order topological phenomena, we construct a higher-order topological insulator model in hyperbolic lattices by breaking the time-reversal symmetry (TRS) of quantum spin Hall insulators. We investigate three kinds of hyperbolic lattices, i.e., hyperbolic $\{4,5\}$, $\{8,3\}$ and $\{12,3\}$ lattices, respectively. The non-Euclidean higher-order topological behavior is characterized by zero-energy effective corner states appearing in hyperbolic lattices. By adjusting the variation period of the TRS breaking term, we obtain 4, 8 and 12 zero-energy effective corner states in these three different hyperbolic lattices, respectively. It is found that the number of zero-energy effective corner states of a hyperbolic lattice depends on the variation period of the TRS breaking term. The real-space quadrupole moment is employed to characterize the higher-order topology of the hyperbolic lattice with four zero-energy effective corner states. Via symmetry analysis, it is confirmed that the hyperbolic zero-energy effective corner states are protected by the particle-hole symmetry $P$, the effective chiral symmetry $Sm_{z}$, and combined symmetries $C_{p}T$ and $C_{p}m_{z}$. The hyperbolic zero-energy effective corner states remain stable unless these four symmetries are broken simultaneously. The topological nature of hyperbolic zero-energy effective corner states is further confirmed by checking the robustness of the zero-energy modes in the hyperbolic lattices in the presence of disorder. Our paper provides a route for research on hyperbolic higher-order topological insulators in non-Euclidean geometric systems.

Two-particle topological Thouless spin pump

We show that two particles interacting via spin exchange exhibit topological features found in one-dimensional single particle lattice models. This is accomplished by absorbing all of the spatial degrees of freedom of the lattices into the spin degrees of freedom of the two particles. Comparing the spin system with the Su-Schrieffer-Heeger model, we show the existence of topologically protected edge spin states and establish the bulk-edge correspondence. Modifying the spin system with a chiral symmetry breaking term results in it resembling the Rice-Mele model and can therefore act as a Thouless spin pump of one of the particles when periodically and adiabatically driven. By using the spin states as a synthetic spatial dimension, we show two particles are enough to simulate well known topological properties in condensed matter physics.

Phase diagram of twisted bilayer graphene at filling factor ν=±3

We study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing translation symmetry breaking terms, we obtain the phase diagram with respect to the ratio of $AA$ interlayer hopping $({w}_{0})$ and $AB$ interlayer hopping $({w}_{1})$. When the interlayer hopping ratio is close to the chiral limit (${w}_{0}/{w}_{1}\ensuremath{\lesssim}0.5$), a quantum anomalous Hall state with Chern number ${\ensuremath{\nu}}_{c}=\ifmmode\pm\else\textpm\fi{}1$ can be observed consistent with previous studies. Around the realistic value ${w}_{0}/{w}_{1}\ensuremath{\approx}0.8$, we find a spin and valley polarized, translation symmetry breaking, state with ${C}_{2z}T$ symmetry, a charge gap and a doubling of the moir\'e unit cell, dubbed the ${C}_{2z}T$ stripe phase. The real-space total charge distribution of this ${C}_{2z}T$ stripe phase in the flat band limit does not have modulation between different moir\'e unit cells, although the charge density in each layer is modulated, and the translation symmetry is strongly broken. Other symmetries, including ${C}_{2z}, {C}_{2x}$, particle-hole symmetry $P$, and the topology of the ${C}_{2z}T$ stripe phase, are also discussed in detail. We observed braiding and annihilation of the Dirac nodes by continuously turning on the order parameter to its fully self-consistent value, and provide a detailed explanation of the mechanism for the charge gap opening despite preserving ${C}_{2z}T$ and valley $\mathrm{U}(1)$ symmetries. In the transition region between the quantum anomalous Hall phase and the ${C}_{2z}T$ stripe phase, we find an additional competing state with comparable energy corresponding to a phase with a tripling of the moir\'e unit cell.

Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms.

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in generalization, and provide dimension reduction. In this work, we introduce a fast-to-compute, translationally invariant and rotationally equivariant wavelet scattering network (EqWS) and filter bank of wavelets (triglets). We demonstrate the interpretability and quantify the invariance/equivariance of the coefficients, briefly commenting on difficulties with implementing scale equivariance. On MNIST, we show that training on a rotationally invariant reduction of the coefficients maintains rotational invariance when generalized to test data and visualize residual symmetry breaking terms. Rotation equivariance is leveraged to estimate the rotation angle of digits and reconstruct the full rotation dependence of each coefficient from a single angle. We benchmark EqWS with linear classifiers on EMNIST and CIFAR-10/100, introducing a new second-order, cross-color channel coupling for the color images. We conclude by comparing the performance of an isotropic reduction of the scattering coefficients and RWST, a previous coefficient reduction, on an isotropic classification of magnetohydrodynamic simulations with astrophysical relevance.

A minimal modular invariant neutrino model

We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus. The neutrino masses are predicted to be normal ordering, the atmospheric angle θ23 is quite close to maximal value and the Dirac CP phase δCP is about 1.34π. We also study the soft supersymmetry breaking terms due to the modulus F-term in this minimal model, which are constrained to be the non-holomorphic modular forms. The radiative lepton flavor violation process μ → eγ is discussed.

Muon and electron (g-2) anomalies with non-holomorphic interactions in MSSM

The recent Fermilab muon g-2 result and the same for electron due to fine-structure constant measurement through {}^{133}textrm{Cs} matter-wave interferometry are probed in relation to MSSM with non-holomorphic (NH) trilinear soft SUSY breaking terms, referred to as NHSSM. Supersymmetric contributions to charged lepton (g-2)_l can be enhanced via the new trilinear terms involving a wrong Higgs coupling with left and right-handed scalars. Bino-slepton loop is used to enhance the SUSY contribution to g-2 where wino mass stays at 1.5 TeV and the left and right slepton mass parameters for the first two generations are considered to be the same. Unlike many MSSM-based analyses completed before, the model does not require a light electroweakino, or light sleptons, or unequal left and right slepton masses, or a very large higgsino mass parameter. In absence of popular UV complete models, we treat the NH terms at par with MSSM soft terms, in a model independent framework of Minimal Effective Supersymmetry. The first part of the analysis involves the study of (g-2)_mu constraint along with the limits from Higgs mass, B-physics, collider data, direct detection of dark matter (DM), while focusing on a higgsino DM which is underabundant in nature. We then impose the constraint from electron g-2 where a large Yukawa threshold correction (an outcome of NHSSM) and opposite signs of trilinear NH coefficients associated with mu and e fields are used to satisfy the dual limits of Delta {a_mu } and Delta {a_e} (where the latter comes with negative sign). Varying Yukawa threshold corrections further provide the necessary flavor-dependent enhancement of Delta {a_e}/m_e^2 compared to that of Delta {a_mu }/m_mu ^2. A larger Yukawa threshold correction through A^prime _e for y_e also takes away the direct proportionality of a_e with respect to tan beta . With a finite intercept, a_e becomes only an increasing function of tan beta . We identified the available parameter space in the two cases while also satisfying the ATLAS data from slepton pair production searches in the plane of slepton mass parameter and the mass of the lightest neutralino.

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Radiative symmetry breaking, cosmic strings and observable gravity waves in \U0001d5b4(1)\U0001d5b1 symmetric \U0001d5b2\U0001d5b4(5) × \U0001d5b4(1)χ

We implement shifted hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ GUT model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The U(1)χ symmetry is radiatevely broken after the end of inflation at an intermediate scale, yielding topologically stable cosmic strings. The Planck's bound on the gravitational interaction strength of these strings, characterized by GNμs are easily satisfied with the U(1)χ symmetry breaking scale which depends on the initial boundary conditions at the GUT scale. The dimension-5 proton lifetime for the decay p → K + ν̅, mediated by color-triplet Higgsinos is found to satisfy current Super-Kamiokande bounds for SUSY breaking scale M SUSY ≳ 12.5 TeV. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital role in bringing the scalar spectral index n_s within the Planck's latest bounds, although with small tensor modes r ≲ 2.5 × 10-6 and SU(5) gauge symmetry breaking scale in the range (2 × 1015≲ Mα ≲ 2 × 1016) GeV. By employing non-minimal terms in the Kähler potential, the tensor-to-scalar ratio approaches observable values (r ≲ 10-3) with the SU(5) symmetry breaking scale Mα ≃ 2 × 1016 GeV.

Modular symmetry of soft supersymmetry breaking terms

Abstract We study the modular symmetry of soft supersymmetry breaking terms. Soft scalar masses and A-term coefficients are invariant under the modular symmetry when we regard the F-term as a spurion with the modular weight −2. Their flavor structure is determined by the same symmetry as Yukawa couplings, i.e., fermion masses. The modular symmetric behavior of the μ-term and B-term depends on how the μ-term is generated.

Explicit form of Berry phase for time dependent harmonic oscillators in noncommutative space

In this paper we look for the existence of Berry phase in time dependent harmonic oscillators in noncommutative space. Two systems are considered in our study in the noncommutative framework. The first one is a system in which a scale invariant term is present in the Hamiltonian from the beginning, and the second one is a system in which a scale invariant term emerges due to a change of variables from the noncommutative to the commutative ones. We first compute the eigenstates of both the systems using the Lewis invariant approach. We then employ the Lewis invariant technique to obtain the geometric phase under adiabatic approximation. We also calculate the Berry phase explicitly by choosing appropriate forms of the time dependent parameters appearing in the Hamiltonian. Our analysis surprisingly reveals that a scale invariant time reversal symmetry breaking term may not always lead to a non trivial Berry phase.

Intermittent attractive interactions lead to microphase separation in nonmotile active matter.

Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equationsnumerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.

Relations among Bc→ J/ψ, ηc form factors

We analyze the form factors parametrizing the Bc→ J/ψ, ηc matrix elements of the operators in a generalized low-energy b → c semileptonic Hamiltonian. We consider an expansion in nonrelativistic QCD, classifying the heavy quark spin symmetry breaking terms and expressing the form factors in terms of universal functions in a selected kinematical range. Using as an input the lattice QCD results for the Bc → J/ψ matrix element of the SM operator, we obtain information on other form factors. The extrapolation to the full kinematical range is also presented.

Flavor-alignment in an S 3-symmetric Higgs sector and its RG-behavior* *NC acknowledges support from DST, India, under Grant Number IFA19-PH237 (INSPIRE Faculty Award). IC acknowledges support from DST, India, under grant number IFA18-PH214 (INSPIRE Faculty Award)

A three Higgs-doublet model exhibiting -symmetry can predict the observed pattern of quark masses and their mixings. However, the same symmetry also introduces potential flavor-changing neutral currents (FCNCs) at the tree level. In this study, we assume that the scalar potential contains appropriate soft -breaking terms to maintain flexible choices of scalar masses. We identify the parameters in the Yukawa Lagrangian of the quark sector responsible for such FCNCs and constrain them using data from flavor physics observables, such as meson-decays and meson-mixings. We also validate the corresponding model parameter space via renormalization group evaluation.

Probing left-right symmetry via gravitational waves from domain walls

We study the possibility of probing the scale of left-right symmetry breaking in the context of left-right symmetric models (LRSM). In LRSM, the right handed fermions transform as doublets under a newly introduced $SU(2{)}_{R}$ gauge symmetry. This, along with a discrete parity symmetry $\mathcal{P}$ ensuring identical gauge couplings of left and right sectors make the model left-right symmetric, providing a dynamical origin of parity violation in electroweak interactions via spontaneous symmetry breaking. The spontaneous breaking of $\mathcal{P}$ leads to the formation of domain walls in the early universe. These walls, if made unstable by introducing an explicit parity breaking term, generate gravitational waves (GW) with a spectrum characterized by the wall tension or the spontaneous $\mathcal{P}$ breaking scale, and the explicit $\mathcal{P}$ breaking term. Considering explicit $\mathcal{P}$ breaking terms to originate from Planck suppressed operators provides one-to-one correspondence between the scale of left-right symmetry and sensitivities of near future GW experiments. This is not only complementary to collider and low energy probes of TeV scale LRSM but also to GW generated from first order phase transition in LRSM with different spectral shape, peak frequencies as well as symmetry breaking scales.

Probing high scale Dirac leptogenesis via gravitational waves from domain walls

We propose a novel way of probing high-scale Dirac leptogenesis, a viable alternative to the canonical leptogenesis scenario where the total lepton number is conserved, keeping light standard model neutrinos purely Dirac. The simplest possible seesaw mechanism for generating light Dirac neutrinos involves heavy singlet Dirac fermions and a singlet scalar. In addition to unbroken global lepton number, a discrete ${Z}_{2}$ symmetry is imposed to forbid direct coupling between right and left chiral parts of light Dirac neutrinos. Generating light Dirac neutrino mass requires the singlet scalar to acquire a vacuum expectation value (VEV) that also breaks the ${Z}_{2}$ symmetry, leading to the formation of domain walls in the early Universe. These walls, if made unstable by introducing a soft ${Z}_{2}$-breaking term, generate gravitational waves (GWs) with a spectrum characterized by the wall tension or the singlet VEV, and the soft symmetry breaking scale. The scale of leptogenesis depends on the ${Z}_{2}$-breaking singlet VEV, which is also responsible for the tension of the domain wall, affecting the amplitude of GWs produced from the collapsing walls. We find that most of the near-future GW observatories will be able to probe Dirac leptogenesis scales all the way up to ${10}^{11}\text{ }\text{ }\mathrm{GeV}$.

Smooth hybrid inflation with low reheat temperature and observable gravity waves in SU(5) × U(1)χ super-GUT

We realize smooth hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ ⊂ SO(10) model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The breaking of U(1)χ symmetry leaves a residual discrete Z 2 symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The d = 5 proton lifetime for the decay p ⟶ K +ν̅, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index ns within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio r ≲ 3.5 × 10-7 are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the d = 5 proton decay. A non-minimal Kähler potential including higher order corrections is required to realize successful inflation with central value of scalar spectral index ns = 0.9655, large tensor modes r ≲ 0.056 and a low reheat temperature (3 × 106 ≲ Tr ≲ 6.5 × 107) GeV consistent with leptogenesis and baryogenesis.

μ -hybrid inflation, gravitino dark matter, and stochastic gravitational wave background from cosmic strings

We present a successful realization of supersymmetric $\mu$-hybrid inflation model based on a gauged $U(1)_{B-L}$ extension of the minimal supersymmetric standard model, with the soft supersymmetry breaking terms are playing an important role. Successful non-thermal leptogenesis with gravitino dark matter yields a reheat temperature in the range $2 \times 10^{7} \lesssim T_R \lesssim 5 \times 10^{9}$ GeV. This corresponds to the predictions $2 \times 10^{-18} \lesssim r\lesssim 4 \times 10^{-13}$ for the tensor to scalar ratio, and $-2 \times 10^{-6} \lesssim dn_s/d\ln k \lesssim -5 \times 10^{-11}$ for the running of the scalar spectral index. The $B-L$ breaking scale is estimated as $ 6 \times 10^{14}\lesssim M/ \text{GeV}\lesssim 10^{16}$, calculated at the central value of the scalar spectral index, $n_s =0.9655$, reported by Planck 2018. Finally, in a grand unified theory setup the dimensionless string tension parameter associated with the metastable strings is in the range $ 10^{-9} \lesssim G\mu_\text{cs} \lesssim 10^{-6}$ corresponding to a stochastic gravitational wave background lying within the 2$\sigma$ bound of the recent NANOGrav 12.5-yr data.