Testing CVC and CKM Unitarity via Superallowed Nuclear Beta Decay

Superallowed nuclear beta decay between 0^+analog states is a sensitive probe of the weak interaction, with the established strength – or F t value – of each such transition being a direct measure of the vector coupling constant, GV. Each transition's F t value depends on the half-life of the parent nucleus as well as on the Q-value and branching ratio for the transition of interest. It also depends on small(~1%) transition-dependent theoretical corrections, of which the most sensitive accounts for isospin symmetry breaking. We have recently published a new survey of world superallowed-decay data, which establishes the F t values of 14 separate superallowed transitions to a precision of order 0.1% or better.The results from this very robust data set yield the value of Vud, the up-down quark mixing element of the Cabibbo-Kobayashi-Maskawa(CKM) matrix, and lead to the most demanding test available of CKM unitarity. The survey results and their outcome are described, as is the current direction of experiments that focus on testing the validity of the isospin-symmetry-breaking corrections.

Investigations on Left Hand Cut Contribution to Determination of κ（700） Pole

The uncertainties of background contributions to J = 0 partial wave πK scattering phase shifts are carefully studied. We firstly point out that the circular cuts exhibit different characters in S1/1 and S3/2 waves. While the former contributes negatively to the scattering length parameter, the latter contributes positively, i.e., has a wrong sign. This fact indicates that short range force contribu tions to the phase shift are non-negligible in the exotic channel. Nevertheless, it is verified that the κ pole will be affected only slightly with respect to the theoretical uncertainty in estimating the left hand cut contributions.

Tunneling dynamics of superfluid Fermi gas in a triple-well potential

The tunneling dynamics of superfluid Fermi gas in a triple-well potential in the unitarity regime is investigated in the present paper. The fixed points of the （0,0） mode and the （π, π） mode are given. We find that the interaction parameter U and the coupling strength k could have an extreme effect on the quantum tunneling dynamics. We also find that, in the zero mode, only Josophson oscillation appears. However, for the mode, the trapping phenomena take place. An irregular oscillation of the particle number in each well could appear by adjusting the scanning period T. It is noted that if the scanning period is less than a critical point T＊, the particle number will come back to the fixed point with small oscillation, while if T 〉 T＊ the particle number cannot come back to the fixed point, but with irregular oscillations. The dependence of the critical point T＊ on the system parameter of coupling strength k is numerically given.

Single Production of Heavy Top Quark from Three-Site Higgsless Model

We consider single production of the heavy top quark T predicted by the three-site Higgsless model in future high energy collider experiments, such as the high energy linear e＋ e- collider （ILC）, the linear-ring type ep collider （THERA）, and the CERN Large Hadron Collider （LHC）. Our numerical results show that the possible signals of the heavy top quark T might be detected via the subproeess qb → q＇T at the LHC.

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev-Petviashvili I （KPI） solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Coope-Schrieffer （BCS） regime, Bose-Einstein condensate （BEC） reginle, and unitarity regime. One- lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.

Condensation of Fermions in the double-well potential

The density distribution of ultracold two-component fermionic gases 6Li, which are confined in a gradient magnetic field and a symmetrical double-well potential, is investigated by employing local-density approximation. It is found that three different regimes including quasi-molecular Bose-Einstein condensation （BECm）, the dimers in the unitarity limit （ULd）, and Bardeen-Cooper-Schrieffer superfluid （BCS） can coexist at the same time. Furthermore, the ranges of these regimes can be controlled to some extent by tuning the gradient of the magnetic field and the parameters characterizing the properties of the double-well potential. This study is of guidance and significance for experimentally realizing the coexistence of BECm, ULd, and BCS in the double-well potential.

Studies on σ Resonance in a New Unitarization Approach

The pole position of the σ meson is determined using the recently proposednew unitarization method combined with the two-loop SU(2) X SU(2) chiral perturbation theoryresults. The scattering length parameters and the effective range parameters predicted by our methodare in good agreement with experimental results. It is found that M_σ = 542 ± 26 ± 39 MeV, Γ_σ= 546 ± 122 ± 25 MeV.

Non-unitary Scattering Theory against Generalized Unitary Scattering Theory

Comparison of non-unitary and generalized unitary scattering theories is done by means of nuclear monodromy （equivalence of Schrodinger and Maxwell time-independent equations）, tunneling and radioactivity. Radioactivity is important part of physics and our life. Its importance stretches from medicine as far as to war strategies. We present theoretical approach to achieve better understanding of the radioactive decay when modified quantum theory is applied. It can be done by updating existing codes to understand better construction of the world and terms and conditions of our existence. The theory modifications are strictly connected with the unimodular M matrix and Wronskian matrices （i.e. their determinants named Wronskians） which create underpinning of so called monodromy being two track wave-function evolution.

Recent QFT of Einstein’s Gravity Simplified via Ultrahyperfunctions

Previously published treatment is rather involved. Here we present a useful approximation to the concomitant derivation that yields a simpler way of handling things and still obtains results quite similar to those yielded by the exact treatment. Our approximation consists of giving the graviton field a simpler, but still quite good approximate form.

Approximate Reformulation a Recent Non-Renormalizable QFT’s Methodology and Einstein’s Gravity

We revisit, advancing a useful approximation, a recently formulated QFT treatment that successfully overcomes any troubles with infinities for non-renormalizable QFTs [J. Phys. Comm. 2 115029 (2018)]. Such methodology was able to successfully deal, in non-relativistic fashion, with Newton’s gravitation potential [Annals of Physics 412, 168013 (2020)]. Our present approximation to the QFT method of [J. Phys. Comm. 2 115029 (2018)] is based on the Einstein’s Lagrangian (EG) elaborated by Gupta [1], save for a different constraint’s selection. This choice allows one to avoid the lack of unitarity for the S matrix that impaired the proceedings of Gupta and Feynman. Moreover, we are able to simplify the handling of such constraint by eliminating the need to involve ghosts for guarantying unitarity. Our approximation consists in setting the graviton field ∅μν=γμν∅, where γμνis a constant tensor and ∅a scalar (graviton) field. The ensuing approximate approach is non-renormalizable, an inconvenience that we are able to overcome in [J. Phys. Comm. 2 115029 (2018)].

Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity

Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz’ tempered distributions. This effort is an application to Einstein’s gravity (EG) of the mathematical theory of convolution of Ultrahyperfunctions developed by Bollini et al. [1] [2] [3] [4]. A simplified version of these results was given in [5] and, based on them;a Quantum Field Theory (QFT) of EG [6] was obtained. Any kind of infinities is avoided by recourse to UHF. We will quantize EG by appealing to the most general quantization approach, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. We follow works by Suraj N. Gupta and Richard P. Feynman so as to undertake the construction of an EG-QFT. We explicitly use the Einstein Lagrangian as elaborated by Gupta [7], but choose a new constraint for the ensuing theory. In this way, we avoid the problem of lack of unitarity for the S matrix that afflicts the procedures of Gupta and Feynman. Simultaneously, we significantly simplify the handling of constraints, which eliminates the need to appeal to ghosts for guarantying unitarity of the theory. Our approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing to the mathematical theory developed by Bollini et al. [1] [2] [3] [4] [5]. Such developments were founded in the works of Alexander Grothendieck [8] and in the theory of Ultradistributions of Jose Sebastiao e Silva [9] (also known as Ultrahyperfunctions). Based on these works, an edifice has been constructed along two decades that are able to quantize non-renormalizable Field Theories (FT). Here we specialize this mathematical theory to discuss EG-QFT. Because we are using a Gupta-Feynman inspired EG Lagrangian, we are able to evade the intricacies of Yang-Mills theories.

Two Kinds of Two-Boson Realizations of Generally Deformed Algebras with Three Generators

In this paper two kinds of two-boson realizations of generally deformed algebras with three generators are obtained by generalizing the Jordan-Schwlnger realizations of SU（2） and SU（1,1）. For each kind, a unitary realization and a non-unitary realizatlon, together with the properties of their acting spaces, are discussed. Similarity transformations that relate the non-unitary realizations to the unitary ones are given by solving unitarization equations.

On-shell methods for form factors in N = 4 SYM and their applications

Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp(soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including(1) tree-level form factors,(2) Sudakov form factor and infrared singularities, and(3) form factors of general operators and their anomalous dimensions. Although most examples we consider are inN= 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories.

Model-independent Veltman condition,naturalness and the little hierarchy problem

We adopt a bottom-up Effective Field Theory(EFT)approach to derive a model-independent Veltman condition to cancel out the quadratic divergences in the Higgs mass.We show using the equivalence theorem that all the deviations in the Higgs couplings to the W and Z from the SM predictions should vanish.We argue based on tree-level unitarity that any new physics that naturally cancels out the quadratic divergences should be ≤19 TeV.We show that the level of fine-tuning required is unless the O(0:1%-1%) UV sector has a symmetry that forces the satisfaction of the model-independent Veltman condition,in which case all fine-tuning is eliminated.We also conjecture that,if no new physics that couples to the Higgs is observed up to~19 TeV,or if the Higgs couplings to the SM particles conform to the SM predictions,then the Higgs either does not couple to any UV sector or is fine-tuned.

Can a non-unitary effect be prominent in neutrino oscillation measurements?

Subject to neutrino experiments, the mixing matrix of ordinary neutrinos can still have small vi-olation from unitarity. We introduce a quasi-unitary matrix to interpret this violation and propose a natural scheme to parameterize it. A quasi-unitary factor △QF is defined to be measured in neutrino oscillation exper-iments and the numerical results show that the improvement in experimental precision may help us figure out the secret of neutrino mixing.

Investigation of the rescattering effect in D decay

With two-body unitarity equations, we demonstrate the relation between the data of Dalitz analysis of a D＋ → K^-π＋π＋ decay experiment and that of Kπ scattering, and point out that there might be some underestimated ambiguity in the existing data sets, if the I = 1/2 component of the Kπ system is dominant in this decay process. It is suggested that the unitarity constraints should be built in to deal with the raw data to obtain an improved result from the Dalitz analysis.

Color-kinematics duality for Sudakov form factor in non-supersymmetric pure Yang-Mills theory

We study the duality between color and kinematics for the Sudakov form factors of tr(F~2)in non-supersymmetric pure Yang-Mills theory.We construct the integrands that manifest the color-kinematics duality up to two loops.The resulting numerators are given in terms of Lorentz products of momenta and polarization vectors,which have the same powers of loop momenta as that from the Feynman rules.The integrands are checked by d-dimensional unitarity cuts and are valid in any dimension.We find that massless-bubble and tadpole topologies are needed at two loops to realize the color-kinematics duality.Interestingly,the two-loop solution contains a large number of free parameters suggesting the duality may hold at higher loop orders.