scholarly journals Perturbative unitarity constraints on generic Yukawa interactions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Lukas Allwicher ◽  
Pere Arnan ◽  
Daniele Barducci ◽  
Marco Nardecchia
Keyword(s):  
Neutral Current ◽  
Adjoint Representation ◽  
Yukawa Couplings ◽  
Quantum Numbers ◽  
Perturbative Regime ◽  
Experimental Values ◽  
Arbitrary Quantum

Abstract We study perturbative unitarity constraints on generic Yukawa interactions where the involved fields have arbitrary quantum numbers under an ∏iSU(Ni) ⊗ U(1) group. We derive compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under the trivial, fundamental or adjoint representation of the various SU(N) factors. We apply our results to specific models formulated to explain the anomalous measurements of (g − 2)μ and of the charged- and neutral-current decays of the B mesons. We show that, while these models can generally still explain the observed experimental values, the required Yukawa couplings are pushed at the edge of the perturbative regime.

ENERGY LEVELS IN THE STATISTICAL ATOM WITH EXCHANGE AND CORRELATION

1967 ◽  
Vol 45 (5) ◽  
pp. 1745-1754 ◽  
Author(s):  
Ashok Jain ◽  
Satish Kumar
Keyword(s):  
Ground State ◽  
Energy Levels ◽  
Argon Atom ◽  
Particle Energy ◽  
Single Particle Energy ◽  
Relativistic Generalization ◽  
Quantum Numbers ◽  
Different Types ◽  
Present Formalism ◽  
Experimental Values

In this paper, quantum numbers are introduced in a statistical model of atoms that includes the correlation and the exchange terms (TFDC model). Two different types of angular momentum assignments have been introduced into the model and, as an application of this, the single-particle energy levels of the argon atom in its ground state have been calculated. A simple relativistic generalization of the present formalism is discussed and is shown to give better agreement with experimental values. Finally, some suggestions for improvement of the present formalism are made.

Energy spectrum for trigonometric Pöschl–Teller potential

2012 ◽  
Vol 90 (12) ◽  
pp. 1259-1265 ◽  
Author(s):  
Babatunde James Falaye
Keyword(s):  
Bound State ◽  
Asymptotic Iteration Method ◽  
Generalized Hypergeometric Functions ◽  
Short Range Potential ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Quantum Numbers ◽  
Special Case ◽  
Arbitrary Quantum ◽  
Good Agreement

We present analytical solutions of the Schrödinger equation for the trigonometric Pöschl–Teller molecular potential by using a proper approximation to the centrifugal term within the framework of the asymptotic iteration method. We obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the generalized hypergeometric functions. Energy eigenvalues for a few diatomic molecules are calculated for arbitrary quantum numbers n and ℓ with various values of parameter α. We also studied special case ℓ = 0 and found that the results are in good agreement with findings of other methods for short-range potential.

scholarly journals MORE EVIDENCE FOR THE WDVV EQUATIONS IN ${\mathcal N} = 2$ SUSY YANG–MILLS THEORIES

2000 ◽  
Vol 15 (08) ◽  
pp. 1157-1206 ◽  
Author(s):  
A. MARSHAKOV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Field Theory ◽  
Adjoint Representation ◽  
Hyperelliptic Curves ◽  
Fundamental Representation ◽  
Wdvv Equations ◽  
Yang Mills ◽  
Perturbative Regime ◽  
String Models ◽  
Supersymmetric Theories ◽  
Moser System

We consider 4D and 5D [Formula: see text] supersymmetric theories and demonstrate that in general their Seiberg–Witten prepotentials satisfy the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. General proof for the Yang–Mills models (with matter in the first fundamental representation) makes use of the hyperelliptic curves and underlying integrable systems. A wide class of examples is discussed; it contains few understandable exceptions. In particular, in the perturbative regime of 5D theories, in addition to naive field theory expectations some extra terms appear, as happens in heterotic string models. We consider also the example of the Yang–Mills theory with matter hypermultiplet in the adjoint representation (related to the elliptic Calogero–Moser system) when the standard WDVV equations do not hold.

scholarly journals Direct production of χc1 at BESIII

2019 ◽  
Vol 202 ◽  
pp. 06009
Author(s):  
Yuping Guo
Keyword(s):  
Data Analysis ◽  
Production Rate ◽  
Neutral Current ◽  
High Luminosity ◽  
Direct Production ◽  
Two Photon ◽  
Quantum Numbers ◽  
Decay Products ◽  
Electron Positron Annihilation ◽  
Electron Positron

The production of resonances in electron-positron annihilation has only been observed for states with quantum numbers JPC = 1−−, while C = +1 resonances appear only among the decay products. The direct production of the 1++ states could happen through two-photon or neutral current. Due to the smallness of the production rate, this process has never been verified experimentally. With the high luminosity and good performance of the BESIII experiment, a search of the direct production of the 1++ state in charmonium region, χc1, is undergoing with dedicated data samples around the χc1 mass. An overview of the data analysis will be presented.

scholarly journals The theory of the change in resistance in a magnetic field

1934 ◽  
Vol 145 (854) ◽  
pp. 268-277 ◽  
Keyword(s):  
Magnetic Field ◽  
Temperature Dependence ◽  
Periodic Potential ◽  
Quadratic Function ◽  
Modern Theory ◽  
Quantum Numbers ◽  
Wrong Direction ◽  
Constant Potential ◽  
The Subject ◽  
Experimental Values

The resistance of a metal is in general increased by a magnetic field. For sufficiently small magnetic fields this dependence may, of course, be expressed by the equation ∆R/R = BH 2 . The calculation of the coefficient B has been the subject of many previous investigations. Sommerfeld has shown that if the electrons are regarded as moving in a constant potential, then the theoretical value of B is 10,000 times smaller than the observed value, and the temperature dependence is in the wrong direction. Peierls has suggested that the correct magnitude of B may be obtained if cognizance is taken of the fact that the electrons are moving in a periodic potential, as is usual in the modern theory of metals. Moreover, he has shown that the correct temperature dependence will then be obtained. Blochinzev and Nordheim have recently investigated in detail the charge of resistance of divalent metals from this standpoint. The periodicity of the lattice was, however, introduced in quite an idealized manner. In place of an actual metal they considered a simple cubic lattice. The surface of the Fermi distribution was assumed to be composed of sections each of which was a quadratic function of the quantum numbers ξ, η , ζ. The coefficient B was obtained in terms of the Fourier coefficient of the potential energy of an electron in the lattice, V 100 . Agreement with the experimental values of B was obtained by taking |V 100 | as small as several hundredths of an electron volt, while the correct value must be of the order of 1 volt. Since in their model B varies inversely as the square of |V 100 |, the comparison with experiment is far from satisfactory.

scholarly journals Rotationally Resolved Rate Constant Measurements for Removal of CH(A2Δ and B2∑−) by Ketene

1994 ◽  
Vol 14 (4) ◽  
pp. 207-216 ◽  
Author(s):  
Jorge Luque ◽  
Javier Ruiz ◽  
Margarita Martin
Keyword(s):  
Quantum Number ◽  
Rate Constant ◽  
Cross Sections ◽  
Rate Constants ◽  
Rotational Quantum Number ◽  
Moderate Increase ◽  
Quantum Numbers ◽  
State Rate ◽  
Experimental Errors ◽  
Experimental Values

Rate constants for total removal of CH(A2Δ) and CH(B2∑−) in collisions with ketene were measured. For the A2Δ state, rate constants increased with vibrational quantum number; measured values were (4.5 ± 0.5) × 10-10 cm3 molec-1 s-1 and (8.0 ± 1) × 10-01 cm3 molec-1 s-1 for v′ = 0 and v′ = 2 respectively. For v′ = 0, rotational levels with quantum numbers from N′ = 4 to N′ = 16 were removed with similar rates within experimental errors; collisional disappearance of levels with higher rotational quantum numbers was faster for a factor of about 1.4. Calculations of cross sections for ketene and other fast colliders, assuming a multipole model, obtained a qualitative correlation with experimental values. CH(B2∑−) was more efficiently removed than CH(A2Δ, v′ = 0); for the lowest rotational levels a rate constant of (5.8 ± 0.3) × 10-10 cm3 molec-1 s-1 was measured and a moderate increase with rotational quantum number was observed.

scholarly journals LIGHT PSEUDO-GOLDSTONE BOSONS WITHOUT EXPLICIT SYMMETRY BREAKING

2007 ◽  
Vol 22 (06) ◽  
pp. 1161-1179
Author(s):  
ANTONIO O. BOUZAS
Keyword(s):  
Orbit Space ◽  
Scalar Fields ◽  
Adjoint Representation ◽  
Dirac Fermion ◽  
Continuous Symmetry ◽  
Yukawa Couplings ◽  
Goldstone Bosons ◽  
Scalar Mass ◽  
Light Scalar ◽  
Massless Fields

A mechanism is discussed to obtain light scalar fields from a spontaneously broken continuous symmetry without explicitly breaking it. If there is a continuous manifold of classical vacua in orbit space, its tangent directions describe classically massless fields that may acquire mass from perturbations of the potential that do not break the symmetry. We consider the simplest possible example, involving a scalar field in the adjoint representation of SU (N). We study the scalar mass spectrum and its renormalization group running at one-loop level including scalar and pseudoscalar Yukawa couplings to a massive Dirac fermion.

ANALYTICAL APPROXIMATIONS TO THE SCHRÖDINGER EQUATION FOR A SECOND PÖSCHL–TELLER-LIKE POTENTIAL WITH CENTRIFUGAL TERM

2008 ◽  
Vol 23 (10) ◽  
pp. 1537-1544 ◽  
Author(s):  
SHI-HAI DONG ◽  
WEN-CHAO QIANG ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Centrifugal Term ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Arbitrary Quantum ◽  
Good Agreement

The bound state solutions of the Schrödinger equation for a second Pöschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.

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