AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

COLOR CONFINEMENT AND FINITE TEMPERATURE QCD PHASE TRANSITION

2004 ◽  
Vol 19 (02) ◽  
pp. 271-285 ◽  
Author(s):  
H. C. PANDEY ◽  
H. C. CHANDOLA ◽  
H. DEHNEN
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Effective Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Expectation Value ◽  
Qcd Phase Transition ◽  
Qcd Vacuum ◽  
Color Confinement

We study an effective theory of QCD in which the fundamental variables are dual magnetic potentials coupled to the monopole field. Dual dynamics are then used to explain the properties of QCD vacuum at zero temperature as well as at finite temperatures. At zero temperature, the color confinement is realized through the dynamical breaking of magnetic symmetry, which leads to the magnetic condensation of QCD vacuum. The flux tube structure of SU(2) QCD vacuum is investigated by solving the field equations in the low energy regimes of the theory, which guarantees dual superconducting nature of the QCD vacuum. The QCD phase transition at finite temperature is studied by the functional diagrammatic evaluation of the effective potential on the one-loop level. We then obtained analytical expressions for the vacuum expectation value of the condensed monopoles as well as the masses of glueballs from the temperature dependent effective potential. These nonperturbative parameters are also evaluated numerically and used to determine the critical temperature of the QCD phase transition. Finally, it is shown that near the critical temperature (Tc≃0.195 GeV ), continuous reduction of vacuum expectation value (VEV) of the condensed monopoles caused the disappearance of vector and scalar glueball masses, which brings a second order phase transition in pure SU(2) gauge QCD.

Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function

2015 ◽  
Vol 70 (10) ◽  
pp. 867-874 ◽  
Author(s):  
Abdelamelk Boumali
Keyword(s):  
Free Energy ◽  
Thermal Properties ◽  
Zeta Function ◽  
Function Method ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Hurwitz Zeta Function ◽  
Expectation Value ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we investigated the thermodynamics properties of the one-dimensional Duffin–Kemmer–Petiau oscillator by using the Hurwitz zeta function method. In particular, we calculated the following main thermal quantities: the free energy, the total energy, the entropy, and the specific heat. The Hurwitz zeta function allowed us to compute the vacuum expectation value of the energy of our oscillator.

scholarly journals AN UPPER BOUND ON THE HIGGS BOSON MASS FROM A POSITIVITY CONDITION ON THE MASS MATRIX

1998 ◽  
Vol 13 (10) ◽  
pp. 753-757 ◽  
Author(s):  
ALI AL-NAGHMOUSH ◽  
MURAT ÖZER ◽  
M. O. TAHA
Keyword(s):  
Higgs Boson ◽  
Upper Bound ◽  
Top Quark ◽  
Mass Matrix ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Boson Mass ◽  
Higgs Boson Mass ◽  
Positivity Condition ◽  
The One

We impose the condition that the eigenvalues of the mass matrix in the shifted Lagrangian density be positive at ϕ=ϕ0, the vacuum expectation value of the scalar field. Using the one-loop effective potential of the standard model, this condition leads to an upper bound on the Higgs boson mass m H :m H <230 GeV, for a top quark mass of 175 GeV.

PHASE TRANSITIONS IN ϕ4 THEORY AT FINITE DENSITIES

1989 ◽  
Vol 04 (08) ◽  
pp. 783-789 ◽  
Author(s):  
V.J. PETER ◽  
M. SABIR
Keyword(s):  
Phase Transitions ◽  
Effective Mass ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Coupling Constant ◽  
Effective Coupling ◽  
Effective Coupling Constant ◽  
The One

We study the effective mass and effective coupling constant of a self interacting O(2) symmetric ϕ4 model at finite temperature and finite chemical potential in the one-loop and improved one-loop approximations. It is shown that the restored symmetry at a finite chemical potential is again broken at a higher value of chemical potential.

scholarly journals Scalar leptoquarks in leptonic processes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Andreas Crivellin ◽  
Christoph Greub ◽  
Dario Müller ◽  
Francesco Saturnino
Keyword(s):  
Standard Model ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Lepton Flavor ◽  
Interaction Terms ◽  
The Standard Model ◽  
The One ◽  
Scalar Leptoquarks

Abstract Leptoquarks are hypothetical new particles, which couple quarks directly to leptons. They experienced a renaissance in recent years as they are prime candidates to explain the so-called flavor anomalies, i.e. the deviations between the Standard Model predictions and measurements in b → sℓ+ℓ− and b → cτν processes and in the anomalous magnetic moment of the muon. At the one-loop level these particles unavoidably generate effects in the purely leptonic processes like Z → ℓ+ℓ−, Z →$$ v\overline{v} $$ v v ¯ , W → ℓν and h → ℓ+ℓ− and can even generate non-zero rates for lepton flavor violating processes such as ℓ → ℓ′γ, Z → ℓ+ℓ′−, h → ℓ+ℓ′− and ℓ → 3ℓ′. In this article we calculate these processes for all five representations of scalar Leptoquarks. We include their most general interaction terms with the Standard Model Higgs boson, which leads to Leptoquark mixing after the former acquires a vacuum expectation value. In our phenomenological analysis we investigate the effects in modified lepton couplings to electroweak gauge bosons, we study the correlations of the anomalous magnetic moment of the muon with h → μ+μ− and Z → μ+μ− as well as the interplay between different lepton flavor violating decays.

scholarly journals MODIFYING GRAVITY IN THE INFRARED BY IMPOSING AN "ULTRASTRONG" EQUIVALENCE PRINCIPLE

2009 ◽  
Vol 18 (14) ◽  
pp. 2181-2188 ◽  
Author(s):  
FEDERICO PIAZZA
Keyword(s):  
Equivalence Principle ◽  
Particle Production ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Energy Tensor ◽  
Dimensional Parameter ◽  
Proposed Modification ◽  
Quantum Phenomena ◽  
The One ◽  
Free Falling

The equivalence principle suggests considering gravity as an infrared phenomenon, whose effects are visible only outside Einstein's free-falling elevator. By curving space–time, general relativity leaves the smallest systems free of classical gravitational effects. However, according to the standard semiclassical treatment, indirect effects of gravity can be experienced inside the elevator through the well-known mechanism of quantum particle production. Here we try a different path than the one historically followed: rather than imposing field quantization on top of a curved manifold, we attempt to upgrade the equivalence principle and extend it to the quantum phenomena. Therefore, we consider, and try to realize in a theoretical framework, a stronger version of the equivalence principle, in which all the effects of gravity are definitely banned from the elevator and confined to the infrared. For this purpose, we introduce infrared modified commutation relations for the global field operators (Fourier modes) that allow us to reabsorb the time-dependent quadratic divergence of the vacuum expectation value of the stress–energy tensor. The proposed modification is effective on length scales comparable to the inverse curvature and, therefore, does not add any dimensional parameter to the theory.

scholarly journals Magnetic Monopoles in Multivector Boson Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Koichiro Kobayashi ◽  
Nahomi Kan ◽  
Kiyoshi Shiraishi
Keyword(s):  
Sigma Model ◽  
Gauge Coupling ◽  
Higgs Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Magnetic Monopoles ◽  
Coupling Constant ◽  
Test Functions ◽  
Boson Theory ◽  
The Common

A classical solution for a magnetic monopole is found in a specific multivector boson theory. We consider the model whose [SU(2)]N+1 gauge group is broken by sigma model fields (à la dimensional deconstruction) and further spontaneously broken by an adjoint scalar (à la triplet Higgs mechanism). In this multivector boson theory, we find the solution for the monopole whose mass is MN~(4πv/g)N+1, where g is the common gauge coupling constant and v is the vacuum expectation value of the triplet Higgs field, by using a variational method with the simplest set of test functions.

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