scholarly journals FIRST LATTICE EVIDENCE FOR A NONTRIVIAL RENORMALIZATION OF THE HIGGS CONDENSATE

1998 ◽  
Vol 13 (29) ◽  
pp. 2361-2367 ◽  
Author(s):  
P. CEA ◽  
L. COSMAI ◽  
M. CONSOLI
Keyword(s):  
Wave Function ◽  
Continuum Limit ◽  
Higgs Mass ◽  
Lattice Simulation ◽  
Wave Function Renormalization ◽  
Renormalization Factor ◽  
Physical Mass ◽  
The Difference ◽  
Ising Limit ◽  
The Continuum

General arguments related to "triviality" predict that, in the broken phase of (λΦ4)4 theory, the condensate <Φ> rescales by a factor Zφ different from the conventional wave function renormalization factor, Z prop . Using a lattice simulation in the Ising limit, we measure Zφ= m2χ from the physical mass and susceptibility and Z prop from the residue of the shifted-field propagator. We find that the two Z's differ, with the difference increasing rapidly as the continuum limit is approached. Since Zφ affects the relation of <Φ> to the Fermi constant, it can sizably affect the present bounds on the Higgs mass.

scholarly journals FURTHER LATTICE EVIDENCE FOR A LARGE RESCALING OF THE HIGGS CONDENSATE

1999 ◽  
Vol 14 (24) ◽  
pp. 1673-1686 ◽  
Author(s):  
P. CEA ◽  
M. CONSOLI ◽  
L. COSMAI ◽  
P. M. STEVENSON
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Continuum Limit ◽  
Higgs Mass ◽  
Lattice Simulation ◽  
The Standard Model ◽  
Ising Limit ◽  
The Continuum

Using a high-statistics lattice simulation of the Ising limit of (λΦ4)4 theory, we have measured the susceptibility and propagator in the broken phase. We confirm our earlier finding of a discrepancy between the field rescaling implied by the propagator data and that implied by the susceptibility. The discrepancy becomes worse as one goes closer to the continuum limit; thus, it cannot be explained by residual perturbative effects. The data are consistent with an unconventional description of symmetry breaking and "triviality" in which the rescaling factor for the finite-momentum fluctuations tends to unity, but the rescaling factor for the condensate becomes larger and larger as one approaches the continuum limit. In the standard model this changes the interpretation of the Fermi-constant scale and its relation to the Higgs mass.

scholarly journals RELATING CALCULATIONS AND RENORMALIZATION IN AXIAL AND LORENTZ GAUGES AND GAUGE-INDEPENDENCE

2005 ◽  
Vol 20 (28) ◽  
pp. 6437-6449
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Wave Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Wave Function Renormalization ◽  
Renormalization Procedure ◽  
Point Function ◽  
Starting Point ◽  
Loop Approximation ◽  
The Difference ◽  
The One

We study further the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the one-loop approximation for the wave function renormalization and the identity of the β-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the one-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the β-functions in the two gauges.

LANDAU POLES, ULTRAVIOLET FIXED POINTS, AND “TRIVIALITY” IN THE PERTURBATIVE EXPANSION OF (λΦ4)4

1996 ◽  
Vol 11 (31) ◽  
pp. 2511-2524 ◽  
Author(s):  
M. CONSOLI ◽  
P.M. STEVENSON
Keyword(s):  
Fixed Points ◽  
Higgs Mass ◽  
Interaction Strength ◽  
Continuum Theory ◽  
Perturbative Approach ◽  
The Standard Model ◽  
Physical Mass ◽  
Group Flow ◽  
Scalar Sector ◽  
The Continuum

The “triviality” of (λΦ4)4 means that the continuum theory has a vanishing renormalized coupling λR. This result inherently conflicts with the standard perturbative approach, which begins by postulating a nonzero, cutoff-independent λR, and which suffers from pathologies — either Landau poles (in odd orders) or spurious ultraviolet fixed points (in even orders). We show how the known structure of perturbation theory can be rearranged, to arbitrarily high orders, to fulfil the condition λR=0. The corresponding renormalization group flow of the bare coupling coincides with that needed to renormalize the effective potential, as calculated in any “triviality”-compatible approximation. Although λR vanishes, the physical mass is finite; there is no proportionality between the two. That implies that the Higgs mass does not represent a measure of the observable interaction strength in the scalar sector of the standard model.

scholarly journals A General Treatment of Oblique Parameters

1997 ◽  
Vol 12 (08) ◽  
pp. 1511-1529 ◽  
Author(s):  
Anirban Kundu ◽  
Probir Roy
Keyword(s):  
Wave Function ◽  
Linear Approximation ◽  
Gauge Boson ◽  
Vacuum Polarization ◽  
Wave Function Renormalization ◽  
Weak Boson ◽  
The Third ◽  
The Difference ◽  
First Time ◽  
Expansion Scheme

A re-examination is made of one-loop oblique electroweak corrections. General definitions are given of the oblique parameters without reference to any q2 expansion scheme. The old oblique parameters S, T and U are defined as differences of gauge boson vacuum polarization Π functions and suffice for describing certain observable ratios on the Z peak and the ρ parameter at q2 = 0. Regarding the new oblique parameters V, W and X, the first two are defined in terms of differences of Π functions as well as the wave function renormalization of the corresponding weak boson, and the third in terms of the difference of differences of two Π functions for γ - Z mixing. Explicit expressions for measurable quantities involving all six oblique parameters are given and experimental bounds are obtained on the latter, some for the first time. A review of these constraints suggests that the linear approximation of Peskin and Takeuchi is robust.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Coupled dynamics of populations supported by discrete sites and their continuum limit

2010 ◽  
Vol 466 (2121) ◽  
pp. 2561-2586 ◽  
Author(s):  
Timothy R. Field ◽  
Robert J. A. Tough
Keyword(s):  
Evolution Equation ◽  
Closed Form ◽  
Generating Function ◽  
Rate Equation ◽  
Continuum Limit ◽  
Infinite Chain ◽  
Migration Process ◽  
The Mean ◽  
The Continuum ◽  
Birth Death

The illumination of single population behaviour subject to the processes of birth, death and immigration has provided a basis for the discussion of the non-Gaussian statistical and temporal correlation properties of scattered radiation. As a first step towards the modelling of its spatial correlations, we consider the populations supported by an infinite chain of discrete sites, each subject to birth, death and immigration and coupled by migration between adjacent sites. To provide some motivation, and illustrate the techniques we will use, the migration process for a single particle on an infinite chain of sites is introduced and its diffusion dynamics derived. A certain continuum limit is identified and its properties studied via asymptotic analysis. This forms the basis of the multi-particle model of a coupled population subject to single site birth, death and immigration processes, in addition to inter-site migration. A discrete rate equation is formulated and its generating function dynamics derived. This facilitates derivation of the equations of motion for the first- and second-order cumulants, thus generalizing the earlier results of Bailey through the incorporation of immigration at each site. We present a novel matrix formalism operating in the time domain that enables solution of these equations yielding the mean occupancy and inter-site variances in the closed form. The results for the first two moments at a single time are used to derive expressions for the asymptotic time-delayed correlation functions, which relates to Glauber’s analysis of an Ising model. The paper concludes with an analysis of the continuum limit of the birth–death–immigration–migration process in terms of a path integral formalism. The continuum rate equation and evolution equation for the generating function are developed, from which the evolution equation of the mean occupancy is derived, in this limit. Its solution is provided in closed form.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

High-resolution spectroscopy near the continuum limit: the microwave spectrum of trans-3-bromo-1,1,1,2,2-pentafluoropropane

2018 ◽  
Vol 117 (9-12) ◽  
pp. 1351-1359 ◽  
Author(s):  
Frank E. Marshall ◽  
Nicole Moon ◽  
Thomas D. Persinger ◽  
David J. Gillcrist ◽  
Nelson E. Shreve ◽  
...  
Keyword(s):  
High Resolution ◽  
Continuum Limit ◽  
Microwave Spectrum ◽  
High Resolution Spectroscopy ◽  
The Continuum

scholarly journals Photon splitting in strongly magnetized medium with taking into account positronium influence

2018 ◽  
Vol 191 ◽  
pp. 08011
Author(s):  
R.A. Anikin ◽  
M.V. Chistyakov ◽  
D.A. Rumyantsev ◽  
D.M. Shlenev
Keyword(s):  
Wave Function ◽  
Absorption Rate ◽  
Wave Function Renormalization ◽  
Selection Rules ◽  
Dispersion Properties ◽  
Photon Splitting

The process of the photon splitting, γ → γγ, is investigated in strongly magnetized vacuum with taking into account positronium influence. The dispersion properties of photons and the new polarization selection rules are obtained. The absorption rate of the leading photon splitting channels are calculated with taking account of the photon dispersion and wave function renormalization.

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