11 research outputs found
Stability of Subsequent-to-Leading-Logarithm Corrections to the Effective Potential for Radiative Electroweak Symmetry Breaking
We demonstrate the stability under subsequent-to-leading logarithm
corrections of the quartic scalar-field coupling constant and the
running Higgs boson mass obtained from the (initially massless) effective
potential for radiatively broken electroweak symmetry in the
single-Higgs-Doublet Standard Model. Such subsequent-to-leading logarithm
contributions are systematically extracted from the renormalization group
equation considered beyond one-loop order. We show to be the dominant
coupling constant of the effective potential for the radiatively broken case of
electroweak symmetry. We demonstrate the stability of and the running
Higgs boson mass through five orders of successively subleading logarithmic
corrections to the scalar-field-theory projection of the effective potential
for which all coupling constants except the dominant coupling constant
are disregarded. We present a full next-to-leading logarithm
potential in the three dominant Standard Model coupling constants
(-quark-Yukawa, , and ) from these coupling constants'
contribution to two loop - and -functions. Finally, we
demonstrate the manifest order-by-order stability of the physical Higgs boson
mass in the 220-231 GeV range. In particular, we obtain a 231 GeV physical
Higgs boson mass inclusive of the -quark-Yukawa and coupling
constants to next-to-leading logarithm order, and inclusive of the smaller
gauge coupling constants to leading logarithm order.Comment: 21 pages, latex2e, 2 eps figures embedded in latex file. Updated
version contains expanded analysis in Section
Pade/renormalization-group improvement of inclusive semileptonic B decay rates
Renormalization Group (RG) and optimized Pade-approximant methods are used to
estimate the three-loop perturbative contributions to the inclusive
semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS}
scheme works favorably in the b \to u case whereas the pole mass scheme shows
better convergence in the b \to c case. Upon the inclusion of the estimated
three-loop contribution, we find the full perturbative decay rate to be
192\pi^3\Gamma(b\to u\bar\nu_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm
GeV^5} and 192\pi^3\Gamma(b\to c\ell^-\bar\nu_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm
198 {\rm GeV^5}, respectively. The errors are inclusive of theoretical
uncertainties and non-perturbative effects. Ultimately, these perturbative
contributions reduce the theoretical uncertainty in the extraction of the CKM
matrix elements |V_{ub}| and |V_{cb}| from their respective measured inclusive
semileptonic branching ratio(s).Comment: 3 pages, latex using espcrc2.sty. Write-up of talk given at BEACH
2002, UBC, Vancouve
Renormalization Group Determination of the Five-Loop Effective Potential for Massless Scalar Field Theory
The five-loop effective potential and the associated summation of subleading
logarithms for O(4) globally-symmetric massless field theory in
the Coleman-Weinberg renormalization scheme (where is the renormalization scale) is calculated via
renormalization-group methods. An important aspect of this analysis is
conversion of the known five-loop renormalization-group functions in the
minimal-subtraction (MS) scheme to the Coleman-Weinberg scheme.Comment: 5 pages. Write-up of talk given at Theory Canada III, June 2007,
University of Albert
Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories
In the absence of a tree-level scalar-field mass, renormalization-group (RG)
methods permit the explicit summation of leading-logarithm contributions to all
orders of the perturbative series for the effective-potential functions
utilized in radiative symmetry breaking. For scalar-field electrodynamics, such
a summation of leading logarithm contributions leads to upper bounds on the
magnitudes of both gauge and scalar-field coupling constants, and suggests the
possibility of an additional phase of spontaneous symmetry breaking
characterized by a scalar-field mass comparable to that of the theory's gauge
boson. For radiatively-broken electroweak symmetry, the all-orders summation of
leading logarithm terms involving the dominant three couplings (quartic
scalar-field, t-quark Yukawa, and QCD) contributing to standard-model radiative
corrections leads to an RG-improved potential characterized by a 216 GeV Higgs
boson mass. Upon incorporation of electroweak gauge couplants we find that the
predicted Higgs mass increases to 218 GeV. The potential is also characterized
by a quartic scalar-field coupling over five times larger than that anticipated
for an equivalent Higgs mass obtained via conventional spontaneous symmetry
breaking, leading to a concomitant enhancement of processes (such as ) sensitive to this coupling. Moreover, if the QCD coupling constant is
taken to be sufficiently strong, the tree potential's local minimum at is shown to be restored for the summation of leading logarithm corrections.
Thus if QCD exhibits a two-phase structure similar to that of
supersymmetric Yang-Mills theory, the weaker asymptotically-free phase of QCD
may be selected by the large logarithm behaviour of the RG-improved effective
potential for radiatively broken electroweak symmetry.Comment: latex2e using amsmath, 36 pages, 7 eps figures embedded in latex.
Section 8.3 errors asociated with electroweak coupling effects are correcte
Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms
Invariance of the effective action under changes of the renormalization scale
leads to relations between those (presumably calculated) terms
independent of at a given order of perturbation theory and those higher
order terms dependent on logarithms of . This relationship leads to
differential equations for a sequence of functions, the solutions of which give
closed form expressions for the sum of all leading logs, next to leading logs
and subsequent subleading logarithmic contributions to the effective action.
The renormalization group is thus shown to provide information about a model
beyond the scale dependence of the model's couplings and masses. This procedure
is illustrated using the model and Yang-Mills theory. In the latter
instance, it is also shown by using a modified summation procedure that the
dependence of the effective action resides solely in a multiplicative
factor of (the running coupling). This approach is also shown to
lead to a novel expansion for the running coupling in terms of the one-loop
coupling that does not require an order-by-order redefinition of the scale
factor . Finally, logarithmic contributions of the instanton
size to the effective action of an SU(2) gauge theory are summed, allowing a
determination of the asymptotic dependence on the instanton size as
goes to infinity to all orders in the SU(2) coupling constant.Comment: latex2e, 30 pages, 2 eps figures embedded in mansucript. v2 corrects
several minor errors in equation
The Renormalization Group with Exact beta-Functions
The perturbative -function is known exactly in a number of
supersymmetric theories and in the 't Hooft renormalization scheme in the
model. It is shown how this allows one to compute the effective
action exactly for certain background field configurations and to relate bare
and renormalized couplings. The relationship between the MS and SUSY
subtraction schemes in super Yang-Mills theory is discussed