540 research outputs found
The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant
We consider a chirally invariant lattice Higgs-Yukawa model based on the
Neuberger overlap operator. As a first step towards the eventual determination
of Higgs mass bounds we study the phase diagram of the model analytically in
the large Nf-limit. We present an expression for the effective potential at
tree-level in the regime of small Yukawa and quartic coupling constants and
determine the order of the phase transitions. In the case of strong Yukawa
couplings the model effectively becomes an O(4)-symmetric non-linear
sigma-model for all values of the quartic coupling constant. This leads to the
existence of a symmetric phase also in the regime of large values of the Yukawa
coupling constant. On finite and small lattices, however, strong finite volume
effects prevent the expectation value of the Higgs field from vanishing thus
obscuring the existence of the symmetric phase at strong Yukawa couplings.Comment: 21 pages, 6 figures, added reference
Lattice chirality and the decoupling of mirror fermions
We show, using exact lattice chirality, that partition functions of lattice
gauge theories with vectorlike fermion representations can be split into
"light" and "mirror" parts, such that the "light" and "mirror" representations
are chiral. The splitting of the full partition function into "light" and
"mirror" is well defined only if the two sectors are separately anomaly free.
We show that only then is the generating functional, and hence the spectrum, of
the mirror theory a smooth function of the gauge field background. This
explains how ideas to use additional non-gauge, high-scale mirror-sector
dynamics to decouple the mirror fermions without breaking the gauge
symmetry--for example, in symmetric phases at strong mirror Yukawa
coupling--are forced to respect the anomaly-free condition when combined with
the exact lattice chiral symmetry. Our results also explain a paradox posed by
a recent numerical study of the mirror-fermion spectrum in a toy
would-be-anomalous two-dimensional theory. In passing, we prove some general
properties of the partition functions of arbitrary chiral theories on the
lattice that should be of interest for further studies in this field.Comment: 29 pages, 2 figures; published version, new addendu
Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
This is a review of the status and outstanding issues in attempts to
construct chiral lattice gauge theories by decoupling the mirror fermions from
a vectorlike theory. In the first half, we explain why studying nonperturbative
chiral gauge dynamics may be of interest, enumerate the problems that a lattice
formulation of chiral gauge theories must overcome, and briefly review our
current knowledge. We then discuss the motivation and idea of mirror-fermion
decoupling and illustrate the desired features of the decoupling dynamics by a
simple solvable toy model. The role of exact chiral symmetries and matching of
't Hooft anomalies on the lattice is also explained. The second, more
technical, half of the article is devoted to a discussion of the known and
unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson
fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo
The dual optimizer for the growth-optimal portfolio under transaction costs
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar et al.(Math. Oper. Res. 13:277-294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341-1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rat
Molecular characterization of Trichomonas gallinae isolates recovered from the Canadian Maritime provincesâ wild avifauna reveals the presence of the genotype responsible for the European finch trichomonosis epidemic and additional strains
Finch trichomonosis, caused by Trichomonas gallinae, emerged in the Canadian Maritime provinces in 2007 and has since caused ongoing mortality in regional purple finch (Carpodacus purpureus) and American goldfinch (Carduelis tristis) populations. Trichomonas gallinae was isolated from (1) finches and rock pigeons (Columbia livia) submitted for post-mortem or live-captured at bird feeding sites experiencing trichomonosis mortality; (2) bird seed at these same sites; and (3) rock pigeons live-captured at known roosts or humanely killed. Isolates were characterized using internal transcribed spacer (ITS) region and iron hydrogenase (Fe-hyd) gene sequences. Two distinct ITS types were found. Type A was identical to the UK finch epidemic strain and was isolated from finches and a rock pigeon with trichomonosis; apparently healthy rock pigeons and finches; and bird seed at an outbreak site. Type B was obtained from apparently healthy rock pigeons. Fe-hyd sequencing revealed six distinct subtypes. The predominant subtype in both finches and the rock pigeon with trichomonosis was identical to the UK finch epidemic strain A1. Single nucleotide polymorphisms in Fe-hyd sequences suggest there is fine-scale variation amongst isolates and that finch trichomonosis emergence in this region may not have been caused by a single spill-over event
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
We present a gauge-invariant and non-perturbative construction of the
Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac
operator satisfying the Ginsparg-Wilson relation. Our construction covers all
SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable
for a description of the baryon number non-conservation. In infinite volume, it
provides a gauge-invariant regularization of the electroweak theory to all
orders of perturbation theory. First we formulate the reconstruction theorem
which asserts that if there exists a set of local currents satisfying cetain
properties, it is possible to reconstruct the fermion measure which depends
smoothly on the gauge fields and fulfills the fundamental requirements such as
locality, gauge-invariance and lattice symmetries. Then we give a closed
formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE
Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions
We study 't Hooft anomaly matching in lattice models with strong Yukawa or
multi-fermion interactions. Strong non-gauge interactions among the mirror
fermions in a vectorlike lattice gauge theory are introduced with the aim to
obtain, in a strong-coupling symmetric phase, a long-distance unbroken gauge
theory with chiral fermions in a complex representation. We show how to use
exact lattice chirality to analyze the anomaly matching conditions on chiral
symmetry current correlators at finite lattice spacing and volume. We perform a
Monte Carlo study of the realization of anomaly matching in a toy
two-dimensional model with an anomalous mirror-fermion content at strong mirror
Yukawa coupling. We show that 't Hooft anomaly matching is satisfied, in most
of the phase diagram, via the minimal solution in either the massless fermion
or "Goldstone" mode, while in some cases there are extra massless vectorlike
mirror fermions. The mirror spectrum at strong coupling is thus consistent with
long-distance unitarity. We discuss the implications of our results for future
studies of the most interesting case of the decoupling of anomaly-free
mirror-fermion sectors.Comment: 46 pages, 8 figures, some typos fixed and references adde
The Nuclear Yukawa Model on a Lattice
We present the results of the quantum field theory approach to nuclear Yukawa
model obtained by standard lattice techniques. We have considered the simplest
case of two identical fermions interacting via a scalar meson exchange.
Calculations have been performed using Wilson fermions in the quenched
approximation. We found the existence of a critical coupling constant above
which the model cannot be numerically solved. The range of the accessible
coupling constants is below the threshold value for producing two-body bound
states. Two-body scattering lengths have been obtained and compared to the non
relativistic results.Comment: 15 page
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