3,368 research outputs found
The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
We present an expression for the leading-color (planar) four-loop four-point
amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms
of eight separate integrals. The expression is based on consistency of
unitarity cuts and infrared divergences. We expand the integrals around e=0,
and obtain analytic expressions for the poles from 1/e^8 through 1/e^4. We give
numerical results for the coefficients of the 1/e^3 and 1/e^2 poles. These
results all match the known exponentiated structure of the infrared
divergences, at four separate kinematic points. The value of the 1/e^2
coefficient allows us to test a conjecture of Eden and Staudacher for the
four-loop cusp (soft) anomalous dimension. We find that the conjecture is
incorrect, although our numerical results suggest that a simple modification of
the expression, flipping the sign of the term containing zeta_3^2, may yield
the correct answer. Our numerical value can be used, in a scheme proposed by
Kotikov, Lipatov and Velizhanin, to estimate the two constants in the
strong-coupling expansion of the cusp anomalous dimension that are known from
string theory. The estimate works to 2.6% and 5% accuracy, providing
non-trivial evidence in support of the AdS/CFT correspondence. We also use the
known constants in the strong-coupling expansion as additional input to provide
approximations to the cusp anomalous dimension which should be accurate to
under one percent for all values of the coupling. When the evaluations of the
integrals are completed through the finite terms, it will be possible to test
the iterative, exponentiated structure of the finite terms in the four-loop
four-point amplitude, which was uncovered earlier at two and three loops.Comment: 72 pages, 15 figures, v2 minor correction
Form factors of descendant operators: Free field construction and reflection relations
The free field representation for form factors in the sinh-Gordon model and
the sine-Gordon model in the breather sector is modified to describe the form
factors of descendant operators, which are obtained from the exponential ones,
\e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra
associated to the field . As a check of the validity of the
construction we count the numbers of operators defined by the form factors at
each level in each chiral sector. Another check is related to the so called
reflection relations, which identify in the breather sector the descendants of
the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi}
for generic values of . We prove the operators defined by the obtained
families of form factors to satisfy such reflection relations. A generalization
of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor
corrections; v4,v5: misprints corrected; v6: minor mistake correcte
Screening of Dirac flavor structure in the seesaw and neutrino mixing
We consider the mechanism of screening of the Dirac flavor structure in the
context of the double seesaw mechanism. As a consequence of screening, the
structure of the light neutrino mass matrix, m_\nu, is determined essentially
by the structure of the (Majorana) mass matrix, M_S, of new super-heavy (Planck
scale) neutral fermions S. We calculate effects of the renormalization group
running in order to investigate the stability of the screening mechanism with
respect to radiative corrections. We find that screening is stable in the
supersymmetric case, whereas in the standard model it is unstable for certain
structures of M_S. The screening mechanism allows us to reconcile the
(approximate) quark-lepton symmetry and the strong difference of the mixing
patterns in the quark and lepton sectors. It opens new possibilities to explain
a quasi-degenerate neutrino mass spectrum, special ``neutrino'' symmetries and
quark-lepton complementarity. Screening can emerge from certain flavor
symmetries or Grand Unification.Comment: 27 pages, 3 figures; references added, discussion of the E6 model
modifie
Quark lepton complementarity and renormalization group effects
We consider a scenario for the Quark-Lepton Complementarity relations between
mixing angles in which the bi-maximal mixing follows from the neutrino mass
matrix. According to this scenario in the lowest order the angle \theta_{12} is
\sim 1\sigma (1.5 - 2^\circ) above the best fit point coinciding practically
with the tri-bimaximal mixing prediction. Realization of this scenario in the
context of the seesaw type-I mechanism with leptonic Dirac mass matrices
approximately equal to the quark mass matrices is studied. We calculate the
renormalization group corrections to \theta_{12} as well as to \theta_{13} in
the standard model (SM) and minimal supersymmetric standard model (MSSM). We
find that in large part of the parameter space corrections \Delta \theta_{12}
are small or negligible. In the MSSM version of the scenario the correction
\Delta \theta_{12} is in general positive. Small negative corrections appear in
the case of an inverted mass hierarchy and opposite CP parities of \nu_1 and
\nu_2 when leading contributions to \theta_{12} running are strongly
suppressed. The corrections are negative in the SM version in a large part of
the parameter space for values of the relative CP phase of \nu_1 and \nu_2:
\phi > \pi/2.Comment: version as published in PRD, 14 pages, 12 figure
Travel time stability in weakly range-dependent sound channels
Travel time stability is investigated in environments consisting of a
range-independent background sound-speed profile on which a highly structured
range-dependent perturbation is superimposed. The stability of both
unconstrained and constrained (eigenray) travel times are considered. Both
general theoretical arguments and analytical estimates of time spreads suggest
that travel time stability is largely controlled by a property of the background sound speed profile. Here, is
the range of a ray double loop and is the ray action variable. Numerical
results for both volume scattering by internal waves in deep ocean environments
and rough surface scattering in upward refracting environments are shown to
confirm the expectation that travel time stability is largely controlled by
.Comment: Submitted to J. Acoust. Soc. Am., 30 June 200
Investigating the local atmospheric response to a realistic shift in the Oyashio Sea surface Temperature Front
Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 28 (2015): 1126–1147, doi:10.1175/JCLI-D-14-00285.1.The local atmospheric response to a realistic shift of the Oyashio Extension SST front in the western North Pacific is analyzed using a high-resolution (HR; 0.25°) version of the global Community Atmosphere Model, version 5 (CAM5). A northward shift in the SST front causes an atmospheric response consisting of a weak surface wind anomaly but a strong vertical circulation extending throughout the troposphere. In the lower troposphere, most of the SST anomaly–induced diabatic heating is balanced by poleward transient eddy heat and moisture fluxes. Collectively, this response differs from the circulation suggested by linear dynamics, where extratropical SST forcing produces shallow anomalous heating balanced by strong equatorward cold air advection driven by an anomalous, stationary surface low to the east. This latter response, however, is obtained by repeating the same experiment except using a relatively low-resolution (LR; 1°) version of CAM5. Comparison to observations suggests that the HR response is closer to nature than the LR response. Strikingly, HR and LR experiments have almost identical vertical profiles of . However, diagnosis of the diabatic quasigeostrophic vertical pressure velocity (ω) budget reveals that HR has a substantially stronger response, which together with upper-level mean differential thermal advection balances stronger vertical motion. The results herein suggest that changes in transient eddy heat and moisture fluxes are critical to the overall local atmospheric response to Oyashio Front anomalies, which may consequently yield a stronger downstream response. These changes may require the high resolution to be fully reproduced, warranting further experiments of this type with other high-resolution atmosphere-only and fully coupled GCMs.We gratefully acknowledge funding provided by NSF to DS and MN (AGS CLD 1035325) and Y-OK and CF (AGS CLD 1035423) and by DOE to Y-OK (DE-SC0007052).2015-08-0
Lepton Mixing and Cancellation of the Dirac Mass Hierarchy in SO(10) GUTs with Flavor Symmetries T7 and Sigma(81)
In SO(10) grand unified theories (GUTs) the hierarchy which is present in the
Dirac mass term of the neutrinos is generically as strong as the one in the
up-type quark mass term. We propose a mechanism to partially or completely
cancel this hierarchy in the light neutrino mass matrix in the seesaw context.
The two main ingredients of the cancellation mechanism are the existence of
three fermionic gauge singlets and of a discrete flavor symmetry G_f which is
broken at a higher scale than SO(10). Two realizations of the cancellation
mechanism are presented. The realization based on the Frobenius group T7 = Z7 x
Z3 leads to a partial cancellation of the hierarchy and relates maximal 2-3
lepton mixing with the geometric hierarchy of the up-quark masses. In the
realization with the group Sigma(81) the cancellation is complete and
tri-bimaximal lepton mixing is reproduced at the lowest order. In both cases,
to fully accommodate the leptonic data we take into account additional effects
such as effects of higher-dimensional operators involving more than one flavon.
The heavy neutral fermion mass spectra are considered. For both realizations we
analyze the flavon potential at the renormalizable level as well as ways to
generate the Cabibbo angle.Comment: 31 page
An Assessment of Policy Measures to Support Russia's Real Economy
"This paper presents the results of an analytical project on the design and approbation of methodology for assessing and monitoring the measures taken by the government of the Russian Federation in response to the recent worldwide fiscal crisis. The paper is based on our analysis of about 100 measures initiated between October 2008 and March 2009 to support Russia's real economy. Within the scope of this analysis, we singled out the main beneficiaries according to industry and enterprise scale, and estimated the effects of the measures during the crisis and recovery phases. The paper also describes the major risks the Russian government will face as a result of implementing the aforementioned measures
and identifies the key problems and inconsistencies of the anti-crisis programme." (author's abstract
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