428 research outputs found
Basis invariant measure of CP-violation and renormalization
We analyze, in the context of a simple toy model, for which renormalization
schemes the CP-properties of bare Lagrangian and its finite part coincide. We
show that this is the case for the minimal subtraction and on-shell schemes.
The CP-properties of the theory can then be characterized by CP-odd basis
invariants expressed in terms of renormalized masses and couplings. For the
minimal subtraction scheme we furthermore show that in CP-conserving theories
the CP-odd basis invariants are zero at any scale but are not renormalization
group invariant in CP-violating ones.Comment: 5 page
Leptogenesis in crossing and runaway regimes
We study the impact of effective thermal masses and widths on resonant
leptogenesis. We identify two distinct possibilities which we refer to as
crossing and runaway regimes. In the runaway regime the mass difference grows
monotonously with temperature, whereas it initially decreases in the crossing
regime, such that the effective masses become equal at some temperature.
Following the conventional logic the source of the asymmetry would vanish in
the latter case. Using non-equilibrium quantum field theory, we analytically
demonstrate that the vanishing of the difference of the effective masses does
however neither imply a suppression nor a strong enhancement of the source for
the lepton asymmetry. In the vicinity of the crossing point the asymmetry
calculated in an (improved) Boltzmann limit develops a spurious peak, which
signals the breakdown of the quasiparticle approximation. In the exact result
this spurious enhancement is compensated by coherent transitions between the
two mass shells. Despite the breakdown of the quasiparticle approximation
off-shell contributions remain negligibly small even at the crossing point.Comment: 41 pages, 9 figures, figures 3 and 6 are animation
A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions
A new formula is derived that generalises an earlier result for the infinite
integral over three spherical Bessel functions. The analytical result involves
a finite sum over associated Legendre functions, , of degree and
order . The sum allows for values of that are greater than . A
generalisation for the associated Legendre functions to allow for any rational
for a specific is also shownComment: Published in J. Phys. A: Math. Theor. 43 (2010) 45520
Medium corrections to the CP-violating parameter in leptogenesis
In two recent papers, arXiv:0909.1559 and arXiv:0911.4122, it has been
demonstrated that one can obtain quantum corrected Boltzmann kinetic equations
for leptogenesis using a top-down approach based on the
Schwinger-Keldysh/Kadanoff-Baym formalism. These "Boltzmann-like" equations are
similar to the ones obtained in the conventional bottom-up approach but differ
in important details. In particular there is a discrepancy between the
CP-violating parameter obtained in the first-principle derivation and in the
framework of thermal field theory. Here we demonstrate that the two approaches
can be reconciled if causal n-point functions are used in the thermal field
theory approach. The new result for the medium correction to the CP-violating
parameter is qualitatively different from the conventional one. The analogy to
a toy model considered earlier enables us to write down consistent quantum
corrected Boltzmann equations for thermal leptogenesis in the Standard Model
(supplemented by three right-handed neutrinos) which include quantum
statistical terms and medium corrected expressions for the CP-violating
parameter.Comment: 13 pages, 9 figure
Systematic approach to leptogenesis in nonequilibrium QFT: self-energy contribution to the CP-violating parameter
In the baryogenesis via leptogenesis scenario the self-energy contribution to
the CP-violating parameter plays a very important role. Here, we calculate it
in a simple toy model of leptogenesis using the Schwinger-Keldysh/Kadanoff-Baym
formalism as starting point. We show that the formalism is free of the
double-counting problem typical for the canonical Boltzmann approach. Within
the toy model, medium effects increase the CP-violating parameter. In contrast
to results obtained earlier in the framework of thermal field theory, the
medium corrections are linear in the particle number densities. In the resonant
regime quantum corrections lead to modified expressions for the CP-violating
parameter and for the decay width. Most notably, in the maximal resonant regime
the Boltzmann picture breaks down and an analysis in the full Kadanoff-Baym
formalism is required.Comment: 28 pages, 14 figure
N=4 superconformal Ward identities for correlation functions
In this paper we study the four-point correlation function of the
energy-momentum supermultiplet in theories with N=4 superconformal symmetry in
four dimensions. We present a compact form of all component correlators as an
invariant of a particular abelian subalgebra of the N=4 superconformal algebra.
This invariant is unique up to a single function of the conformal cross-ratios
which is fixed by comparison with the correlation function of the lowest
half-BPS scalar operators. Our analysis is independent of the dynamics of a
specific theory, in particular it is valid in N=4 super Yang-Mills theory for
any value of the coupling constant. We discuss in great detail a subclass of
component correlators, which is a crucial ingredient for the recent study of
charge-flow correlations in conformal field theories. We compute the latter
explicitly and elucidate the origin of the interesting relations among
different types of flow correlations previously observed in arXiv:1309.1424.Comment: 41 page
From correlation functions to event shapes
We present a new approach to computing event shape distributions or, more
precisely, charge flow correlations in a generic conformal field theory (CFT).
These infrared finite observables are familiar from collider physics studies
and describe the angular distribution of global charges in outgoing radiation
created from the vacuum by some source. The charge flow correlations can be
expressed in terms of Wightman correlation functions in a certain limit. We
explain how to compute these quantities starting from their Euclidean analogues
by means of a non-trivial analytic continuation which, in the framework of CFT,
can elegantly be performed in Mellin space. The relation between the charge
flow correlations and Euclidean correlation functions can be reformulated
directly in configuration space, bypassing the Mellin representation, as a
certain Lorentzian double discontinuity of the correlation function integrated
along the cuts. We illustrate the general formalism in N=4 SYM, making use of
the well-known results on the four-point correlation function of half-BPS
scalar operators. We compute the double scalar flow correlation in N=4 SYM, at
weak and strong coupling and show that it agrees with known results obtained by
different techniques. One of the remarkable features of the N=4 theory is that
the scalar and energy flow correlations are proportional to each other.
Imposing natural physical conditions on the energy flow correlations
(finiteness, positivity and regularity), we formulate additional constraints on
the four-point correlation functions in N=4 SYM that should be valid at any
coupling and away from the planar limit.Comment: 40 pages, 1 figure; v2: typos correcte
Energy-energy correlations in N=4 SYM
We present a new approach to computing energy-energy correlations in gauge
theories that exploits their relation to correlation functions and bypasses the
use of scattering amplitudes. We illustrate its power by calculating
energy-energy correlations in the maximally supersymmetric Yang-Mills theory
(N=4 SYM) in the next-to-leading order approximation.Comment: 5 page
Event shapes in N=4 super-Yang-Mills theory
We study event shapes in N=4 SYM describing the angular distribution of
energy and R-charge in the final states created by the simplest half-BPS scalar
operator. Applying the approach developed in the companion paper
arXiv:1309.0769, we compute these observables using the correlation functions
of certain components of the N=4 stress-tensor supermultiplet: the half-BPS
operator itself, the R-symmetry current and the stress tensor. We present
master formulas for the all-order event shapes as convolutions of the Mellin
amplitude defining the correlation function of the half-BPS operators, with a
coupling-independent kernel determined by the choice of the observable. We find
remarkably simple relations between various event shapes following from N=4
superconformal symmetry. We perform thorough checks at leading order in the
weak coupling expansion and show perfect agreement with the conventional
calculations based on amplitude techniques. We extend our results to strong
coupling using the correlation function of half-BPS operators obtained from the
AdS/CFT correspondence.Comment: 52 pages, 6 figures; v2: typos correcte
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