254 research outputs found
Jets in Effective Theory: Summing Phase Space Logs
We demonstrate how to resum phase space logarithms in the Sterman-Weinberg
(SW) dijet decay rate within the context of Soft Collinear Effective theory
(SCET). An operator basis corresponding to two and three jet events is defined
in SCET and renormalized. We obtain the RGE of the two and three jet operators
and run the operators from the scale to the phase space scale . This phase space scale, where is the
cone half angle of the jet, defines the angular region of the jet. At we determine the mixing of the three and two jet operators. We
combine these results with the running of the two jet shape function, which we
run down to an energy cut scale . This defines the resumed SW
dijet decay rate in the context of SCET. The approach outlined here
demonstrates how to establish a jet definition in the context of SCET. This
allows a program of systematically improving the theoretical precision of jet
phenomenology to be carried out.Comment: 25 pages, 4 figures, V2: Typos fixed, writing clarified, detail on
PSRG added. Matching onto jet definition changed to taking place at collinear
scal
Drift dependence of optimal trade execution strategies under transient price impact
We give a complete solution to the problem of minimizing the expected
liquidity costs in presence of a general drift when the underlying market
impact model has linear transient price impact with exponential resilience. It
turns out that this problem is well-posed only if the drift is absolutely
continuous. Optimal strategies often do not exist, and when they do, they
depend strongly on the derivative of the drift. Our approach uses elements from
singular stochastic control, even though the problem is essentially
non-Markovian due to the transience of price impact and the lack in Markovian
structure of the underlying price process. As a corollary, we give a complete
solution to the minimization of a certain cost-risk criterion in our setting
Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions
A light-like Wilson loop is computed in perturbation theory up to for pure Yang--Mills theory in 1+1 dimensions, using Feynman and
light--cone gauges to check its gauge invariance. After dimensional
regularization in intermediate steps, a finite gauge invariant result is
obtained, which however does not exhibit abelian exponentiation. Our result is
at variance with the common belief that pure Yang--Mills theory is free in 1+1
dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
Instanton Contribution to the Quark Form Factor
The nonperturbative effects in the quark form factor are considered in the
Wilson loop formalism. The properties of the Wilson loops with cusp
singularities are studied taking into account the perturbative and
nonperturbative contributions, where the latter are considered within the
framework of the instanton liquid model. For the integration path corresponding
to this form factor -- the angle with infinite sides -- the explicit expression
for the vacuum expectation value of the Wilson operator is found to leading
order. The calculations are performed in the weak-field limit for the instanton
vacuum contribution and compared with the one- and two-loop order results for
the perturbative part. It is shown that the instantons produce the powerlike
corrections to the perturbative result, which are comparable in magnitude with
the perturbative part at the scale of order of the inverse average instanton
size. It is demonstrated that the instanton contributions to the quark form
factor are exponentiated to high orders in the small instanton density
parameter.Comment: Version coincident with the journal publication. LaTeX, 15 pages, 1
figur
Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
It has been observed that in the DIS scheme the refactorization of the
Drell-Yan cross section leading to exponentiation of threshold logarithms can
also be used to organize a class of constant terms, most of which arise from
the ratio of the timelike Sudakov form factor to its spacelike counterpart. We
extend this exponentiation to include all constant terms, and demonstrate how a
similar organization may be achieved in the MSbar scheme. We study the
relevance of these exponentiations in a two-loop analysis.Comment: 20 pages, JHEP style, no figure
Dijet Event Shapes as Diagnostic Tools
Event shapes have long been used to extract information about hadronic final
states and the properties of QCD, such as particle spin and the running
coupling. Recently, a family of event shapes, the angularities, has been
introduced that depends on a continuous parameter. This additional
parameter-dependence further extends the versatility of event shapes. It
provides a handle on nonperturbative power corrections, on non-global
logarithms, and on the flow of color in the final state.Comment: 18 pages, 3 figure
Electroweak Gauge-Boson Production at Small q_T: Infrared Safety from the Collinear Anomaly
Using methods from effective field theory, we develop a novel, systematic
framework for the calculation of the cross sections for electroweak gauge-boson
production at small and very small transverse momentum q_T, in which large
logarithms of the scale ratio M_V/q_T are resummed to all orders. These cross
sections receive logarithmically enhanced corrections from two sources: the
running of the hard matching coefficient and the collinear factorization
anomaly. The anomaly leads to the dynamical generation of a non-perturbative
scale q_* ~ M_V e^{-const/\alpha_s(M_V)}, which protects the processes from
receiving large long-distance hadronic contributions. Expanding the cross
sections in either \alpha_s or q_T generates strongly divergent series, which
must be resummed. As a by-product, we obtain an explicit non-perturbative
expression for the intercept of the cross sections at q_T=0, including the
normalization and first-order \alpha_s(q_*) correction. We perform a detailed
numerical comparison of our predictions with the available data on the
transverse-momentum distribution in Z-boson production at the Tevatron and LHC.Comment: 34 pages, 9 figure
The Extraction of from Inclusive B Decays and the Resummation of End Point Logs
In this paper we discuss the theoretical difficulties in extracting
using the data from inclusive B decays. Specifically, we address the issue of
the end point singularities. We perform the resummation of both the leading and
next to leading end point logs and include the leading corrections to the hard
scattering amplitude. We find that the resummation is a effect in
the end point region where the resummation is valid. Furthermore, the resummed
sub-leading logs dominate the resummed double logs. The consequences of this
result for a model independent extraction of the mixing angle are
explored.Comment: Published Version. Minor changes in discussion. 31 pages, 4 figure
Instanton Corrections to Quark Form Factor at Large Momentum Transfer
Within the Wilson integral formalism, we discuss the structure of
nonperturbative corrections to the quark form factor at large momentum transfer
analyzing the infrared renormalon and instanton effects. We show that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and attribute their general structure to the
renormalon ambiguities of the perturbative series. It is demonstrated that the
instanton contributions result in the finite renormalization of the
next-to-leading perturbative result and numerically are characterized by a
small factor reflecting the diluteness of the QCD vacuum within the instanton
liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe
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