1,548 research outputs found
Infrared regulators and SCETII
We consider matching from SCETI, which includes ultrasoft and collinear
particles, onto SCETII with soft and collinear particles at one loop. Keeping
the external fermions off their mass shell does not regulate all IR divergences
in both theories. We give a new prescription to regulate infrared divergences
in SCET. Using this regulator, we show that soft and collinear modes in SCETII
are sufficient to reproduce all the infrared divergences of SCETI. We explain
the relationship between IR regulators and an additional mode proposed for
SCETII.Comment: 9 pages. Added discussion about relationship between IR regulators
and messenger mode
On Power Suppressed Operators and Gauge Invariance in SCET
The form of collinear gauge invariance for power suppressed operators in the
soft-collinear effective theory is discussed. Using a field redefinition we
show that it is possible to make any power suppressed ultrasoft-collinear
operators invariant under the original leading order gauge transformations. Our
manipulations avoid gauge fixing. The Lagrangians to O(lambda^2) are given in
terms of these new fields. We then give a simple procedure for constructing
power suppressed soft-collinear operators in SCET_II by using an intermediate
theory SCET_I.Comment: 15 pages, journal versio
KNEE TORQUE KINETICS DURING HIGHLAND DANCING
The purpose of the study is to measure torque variations in the knees of malaligned Highland dancers during the early and late stages of a six step Highland Fling. A secondary objective is to measure variations in knee malalignment at impact, maximum flexion and extension. The most frequently occurring injuries in dance involve the knee (Arnheim, 1980; Schafle, Requa & Garrick, 1990; Solomon & Micheli, 1986). More specifically, knee injuries in dance develop largely from knee malalignrnent (Arnheim, 1980; Clarkson & Skrinar, 1988; Clippinger-Robertson, 1987; Ende & Wickstrom, 1982; Reid, 1988; Solomon & Micheli, 1986; Teitz, 1987; Watkins & Clarkson, 1990). Quantifying knee torque due to malalignment provides a measure to better understand malalignment and the prevention of injury due to incorrect dance technique. Seven subjects, dancing a six step Highland Fling, were video taped from both a frontal and oblique view (45 degrees to the frontal view) while performing on a force platform. Video analysis provided knee displacement measures from both frontal and oblique views. Ground reaction forces (GRF) provided the force component for knee torque calculations. Knee malalignment displacements at impact, maximum flexion and extension were measured from the oblique view. Results were analyzed using a single subject baseline design and indicated mixed trends in knee torque, knee malalignment, and knee flexion from early to late stages of the dance. The decrease in knee torque is explained by a decrease, therefore, malalignment could have increased to aid in the absorption of shock. Maximum knee malalignment occurred at maximum knee flexion in the last step for all subjects and for five subjects in the first step. Increased knee malalignment measures, in the oblique plane, demonstrate potential for injury unless the dancer's technique and lower extremity alignment is corrected. The research utilizes Highland dancers, however the research concentration is on dancing in the turned-out position, a position common to other dance forms, such as ballet, jazz, and modern dance
Rare radiative exclusive B decays in soft-collinear effective theory
We consider rare radiative B decays such as B -> K^* gamma or B -> rho gamma
in soft-collinear effective theory, and show that the decay amplitudes are
factorized to all orders in alpha_s and at leading order in Lambda/m_b.By
employing two-step matching, we classify the operators for radiative B decays
in powers of a small parameter lambda(~ \sqrt{Lambda/m_b}) and obtain the
relevant operators to order lambda in SCET_I. These operators are constructed
with or without spectator quarks including the four-quark operators
contributing to annihilation and W-exchange channels. And we employ SCET_II
where the small parameter becomes of order Lambda/m_b, and evolve the operators
in order to compute the decay amplitudes for rare radiative decays in
soft-collinear effective theory. We show explictly that the contributions from
the annihilation channels and the W-exchange channels vanish at leading order
in SCET. We present the factorized result for the decay amplitudes in rare
radiative B decays at leading order in SCET, and at next-to-leading order in
alpha_s.Comment: v2: 31 pages, 11 figures. An appendix is added about the quark mass
effects on radiative B decay
Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions
For the hard-core lattice gas model defined on independent sets weighted by
an activity , we study the critical activity
for the uniqueness/non-uniqueness threshold on the 2-dimensional integer
lattice . The conjectured value of the critical activity is
approximately . Until recently, the best lower bound followed from
algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating
the partition function for graphs of constant maximum degree when
where is the
infinite, regular tree of degree . His result established a certain
decay of correlations property called strong spatial mixing (SSM) on
by proving that SSM holds on its self-avoiding walk tree
where and is an ordering on the neighbors of vertex . As
a consequence he obtained that . Restrepo et al. (2011) improved Weitz's approach for
the particular case of and obtained that
. In this paper, we establish an upper bound for
this approach, by showing that, for all , SSM does not hold on
when . We also present a
refinement of the approach of Restrepo et al. which improves the lower bound to
.Comment: 19 pages, 1 figure. Polished proofs and examples compared to earlier
versio
External Operators and Anomalous Dimensions in Soft-Collinear Effective Theory
It has recently been argued that soft-collinear effective theory for
processes involving both soft and collinear partons contains a new
soft-collinear mode, which can communicate between the soft and collinear
sectors of the theory. The formalism incorporating the corresponding fields
into the effective Lagrangian is extended to include external current and
four-quark operators relevant to weak interactions. An explicit calculation of
the anomalous dimensions of these operators reveals that soft-collinear modes
are needed for correctly describing the ultraviolet behavior of the effective
theory.Comment: 15 pages, 2 figure
Strong Phases and Factorization for Color Suppressed Decays
We prove a factorization theorem in QCD for the color suppressed decays B0->
D0 M0 and B0-> D*0 M0 where M is a light meson. Both the color-suppressed and
W-exchange/annihilation amplitudes contribute at lowest order in LambdaQCD/Q
where Q={mb, mc, Epi}, so no power suppression of annihilation contributions is
found. A new mechanism is given for generating non-perturbative strong phases
in the factorization framework. Model independent predictions that follow from
our results include the equality of the B0 -> D0 M0 and B0 -> D*0 M0 rates, and
equality of non-perturbative strong phases between isospin amplitudes,
delta(DM) = delta(D*M). Relations between amplitudes and phases for M=pi,rho
are also derived. These results do not follow from large Nc factorization with
heavy quark symmetry.Comment: 38 pages, 6 figs, typos correcte
Subleading Shape Functions in Inclusive B Decays
The contributions of subleading shape functions to inclusive decay
distributions of B mesons are derived from a systematic two-step matching of
QCD current correlators onto soft-collinear and heavy-quark effective theory.
At tree-level, the results can be expressed in terms of forward matrix elements
of bi-local light-cone operators. Four-quark operators, which arise at O(g^2),
are included. Their effects can be absorbed entirely into a redefinition of
other shape functions. Our results are in disagreement with some previous
studies of subleading shape-function effects in the literature. A numerical
analysis of B->X_u+l+nu decay distributions suggests that power corrections are
small, with the possible exception of the endpoint region of the charged-lepton
energy spectrum.Comment: 22 pages, 2 figures; several typos corrected; version published in
JHE
Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium
We analyze the end-point region of the photon spectrum in semi-inclusive
radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We
discuss the interplay of the scales arising in the Soft-Collinear Effective
Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy
quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2.
For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be
relevant, but the recently discovered soft-collinear modes show up for 1-z <<
alpha_s^2. The S- and P-wave octet shape functions are calculated. When they
are included in the analysis of the photon spectrum of the Upsilon (1S) system,
the agreement with data in the end-point region becomes excellent. The NRQCD
matrix elements and
are also obtained.Comment: Revtex, 11 pages, 6 figures. Minor improvements and references added.
Journal versio
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