117,735 research outputs found
Breakdown of QCD Factorization for P-Wave Quarkonium Production at Low Transverse Momentum
Quarkonium production at low transverse momentum in hadron collisions can be
used to extract Transverse-Momentum-Dependent(TMD) gluon distribution
functions, if TMD factorization holds there. We show that TMD factorization for
the case of P-wave quarkonium with holds at one-loop
level, but is violated beyond one-loop level. TMD factorization for other
P-wave quarkonium is also violated already at one-loop.Comment: Published version in Physics Letters B (2014), pp. 103-10
Transverse Momentum Dependent Factorization for Quarkonium Production at Low Transverse Momentum
Quarkonium production in hadron collisions at low transverse momentum
with as the quarkonium mass can be used for probing
transverse momentum dependent (TMD) gluon distributions. For this purpose, one
needs to establish the TMD factorization for the process. We examine the
factorization at the one-loop level for the production of or .
The perturbative coefficient in the factorization is determined at one-loop
accuracy. Comparing the factorization derived at tree level and that beyond the
tree level, a soft factor is, in general, needed to completely cancel soft
divergences. We have also discussed possible complications of TMD factorization
of p-wave quarkonium production.Comment: Title changed in the journal, published versio
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
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Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations
As the use of viscoelastic materials becomes increasingly popular, stability of viscoelastic structures under random loads becomes increasingly important. This paper aims at studying the asymptotic stability of viscoelastic systems under Gaussian and Poisson white noise excitations with Lyapunov functions. The viscoelastic force is approximated as equivalent stiffness and damping terms. A stochastic differential equation is set up to represent randomly excited viscoelastic systems, from which a Lyapunov function is determined by intuition. The time derivative of this Lyapunov function is then obtained by stochastic averaging. Approximate conditions are derived for asymptotic Lyapunov stability with probability one of the viscoelastic system. Validity and utility of this approach are illustrated by a Duffing-type oscillator possessing viscoelastic forces, and the influence of different parameters on the stability region is delineated
Constrained structure of ancient Chinese poetry facilitates speech content grouping
Ancient Chinese poetry is constituted by structured language that deviates from ordinary language usage [1, 2]; its poetic genres impose unique combinatory constraints on linguistic elements [3]. How does the constrained poetic structure facilitate speech segmentation when common linguistic [4, 5, 6, 7, 8] and statistical cues [5, 9] are unreliable to listeners in poems? We generated artificial Jueju, which arguably has the most constrained structure in ancient Chinese poetry, and presented each poem twice as an isochronous sequence of syllables to native Mandarin speakers while conducting magnetoencephalography (MEG) recording. We found that listeners deployed their prior knowledge of Jueju to build the line structure and to establish the conceptual flow of Jueju. Unprecedentedly, we found a phase precession phenomenon indicating predictive processes of speech segmentation—the neural phase advanced faster after listeners acquired knowledge of incoming speech. The statistical co-occurrence of monosyllabic words in Jueju negatively correlated with speech segmentation, which provides an alternative perspective on how statistical cues facilitate speech segmentation. Our findings suggest that constrained poetic structures serve as a temporal map for listeners to group speech contents and to predict incoming speech signals. Listeners can parse speech streams by using not only grammatical and statistical cues but also their prior knowledge of the form of language
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