QCD Factorization for heavy quarkonium production at collider energies

In this talk, I briefly review several models of the heavy quarkonium production at collider energies, and discuss the status of QCD factorization for these production models.Comment: 7 pages, 12 figures, Talk presented at the Conference on Quark Confinement and Hadron Spectrum VII, Ponta Delgada, Portugal, 2-7 September, 200

Knot Weight Systems from Graded Symplectic Geometry

We show that from an even degree symplectic NQ-manifold, whose homological vector field Q preserves the symplectic form, one can construct a weight system for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX relation. Likewise, given a representation of the homological vector field, one can construct a weight system for the chord diagrams, satisfying the IHX and STU relations. Moreover we show that the use of the 'Gronthendieck connection' in the construction is essential in making the weight system dependent only on the choice of the NQ-manifold and its representation.Comment: 26 pages, revised versio

Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV-formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.Comment: 67 pages, typos corrected, published versio

5D Super Yang-Mills on Yp,qY^{p,q} Sasaki-Einstein manifolds

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as $Y^{p,q}$ manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large $N$ behaviour for the case of single hypermultiplet in adjoint representation and we derive the $N^3$-behaviour in this case.Comment: 43 pages, typos and mistakes correcte

Knot Invariants and New Weight Systems from General 3D TFTs

We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich's graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley-Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKahler manifolds.Comment: 55 pages, typos correcte

Collinear factorization for deep inelastic scattering structure functions at large Bjorken xB

We examine the uncertainty of perturbative QCD factorization for hadron structure functions in deep inelastic scattering at a large value of the Bjorken variable xB. We analyze the target mass correction to the structure functions by using the collinear factorization approach in the momentum space. We express the long distance physics of structure functions and the leading target mass corrections in terms of parton distribution functions with the standard operator definition. We compare our result with existing work on the target mass correction. We also discuss the impact of a final-state jet function on the extraction of parton distributions at large fractional momentum x.Comment: 18 pages, 10 figures; discussion on baryon number conservation clarifie

Heavy quarkonium production in hadronic collisions in TMD framework

Heavy quarkonium ($\Upsilon$) production at low transverse momentum ($P_\perp$) in high-energy hadronic collisions is revisited from the point of view of transverse momentum dependent (TMD) framework. We perform resummation of double logarithmic correction associated with initial-state soft gluon shower for $b\bar b$ production by employing Collins-Soper-Sterman (CSS) formalism. We show that the CSS formalism provides a nice description of $\Upsilon$ production data in p+$\rm\bar{p}$ collisions at Tevatron and p+p collisions at the LHC.Comment: 6 pages, 2 figures, proceedings of QCD Evolution 2017, 22-26 May 2017, Newport News, VA-US

Novel Phenomenology of Parton Distributions from the Drell-Yan Process

The Drell-Yan massive lepton-pair production in hadronic collisions provides a unique tool complementary to the Deep-Inelastic Scattering for probing the partonic substructures in hadrons. We review key concepts, approximations, and progress for QCD factorization of the Drell-Yan process in terms of collinear or transverse momentum dependent (TMD) parton distribution functions. We present experimental results from recent fixed-target Drell-Yan as well as $W$ and $Z$ boson production at colliders, focussing on the topics of flavor structure of the nucleon sea as well as the extraction of novel Sivers and Boer-Mulders functions via single transverse spin asymmetries and azimuthal lepton angular distribution of the Drell-Yan process. Prospects for future Drell-Yan experiments are also presented.Comment: 50 pages and 23 figures, and references added and minor typos correcte

Wilson Lines from Representations of NQ-Manifolds

An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction.Comment: 37 page