121609581
Elastic amplitudes and power corrections in QCD
Abstract We discuss two power-suppressed quantities in hadronic scattering: elastic amplitudes at fixed angles and power corrections to inclusive hadronic cross sections. Generalized factorization theorems allow us to determine the asymptotic behavior of elastic scattering and to relate 1 Q 2 corrections in deeply inelastic scattering and the Drell-Yan process.
37897181
Gluonic contribution to g1 and its relationship to the spin-dependent parton distributions.
We examine the suggestion of Altarelli and Ross and of Carlitz, Collins, and Mueller that there is a hard gluonic contribution to the first moment of the proton's spin-dependent structure function {ital g}{sub 1}. We find that if the soft (collinear) divergence in the gluonic contribution is regulated dimensionally or with a quark mass, then the first moment vanishes. More generally, we suggest that the hard gluonic contribution to {ital g}{sub 1} be identified by subtracting certain contributions that are attributable to the spin-dependent quark distributions. We show that the first moment of the resulting hard gluonic contribution vanishes, provided that the UV regulator for the spin-dependent quark distributions respects gauge invariance, Lorentz invariance, and the analyticity structure of the unregulated distributions. However, by relaxing the Lorentz-invariance requirement, we are able to construct quark distributions such that the hard gluonic contribution to the first moment of {ital g}{sub 1} is nonzero. The corresponding quark distributions are related to matrix elements of Lorentz-variant operators. Hence, they have no analogue in the standard operator-product expansion and do not satisfy the usual forms of the quark sum rules. We conclude that the size of the gluonic contribution to the first moment of {italmore » g}{sub 1} is entirely a matter of the convention used in defining the quark distributions.« less
121107230
Universal nuclear dependence in high energy nuclear collisions
In this talk, I present a systematic calculation of process independent nuclear dependence to nuclear parton distribution functions (nPDFS). In terms of the collinear QCD factorization approach, we calculate the leading-pole contributions to DGLAP evolution equations of nPDFs, and we evaluate both real and virtual Feynman diagrams without using the AGK cutting rule. Our result has an advantage for studying nuclear dependence in a region where active parton momentum fraction x is not too small.
119631335
Nuclear Shadowing at Small Values of x
The nuclear parton distributions are given in a model where the nucleus is viewed as a collection of uncorrelated nucleons. Using these distributions, we determine nuclear shadowing at small values of x. We find that the effect of nuclear shadowing goes away very slowly when Q2 increases. Our results are consistent with the experiment of Goodman et al. The amount of nuclear shadowing expected at higher energies is discussed.
15462403
Nuclear dependence in direct photon production.
We calculate the nuclear dependence of direct photon production in hadron-nucleus collisions. In terms of a multiple scattering picture, we factorize the cross section for direct photon production into calculable short-distance partonic parts times multiparton correlation functions in nuclei. We present the hadron-nucleus cross section as {ital A}{sup {alpha}} times the hadron-nucleon cross section. Using information on the multiparton correlation functions extracted from photon-nucleus experiments, we compute the value of {alpha} as a function of transverse momentum of the direct photon. We also compare our results with recent data from Fermilab experiment E706. {copyright} {ital 1996 The American Physical Society.}
121725996
Single transverse spin asymmetries in direct photon production
Abstract We derive single transverse spin asymmetries for direct photon production cross sections in perturbative QCD, relating them to partonic matrix elements that couple the quark and gluon fields. Our method may be generalized to asymmetries for other reactions.
15055597
Dimensional regularization and dimensional reduction in the light cone
We calculate all of the 2 to 2 scattering process in Yang-Mills theory in the light cone gauge, with the dimensional regulator as the UV regulator. The IR is regulated with a cutoff in ${q}^{+}$. It supplements our earlier work, where a Lorentz noncovariant regulator was used, and the final results bear some problems in gauge fixing. Supersymmetry relations among various amplitudes are checked by using the light cone superfields.
119614535
Knot invariants and new weight systems from general 3D TFTs
Abstract We introduce and study the Wilson loops in general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in the Chern–Simons theory. We study the TFTs within the Batalin–Vilkovisky (BV) and the 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.
116908028
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.
49984581
On the infinity category of homotopy Leibniz algebras
We discuss various concepts of $\infty$-homotopies, as well as the relations between them (focussing on the Leibniz type). In particular $\infty$-$n$-homotopies appear as the $n$-simplices of the nerve of a complete Lie ${\infty}$-algebra. In the nilpotent case, this nerve is known to be a Kan complex \cite{Get09}. We argue that there is a quasi-category of $\infty$-algebras and show that for truncated $\infty$-algebras, i.e. categorified algebras, this $\infty$-categorical structure projects to a strict 2-categorical one. The paper contains a shortcut to $(\infty,1)$-categories, as well as a review of Getzler's proof of the Kan property. We make the latter concrete by applying it to the 2-term $\infty$-algebra case, thus recovering the concept of homotopy of \cite{BC04}, as well as the corresponding composition rule \cite{SS07}. We also answer a question of \cite{BS07} about composition of $\infty$-homotopies of $\infty$-algebras.
59473327
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.