12342577
Fragmentation, factorization and infrared poles in heavy quarkonium production
We explore the role of soft gluon exchange in heavy quarkonium production at large transverse momentum. We find uncanceled infrared poles at NNLO that are not matched by conventional NRQCD matrix elements. We show, however, that gauge invariance and factorization require that conventional NRQCD production operators be modified to include non-Abelian phases or Wilson lines. With appropriately modified operators, factorization is restored at NNLO. We also argue that, in the absence of special cancellations, infrared poles at yet higher orders may require the inclusion of additional nonlocal operators, not present in the NRQCD expansion in relative velocity.
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
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.}
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.
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.
55788912
On Twisted N = 2 5D Super Yang–Mills Theory
On a five-dimensional simply connected Sasaki–Einstein manifold, one can construct Yang–Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys–Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa–Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys–Witten equations on product manifolds $${M_5 = M_4 \times \mathbb{R}}$$M5=M4×R arise in the context of twisting the 5D maximally supersymmetric Yang–Mills theory. In this paper, we present the construction of twisted N = 2 Yang–Mills theory on Sasaki–Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys–Witten equation.
119326742
Equivariant Rozansky-Witten classes and TFTs
Abstract We first construct the Rozansky–Witten model coupled to BF theory and Chern–Simons theory using the Alexandrov–Kontsevich–Schwarz–Zaboronsky (AKSZ) method. Then we apply the machinery developed in some earlier papers about AKSZ theories and characteristic classes to these concrete models: the BF–Rozansky–Witten model and the Chern–Simons–Rozansky–Witten model. In the former case, we obtain characteristic classes on the target hyperKahler manifold equipped with a group action as a generalization of the original Rozansky–Witten classes. We also give the prescription for similar classes associated with a holomorphic symplectic manifold and demonstrate the invariance of such classes explicitly.
119325793
Gluing Nekrasov Partition Functions
In this paper we summarise the localisation calculation of 5D super Yang-Mills on simply connected toric Sasaki-Einstein (SE) manifolds. We show how various aspects of the computation, including the equivariant index, the asymptotic behaviour and the factorisation property are governed by the combinatorial data of the toric geometry. We prove that the perturbative partition function on a simply connected SE manifold corresponding to an n-gon toric diagram factorises to n copies of perturbative part (zero instanton sector) of the Nekrasov partition function. This leads us to conjecture a prescription for the computation of the complete partition function, by gluing n copies of the full Nekrasov partition functions. This work is a generalisation of some earlier computation carried out on Yp,q manifolds, whose moment map cone has a quadrangle base and our result is valid for manifolds whose moment map cones have pentagon base, hexagon base, etc. The algorithm we used for dealing with general cones may also be of independent interest.
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.
56282767
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
A bstractBased on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of $ {{{r} \left/ {{g_Y^2}} \right.}_M} $, where $ {g_Y}_M $ is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.