scholarly journals An Operator Product Expansion for Form Factors II. Born level

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Amit Sever ◽  
Alexander G. Tumanov ◽  
Matthias Wilhelm
Keyword(s):  
Form Factor ◽  
Operator Product Expansion ◽  
Wilson Loop ◽  
Form Factors ◽  
Building Blocks ◽  
Operator Product ◽  
Yang Mills ◽  
Singlet States ◽  
Particle Form ◽  
Elementary Building

Abstract Form factors in planar $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in [1]. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.

scholarly journals A three-point form factor through five loops

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Lance J. Dixon ◽  
Andrew J. McLeod ◽  
Matthias Wilhelm
Keyword(s):  
Form Factor ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Loop Order ◽  
Present Evidence ◽  
Yang Mills ◽  
High Loop ◽  
Transcendental Functions ◽  
Point Form ◽  
Super Yang Mills Theory

Abstract We bootstrap the three-point form factor of the chiral part of the stress­tensor supermultiplet in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ* → $$ q\overline{q}g $$ q q ¯ g . We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$ N = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

scholarly journals Hexagon bootstrap in the double scaling limit

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Vsevolod Chestnov ◽  
Georgios Papathanasiou
Keyword(s):  
Function Space ◽  
Operator Product Expansion ◽  
General Pattern ◽  
Scaling Limit ◽  
Kinematic Region ◽  
Operator Product ◽  
Yang Mills ◽  
Codimension One ◽  
Double Scaling Limit ◽  
Super Yang Mills Theory

Abstract We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

scholarly journals Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Hiroshi Suzuki ◽  
Hiromasa Takaura
Keyword(s):  
Operator Product Expansion ◽  
Density Operator ◽  
Gradient Flow ◽  
Gluon Condensate ◽  
Operator Product ◽  
Clear Definition ◽  
Lattice Data ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Definition Of

Abstract We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang–Mills gradient flow.

scholarly journals RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME

2008 ◽  
Vol 20 (09) ◽  
pp. 1033-1172 ◽  
Author(s):  
STEFAN HOLLANDS
Keyword(s):  
Operator Product Expansion ◽  
Poisson Algebra ◽  
Technical Difficulty ◽  
Operator Product ◽  
Quantum Field ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Brst Charge ◽  
A New Technique ◽  
Formal Power

We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang–Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensures conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators. The key technical tool behind these arguments is a new universal Ward identity that is formulated at the algebraic level, and that is proven to be consistent with a local and covariant renormalization prescription. We also develop a new technique to accomplish this renormalization process, and in particular give a new expression for some of the renormalization constants in terms of cycles.

Constraints on the ωπ form factor from analyticity and unitarity

2016 ◽  
Vol 31 (14n15) ◽  
pp. 1630020 ◽  
Author(s):  
B. Ananthanarayan ◽  
Irinel Caprini ◽  
Bastian Kubis
Keyword(s):  
Experimental Data ◽  
Form Factor ◽  
Information Needs ◽  
Theoretical Calculations ◽  
Form Factors ◽  
Experimental Information ◽  
Upper And Lower Bounds ◽  
Strong Interactions ◽  
Operator Product ◽  
Using Data

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review our recent work on the electromagnetic [Formula: see text] form factor in a model-independent framework known as the method of unitarity bounds, partly motivated by the discrepancies noted recently between the theoretical calculations of the form factor based on dispersion relations and certain experimental data measured from the decay [Formula: see text]. We have applied a modified dispersive formalism, which uses as input the discontinuity of the [Formula: see text] form factor calculated by unitarity below the [Formula: see text] threshold and an integral constraint on the square of its modulus above this threshold. The latter constraint was obtained by exploiting unitarity and the positivity of the spectral function of a QCD correlator, computed on the spacelike axis by operator product expansion and perturbative QCD. An alternative constraint is obtained by using data available at higher energies for evaluating an integral of the modulus squared with a suitable weight function. From these conditions we derived upper and lower bounds on the modulus of the [Formula: see text] form factor in the region below the [Formula: see text] threshold. The results confirm the existence of a disagreement between dispersion theory and experimental data on the [Formula: see text] form factor around 0.6 GeV, including those from NA60 published in 2016.

scholarly journals Operator Product Expansion for Form Factors

2021 ◽  
Vol 126 (3) ◽  
Author(s):  
Amit Sever ◽  
Alexander G. Tumanov ◽  
Matthias Wilhelm
Keyword(s):  
Operator Product Expansion ◽  
Form Factors ◽  
Operator Product

scholarly journals ANNIHILATION POLES FOR FORM FACTORS IN THE XXZ MODEL

1994 ◽  
Vol 09 (12) ◽  
pp. 2087-2102 ◽  
Author(s):  
S. PAKULIAK
Keyword(s):  
Form Factor ◽  
Linear Combination ◽  
Form Factors ◽  
Vertex Operators ◽  
Xxz Model ◽  
Particle Form

The annihilation poles for the form factors in the XXZ model are studied using vertex operators introduced in Ref. 1. An annihilation pole is the property of form factors according to which the residue of the 2n-particle form factor in such a pole can be expressed through linear combination of the (2n−2)-particle form factors. To prove this property we use the bosonization of the vertex operators in the XXZ model which was invented in Ref. 2.

scholarly journals Celestial operator products of gluons and gravitons

2021 ◽  
pp. 2140003
Author(s):  
Monica Pate ◽  
Ana-Maria Raclariu ◽  
Andrew Strominger ◽  
Ellis Ye Yuan
Keyword(s):  
Operator Product Expansion ◽  
Beta Function ◽  
Tree Level ◽  
Operator Product ◽  
Recursion Relations ◽  
Yang Mills ◽  
Euler Beta Function ◽  
Celestial Sphere ◽  
Asymptotic Symmetries

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein–Yang–Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.

scholarly journals Branch point twist field form factors in the sine-Gordon model I: Breather fusion and entanglement dynamics

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Olalla Castro-Alvaredo ◽  
David Horvath
Keyword(s):  
Branch Point ◽  
Form Factors ◽  
Building Blocks ◽  
Small Mass ◽  
Particle Spectrum ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Fusion Procedure ◽  
Particle Form ◽  
Sine Gordon Model

The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap program. In this paper we compute low particle-number form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory possesses a particle spectrum consisting of a soliton, an antisoliton (of opposite U(1) charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and Rényi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's one-particle form factor.

scholarly journals Bonus symmetry and the operator product expansion of super-Yang-Mills

1999 ◽  
Vol 559 (1-2) ◽  
pp. 165-183 ◽  
Author(s):  
Kenneth Intriligator ◽  
Witold Skiba
Keyword(s):  
Operator Product Expansion ◽  
Operator Product ◽  
Yang Mills
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