Nonperturbative Constraints Research Articles

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel

There is considerable controversy about the size and importance of nonperturbative contributions to the evolution of transverse-momentum-dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that nonperturbative contributions at large transverse distance b_T are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and nonperturbative. We make a motivated proposal for the parameterization of the nonperturbative part of the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical nonperturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(b_T) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(b_T) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell-Yan experiments to measure the Sivers function.

Dispersive approach to QCD: τ lepton hadronic decay in vector and axial–vector channels

The dispersive approach to QCD, which extends the applicability range of perturbation theory towards the infrared domain, is developed. This approach properly accounts for the intrinsically nonperturbative constraints, which originate in the low–energy kinematic restrictions on pertinent strong interaction processes. The dispersive approach proves to be capable of describing OPAL (update 2012) and ALEPH (update 2014) experimental data on inclusive τ lepton hadronic decay in vector and axial–vector channels in a self–consistent way.

Non-perturbative constraints on light sparticles from properties of the RG flow

We study certain small supersymmetry-breaking perturbations of a large class of strongly coupled four-dimensional R-symmetric renormalization group (RG) flows between superconformal field theories in the ultraviolet (UV) and the infrared (IR). We analyze the conditions under which these perturbations scale to zero at leading order in the deep IR, resulting in accidental supersymmetry. Furthermore, we connect the emergence of IR supersymmetry in this context with a quantity that was recently conjectured to be larger at the UV starting points of the underlying supersymmetric flows than at the corresponding IR endpoints, and we propose a bound on emergent supersymmetry. Along the way, we prove a simple and useful non-perturbative theorem regarding the IR behavior of global flavor currents. Our results suggest general ways in which light stop particles can emerge and potentially influence physics at the Large Hadron Collider.

Dispersive approach to QCD and inclusiveτlepton hadronic decay

The dispersive approach to QCD is applied to the study of the inclusive $\ensuremath{\tau}$ lepton hadronic decay. This approach provides the unified integral representations for the hadronic vacuum polarization function, related $R$ function, and Adler function. These representations account for the intrinsically nonperturbative constraints, which originate in the kinematic restrictions on the functions on hand, and retain the effects due to hadronization, which play a valuable role in the analysis of the strong interaction processes at low energies. The dispersive approach proves to be capable of describing recently updated ALEPH and OPAL experimental data on inclusive $\ensuremath{\tau}$ lepton hadronic decay in vector and axial-vector channels. The vicinity of values of the QCD scale parameter obtained in both channels testifies to the potential ability of the developed approach to describe the aforementioned data in a self-consistent way.

F-theorem, duality and SUSY breaking in one-adjoint Chern–Simons–Matter theories

We extend previous work on N = 2 Chern–Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S 3 partition functions. An explicit illustration based on the known analytic solution of the Chern–Simons matrix model is presented.

On D = 5 super Yang-Mills theory and (2, 0) theory

We discuss how D=5 maximally supersymmetric Yang-Mills theory (MSYM) might be used to study or even to define the (2,0) theory in six dimensions. It is known that the compactification of (2,0) theory on a circle leads to D=5 MSYM. A variety of arguments suggest that the relation can be reversed, and that all of the degrees of freedom of (2,0) theory are already present in D=5 MSYM. If so, this relation should have consequences for D=5 SYM perturbation theory. We explore whether it might imply all orders finiteness, or else an unusual relation between the cutoff and the gauge coupling. S-duality of the reduction to D=4 may provide nonperturbative constraints or tests of these options.

Functional integral approach for multiplicative stochastic processes

We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green's functions in the Grassman sector of the theory. We also study nonperturbative constraints imposed by Becchi, Rouet and Stora symmetry (BRS) and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory, the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.

Perturbatively stable resummed small x evolution kernels

We present a small x resummation for the GLAP anomalous dimension and its corresponding dual BFKL kernel, which includes all the available perturbative information and non-perturbative constraints. Specifically, it includes all the information coming from next-to-leading order GLAP anomalous dimensions and BFKL kernels, from the constraints of momentum conservation, from renormalization-group improvement of the running coupling and from gluon interchange symmetry. The ensuing evolution kernel has a uniformly stable perturbative expansion. It is very close to the unresummed NLO GLAP kernel in most of the HERA kinematic region, the small x BFKL behaviour being softened by momentum conservation and the running of the coupling. Next-to-leading corrections are small thanks to the constraint of gluon interchange symmetry. This result subsumes all previous resummations in that it combines optimally all the information contained in them.

B meson structure function in the heavy quark limit

We present an operator analysis of the light-cone structure function for inclusive B decays in the heavy quark limit. Using heavy quark symmetry and the HQET equations of motion, we derive non-perturbative constraints between the light-cone structure function and the B meson matrix elements of higher dimensional non-local operators.

A Thomas-Fermi-Weizsäcker approach to the total positron annihilation in electron gas

Abstract An efficient formulation for the problem of a charged light impurity in a homogeneous electron gas is presented. The approach is based on a parametric dielectric function obtained from the linearized Thomas-Fermi-von Weizsacker treatment of screening in an extended system. A nonperturbative constraint, provided by the cusp condition, is used to determine the value of the parameter. Analytic expressions for the static effective potential and screening electron density are given. The calculated annihilation rates are in impressive agreement with experiments.

Stopping power of an electron gas for antiprotons at intermediate velocities.

The stopping power of antiprotons moving at energies up to 400 keV through a uniform zero-temperature electron gas is calculated within the framework of the kinetic theory. The momentum-transfer cross section required is determined with the aid of a parametric velocity-dependent scattering potential. A nonperturbative constraint, provided by the nuclear-cusp condition, is used to fix the parameter value. A comparison with the result of a quadratic-response-function approach is made. The calculated stopping powers are in good agreement with recent experimental predictions.

Stopping power of a finite-temperature electron gas for slow unit charges.

The stopping power of protons and antiprotons moving at low velocities through a uniform temperature-dependent electron gas is calculated by making use of the momentum-transfer cross section. The screened scattering potential required is determined with the aid of a parametric dielectric function obtained from the linearized Thomas--Fermi--von Weizsaecker treatment for screening in extended systems. A nonperturbative constraint, provided by the nuclear-cusp condition for the total electron density at the position of the probe charge, is used to fix the parameter value. The temperature-dependent higher-order effect on the stopping power is discussed for metallic densities of the system, showing that first-order approximations are valid only asymptotically.

General results on glueball masses in QCD

A number of authors have investigated mass inequalities for mesons and baryons in QCD. These provide rigorous non-perturbative constraints on the mass spectrum. Similar inequalities for glueballs are investigated. For nonzero spin J, in the large- N c approximation, m J −⩾ m J + is found. (For J = 0, the existence of a gluon condensate can modify this statement.) There are also constraints on how fast m J can grow with J. For example, for m J = a + bJ α , 0 ⩽ α ⩽ 1 is found, a result consistent with Regge behaviour.

Constraints on supersymmetry breaking

Some non-perturbative constraints on supersymmetry breaking are derived. It is demonstrated that dynamical supersymmetry breaking does not occur in certain interesting classes of theories.