Small Momentum Limit Research Articles

Transverse momentum dependent shape function for J/ψ production in SIDIS

It has been shown previously that the transverse momentum dependent (TMD) factorization of heavy quarkonium production requires a TMD shape function. Its perturbative tail can be extracted by matching the cross sections valid at low and high transverse momenta. In this article we compare the order-αs TMD expressions with the order- {alpha}_s^2 collinear ones for J/ψ production in semi-inclusive deep inelastic scattering (SIDIS), employing nonrelativistic QCD in both cases. In contrast to previous studies, we find that the small transverse momentum limit of the collinear expressions contains discontinuities. We demonstrate how to properly deal with them and include their finite contributions to the TMD shape functions. Moreover, we show that soft gluon emission from the low transverse momentum Born diagrams provide the same leading order TMD shape functions as required for the matching. Their revised perturbative tails have a less divergent behavior as compared to the TMD fragmentation functions of light hadrons. Finally, we investigate the universality of TMD shape functions in heavy quarkonium production, identify the need for process dependent factorization and discuss the phenomenological implications.

On the NLO QCD corrections to gluon-initiated ZH production

We compute the QCD corrections at next-to-leading order for the process gg → ZH, including both the virtual two-loop terms and real-emission contributions. The two-loop box diagrams in the virtual corrections are approximated analytically over the complete phase space, combining the results of an expansion in the limit of small transverse momentum and an expansion in the regime of high energy. We obtain both inclusive and differential results for the cross section. We find that the NLO QCD corrections are of the same size as the LO contribution up to ZH invariant masses close to 1 TeV, but they increase significantly when higher energies are considered, due to a class of real-emission diagrams in which the Z boson is radiated from an open quark line. Finally, we estimate the uncertainty due to the renormalization scheme used for the top-quark mass both on the total and differential cross section.

Treating divergence in quark matter by using energy projectors

We calculate the gluon self-energy using quark energy projectors in a general quark-gluon plasma. By separating the quark field into positive- and a negative-energy modes, the quark loop constructed with the same mode is always convergent, and the divergence appears only in the mixed loop with different modes and is medium independent. After removing the divergence in vacuum, we obtain the one-loop gluon self-energy at finite temperature, chemical potential, and quark mass without approximation. With the method of quark-loop resummation, we calculate nonperturbatively the gluon Debye mass and thermodynamic potential. In the limit of small gluon momentum in comparison with temperature, chemical potential, and quark mass, our calculation comes back to the known HTL/HDL results in literature.

QCD resummation on single hadron transverse momentum distribution with the thrust axis

We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution (jT) for the single hadron production with the thrust axis in an electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit jT « Q, and joint transverse momentum and threshold limit jT « Q(1 − zh) « Q, where Q and zh are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms ln(Q/jT) and ln(1 − zh) to all orders. In the end, we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.

Nonrelativistic giant magnons from Newton Cartan strings

We show nonrelativistic (NR) giant magnon dispersion relations by probing the torsional Newton Cartan (TNC) geometry with (semi)classical nonrelativistic rigidly rotating strings. We construct NR sigma models over R × S2 and consider two specific limiting cases those are of particular interest. Both of these limiting conditions give rise to what we identify as the small momentum limit of the giant magnon dispersion relation in the dual SMT at strong coupling. We further generalize our results in the presence of background NS-NS fluxes. Our analysis reveals that unlike its relativistic counterpart, the NR string theory lacks of single spike solutions.

Recovering P(X) from a canonical complex field

We study the correspondence between models of a self-interacting canonical complex scalar field and P(X)-theories/shift-symmetric k-essence. Both describe the same background cosmological dynamics, provided that the amplitude of the complex scalar is frozen modulo the Hubble drag. We compare perturbations in these two theories on top of a fixed cosmological background. The dispersion relation for the complex scalar has two branches. In the small momentum limit, one of these branches coincides with the dispersion relation of the P(X)-theory. Hence, the low momentum phase velocity agrees with the sound speed in the corresponding P(X)-theory. The behavior of high frequency modes associated with the second branch of the dispersion relation depends on the value of the sound speed. In the subluminal case, the second branch has a mass gap. On the contrary, in the superluminal case, this branch is vulnerable to a tachyonic instability. We also discuss the special case of the P(X)-theories with an imaginary sound speed leading to the catastrophic gradient instability. The complex field models provide with a cutoff on the momenta involved in the instability.

Phonon Scattering by Externded Defects in Polycrystalline Graphene

Phonon scattering by static stress fields created by grain boundaries (GBs) in graphene was studied with the deformation potential method. This method provides exact analytical expressions for phonon mean free paths as a result of scattering by GBs with arbitrary geometries in the Born approximation. Two regimes, k–1 and k–3, of the mean free path behavior are discovered in the limit of small momenta. The first (dislocation) regime is realized for open configurations in polycrystalline graphene, while the second regime is realized for closed configurations and Stone-Wales defects in pure graphene. The mean free path does not depend on k for any GB in the short-wave limit (large k). Thermal conductivity in graphene with GBs was calculated using the Callaway model which considers both normal phonon processes and umklapp processes. The contribution from these defects to the thermal conductivity is shown to exceed substantially the contribution from point defects and vacancies in a wide range of temperatures.

Particle-hole pairs and density–density correlations in the Lieb–Liniger model

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb–Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.

Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

We study the density-density correlation function of the 1D Lieb–Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.

Relativistic quantum correlations in bipartite fermionic states

The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spin correlations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the other hand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.

High energy resummation of transverse momentum distributions: Higgs in gluon fusion

We derive a general resummation formula for transverse-momentum distributions of hard processes at the leading logarithmic level in the high-energy limit, to all orders in the strong coupling. Our result is based on a suitable generalization of high-energy factorization theorems, whereby all-order resummation is reduced to the determination of the Born-level process but with incoming off-shell gluons. We validate our formula by applying it to Higgs production in gluon fusion in the infinite top mass limit. We check our result up to next-to-leading order by comparison to the high energy limit of the exact expression and to next-to-next-to leading by comparison to NNLL order trasverse momentum (Sudakov) resummation, and we predict the high-energy behaviour at next$^3$-to-leading order. We also show that the structure of the result in the small transverse momentum limit agrees to all orders with general constraints from Sudakov resummation.

Slowly rotating dilatonic black holes with exponential form of nonlinear electrodynamics

The generalization of the four-dimensional Kerr–Newman black holes to include the nonlinear electrodynamics has been one of the famous problems in black hole physics. In this paper, we address the effects of the small rotation parameter on the exact black hole solutions of Einstein-dilaton gravity coupled to the exponential nonlinear electrodynamics. We find a new stationary black hole solutions of this theory, in the limit of small angular momentum, and in the presence of Liouville-type potential for the dilaton field and an arbitrary value of the dilaton coupling constant. We compute the angular momentum and the gyromagnetic ratio of these rotating dilaton black holes. Interestingly enough, we find that the nonlinearity of the electrodynamics do not affect the angular momentum and the gyromagnetic ratio of the spacetime, while in contrast, the dilaton field can modify the angular momentum as well as the gyromagnetic ratio of the rotating black holes. We find the gyromagnetic ratio as \(g=6/(3-\alpha ^2)\), where \(\alpha \) is the coupling constant of the dilaton and the electrodynamic fields. For \(\alpha =0\), we arrive at \(g=2\), which is the gyromagnetic ratio of the Kerr–Newman black holes in four dimensions.

Cosmological perturbation theory at three-loop order

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times theloop expansion does not converge even for large scales (small momenta) well within the linear regime,but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum,and use it to obtain a perturbative expansion with improved convergencefor momenta in the range where baryonic acoustic oscillations are present. Our numerical three-loop results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

Two-Exciton States and Coherent Third-Order Response from Semiconductor Quantum Wells

We present a microscopic description of the coherent third-order response from a quantum well, treated as a quasi-two-dimensional semiconductor, in the exciton representation. We establish a closed system of dynamic equations including those for coherent spin-polarized photons and excitons and for correlated two-exciton structures, called molecules. We employ such a system of equations as a starting point for calculating all third-order contributions to the semiconductor coherent polarization in the case where the eigenenergies and eigenfunctions of the molecules are available. Considering the molecular problem, we calculate the interaction potential between excitons in molecules for quantum-well samples in the limit of small exciton momentum taking place in the close-to-normal-incidence excitation geometry. The potential computed allows an approximate explicit determination of the molecular eigenenergies and eigenfunctions in the slow scattering limit. The criterion for a coherent pump-probe experiment to support the limit is pointed out.

D-wave superconductivity on the honeycomb bilayer

We introduce a microscopic model on the honeycomb bilayer, which in the small-momentum limit captures the usual (quadratic dispersion in the kinetic term) description of bilayer graphene. In the limit of strong interlayer hopping it reduces to an effective honeycomb monolayer model with also third-neighbor hopping. We study interaction effects in this effective model, focusing on possible superconducting instabilities. We find ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the strong-coupling limit of an effective $tJ$-model-like description that gradually transforms into $d+id$ time-reversal symmetry-breaking superconductivity at weak couplings. In this limit the small-momentum order-parameter expansion is ${({k}_{x}+i{k}_{y})}^{2}$ [or ${({k}_{x}\ensuremath{-}i{k}_{y})}^{2}$] in both valleys of the effective low-energy description. The relevance of our model and investigation for the physics of bilayer graphene is also discussed.

VERTEX FUNCTION OF VIRTUAL NEUTRINO AT SMALL MOMENTUM TRANSFERRED

The vertex function at the limit of small momentum transferred of a virtual massive neutrino in ξ-gauge is calculated via neutrino self-energy operator in a constant electromagnetic field. The expressions for neutrino magnetic moment under various relations between masses of neutrino, W-boson and charged lepton are presented.

Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes

Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity violating term. We study perturbations of anti-de Sitter black holes and branes in such a theory, and show that the relevant equations reduce to a set of coupled ODEs which can be solved efficiently through a series expansion. We prove numerically that black holes and branes in DCS gravity are stable against gravitational and scalar perturbations in the entire parameter space. Furthermore, by applying the AdS/CFT duality, we relate black hole perturbations to hydrodynamic quantities in the dual field theory, which is a (2+1)-dimensional isotropic fluid with broken spatial parity. The Chern-Simons term does not affect the entropy to viscosity ratio and the relaxation time, but instead quantities that enter the shear mode at order q^4 in the small momentum limit, for example the Hall viscosity and other quantities related to second and third order hydrodynamics. We provide explicit corrections to the gravitational hydrodynamic mode to first relevant order in the couplings.

Spin-charge coupling in quantum wires at zero magnetic field

We discuss an approximation for the dynamic charge response of nonlinear spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting for the broadening of the charge peak due to two-holon excitations, the nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero temperature has an asymmetric line shape. At finite temperature the spin peak is broadened by diffusion. As an application, we discuss the density and temperature dependence of the Coulomb drag resistivity due to long-wavelength scattering between quantum wires.

The Ising model and planar Yang–Mills

The scattering matrix for planar Yang–Mills with supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this paper we define a map from the spectral variables , parameterizing the long-range magnon momenta, to couplings in a two-dimensional Ising model. Under this map integrability of planar Yang–Mills becomes equivalent to the Yang–Baxter equation for the two-dimensional Ising model, and the long-range variables translate into the entries of the Ising transfer matrices. We explore the Ising correlation length which equals the inverse magnon momentum in the small-momentum limit. The critical regime is thus reached for vanishing magnon momentum. We also discuss the meaning of the Kramers–Wannier duality transformation on the gauge theory, together with that of the Ising model critical points.

Magnon bound-state scattering in gauge and string theory

It has been shown that, in the infinite length limit, the magnons of the gauge theory spin chain can form bound states carrying one finite and one strictly infinite R-charge. These bound states have been argued to be associated to simple poles of the multi-particle scattering matrix and to world sheet solitons carrying the same charges. Classically, they can be mapped to the solitons of the complex sine-Gordon theory. Under relatively general assumptions we derive the condition that simple poles of the two-particle scattering matrix correspond to physical bound states and construct higher bound states ``one magnon at a time''. We construct the scattering matrix of the bound states of the BDS and the AFS S-matrices. The bound state S-matrix exhibits simple and double poles and thus its analytic structure is much richer than that of the elementary magnon S-matrix. We also discuss the bound states appearing in larger sectors and their S-matrices. The large 't Hooft coupling limit of the scattering phase of the bound states in the SU(2) sector is found to agree with the semiclassical scattering of world sheet solitons. Intriguingly, the contribution of the dressing phase has an independent world sheet interpretation as the soliton-antisoliton scattering phase shift. The small momentum limit provides independent tests of these identifications.