Maximal Helicity Research Articles

Celestial Dual for Maximal Helicity Violating Amplitudes.

It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight -3/2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-N and semiclassical large-c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti-de Sitter Witten diagrams.

Primordial magnetogenesis in the two-Higgs-doublet model

γ-ray emission of blazars infer the presence of large-scale magnetic fields in the intergalactic medium, but their origin remains a mystery. Using recent data from MAGIC, H.E.S.S., and Fermi-LAT, we investigate whether the large-scale magnetic fields in the intergalactic medium could have been generated by a first-order electroweak phase transition in the two-Higgs-doublet model (2HDM). We study two representative scenarios where we vary the initial conditions of the magnetic field and the plasma, assuming either a primordial magnetic field with maximal magnetic helicity or a primordial magnetic field with negligible magnetic helicity in a plasma with kinetic helicity. By considering a primordial magnetic field with maximal helicity and applying the conservative constraints derived from MAGIC and Fermi-LAT data, we demonstrate that a first-order electroweak phase transition within the 2HDM may account for the observed intergalactic magnetic fields in the case of the strongest transitions. We show that this parameter space also predicts strong gravitational wave signals in the reach of space-based detectors such as LISA, providing a striking multimessenger signal of the 2HDM. Published by the American Physical Society 2024

Higher-spin Yang–Mills, amplitudes and self-duality

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude.

All-order celestial OPE in the MHV sector

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

Investigating the hemodynamic implications of triangular cross-sectioned superior sagittal sinus vessels and the errors associated with idealised modelling

The superior sagittal sinus (SSS) is a blood vessel that is often observed to be approximately triangular in cross-section, due to how the venous wall attaches to the surrounding tissue. Despite this, the vessel has been assumed to be circular, when models are generated without patient-specific data. In this study, the differences between the cerebral hemodynamics of one circular, three triangular and five patient-specific cross-sectional models of a SSS were conducted. The errors associated with using circular cross-sectioned flow extensions were also determined. Computational fluid dynamics (CFD) models were generated from these geometries, with a population mean transient blood flow profile incorporated. The maximal helicity of the fluid flow was found to be elevated in the triangular cross-section, compared to the circular, with a higher wall shear stress (WSS) observed over a smaller, more concentrated region on the posterior sinus wall. The errors associated with using a circular cross-section were detailed, with the cross-sectional area appearing to have a greater influence on the hemodynamic parameters than the triangularity or circularity of the cross-section. This highlighted the importance of exhibiting caution when incorporating idealised modelling, especially when commenting on the true hemodynamics of these models. Errors were also found to be induced when using a circular cross-sectioned flow extension, for a geometry which was non-circular. This study highlights the importance of understanding the human anatomy when modelling blood vessels.

Topology and transport in generalized helical flows

Pure helical or screw flow presents a unique combination of zero net advection, alignment of vorticity dissipation with vorticity field, and maximal helicity. Helicity is a measure of knottedness in a flow structure as manifested in terms of a net imbalance between right and left handed helical motion. Topology, which is intrinsic to helicity, provides a geometric perspective to vortex reconnection in helical flow. However, the topological evolution and the resulting transport in helical flows remain unclear. Here, we investigate the evolution of isosurfaces associated with the Galilean invariant Q-criterion in generalized models of helical flow. While we categorize the stagnation points with Δ-criterion, the Gaussian curvature shows that the creation and annihilation of these points occur in pairs for specific instances of helical flow. The contours of finite-time Lyapunov exponent reveal the fluidic mixing due to the strain and shear transport barriers. These findings have far-reaching implications in diverse fields, ranging from classical turbulence in superfluid helium to dynamos in growing magnetic field. The present article sheds insights into these applications.

Maximal-Helicity-Violating Scattering of Gluons and Gravitons in Chiral Strong Fields.

We present all-multiplicity formulas for the tree-level scattering of gluons and gravitons in the maximal helicity violating (MHV) helicity configuration, calculated in certain chiral strong fields. The strong backgrounds we consider are self-dual plane waves in gauge theory and general relativity, which are treated exactly and admit a well-defined S matrix. The gauge theory background-coupled MHV amplitude is simply a dressed analog of the familiar Parke-Taylor formula, but the gravitational version has nontrivial new structures due to graviton tails. Both formulas have just one residual integral rather than the n-2 expected at n points from space-time perturbation theory; this simplification arises from the integrability of self-dual backgrounds and their corresponding twistor description. The resulting formulas pass several consistency checks and limit to the well-known expressions for MHV scattering of gluons and gravitons when the background becomes trivial.

Determining the strong phase of the a1 meson decay amplitude using the W→ντ(→νa1(→π∓π∓π±)) process

To measure the helicity of a spin-1 meson from the triple vector product of the three-momenta of its decay products, one needs information about the strong phase of the decay amplitude. In this paper, taking $a_1(1260)$ meson as an example, we present a method to extract information about the strong phase from the triple vector product of the pion momenta in $W \to \nu \tau(\to \nu a_1(\to\pi^\mp \pi^\mp \pi^\pm))$ process, where the $a_1$ helicity is known a priori from electroweak theory. This process is advantageous in that highly-boosted $a_1^-$ mesons from $\tau_L^-$ decays have nearly maximal helicity asymmetry and thus most reflect the strong phase. We revisit the theoretical calculation of the $a_1$ meson helicity in $W \to \nu \tau(\to \nu a_1)$ process. We formulate the differential decay rate of polarized $a_1$ mesons in a manner convenient for the study of the $a_1$ meson helicity asymmetry. Finally, we present the method for extracting information about the strong phase, and assess its feasibility at the LHC.

Correction to the Probability Distribution of Induced Gluon

We present a novel technique for the calculation of the probability for emission of gluon radiated from a high-pT quark through a medium (QGP). Our work is an extension of the maximal helicity violating (MHV) method to compute the non-abelian correction for 2 gluon emissions.

Beyond the Poisson Approximation: n-gluon radiation in QGP

We present a novel technique for the calculation of the probability for emission of gluon radiated from a high-pT quark through a medium (QGP). Our work is an extension of the maximal helicity violating (MHV) method in which the usual soft-collinear factor is classified according to its symmetry under gluon permutation. For the purposes of illustration, we show the result from 1 to 3 gluon radiation.

Medium-induced radiation beyond the Poisson approximation

We present a novel technique for the calculation of the probability for emission of gluons, radiated from a high-pT quark, through a medium (QGP). Our work is an extension of the maximal helicity violating method to compute the non-Abelian correction for 2 gluon emissions.

Protostring scattering amplitudes

We calculate some tree level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a lightcone worldsheet which supports $s$ integer moded Grassmann fields. In the generalization we supplement this Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$. The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that $s$ is even we calculate the multi-string scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic worldsheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then study in detail some simple special cases. Multi-string processes with maximal helicity violation have much simplified amplitudes. We also specialize to general four string amplitudes and discuss their high energy behavior. Most of these models are not covariant under the full Lorentz group $O(d+1,1)$. The exceptions are the bosonic string whose Lorentz group is $O(25,1)$ and the protostring whose Lorentz group is $O(1,1)$. The models in between only enjoy an $O(1,1)\times O(d)$ spacetime symmetry.

Massive to gauge field reduction and gravitational wave zone information

We show explicitly that massive, Abelian, vector, just like (properly defined) massive tensor, fields limit smoothly to their massless, gauge, versions: they emit only maximal helicity radiation and mediate Coulomb and (special relativistic) Newtonian, forces between their (conserved) sources. Our main motivation, though, is to show that the recent gravitational wave detection probably cannot directly rule out very long-range gravity: Even though the waves were emitted in a strong field regime, their being detected in the weak field wave zone means the above equivalences apply. There remains the, not unlikely, possibility that no strong field generation of radiation in massive models can reproduce the observed ring-down patterns. Separately, the smooth linear limiting behaviors show that the discontinuity lies not in the mass alone, but rather in Abelian versus non-Abelian, Yang-Mills and General Relativity, regimes, whose respective massive versions are known to be non-physical.

Dual-plane PIV investigation of acoustically excited jets in a swirl nozzle

Abstract. A novel dual-plane dye laser particle image velocimetry (PIV) technique used to analyze helicity and energy dissipation in an unexcited turbulent swirling jet of pressurized cold air has established that regions within the flow field of the jet exhibiting high helicity are correlated regions of high turbulent kinetic energy dissipation. This PIV configuration provides estimates of all components of the velocity gradient tensor, facilitating calculation of the helicity from the vorticity components. Application of this novel dual-plane PIV technique is extended in this study to investigate helical structures in a turbulent swirling jet where the underlying shear flow is subjected to external acoustic sinusoidal forcing in a plane perpendicular to the central axis of the jet. It was found that acoustic excitation had a significant effect on the mean velocity profile parallel to the direction of the jet. The horizontal forcing resulted in the generation of vorticity that was skewed with a pitch that favored a distribution of angles around 90° with respect to the velocity vector. The distribution of the time-averaged helicity angle indicated organized helical activity, but such activity is not dominated by large-scale coherent structures of maximal helicity.

Discontinuities of BFKL amplitudes and the BDS ansatz

We perform an examination of discontinuities of multiple production amplitudes, which are required for further development of the BFKL approach. It turns out that the discontinuities of 2→2+n amplitudes obtained in the BFKL approach contradict to the BDS ansatz for amplitudes with maximal helicity violation in N=4 supersymmetric Yang–Mills theory with large number of colors starting with n=2. Explicit expressions for the discontinuities of the 2→3 and 2→4 amplitudes in the invariant mass of pairs of produced gluons are obtained in the planar N=4 SYM in the next-to-leading logarithmic approximation. These expressions can be used for checking the conjectured duality between the light-like Wilson loops and the MHV amplitudes.

Generation of the magnetic helicity in a neutron star driven by the electroweak electron-nucleon interaction

We study the instability of magnetic fields in a neutron star core driven by the parity violating part of the electron-nucleon interaction in the Standard Model. Assuming a seed field of the order 1012 G, that is a common value for pulsars, one obtains its amplification due to such a novel mechanism by about five orders of magnitude, up to 1017 G, at time scales ∼ (103–105) yr. This effect is suggested to be a possible explanation of the origin of the strongest magnetic fields observed in magnetars. The growth of a seed magnetic field energy density is stipulated by the corresponding growth of the magnetic helicity density due to the presence of the anomalous electric current in the Maxwell equation. Such an anomaly is the sum of the two competitive effects: (i) the chiral magnetic effect driven by the difference of chemical potentials for the right and left handed massless electrons and (ii) constant chiral electroweak electron-nucleon interaction term, which has the polarization origin and depends on the constant neutron density in a neutron star core. The remarkable issue for the decisive role of the magnetic helicity evolution in the suggested mechanism is the arbitrariness of an initial magnetic helicity including the case of non-helical fields from the beginning. The tendency of the magnetic helicity density to the maximal helicity case at large evolution times provides the growth of a seed magnetic field to the strongest magnetic fields in astrophysics.

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

AbstractA weak turbulence theory is derived for magnetohydrodynamics (MHD) under rapid rotation and in the presence of a uniform large-scale magnetic field which is associated with a constant Alfvén velocity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\boldsymbol {b}}_{{0}}$. The angular velocity ${\boldsymbol{\Omega}}_{{0}}$ is assumed to be uniform and parallel to ${\boldsymbol {b}}_{{0}}$. Such a system exhibits left and right circularly polarized waves which can be obtained by introducing the magneto-inertial length $d \equiv b_0/\varOmega _0$. In the large-scale limit ($kd \to 0$, with $k$ being the wavenumber) the left- and right-handed waves tend to the inertial and magnetostrophic waves, respectively, whereas in the small-scale limit ($kd \to + \infty $) pure Alfvén waves are recovered. By using a complex helicity decomposition, the asymptotic weak turbulence equations are derived which describe the long-time behaviour of weakly dispersive interacting waves via three-wave interaction processes. It is shown that the nonlinear dynamics is mainly anisotropic, with a stronger transfer perpendicular than parallel to the rotation axis. The general theory may converge to pure weak inertial/magnetostrophic or Alfvén wave turbulence when the large- or small-scale limits are taken, respectively. Inertial wave turbulence is asymptotically dominated by the kinetic energy/helicity, whereas the magnetostrophic wave turbulence is dominated by the magnetic energy/helicity. For both regimes, families of exact solutions are found for the spectra, which do not correspond necessarily to a maximal helicity state. It is shown that the hybrid helicity exhibits a cascade whose direction may vary according to the scale $k_f$ at which the helicity flux is injected, with an inverse cascade if $k_fd < 1$ and a direct cascade otherwise. The theory is relevant to the magnetostrophic dynamo, whose main applications are the Earth and the giant planets, such as Jupiter and Saturn, for which a small (${\sim }10^{-6}$) Rossby number is expected.

Permutation relations of generalized Yangian Invariants, unitarity cuts, and scattering amplitudes

We find a permutation relation among Yangian Invariants -- two Yangian Invariants with adjacent external lines exchanged are related by a simple kinematic factor. This relation is shown to be equivalent to U(1) decoupling and Bern-Carrasco-Johansson (BCJ) relation at the level of maximal helicity violating (MHV) amplitudes. Together with the newly found permutation relation and using unitarity cuts to remove ambiguity in the definition of loop momenta of cut amplitudes due to the nonplanar legs, we propose a systematic way of reconstructing the the integrands of nonplanar MHV amplitudes up to a rational function which vanishes under all possible unitarity cuts. This method when applied to planar diagrams reproduces results from the single cut method. As explicit examples the construction of one-loop double-trace MHV amplitudes of 4- and 5-point interactions are presented using on-shell diagrams. The kinematic factors and the resultant planar diagrams are carefully dealt with using the unitarity cut condition. The first next-to-MHV amplitudes are addressed using generalized unitarity cuts. Their leading singularities can be identified as residues of the Grassmanian integral. This example also serve to demonstrate the power of the newly found relation of Yangian Invariants.

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N3LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.

Theory for helical turbulence under fast rotation.

Recent numerical simulations have shown the strong impact of helicity on homogeneous rotating hydrodynamic turbulence. The main effect can be summarized through the law n+ñ=-4, where n and ñ are the power law indices of the one-dimensional energy and helicity spectra, respectively. We investigate this rotating turbulence problem in the small Rossby number limit by using the asymptotic weak turbulence theory derived previously. We show that the empirical law is an exact solution of the helicity equation where the power law indices correspond to perpendicular (to the rotation axis) wave number spectra. It is proposed that when the cascade towards small scales tends to be dominated by the helicity flux the solution tends to ñ=-2, whereas it is ñ=-3/2 when the energy flux dominates. The latter is compatible with the solution previously observed numerically and derived theoretically in the weak turbulence regime when only the energy equation is used, whereas the former solution is constrained by a locality condition.