Positive Helicity Research Articles

Magnetic helicity and active filament configuration

Context. The role of magnetic helicity in active filament formation and destabilization is still under debate. Aims. Although active filaments usually show a sigmoid shape and a twisted configuration before and during their eruption, it is unclear which mechanism leads to these topologies. In order to provide an observational contribution to clarify these issues, we describe a filament evolution whose characteristics seem to be directly linked to the magnetic helicity transport in corona. Methods. We applied different methods to determine the helicity sign and the chirality of the filament magnetic field. We also computed the magnetic helicity transport rate at the filament footpoints. Results. All the observational signatures provided information on the positive helicity and sinistral chirality of the flux rope containing the filament material: its forward S shape, the orientation of its barbs, the bright and dark threads at 195 A. Moreover, the magnetic helicity transport rate at the filament footpoints showed a clear accumulation of positive helicity. Conclusions. The study of this event showed a correspondence between several signatures of the sinistral chirality of the filament and several evidences of the positive magnetic helicity of the filament magnetic field. We also found that the magnetic helicity transported along the filament footpoints showed an increase just before the change of the filament shape observed in Hα images. We argued that the photospheric regions where the filament was rooted might be the preferential ways where the magnetic helicity was injected along the filament itself and where the conditions to trigger the eruption were yielded.

Manifestation of helical edge states as zero bias magneto-tunneling-conductance peaks innoncentrosymmetric superconductors

Helical edge states exist in the mixed spin singlet and triplet phase of a noncentrosymmetricsuperconductor (NCSS) when the pair amplitude (PA) in the negative helicity band,Δ−, is smaller than the PA in the positive helicity band,Δ+, i.e., when the PA in the triplet component is more than the same in the singletcomponent. We numerically determine energies of these edge states as a function ofγ = Δ−/Δ+. The presence of these edge states is reflected in the tunnelingprocess from a normal metal to an NCSS across a bias energyeV. (i) Angle resolved spin conductance (SC) obeying the symmetrygs(ϕ) = −gs(−ϕ) shows peaks when the bias energy equals the available quasiparticle edge state energyprovided . (ii) The total SC, Gs, iszero but modulates with eV for finite magnetic field H.(iii) The zero bias peaks of Gs and total charge conductance, Gc, at finite H splitinto two at finite eV for moderate H.(iv) At zero bias, Gc and Gs increasewith H andshow peaks at |H|∼γH0, where H0 is a characteristic field.

Evidence of Magnetic Helicity in Emerging Flux and Associated Flare

The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multiwavelength analysis of an M1.6 flare occurring in the NOAA active region 10365 on 27 May 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the “tongue” shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues indicates the emergence of a flux tube with a right-hand twist (i.e., positive magnetic helicity). The flare signatures in the chromosphere are ribbons observed in Hα by the MSDP spectrograph in the Meudon solar tower and in 1600 Å by TRACE. These ribbons have a J shape and are shifted along the inversion line. The pattern of these ribbons suggests that the flare was triggered by magnetic reconnection at coronal heights below a twisted flux tube of positive helicity, corresponding to that of the observed emergence. It is the first time that such a consistency between the signatures of the emerging flux through the photosphere and flare ribbons has been clearly identified in observations. Another type of ribbons observed during the flare at the periphery of the active region by the MSDP and SOHO/EIT is related to the existence of a null point, which is found high in the corona in a potential field extrapolation. We discuss the interpretation of these secondary brightenings in terms of the “breakout” model and in terms of plasma compression/heating within large-scale separatrices.

S-matrix equivalence restored

The canonical transformation that maps light-cone Yang-Mills theory to a Lagrangian description of the MHV rules is non-local, consequently the two sets of fields do not necessarily generate the same S-matrix. By deriving a new recursion relation for the canonical transformation expansion coefficients, we find a direct map between these coefficients and tree level light-cone diagrams. We use this to show that, at least up to one-loop with dimensionally regularised MHV vertices, the only difference is the omission of the one-loop amplitudes in which all gluons have positive helicity.

Magnetic helicity accumulation and tilt angle evolution of newly emerging active regions

Context. It has been known for years that there is a general dominance of negative (positive) helicity of active regions (ARs) in the northern (southern) solar hemisphere. For a better understanding of the role of helicity in the evolution of active regions, it is necessary to know more about the accumulation of helicity during the emergence of active regions. In particular, different conclusions were drawn in the past about the relationship between the accumulated helicity and the writhe of active regions. Aims. We investigate the accumulation of helicity in newly emerging simple bipolar solar active regions. We also investigate the relation between the accumulated helicity and writhe. Methods. We obtain helicity accumulation by applying Fast Fourier Transforms (FFT) and local correlation tracking (LCT) to MDI data. We deduce the writhe of the active regions according to the evolution of the tilt angle between the connecting line of the weighting centers of opposite polarities in the ARs. Results. It is found that the accumulated helicity is proportional to the exponent of magnetic flux $(|H| \propto \Phi^{1.85})$ in the 58 selected newly emerged simple ARs. 74% of ARs have a negative (positive) helicity when the above defined tilt angle rotates clockwise (counter-clockwise). This means that the accumulated helicity and writhe have the same sign for most of the investigated ARs according to the tilt angle evolution of ARs. We also found that 56% (57.6%) of these ARs in the northern (southern) photosphere provide negative (positive) helicity to the corona in the course of the emergence of magnetic flux.

LOCAL TWIST AND CURRENT HELICITY DISTRIBUTIONS OF ACTIVE REGION NOAA 10930

Hinode high-quality vector magnetograms and G-band data are utilized to study the distributions of local twist alpha(z) and current helicity h(c) on the active region of NOAA 10930. The new findings are as follows. (1) The patches of positive and negative helicities were intermixed showing a mesh pattern in the umbra and a thread pattern in the penumbra. (2) For its main stable sunspot (MSS), there was a positive-helicity patch accounting for similar to 43% of the umbra area surrounding the inner umbra, which had a predominantly negative helicity. For its minor rotating sunspot (MRS), there was a negative-helicity patch appearing in the umbra. (3) The fine distributions of alpha(z) and h(c) on a penumbral filament indicated that it may be possible for the two opposite helicities to coexist in a filament and their magnitudes were nearly equivalent.

MAGNETIC HELICITY EXCHANGE BETWEEN NEIGHBORING ACTIVE REGIONS

Addressing the long-lasting problem of the magnetic helicity distribution in the solar corona, a proof for magnetic helicity exchange between two neighboring emerging active regions (ARs) was found: when AR 9188 emerged, it first started to accumulate positive helicity, while the later neighboring emerging AR 9192 accumulated negative helicity. At a later time, after the bright connecting loops became visible between the two ARs, AR 9188 also suddenly started to gain negative helicity. At the same time AR 9192 started to loose negative helicity. It was found that the magnetic helicity fluxes of the two ARs changed simultaneously by almost the same amount. At one instant it was even possible to determine that the connecting loop between the two ARs carried negative helicity. We excluded the possibility that magnetic flux emergence was causing the observed variation of the magnetic helicity. Hence, magnetic helicity was indeed transferred from the late emerging AR 9192 to AR 9188 via an unbalanced magnetic torque along the loop. Such kinds of helicity transfer might be a common mechanism of redistribution of magnetic helicity in the solar atmosphere, which has just not been widely observed yet.

MAGNETIC HELICITY INJECTION DURING THE FORMATION OF AN INTERMEDIATE FILAMENT

A necessary condition for the formation of a filament is magnetic helicity. In the present paper we seek the origin of magnetic helicity of intermediate filaments. We observed the formation of a sinistral filament at the boundary of a decaying active region using full-disk H images obtained from Big Bear Solar Observatory. We have measured the rate of helicity injection during the formation of the filament using full-disk 96 minute-cadence magnetograms taken by SOHO MDI. As a result we found that 1) no significant helicity was injected around the region (polarity inversion line; PIL) of filament formation and 2) negative helicity was injected in the decaying active region. The negative sign of the injected helicity was opposite to that of the filament helicity. On the other hand, at earlier times when the associated active region emerged and grew, positive helicity was intensively injected. Our results suggest that the magnetic helicity of the intermediate filament may have originated from the helicity accumulated during the period of the growth of its associated active region.

The three-dimensional structure of the magnetic field of a sunspot

AbstractSpectro-polarimetric observations in several spectral lines allow to determine the height variation of the magnetic field of a small sunspot throughout the solar photosphere. The full Stokes-vector is measured with high spatial resolution. From these data we derive the magnetic field vector. The magnetic field strength decreases with height everywhere in the spot, even in the outer penumbra where some other authors have reported the opposite. The precise value of this decrease depends on the exact position in the spot. Values vary between 0.5 and 2.2 G km−1 when they are determined from an iron and a silicon line in the near infrared. The magnetic field is less inclined in the higher layers where the silicon line is formed. Once the magnetic vector field is known, it is straight forward to determine current densities and helicities. Current densities exhibit a radial structure in the penumbra, although it is still difficult to correlate this with the structure seen in the intensity continuum. In spite of this, current densities have a potential to serve as diagnostic tools to understand the penumbra, at least with the spatial resolution of the upcoming telescopes. The mean infered helicity is negative, as expected for a spot in the northern hemisphere. Nevertheless, there are locations inside the spot with positive helicity.

One-loop ϕ-MHV amplitudes using the unitarity bootstrap: the general helicity case

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν. We treat H as the real part of a complex field that couples to the selfdual gluon field strengths and compute the one-loop corrections to the -MHV amplitudes involving , two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work where the two negative helicity gluons were constrained to be colour adjacent. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

FROM HADRONIC PARITY VIOLATION TO PARITY-VIOLATING ELECTRON SCATTERING AND TESTS OF THE STANDARD MODEL

Searches for parity violation in hadronic systems started soon after the evidence for parity violation in β-decay of 60 Co was presented by Madame Chien-Shiung Wu and in π and μ decay by Leon Lederman in 1957. The early searches for parity violation in hadronic systems did not reach the sensitivity required and only after technological advances in later years was parity violation unambiguously established. Within the meson-exchange description of the strong interaction, theory and experiment meet in a set of seven weak meson-nucleon coupling constants. Even today, after almost five decades, the determination of the seven weak meson-nucleon couplings is incomplete. Parity violation in nuclear systems is rather complex due to the intricacies of QCD. More straight forward in terms of interpretation are measurements of the proton-proton parity-violating analyzing power (normalized differences in scattering yields for positive and negative helicity incident beams), for which there exist three precision experiments (at 13.6, at 45, and 221 MeV). To-date, there are better possibilities for theoretical interpretation using effective field theory approaches. The situation with regard to the measurement of the parity-violating analyzing power or asymmetry in polarized electron scattering is quite different. Although the original measurements were intended to determine the electro-weak mixing angle, with the current knowledge of the electro-weak interaction and the great precision with which electro-weak radiative corrections can be calculated, the emphasis has been to study the structure of the nucleon, and in particular the strangeness content of the nucleon. A whole series of experiments (the SAMPLE experiment at MIT-Bates, the G0 experiment and HAPPEX experiments at Jefferson Laboratory (JLab), and the PVA4 experiment at MAMI) have indicated that the strange quark contributions to the charge and magnetization distributions of the nucleon are tiny. These measurements if extrapolated to zero degrees and zero momentum transfer have also provided a factor five improvement in the knowledge of the neutral weak couplings to the quarks. Choosing appropriate kinematics in parity-violating electron-proton scattering permits nucleon structure effects on the measured analyzing power to be precisely controlled. Consequently, a precise measurement of the ‘running’ of sin 2θw or the electro-weak mixing angle has become within reach. The [Formula: see text] experiment at Jefferson Laboratory is to measure this quantity to a precision of about 4%. This will either establish conformity with the Standard Model of quarks and leptons or point to New Physics as the Standard Model must be encompassed in a more general theory required, for instance, by a convergence of the three couplings (strong, electromagnetic, and weak) to a common value at the GUT scale. The upgrade of CEBAF at Jefferson Laboratory to 12 GeV, will allow a new measurement of sin 2θW in parity-violating electron-electron scattering with an improved precision to the current better measurement (the SLAC E158 experiment) of the ‘running’ of sin 2θW away from the Z0 pole. Preliminary design studies of such an experiment show that a precision comparable to the most precise individual measurements at the Z0 pole (to about ±0.00025) can be reached. The result of this experiment will be rather complementary to the [Formula: see text] experiment in terms of sensitivity to New Physics.

Hamilton–Jacobi approach to photon wave mechanics: near‐field aspects

After having briefly reviewed the Hamilton-Jacobi theory of classical point-particle mechanics, its extension to the quantum regime and the formal identity between the Hamilton-Jacobi equation for Hamilton's characteristic function and the eikonal equation of geometrical optics, an eikonal theory for free photons is established. The space-time dynamics of the photon is described on the basis of the six-component Riemann-Silberstein energy wave function. Form-identical eikonal equations are obtained for the positive and negative helicity dynamics. Microscopic response theory is used to describe the linear photon-matter interaction. In the presence of matter the free-photon concept is replaced by a quasi-photon concept, and there is a quasi-photon for each of the two helicity states. After having established integro-differential equations for the wave functions of the two quasi-photons, the eikonal conditions for the quasi-photons are determined. It appears that the eikonal condition contains complicated space integrals of the gradient of the eikonal over volumes of near-field domain size. In these space integrals the dynamics of the electrons (matter particles) appears via transverse transition current densities between pairs of many-body states. Generalized microscopic polarization and magnetization fields are introduced to establish the connection between the quasi-photon and macroscopic eikonal theories.

Transient Coronal Sigmoids and Rotating Erupting Flux Ropes

To determine the relationship between transient coronal (soft X-ray or EUV) sigmoids and erupting flux ropes, we analyse four events in which a transient sigmoid could be associated with a filament whose apex rotates upon eruption and two further events in which the two phenomena were spatially but not temporally coincident. We find the helicity sign of the erupting field and the direction of filament rotation to be consistent with the conversion of twist into writhe under the ideal MHD constraint of helicity conservation, thus supporting our assumption of flux rope topology for the rising filament. For positive (negative) helicity the filament apex rotates clockwise (counterclockwise), consistent with the flux rope taking on a reverse (forward) S shape, which is opposite to that observed for the sigmoid. This result is incompatible with two models for sigmoid formation: one identifying sigmoids with upward arching kink-unstable flux ropes and one identifying sigmoids with a current layer between two oppositely sheared arcades. We find instead that the observations agree well with the model by Titov and Demoulin (Astron. Astrophys.351, 707, 1999), which identifies transient sigmoids with steepened current layers below rising flux ropes.

Electroweak structure of the nucleon, meson cloud, and light-cone wave functions

The meson-cloud model of the nucleon consisting of a system of three valence quarks surrounded by a meson cloud is applied to study the electroweak structure of the proton and neutron. Light-cone wave functions are derived for the dressed nucleon as pictured to be part of the time a bare nucleon and part of the time a baryon-meson system. Configurations are considered where the baryon can be a nucleon or a {delta} and the meson can be a pion as well as a vector meson such as the {rho} or the {omega}. An overall good description of the electroweak form factors is obtained. The contribution of the meson cloud is small and only significant at low Q{sup 2}. Mixed-symmetry S{sup '}-wave components in the wave function are most important to reproduce the neutron electric form factor. Charge and magnetization densities are deduced as a function of both the radial distance from the nucleon center and the transverse distance with respect to the direction of the three-momentum transfer. In the latter case, a central negative charge is found for the neutron. The up and down quark distributions associated with the Fourier transform of the axial form factor have opposite sign, withmore » the consequence that the probability to find an up (down) quark with positive helicity is maximal when it is (anti)aligned with the proton helicity.« less

One-loop phi-MHV amplitudes using the unitarity bootstrap

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν produced by considering the heavy top quark limit of the one-loop coupling of Higgs and gluons in the standard model. We treat H as the real part of a complex field that couples to the selfdual gluon field strengths and compute the one-loop corrections to amplitudes involving , two colour adjacent negative helicity gluons and an arbitrary number of positive helicity gluons - the so-called -MHV amplitudes. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

Potential Magnetic Field around a Helical Flux Rope Current Structure in the Solar Corona

We consider the potential magnetic field associated with a helical electric line current flow, idealizing the near-potential coronal field within which a highly localized twisted current structure is embedded. It is found that this field has a significant axial component off the helical magnetic axis where there is no current flow, such that the flux winds around the axis. The helical line current field, in including the effects of flux rope writhe, is therefore more topologically complex than straight line and ring current fields sometimes used in solar flux rope models. The axial flux in magnetic fields around confined current structures may be affected by the writhe of these current structures such that the field twists preferentially with the same handedness as the writhe. This property of fields around confined current structures with writhe may be relevant to classes of coronal magnetic flux rope, including structures observed to have sigmoidal forms in soft X-rays and prominence magnetic fields. For example, ``bald patches'' and the associated heating by Parker current sheet dissipation seem likely. Thus some measurements of flux rope magnetic helicities may derive from external, near-potential fields. The predicted hemispheric preference for positive and negative magnetic helicities is consistent with observational results for prominences and sigmoids and past theoretical results for flux rope internal fields.

S-matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV lagrangian

We demonstrate that the canonical change of variables that yields the MHV lagrangian, also provides contributions to scattering amplitudes that evade the equivalence theorem. This `ET evasion' in particular provides the tree-level (-++) amplitude, which is non-vanishing off shell, or on shell with complex momenta or in (2,2) signature, and is missing from the MHV (aka CSW) rules. At one loop there are ET-evading diagrammatic contributions to the amplitudes with all positive helicities. We supply the necessary regularisation in order to define these contributions (and quantum MHV methods in general) by starting from the light-cone Yang-Mills lagrangian in D dimensions and making a canonical change of variables for all D-2 transverse degrees of freedom of the gauge field. In this way, we obtain dimensionally regularised three- and four-point MHV amplitudes. Returning to the one-loop (++++) amplitude, we demonstrate that its quadruple cut coincides with the known result, and show how the original light-cone Yang-Mills contributions can in fact be algebraically recovered from the ET-evading contributions. We conclude that the canonical MHV lagrangian, supplemented with the extra terms brought to correlation functions by the non-linear field transformation, provide contributions which are just a rearrangement of those from light-cone Yang-Mills and thus coincide with them both on and off shell.

On-shell recursion relations for all Born QCD amplitudes

We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z --> infinity. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.

Recursion Relations for one-loop gravity amplitudes

We study the application of recursion relations to the calculation of finite one-loop gravity amplitudes. It is shown explicitly that the known four, five, and six graviton one-loop amplitudes for which the external legs have identical outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+) can be derived from simple recursion relations. The latter amplitude is derived by introducing a one-loop three-point vertex of gravitons of positive helicity, which is the counterpart in gravity of the one-loop three-plus vertex in Yang-Mills. We show that new issues arise for the five point amplitude with helicities (-,+,+,+,+), where the application of known methods does not appear to work, and we discuss possible resolutions.

Amplitudes in pure Yang-Mills and MHV Diagrams

We show how to calculate the one-loop scattering amplitude with all gluons of negative helicity in non-supersymmetric Yang-Mills theory using MHV diagrams. We argue that the amplitude with all positive helicity gluons arises from a Jacobian which occurs when one performs a Bäcklund-type holomorphic change of variables in the lightcone Yang-Mills Lagrangian. This also results in contributions to scattering amplitudes from violations of the equivalence theorem. Furthermore, we discuss how the one-loop amplitudes with a single positive or negative helicity gluon arise in this formalism. Perturbation theory in the new variables leads to a hybrid of MHV diagrams and lightcone Yang-Mills theory.