Spin-0 Case Research Articles

Vetoing all the Higgs imposters in H→ℓ-ℓ+Z

We develop an effective and methodical algorithm for the construction of general covariant four-point HℓℓZ vertices, accommodating leptons ℓ=e,μ, and designed to handle a boson H of any integer spin, not merely confined to spins up to 2. While our numerical analysis assumes the H-boson mass to be mH=125GeV, the analytical framework we propose is versatile, enabling the examination of various mass as well as spin scenarios. These meticulously devised general covariant four-point HℓℓZ vertices are pivotal in vetoing all the imposters of the Standard Model Higgs boson holding the spin-0 and even-parity quantum numbers, especially in one of its primary decay channels, the three-body decay process H→ℓ-ℓ+Z, observable at the Large Hadron Collider. Our innovative strategy encompasses the analysis of all the effectively allowed scenarios, extending beyond the limitations of previous investigations on the Higgs spin and parity determinations in the decay H→ℓ-ℓ+Z. Based on the significantly expanded scheme, we demonstrate that the Higgs boson imposter of any spin and parity can be definitively vetoed by leveraging angular and invariant mass distributions focusing on threshold effects. Even though achieving such conclusive results in practical and exhaustive analyses may necessitate high event rates, especially in the spin-0 contact-interaction case.

Superradiance in massive vector fields with spatially varying mass

Superradiance is a process by which massive bosonic particles can extract energy from spinning black holes, leading to the build up of a condensate if the particle has a Compton wavelength comparable to the black hole's Schwarzschild radius. One interesting possibility is that superradiance may occur for photons in a diffuse plasma, where they gain a small effective mass. Studies of the spin-0 case have indicated that such a build up is suppressed by a spatially varying effective mass, supposed to mimic the photons' interaction with a physically realistic plasma density profile. We carry out relativistic simulations of a massive Proca field evolving on a Kerr background, with modifications to account for the spatially varying effective mass. This allows us to treat the spin-1 case directly relevant to photons, and to study the effect of thinner disk profiles in the plasma. We find similar qualitative results to the scalar case, and so support the conclusions of that work: either a constant asymptotic mass or a shell-like plasma structure is required for superradiant growth to occur. We study thin disks and find a leakage of the bosonic condensate that suppresses its growth, concluding that thick disks are more likely to support the instability.

Shining light on polarizable dark particles

We investigate the possibilities of searching for a self-conjugate polarizable particle in the self-interactions of light. We first observe that polarizability can arise either from the exchange of mediator states or as a consequence of the inner structure of the particle. To exemplify this second possibility we calculate the polarizability of a neutral bosonic open string, and find it is described only by dimension-8 operators. Focussing on the spin-0 case, we calculate the light-by-light scattering amplitudes induced by the dimension-6 and 8 polarizability operators. Performing a simulation of exclusive diphoton production with proton tagging at the LHC, we find that the imprint of the polarizable dark particle can be potentially detected at 5σ significance for mass and cutoff reaching values above the TeV scale, for sqrt{s}=13 TeV and 300 fb−1 of integrated luminosity. If the polarizable dark particle is stable, it can be a dark matter candidate, in which case we argue this exclusive diphoton search may complement the existing LHC searches for polarizable dark matter.

Wide or narrow? The phenomenology of 750 GeV diphotons

I perform a combined analysis of the ATLAS and CMS diphoton data, using both Run-I and Run-II results, including those released at the 2016 Moriond conference. I find combining the ATLAS and CMS results from Run-II increases the statistical significance of the reported 750 GeV anomaly, assuming a spin-0 mediator coupling to gluons or heavy quarks with a width much smaller than the detector resolution. This significance does not decrease when the 8 TeV data is included. A spin-2 mediator is disfavored compared to the spin-0 case. The cross section required to fit the ATLAS anomaly is in tension with the aggregate data, all of which prefers a smaller value. The best fit for all models I consider is a $4.0\sigma$ local significance for a 750 GeV spin-0 mediator coupling to gluons with a cross section of 4 fb at 13 TeV (assuming narrow width) or 10~fb (assuming $\Gamma=45$ GeV).

A relativistic one-particle Time of Arrival operator for a free spin-[formula omitted] particle in [formula omitted] dimensions

As a follow-up to a recent study in the spin-0 case (Bunao and Galapon, 2015), we construct a one-particle Time of Arrival (TOA) operator conjugate to a Hamiltonian describing a free relativistic spin-1/2 particle in one spatial dimension. Upon transformation in a representation where the Hamiltonian is diagonal, it turns out that the constructed operator consists of an operator term Tˆ whose action is the same as in the spin-0 case, and another operator term Tˆ0 which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away Tˆ0 so that the TOA operator is just Tˆ.

Enhancement of [formula omitted] via spin-0 and spin-1/2 charged unparticle loops

We calculate the spin-0 and spin-1/2 charged unparticle loop contributions to the Higgs diphoton decay within an unparticle gauge model and show that they can significantly enhance or suppress SM predictions for the same. In the SM limits of scalar and fermion conformal dimensions, dUs→1 and dUf→3/2 respectively, our results exactly reproduce the contributions of the spin-0 and spin-1/2 particle cases. Furthermore the decoupling from the Higgs boson occurs only for the spin-0 case in the critical limit dUs→2. Using the recent ATLAS data which reported an excess of diphoton decay rate of SM-like Higgs boson around 125 GeV, and taking into account the vacuum stability and perturbativity conditions, the parameters of the gauge unparticle model are constrained.

On the uniqueness of paths for spin-0 and spin-1 quantum mechanics

The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-(1/2) was dealt with by Holland. It appears that the uniqueness of boson paths can be enforced under well determined conditions. This in turn fixes the nonrelativistic particle equations of the nonrelativistic Schrödinger equation, which appear to correspond with the original definitions given by de Broglie and Bohm only in the spin-0 case. Similar to the spin-(1/2) case, there appears an additional spin-dependent term in the guidance equation in the spin-1 case. We also discuss the ambiguity associated with the introduction of an electromagnetic coupling in the Kemmer theory. We argue that when the minimal coupling is correctly introduced, then the current constructed from the energy–momentum tensor is no longer conserved. Hence this current cannot serve as a particle probability four-vector.

Pair term in the electromagnetic current within the Front-Form dynamics: spin-0 case

The frame and scale dependence of the pair-term contribution to the electromagnetic form factor of a spin-zero composite system of two-fermions is studied within the Light Front. The form factor is evaluated from the plus-component of the current in the Breit frame, using for the first time a nonconstant, symmetric ansatz for the Bethe–Salpeter amplitude. The frame dependence is analyzed by allowing a nonvanishing plus component of the momentum transfer, while the dynamical scale is set by the masses of the constituents and by mass and size of the composite system. A transverse momentum distribution, associated with the Bethe–Salpeter amplitude, is introduced which allows to define strongly and weakly relativistic systems. In particular, for strongly relativistic systems, the pair term vanishes for the Drell–Yan condition, while is dominant for momentum transfer along the light-front direction. For a weakly relativistic system, fitted to the deuteron scale, the pair term is negligible up to momentum transfers of 1 (GeV/ c) 2. A comparison with results obtained within the Front-Form Hamiltonian dynamics with a fixed number of constituents is also presented.

The quantum mechanical current of the Pauli equation

We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of argument used in the spin-0 case, i.e., the Schrödinger equation, is ambiguous. We show that a nonrelativistic reduction of the relativistic Dirac four-vector current is, however, capable of fully resolving the problem. This analysis reveals that the nonrelativistic current of the Pauli equation should include an extra term of the form ∇×(ψ†σψ). We present an initial exploration of the potential consequences of this new “spin term” by solving the Pauli equation for crossed magnetic and electric fields and calculating the corresponding current.

Perturbative expansion in the Galilean-invariant spin-1/2Chern-Simons field theory

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-$1/2$ fields of distinct masses $M$ and ${M}^{\ensuremath{'}}.$ A method for the construction of states containing $N$ particles of mass $M$ and ${N}^{\ensuremath{'}}$ particles of mass ${M}^{\ensuremath{'}}$ is given which is subsequently used to display equivalence to the spin-$1/2$ Aharonov-Bohm effect in the ${N=N}^{\ensuremath{'}}=1$ sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one-loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin-0 case in field theory as well as in quantum mechanics.

Nonlinear quantum mechanics as weyl geometry of a classical statistical ensemble

We derive nonlinear relativistic and non-relativistic wave equations for spin-0 and 1/2 particles. For a suitable choice of coupling constants, the equations become linear and Weyl gauge invariant in the spin-0 case. The Dirac particle is much more subtle. When a suitable gauge is chosen and, when the Compton wavelength of the particle is much larger than Planck's length, we recover the standard Dirac equation. Nonlinear corrections to the Schrodinger equation are obtained and these appear as the first-order relativistic corrections to the non-relativistic Hamilton-Jacobi equation. Consequently, we construct nonbilinear homogeneous realizations of anapproximate Galilean symmetry. We put forth the idea that not only a modification of quantum mechanics might be necessary in order to accommodate gravity, but quantum mechanics itself might have a geometrical origin with Planck's constant as the coupling between matter and curvature.

Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems

We develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short-range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large-distance Schwinger functions in terms of a family of running couplings consisting of one- and two-body quasiparticle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in thenth order,n! bounds. The flow equations are written in general dimensiond⩾1 for the spinless case (for simplicity). The picture that emerges is that on a large scale the system looks like a system of fermions interacting via aδ-like interaction potential (i.e., a potential approaching 0 everywhere except at the origin, where it diverges, although keeping the integral bounded); the theory is not asymptotically free in the usual sense and the freedom mechanism is thus more delicate than usual: the technical problem of dealing with unbounded effective potentials is solved by introducing a mathematically precise notion ofquasiparticles, which turn out to be natural objects with finite interaction even when the physical potential diverges as a deltalike function. A remarkable kind of gauge symmetry is associated with the quasiparticles. To substantiate the analogy with the quasiparticle theory we discuss the mean field theory using our notion of quasiparticles: the resulting self-consistency relations are closely reminiscent of those of the BCS model. The formalism seems suited for a joint theory of normal states of Fermi liquids and of BCS states: the first are associated with the trivial fixed point of our flow or with nearby nontrivial fixed points (or invariant sets) and the second may naturally correspond to really nontrivial fixed points (which may nevertheless turn out to be accessible to analysis because the BCS state is a quasi free state, hence quite simple, unlike the nontrivial fixed points of field theory). Thed=1 case is deeply different from thed> 1 case, for our spinless fermions: we can treat it essentially completely for small coupling. The system is not asymptotically free and presents anomalous renormalization group flow with a vanishing beta function, and the discontinuity of the occupation number at the Fermi surface is smoothed by the interaction (remaining singular with a coupling-dependent singularity of power type with exponent identified with the anomalous dimension). Finally, we present a heuristic discussion of the theory for the flow of the running coupling constants in spinlessd> 1 systems: their structure is simplified further and the relevant part of the running interaction is precisely the interaction between pairs of quasiparticles which we identify with the Cooper pairs of superconductivity. The formal perturbation theory seems to have a chance to work only if the interaction between the Cooper pairs is repulsive: and to second order we show that in the spin-0 case this happens if the physical potential is repulsive. Our results indicate the possibility of the existence of a normal Fermi surface only if the interaction is repulsive.

New approach to quantum corrections in synchrotron radiation. II

Continuing our efforts to provide a simple and elegant derivation of a compact (exact) expression for the radiated power of the synchrotron radiation, we here generalize our previous discussion of the radiation by a spin-0 charged particle to that of a spin-\textonehalf{} particle. As in the spin-0 case, we compute the spectrum of the radiated power by using the proper-time method to first calculate the forward Compton scattering amplitude and then apply the optical theorem. The complication due to the inclusion of spin is handled by first decomposing the spin-\textonehalf{} states into the two subspaces of ${\ensuremath{\gamma}}^{0}$, and then using the connection between the two subspaces that is provided by the Dirac equation. Aside from the simple and straightforward operator procedures in computing the result, we also obtain a very simple and compact (one parameter) integral expression for the spectral and angular distribution of the radiated power. Its high-energy, weak-field limit agrees with that obtained from the conventional approach and that from the mass operator method.

New Low-Energy Theorems for Nucleon Compton Scattering

Two new low-energy theorems for Compton scattering from spin-\textonehalf{} targets, giving some terms of order ${\ensuremath{\omega}}^{2}$, are derived using a recently obtained lemma. One of these theorems is a generalization to the spin-\textonehalf{} case of a similar theorem for the spin-0 case. The other theorem involves magnetic moment radius, i.e., ${[\frac{d{G}_{M}(t)}{\mathrm{dt}}]}_{t=0}$, which does not occur in any of the low-energy theorems obtained earlier.

Search for a Spin-1 Intermediate Meson in Neutral Pion Photoproduction

If a spin-1 meson exists it might act as an intermediate particle in a meson current graph for neutral pion photoproduction. It is shown that the singularities from this graph are likely to be much closer to the physical region in the complex $x=cos\ensuremath{\theta}$ plane than any other singularities with the possible exception of those coming from a pion-pion interaction. Thus an extrapolation can be carried out in $x$ to determine the residue of the pole due to the spin-1 meson if it exists. This residue is calculated for vector ($V$) and pseudovector ($\mathrm{PV}$) mesons and is found to have the same negative sign for both cases, unlike in the spin-0 case. Experimental data at 300, 450, 700, and 800 Mev are used for the extrapolation which is carried out as a function of intermediate meson mass. It is found that the results are consistent with zero residue for all energies with the possible exception of 450 Mev where there is a slight evidence for a positive residue. Thus present evidence favors the conclusion that there is no contribution to neutral photoproduction from a spin-1 meson. One can place an upper limit of about 0.01 for the $V$ case and 0.05 for the $\mathrm{PV}$ case on the magnitude of ${g}^{2}{(\frac{\mathfrak{M}}{2m})}^{2}$, where $g$ is the coupling constant between the nucleon and the spin-1 meson, and the latter has a mass $m$ and a magnetic moment $\mathfrak{M}$. A detailed analysis is also given of the error in the residue determined from a set of experimental data, as a function of the location and number of data points, the extrapolation distance, and the order of the extrapolating polynomial. It is concluded that the present error in the residue could be improved by a factor of 3 to 5 by an experiment measuring the differential cross section of neutral pion photoproduction at a photon energy of 800 Mev in the laboratory system at every 10\ifmmode^\circ\else\textdegree\fi{} from 10\ifmmode^\circ\else\textdegree\fi{} with an error of \ifmmode\pm\else\textpm\fi{}0.2 \ensuremath{\mu}b/sr on the individual measurements.