Scalar States Research Articles

Spinning amplitudes from scalar amplitudes

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin J exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.

Squeezing the Axion

We apply the squeezed state formalism to scalar field dark matter (e.g. axion) perturbations generated during inflation. As for the inflationary perturbations, the scalar field state becomes highly squeezed as modes exit the horizon. For as long as $H>m_\phi$ (with $H$ the Hubble rate and $m_\phi$ the scalar mass) the scalar field field does not interact during reheating, and we follow its evolution exactly as modes re-enter the horizon. We find that the quantum state remains squeezed after horizon re-entry during the hot big bang. This demonstrates a fact well-known in the theory of inflation: cosmological observables for scalar dark matter are accurately modelled by a classical stochastic field with a fixed phase. Our calculation covers all modes smaller than the present-day cosmic de Broglie wavelength. Larger scale modes mix gravitationally with the environment when $H<m_\phi$, and are thus expected to decohere.

Bottomonium melting from screening correlators at high temperature

We study the bottomonium screening masses in a 2+1 flavor QCD medium on the lattice using the Highly Improved Staggered Quark(HISQ) discretization for the quarks. We focus on a wide temperature range in the region $350~{\rm MeV}\le T < 1000 ~{\rm MeV}$, and perform our calculations on three different lattice spacings to control the lattice cut-off effects, corresponding to temporal lattice extent of $N_\tau=8,10,12$. From a detailed study of the temperature dependence of screening masses we conclude that while the $\eta_b(1S)$ and $\Upsilon(1S)$ states melt at $T>500$ MeV, the scalar and axial-vector states $\chi_{b0}(1P)$ and $h_b(1P)$ melt already at $T>350$ MeV.

Demonstrating Arago-Fresnel laws with Bessel beams from vectorial axicons.

Two-dimensional Bessel beams, both vectorial and scalar, have been extensively studied to date, finding many applications. Here we mimic a vectorial axicon to create one-dimensional scalar Bessel beams embedded in a two-dimensional vectorial field. We use a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and study the boundary of scalar and vectorial states in the context of structured light using the Arago-Fresnel laws. We show that the entire field resembles a vectorial combination of parabolic beams, exhibiting dependence on solutions to the inhomogeneous Bessel equation and asymmetry due to the orbital angular momentum associated rotational diffraction. Our work reveals the rich optical processes involved at the interplay between scalar and vectorial interference, opening intriguing questions on the duality, complementarity, and non-separability of vectorial light fields.

Semileptonic decays D→ηπe+νe in the a0(980) region

The mechanism of the four-quark production of the light scalar isovector four-quark state ${a}_{0}(980)$ in the $D\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\pi}{e}^{+}{\ensuremath{\nu}}_{e}$ decays is discussed. It is shown that the characteristic features of the shape of the $\ensuremath{\eta}\ensuremath{\pi}$ mass spectra expected in our scheme can serve as the indicator of the production mechanism and internal structure of the ${a}_{0}(980)$ resonance.

Completing Multiparticle Representations of the Poincaré Group.

We extend the definition of asymptotic multiparticle states of the S-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or q_{ij}, associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing q_{ij}, while for vanishing spins they reproduce Zwanziger's scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as q_{ij}=e_{i}g_{j}-e_{j}g_{i}.

Probing Gravitational Waves from Pulsars in Brans–Dicke Theory

This paper comprises the theoretical background for the data analysis of gravitational waves (GWs) from spinning neutron stars in Brans–Dicke (BD) theory. Einstein’s general theory of relativity (GR) predicts only two tensor polarization states, but a generic metric theory of gravity can also possess scalar and vector polarization states. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third one is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters.

The New Charm-Strange Resonances in the D−K+ Channel

We evaluate the masses and decay constants of the 0+ and 1− open-charm (c¯d¯)(us) tetraquarks and molecular states from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR). This method takes into account the stability criteria where the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the D−K+ invariant mass recently reported by LHCb from B+ → D+(D−K+) decays. We expect that the resonance near the D−K+ threshold can be originated from the 0++(D−K+) molecule and/or D−K+ scattering. The X0(2900) scalar state and the resonance XJ(3150) (if J = 0) can emerge from a minimal mixing model, with a tiny mixing angle θ0 ≃ (5.2 ± 1.9)0, between a scalar Tetramole (TM0) (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers), having a mass MTM0=2743(18)MeV, and the first radial excitation of the D−K+ molecule with mass M(DK)1 = 3678(310) MeV. In an analogous way, the X1(2900) and the XJ(3350) (if J = 1) could be a mixture between the vector Tetramole (TM1), with a mass MTM1=2656(20)MeV, and its first radial excitation having a mass MTM1=4592(141)MeV with an angle θ0 ≃ (9.1 ± 0.6)0. A (non)-confirmation of these statements requires experimental findings of the quantum numbers of the resonances at 3150 and 3350 MeV.

(2, 2) Scattering and the celestial torus

Analytic continuation from Minkowski space to (2, 2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to an S3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, ℝ)L×SL(2, ℝ)R conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

Isospin-1/2 D\u03c0 scattering and the lightest {D}_0^{ast } resonance from lattice QCD

Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a {D}_0^{ast } resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the {D}_{s0}^{ast } , and {D}_0^{ast } with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the {D}_0^{ast } is consistently found well below that of the {D}_{s0}^{ast } , in contrast to the currently reported experimental result.

Quadratic gravity and restricted Weyl symmetry

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

Dilatonic states near holographic phase transitions

The spectrum of bound states of special strongly coupled confining field theories might include a parametrically light dilaton, associated with the formation of enhanced condensates that break (approximate) scale invariance spontaneously. It has been suggested in the literature that such a state may arise in connection with the theory being close to the unitarity bound in holographic models. We extend these ideas to cases where the background geometry is non-AdS, and the gravity description of the dual confining field theory has a top-down origin in supergravity. We exemplify this programme by studying the circle compactification of Romans six-dimensional half-maximal supergravity. We uncover a rich space of solutions, many of which were previously unknown in the literature. We compute the bosonic spectrum of excitations, and identify a tachyonic instability in a region of parameter space for a class of regular background solutions. A tachyon only exists along an energetically disfavoured (unphysical) branch of solutions of the gravity theory; we find evidence of a first-order phase transition that separates this region of parameter space from the physical one. Along the physical branch of regular solutions, one of the lightest scalar particles is approximately a dilaton, and it is associated with a condensate in the underlying theory. Yet, because of the location of the phase transition, its mass is not parametrically small, and it is, coincidentally, the next-to-lightest scalar bound state, rather than the lightest one.

Search for new phenomena in final states with b-jets and missing transverse momentum in sqrt{mathrm{s}} = 13 TeV pp collisions with the ATLAS detector

The results of a search for new phenomena in final states with b-jets and missing transverse momentum using 139 fb−1 of proton-proton data collected at a centre-of-mass energy sqrt{s} = 13 TeV by the ATLAS detector at the LHC are reported. The analysis targets final states produced by the decay of a pair-produced supersymmetric bottom squark into a bottom quark and a stable neutralino. The analysis also seeks evidence for models of pair production of dark matter particles produced through the decay of a generic scalar or pseudoscalar mediator state in association with a pair of bottom quarks, and models of pair production of scalar third-generation down-type leptoquarks. No significant excess of events over the Standard Model background expectation is observed in any of the signal regions considered by the analysis. Bottom squark masses below 1270 GeV are excluded at 95% confidence level if the neutralino is massless. In the case of nearly mass-degenerate bottom squarks and neutralinos, the use of dedicated secondary-vertex identification techniques permits the exclusion of bottom squarks with masses up to 660 GeV for mass splittings between the squark and the neutralino of 10 GeV. These limits extend substantially beyond the regions of parameter space excluded by similar ATLAS searches performed previously.

Triple Higgs boson production at the Large Hadron Collider with Two Real Singlet scalars

We investigate the production of three Higgs bosons in the Two Real Singlet extension of the Standard Model, where the scalar sector is augmented by two additional real scalar fields which are singlets under the Standard Model gauge group. The model contains three neutral CP-even scalars, allowing for resonant production and asymmetric decay chains. We focus on the signature pp → h3→ h1h2→ h1h1h1, where we identify h3 as the heaviest scalar state, h2 as the second heaviest and the lightest, h1, as the Standard Model-like Higgs boson discovered by the Large Hadron Collider experiments. The dominant final state occurs when all three Higgs bosons decay to bottom-anti-bottom quark pairs, h1→ boverline{b} , leading to 6 b-jets. Taking into account all current theoretical and experimental constraints, we determine the discovery prospects for this channel in future runs of the Large Hadron Collider, as well as in the high-luminosity phase.

On the stress tensor light-ray operator algebra

We study correlation functions involving generalized ANEC operators of the form int {dx}^{-}{left({x}^{-}right)}^{n+2}{T}_{--}left(overrightarrow{x}right) in four dimensions. We compute two, three, and four-point functions involving external scalar states in both free and holographic Conformal Field Theories. From this information, we extract the algebra of these light-ray operators. We find a global subalgebra spanned by n = {−2, −1, 0, 1, 2} which annihilate the conformally invariant vacuum and transform among themselves under the action of the collinear conformal group that preserves the light-ray. Operators outside this range give rise to an infinite central term, in agreement with previous suggestions in the literature. In free theories, even some of the operators inside the global subalgebra fail to commute when placed at spacelike separation on the same null-plane. This lack of commutativity is not integrable, presenting an obstruction to the construction of a well defined light-ray algebra at coincident overrightarrow{x} coordinates. For holographic CFTs the behavior worsens and operators with n ≠ −2 fail to commute at spacelike separation. We reproduce this result in the bulk of AdS where we present new exact shockwave solutions dual to the insertions of these (exponentiated) operators on the boundary.

Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-color-singlet-color-singlet type currents to study the scalar , tetraquark molecular states and the vector , hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula and for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar , tetraquark molecular states and the vector hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector hexaquark molecular state. The connected (nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar tetraquark molecular state, but make negative or destructive contributions for the vector hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.

Scalar isoscalar mesons and the scalar glueball from radiative J/ψ decays

A coupled-channel analysis of BESIII data on radiative J/ψ decays into ππ, KK¯, ηη and ωϕ has been performed. The partial-wave amplitude is constrained by a large number of further data. The analysis finds ten isoscalar scalar mesons. Their masses, widths and decay modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet and mainly octet states. Octet isoscalar scalar states are observed with significant yields only in the 1500-2100MeV mass region. Singlet scalar mesons are produced over a wide mass range but their yield peaks in the same mass region. The peak is interpreted as scalar glueball. Its mass and width are determined to M=1865±25−30+10MeV and Γ=370±50−20+30MeV, its yield in radiative J/ψ decays to (5.8±1.0)10−3.

Light dilaton in a metastable vacuum

We identify a parametrically light dilaton by studying the perturbations of metastable vacua along a branch of regular supergravity backgrounds that are dual to four-dimensional confining field theories. The branch includes also stable and unstable solutions. The former encompass, as a special case, the geometry proposed by Witten as a holographic model of confinement. The latter approach a supersymmetric solution, by enhancing a condensate in the dual field theory. A phase transition separates the space of stable backgrounds from the metastable ones. In proximity of the phase transition, one of the lightest scalar states inherits some of the properties of the dilaton, despite not being particularly light.

Deep neural network application: Higgs boson CP state mixing angle in H→ττ decay and at the LHC

The consecutive steps of cascade decay initiated by H to tau tau can be useful for the measurement of Higgs couplings and in particular of the Higgs boson parity. In the previous papers we have found, that multi-dimensional signatures of the tau^pm to pi^pm pi^0 nu and tau^pm to 3pi^pm nu decays can be used to distinguish between scalar and pseudoscalar Higgs state. The Machine Learning techniques (ML) of binary classification, offered break-through opportunities to manage such complex multidimensional signatures. The classification between two possible CP states: scalar and pseudoscalar, is now extended to the measurement of the hypothetical mixing angle of Higgs boson parity states. The functional dependence of H to tau tau matrix element on the mixing angle is predicted by theory. The potential to determine preferred mixing angle of the Higgs boson events sample including $\tau$-decays is studied using Deep Neural Network. The problem is adressed as classification or regression with the aim to determine the per-event: a) probability distribution (spin weight) of the mixing angle; b) parameters of the functional form of the spin weight; c) the most preferred mixing angle. Performance of methods are evaluated and compared. Numerical results are collected.

Exotic ΩΩ dibaryon states in a molecular picture * *Supported by the National Natural Science Foundation of China (11722540, 12075019), the Fundamental Research Funds for the Central Universities, and the National Key Research and Development Program of China (2020YFA0406400)

We investigate the exotic dibaryon states with and in a molecular picture. We construct a tensor molecular interpolating current and calculate the two-point correlation function within the method of QCD sum rules. Our calculations indicate that the masses of the scalar and tensor dibaryon states are and , respectively, which are below the threshold. Within error, these results do not negate the existence of loosely bound molecular dibaryon states. These exotic strangeness and doubly-charged dibaryons, if they exist, may be identified in heavy-ion collision processes in the future.