Tensor Contributions Research Articles

Multi-stress tensors and next-to-leading singularities in the Regge limit

The stress tensor sector of a heavy-heavy-light-light scalar correlator in CFTs with a large central charge and a large gap is defined by the exchange of multi-stress tensor operators. The Regge limit of this correlator is determined by the phase shift of a highly energetic particle propagating in a dual black hole background. Assuming Einstein gravity in the bulk, the phase shift is known perturbatively to all orders in the ratio of the heavy scaling dimension over the central charge. In the CFT, the order counts the number of stress tensors in the multi-stress tensor operator. By Fourier transforming the correlator to position space, the multi-stress tensor contributions to the leading and next-to-leading singularities in the Regge limit are found to all orders in four dimensions. The leading singularity at each order agrees with known results obtained by considering a particle in a dual shockwave background. Moreover, the leading and next-to-leading singularities due to double- and triple-stress tensors with minimal twist are known from lightcone bootstrap and agree with the results derived from the phase shift.

Characterizing the cosmological gravitational wave background: Anisotropies and non-Gaussianity

A future detection of the Stochastic Gravitational Wave Background (SGWB) with GW experiments is expected to open a new window on early universe cosmology and on the astrophysics of compact objects. In this paper we study SGWB anisotropies, that can offer new tools to discriminate between different sources of GWs. In particular, the cosmological SGWB inherits its anisotropies both (i) at its production and (ii) during its propagation through our perturbed universe. Concerning (i), we show that it typically leads to anisotropies with order one dependence on frequency. We then compute the effect of (ii) through a Boltzmann approach, including contributions of both large-scale scalar and tensor linearized perturbations. We also compute for the first time the three-point function of the SGWB energy density, which can allow one to extract information on GW non-Gaussianity with interferometers. Finally, we include non-linear effects associated with long wavelength scalar fluctuations, and compute the squeezed limit of the 3-point function for the SGWB density contrast. Such limit satisfies a consistency relation, conceptually similar to what found in the literature for the case of CMB perturbations.

Vibrational Raman optical activity of camphor: The importance of electric‐dipole—electric‐quadrupole polarizability contribution

AbstractThe importance of the electric‐dipole—electric‐quadrupole polarizability contribution to the vibrational Raman optical activity (VROA) and dimensionless circular intensity difference spectra of (1S)‐camphor is examined. The spectra are simulated with and without this tensor contribution using density functional theory calculations, and similarity is evaluated for each against the experimental spectra. Careful examination of the comparison between experimental and calculated spectra reveals multiple vibrational bands, in the ~1,130–950 cm−1 region, originating from −C–H bending vibrations that are dominated by the electric‐dipole—electric‐quadrupole polarizability contributions. The similarity overlap analysis also reveals that the similarity overlap between experimental and predicted spectra in the measured spectral range increases, by up to 12%, when electric‐dipole—electric‐quadrupole polarizability contributions are included. The negative VROA band at 1,125 cm−1 in the experimental spectrum of (1S)‐(‐)‐camphor can only be reproduced in the predicted spectra when electric‐dipole—electric‐quadrupole polarizability contribution is included. Investigations on additional molecules indicated that (a) two experimental VROA bands of (1S,4R)‐(+)‐fenchone at ~1,740 and 220 cm−1 originate from dominating electric‐dipole—electric‐quadrupole polarizability contribution and (b) the symmetric and antisymmetric ring deformation modes of dimethyloxirane have dominating electric‐dipole—electric‐quadrupole polarizability contribution. These observations establish the importance of electric‐dipole—electric‐quadrupole polarizability contribution to VROA for the first time.

Revisiting the new-physics interpretation of the b \u2192 c\u03c4\u03bd data

We revisit the status of the new-physics interpretations of the anomalies in semileptonic B decays in light of the new data reported by Belle on the lepton-universality ratios RD(*) using the semileptonic tag and on the longitudinal polarization of the D* in B → D*τν, {F}_L^{Dast } . The preferred solutions involve new left-handed currents or tensor contributions. Interpretations with pure right-handed currents are disfavored by the LHC data, while pure scalar models are disfavored by the upper limits derived either from the LHC or from the Bc lifetime. The observable {F}_L^{Dast } also gives an important constraint leading to the exclusion of large regions of parameter space. Finally, we investigate the sensitivity of different observables to the various scenarios and conclude that a measurement of the tau polarization in the decay mode B → Dτν would effectively discriminate among them.

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε, turning them into a simple diagrammatic perturbation theory at large central charge.Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode.These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.

Subleading eikonal, AdS/CFT and double stress tensors

The eikonal phase which determines the Regge limit of the gravitational scat- tering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been com- puted to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single stress tensor conformal block, but the subleading term is a result of an infinite sum of the double stress tensor contributions. We provide a closed form expression for the OPE coef- ficients of the leading twist double stress tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.

Constraining graviton non-Gaussianity through the CMB bispectra

Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that forthcoming experiments, such as LiteBIRD, CMB-S4 and CORE, will detect the presence of the (Weyl)$^3$ term if $M_p^4 L^4 \sim 10^{17} r^{-4}$, where $L$ parametrizes the strength of the (Weyl)$^3$ term and $r$ is the tensor-to-scalar ratio, which corresponds to $L\gtrsim 3.2 \times 10^5 M_p^{-1}$, while the current upper limit is $M_p^4 L^4 = (1.1 \pm 4.0) \times 10^{19} r^{-4}$ (68%CL).

New approach to the adiabaticity concepts in the collective nuclear motion: Impact for the collective-inertia tensor and comparisons with experiment

We propose a new derivation of the cranking-model expression for the nuclear collective inertia tensor, introducing explicitly the slow- and fast-motion timescales together with a parameter controlling the interplay between the two modes. The new cranking formula is free from the mass tensor divergencies originating from the nucleon-level crossings in the denominators of the first-order perturbation theory expressions and allows the exploration of the unrestricted deformation space without spurious mass tensor contributions caused by those divergencies. We apply the new formalism without extra parameter adjustments to the collective vibrations in $^{208}\mathrm{Pb}$.

Imprints of local lightcone projection effects on the galaxy bispectrum IV: second-order vector and tensor contributions

The galaxy bispectrum on scales around and above the equality scale receives contributions from relativistic effects. Some of these arise from lightcone deformation effects, which come from local and line-of-sight integrated contributions. Here we calculate the local contributions from the generated vector and tensor background which is formed as scalar modes couple and enter the horizon. We show that these modes are sub-dominant when compared with other relativistic contributions.

Tensor correlations in He4 and Be8 within an antisymmetrized quasicluster model

In this paper, we extend the framework of improved version of simplified method to take into account the tensor contribution ($i$SMT) and propose AQCM-T, tensor version of antisymmetrized quasi cluster model (AQCM). Although AQCM-T is phenomenological, we can treat the $^3S$-$^3D$ coupling in the deuteron-like $T=0$ $NN$-pair induced by the tensor interaction in a very simplified way, which allows us to proceed to heavier nuclei. Also we propose a new effective interaction, V2m, where the triplet-even channel of the Volkov No.2 interaction is weakened to 60% so as to reproduce the binding energy of $^4$He after including the tensor term of a realistic interaction. Using AQCM-T and the new interaction, the significant tensor contribution in $^4$He is shown, which is almost comparable the central interaction, where $D$-state mixes by 8% to the major $S$-state. The AQCM-T model with the new interaction is also applied to $^8$Be. It is found that the tensor suppression gives significant contribution to the short-range repulsion between two {\alpha} clusters.

Quantitative analysis of tensor effects in the relativistic Hartree-Fock theory

Tensor force is identified in each meson-nucleon coupling in the relativistic Hartree-Fock theory. It is found that all the meson-nucleon couplings, except the $\sigma$-scalar one, give rise to the tensor force. The effects of tensor force on various nuclear properties can now be investigated quantitatively, which allows fair and direct comparisons with the corresponding results in the non-relativistic framework. The tensor effects on nuclear binding energies and the evolutions of the $Z,\,N = 8,\,20$, and $28$ magic gaps are studied. The tensor contributions to the binding energies are shown to be tiny in general. The $Z,\,N = 8$ and $20$ gaps are sensitive to the tensor force, but the $Z,\,N = 28$ gaps are not.

Modified gravitational-wave propagation and standard sirens

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(\Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(\Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1\%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $\Xi_0$ can be measured to $0.8\%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.

Using the full power of the cosmic microwave background to probe axion dark matter

The cosmic microwave background (CMB) places strong constraints on models of dark matter (DM) that deviate from standard cold DM (CDM), and on initial conditions beyond the scalar adiabatic mode. Here, the full \textit{Planck} data set (including temperature, $E$-mode polarisation, and lensing deflection) is used to test the possibility that some fraction of the DM is composed of ultralight axions (ULAs). This represents the first use of CMB lensing to test the ULA model. We find no evidence for a ULA component in the mass range $10^{-33}\leq m_a\leq 10^{-24}\text{ eV}$. We put percent-level constraints on the ULA contribution to the DM, improving by up to a factor of two compared to the case with temperature anisotropies alone. Axion DM also provides a low-energy window onto the high-energy physics of inflation through the interplay between the vacuum misalignment production of axions and isocurvature perturbations. We perform the first systematic investigation into the parameter space of ULA isocurvature, using an accurate isocurvature transfer function at all $m_{a}$ values. We precisely identify a "window of co-existence" for $10^{-25}\text{ eV}\leq m_a\leq10^{-24}\text{ eV}$ where the data allow, simultaneously, a $\sim10\%$ contribution of ULAs to the DM, and $\sim 1\%$ contributions of isocurvature and tensors to the CMB power. ULAs in this window (and \textit{all} lighter ULAs) are shown to be consistent with a large inflationary Hubble parameter, $H_I\sim 10^{14}\text{ GeV}$. The window of co-existence will be fully probed by proposed CMB-S4 observations with increased accuracy in the high-$\ell$ lensing power and low-$\ell$ $E$ and $B$-mode polarisation. If ULAs in the window exist, this could allow for two independent measurements of $H_I$ in the CMB using the axion DM content and isocurvature, and the tensor contribution to $B$-modes.

Improved version of a simplified method for including tensor effects in cluster models

The tensor contribution can be directly incorporated in the cluster model in a simplified way. In conventional $\alpha$ cluster models, the contribution of the non-central interactions exactly cancels because of the antisymmetrization effect and spatial symmetry of $\alpha$ clusters. The mixing of breaking components of $\alpha$ clusters to take into account the spin-orbit and tensor effects is needed. Previously we proposed a simplified method to include the spin-orbit effect, and also for the tensor part, a simplified model to directly take into account the contribution of the tensor interaction (called SMT) was introduced; however the contribution of the tensor interaction was quite limited. Here we improve SMT, which is called $i$SMT. Using newly proposed $i$SMT, the contribution of the tensor interaction in $^4$He is more than $-40$ MeV, four times larger than the previous version. The method is applied to four-$\alpha$ cluster structure of $^{16}$O. In $^{16}$O, the tensor contribution is also large, and this is coming from the finite size effect for the distances among $\alpha$ clusters with a tetrahedral configuration.

Ke3 Decay Studies in the OKA Experiment

Recent results from OKA setup concerning form factor studies in $K_{e3}$ decay are presented. About 5.25M events are selected for the analysis. The linear and quadratic slopes for the decay formfactor $f_{+}(t)$ are measured: $\lambda'_{+}=(26.1 \pm 0.35 \pm 0.28 )\times 10^{-3}$, $\lambda"_{+}=(1.91 \pm 0.19 \pm 0.14)\times 10^{-3}$. The scalar and tensor contributions are compatible with zero. Several alternative parametrizations are tried: the Pole fit parameter is found to be $M_V = 891 \pm 2.0$ MeV ; the parameter of the Dispersive parametrization is measured to be $\Lambda_+ =(24.58 \pm 0.18) \times 10^{-3}$. The presented results are considered as preliminary.

Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the 6S1/2 5D3/2 clock transition in Yb+

We present precise values of the dipole polarizabilities (α) of the ground and metastable states of Yb+, that are important in reducing systematics in the clock frequency of the transition. The static values of α for the ground and states are estimated to be and , respectively, while the tensor contribution to the state as compared to the experimental value . This corresponds to the differential scalar polarizability value of the above transition as −7.8(5) in contrast to the available experimental value −6.9(1.4) J m2 V−2 . This results in the black-body radiation shift of the clock transition as Hz at the room temperature, which is large as compared to the previously estimated values. Using the dynamic α values, we report the tune-out and magic wavelengths that could be of interest to subdue systematics due to the Stark shifts and for constructing lattice optical clock using Yb+.

Weak interaction physics at ISOLDE

Radioactive nuclei offer unique possibilities to study the structure and symmetries of the weak interaction in nuclear β decay. The large variety of nuclear states available allows selecting the ones that are best suited to study the phenomena of interest with optimal sensitivity, while at the same time minimising the effects of nuclear structure. The ISOLDE facility, offering worldwide the largest variety and intensity of radioactive beams, is one of the best suited laboratories in this respect. Over the last decade or so different aspects of the weak interaction have been studied at ISOLDE, ranging from half-lives, branching ratios and nuclear masses relevant for the determination of the Vud quark-mixing matrix element, over β-asymmetry and correlation measurements searching for possible tensor and/or scalar contributions to the weak interaction, up to a measurement showing the effect of parity violation in the weak interaction in gamma decay. In addition, new projects respectively searching for scalar currents in the β-delayed proton decay of 32Ar, or to determine the Vud quark-mixing matrix element from the β-asymmetry parameter in the mirror decay of 35Ar, have just started.

Limited true polar wander as evidence that Earth's nonhydrostatic shape is persistently triaxial

AbstractEarth's spin axis follows the maximum moment of inertia axis of mantle convection, with some delay due to adjustment of the rotational bulge. Here we compute this axis for geodynamic models based on subduction history, assuming constant slab sinking speed, with another contribution due to thermochemical piles. For a wide range of parameters, a large shift of ≈90° is predicted around 80–90 Ma. It can be largely attributed to a change in circum‐Pacific subduction from predominantly in the North and South toward East and West. Actual amounts of true polar wander are much smaller, pointing toward additional inertia tensor contributions, possibly due to slabs in the lowermost mantle below both polar regions. These slabs would have been subducted before ≈150 Ma, when plate motions in the Panthalassa basin are largely unknown. Matching predicted and observed true polar wander can serve at constraining such plate motions.

Large Hyperpolarizabilities at Telecommunication-Relevant Wavelengths in Donor-Acceptor-Donor Nonlinear Optical Chromophores.

Octopolar D2-symmetric chromophores, based on the MPZnM supermolecular motif in which (porphinato)zinc(II) (PZn) and ruthenium(II) polypyridyl (M) structural units are connected via ethyne linkages, were synthesized. These structures take advantage of electron-rich meso-arylporphyrin or electron-poor meso-(perfluoroalkyl)porphyrin macrocycles, unsubstituted terpyridyl and 4′-pyrrolidinyl-2,2′;6′,2″-terpyridyl ligands, and modulation of metal(II) polypyridyl-to-(porphinato)zinc connectivity, to probe how electronic and geometric factors impact the measured hyperpolarizability. Transient absorption spectra obtained at early time delays (tdelay < 400 fs) demonstrate fast excited-state relaxation, and formation of a highly polarized T1 excited state; the T1 states of these chromophores display expansive, intense T1 → Tn absorption manifolds that dominate the 800–1200 nm region of the NIR, long (μs) triplet-state lifetimes, and unusually large NIR excited absorptive extinction coefficients [ε(T1 → Tn) ∼ 105 M–1 cm–1]. Dynamic hyperpolarizability (βλ) values were determined from hyper-Rayleigh light scattering (HRS) measurements, carried out at multiple incident irradiation wavelengths spanning the 800–1500 nm spectral domain. The measured βHRS value (4600 ± 1200 × 10–30 esu) for one of these complexes, RuPZnRu, is the largest yet reported for any chromophore at a 1500 nm irradiation wavelength, highlighting that appropriate engineering of strong electronic coupling between multiple charge-transfer oscillators provides a critical design strategy to realize octopolar NLO chromophores exhibiting large βHRS values at telecom-relevant wavelengths. Generalized Thomas–Kuhn sum (TKS) rules were utilized to compute the effective excited-state-to-excited-state transition dipole moments from experimental linear-absorption spectra; these data were then utilized to compute hyperpolarizabilities as a function of frequency, that include two- and three-state contributions for both βzzz and βxzx tensor components to the RuPZnRu hyperpolarizability spectrum. This analysis predicts that the βzzz and βxzx tensor contributions to the RuPZnRu hyperpolarizability spectrum maximize near 1550 nm, in agreement with experimental data. The TKS analysis suggests that relative to analogous dipolar chromophores, octopolar supermolecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Optical trapping of ultracold dysprosium atoms: transition probabilities, dynamic dipole polarizabilities and van der Waals C6 coefficients

The efficiency of the optical trapping of ultracold atoms depends on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited levels. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-orders-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. Finally, our anisotropic C6 coefficients are much smaller than those published in the literature.