Scalar Channel Research Articles

Exponential error reduction for glueball calculations using a two-level algorithm in pure gauge theory

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional SU(3) pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multilevel method. We discuss the physical distance at which the multilevel sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels. Published by the American Physical Society 2024

Numerical conformal bootstrap with analytic functionals and outer approximation

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these functionals to a more comprehensive backdrop, demonstrating their adaptability and efficacy in general spacetime dimensions above two. The bootstrap is implemented using the outer approximation methodology, with computations conducted in double precision. The crux of our study lies in comparing the performance of this category of analytic functionals with conventional derivatives at crossing symmetric points. It is worth highlighting that in our study, we identified some novel kinks in the scalar channel during the maximization of the gap in two-dimensional conformal field theory. Our numerical analysis indicates that these analytic functionals offer a superior performance, thereby revealing a potential alternative paradigm in the application of conformal bootstrap.

Topological susceptibility and axion potential in two-flavor superconductive quark matter

We study the potential of the axion, a, of Quantum Chromodynamics, in the two-flavor color superconducting phase of cold and dense quark matter. We adopt a Nambu-Jona-Lasinio-like model. Our interaction contains two terms, one preserving and one breaking the U(1)A symmetry: the latter is responsible of the coupling of axions to quarks. We introduce two quark condensates, hL and hR, describing condensation for left-handed and right-handed quarks respectively; we then study the loci of the minima of the thermodynamic potential, Ω, in the (hL,hR) plane, noticing how the instanton-induced interaction favors condensation in the scalar channel when the θ angle, θ=a/fa, vanishes. Increasing θ we find a phase transition where the scalar condensate rotates into a pseudoscalar one. We present an analytical result for the topological susceptibility, χ, in the superconductive phase, which stands both at zero and at finite temperature. Finally, we compute the axion mass and its self-coupling. In particular, the axion mass ma is related to the full topological susceptibility via χ=ma2fa2; hence our result for χ gives an analytical result for ma in the superconductive phase of high-density Quantum Chromodynamics. Published by the American Physical Society 2024

Holographic Euclidean thermal correlator

In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein’s gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels.

Mass and spectral function of scalar and pseudoscalar mesons in a hot and chirally imbalanced medium using the two-flavor NJL model

We explore the properties of neutral mesons within the context of a chirally imbalanced medium, employing the two-flavor Nambu–Jona-Lasinio model. The temperature dependence of the constituent quark mass at finite values of the chiral chemical potential (CCP) demonstrates the well-established phenomena of chiral catalysis at lower temperatures and inverse chiral catalysis at higher temperatures. The polarization functions in both the scalar (σ) and pseudoscalar (π0) channels have been evaluated using the real-time formalism of thermal field theory. These have been used to determine the masses and spectral functions of σ and π mesons. Detailed investigation of the analytic structure of the imaginary part of the polarization function for σ and π mesons results in the emergence of nontrivial Landau-cut contributions due to the presence of chiral imbalance. The multiple solutions for the mass of the π meson for specific values of CCP have been analyzed on the basis of their residue at the pole. Furthermore, we have observed abrupt changes in the masses of both scalar and pseudoscalar mesons at finite CCP values, particularly at higher temperatures. A decreasing trend in the Mott transition temperature is seen with the increase in CCP. Published by the American Physical Society 2024

On Second Order Rate Regions for the Static Scalar Gaussian Broadcast Channel

This paper considers the single antenna, static, scalar Gaussian broadcast channel in the finite blocklength regime. Second order achievable and converse rate regions are presented. Both a global reliability and per-user reliability requirements are considered. The two-user case is analyzed in detail, and generalizations to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user case are also discussed. The largest second order achievable regions presented here require both superposition and rate splitting in the code construction, as opposed to the (infinite blocklength, first order) capacity region which does not require rate splitting. Indeed, the finite blocklength penalty causes superposition alone to underperform other coding techniques in some parts of the region. In addition, the proposed scheme uses joint simultaneous decoding as opposed to successive interference cancellation. Interestingly, in the two-user case with per-user reliability requirements, the capacity achieving superposition encoding order (with the codeword intended for the user with the smallest received SNR as cloud center) does not necessarily give the largest second order region. Instead, the message of the user with the smallest point-to-point second order capacity should be encoded in the cloud center in order to obtain the largest second order region for the proposed scheme.

Color Processing System of Art Color Based on Fractional Differential Equation

Abstract This paper mainly studies a high-precision correction method for warp knitting seamless images. The color factor conversion method is used to transform the gray level of the center point in the frequency domain. Then this paper proposes an image-denoising method based on an average way to improve image quality. The multichannel scalar channel is solved using the gradient domain method, and the fractional differential equations of two images are given. A structure tensor matrix is constructed to describe the geometric properties of images. The regional contrast of the image is calculated by using the characteristics of adjacent layers of pixels. The fusion of multiple images is based on the limitations of object functionality. This can make the texture structure of artistic color pictures more obvious. The experiment of color restoration shows that this method has a good interpretation effect. The color image processing technique has obtained an excellent restoration effect.

Information Rates for Channels with Fading, Side Information and Adaptive Codewords.

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

Strongly Bound Dibaryon with Maximal Beauty Flavor from Lattice QCD.

We report the first lattice QCD study of the heavy dibaryons in which all six quarks have the bottom (beauty) flavor. Performing a state-of-the-art lattice QCD calculation we find clear evidence for a deeply bound Ω_{bbb}-Ω_{bbb} dibaryon in the ^{1}S_{0} channel, as a pole singularity in the S-wave Ω_{bbb}-Ω_{bbb} scattering amplitude with a binding energy -81( _{-16}^{+14}) MeV. With such a deep binding, Coulomb repulsion serves only as a perturbation on the ground state wave function of the parametrized strong potential and may shift the strong binding only by a few percent. Considering the scalar channel to be the most bound for single flavored dibaryons, we conclude this state is the heaviest possible most deeply bound dibaryon in the visible universe.

A Simple Capacity-Achieving Scheme for Channels With Polarization-Dependent Loss

We demonstrate, for a widely used model of channels with polarization dependent loss (PDL), that channel capacity is achieved by a simple interference cancellation scheme in conjunction with a universal precoder. Crucially, the proposed scheme is not only information-theoretically optimal, but it is also exceptionally simple and concrete. It transforms the PDL channel into separate scalar additive white Gaussian noise channels, allowing off-the-shelf coding and modulation schemes designed for such channels to approach capacity. The signal-to-noise ratio (SNR) penalty incurred under 6 dB of PDL is reduced to the information-theoretic minimum of a mere 1 dB as opposed to the 4 dB SNR penalty incurred under naive over-provisioning.

MEMS co-vibration combined hydrophone

This paper proposes a MEMS co-vibration combined hydrophone (CCH) to position the weak acoustic source of small-volume UUV acoustic self-guided cabins. With an external diameter of 36 mm, it adopts the MEMS triaxial accelerometer to form the vector channel and the MEMS capacitive omnidirectional microphone to form the scalar channel. This paper first analyzes the acoustic receiving model of an elastic-free sphere in water, designs a MEMS co-vibration combined hydrophone packaging and then simulates its acoustic performance. The average density of the encapsulated CCH is 1.01 g/cm3. The vector channel bandwidth is 20 Hz−1,000 Hz, and the sensitivity is −173 dB @ 1 kHz (re 1 V/ μPa) with good cosine directivity. The scalar channel sensitivity is −171 dB @ 1 kHz (re 1 V/ μPa) with omnidirectional directivity. The error of the orientation test in the standing wave tube is less than 1 degree. The sound source-level test results are mostly consistent with the theoretical calculation based on the actual distance. The above results indicate that the hydrophone can be mounted to UUV to perform sound source detection, which can meet the need for precise positioning, and has a specific application value.

Machine learning etudes in conformal field theories

We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and identify a crossing-symmetric four-point function to nearly 100% accuracy. Furthermore, neural networks are also able to identify conformal blocks appearing in a putative CFT four-point function and predict the values of the corresponding operator product expansions (OPE) coefficients. Neural networks also successfully classify primary operators by their quantum numbers under discrete symmetries in the CFT from examining OPE data. We also demonstrate that neural networks are able to learn the available OPE data for scalar correlation function in the 3D Ising model and predict the twists of higher-spin operators that appear in scalar OPE channels by regression.

Private Key and Decoder Side Information for Secure and Private Source Coding.

We extend the problem of secure source coding by considering a remote source whose noisy measurements are correlated random variables used for secure source reconstruction. The main additions to the problem are as follows: (1) all terminals noncausally observe a noisy measurement of the remote source; (2) a private key is available to all legitimate terminals; (3) the public communication link between the encoder and decoder is rate-limited; and (4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region for the lossless case as well. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established. An achievable lossy rate region that can be numerically computed is also provided for binary-input multiple additive discrete-time Gaussian noise measurement channels.

Nucleon isovector couplings in Nf=2+1 lattice QCD at the physical point

We present results for the scalar and tensor isovector-couplings ($g_S$ and $g_T$) of the nucleon measured at the physical point ($M_{\pi}=135$ MeV) with a single lattice spacing of $0.085\ \mathrm{fm}$ in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively ${\cal O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\ {\rm fm})^4$ and $(5.5\ {\rm fm})^4$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of the statistical precision less than 0.5%. We compute the nucleon three-point correlation functions in the vector, axial, scalar, and tensor channels. We confirm that our previous result of the nucleon axial coupling on the large spatial volume of $(10.9\ {\rm fm})^4$ has no finite-size effect at the level of the statistical precision of 1.9%. For the renormalization, we first renormalize $g_S$ and $g_T$ nonperturbatively using the RI/SMOM$_{(\gamma_\mu)}$ scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the intermediate scheme. We evaluate our final results at the renormalization scale of 2 GeV in the $\overline{\rm MS}$ scheme through matching procedure between the RI/SMOM$_{(\gamma_\mu)}$ and $\overline{\rm MS}$ schemes with the help of perturbation theory, and then obtain $g_S=0.927(71)_{\rm stat}(22)_{\rm syst}$ and $g_T=1.036(6)_{\rm stat}(20)_{\rm syst}$.

Hartree-Fock approach to dynamical mass generation in the generalized ( 2+1 )-dimensional Thirring model

The (2+1)-dimensional generalized massless Thirring model with 4-component Fermi-fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector$\times$vector channel of fermion interaction with coupling constant $G_v$, the other - the scalar$\times$scalar channel with coupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearing of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. It is shown that in the particular case of pure Thirring model, i.e. at $G_s=0$, the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi-fields.

Updated constraints on the Georgi-Machacek model and its electroweak phase transition and associated gravitational waves

With theoretical constraints such as perturbative unitarity and vacuum stability conditions and updated experimental data of Higgs measurements and direct searches for exotic scalars at the LHC, we perform an updated scan of the allowed parameter space of the Georgi-Machacek (GM) model. With the refined global fit, we examine the allowed parameter space for inducing strong first-order electroweak phase transitions (EWPTs) and find only the one-step phase transition is phenomenologically viable. Based upon the result, we study the associated gravitational wave (GW) signals and find most of which can be detected by several proposed experiments. We also make predictions on processes that may serve as promising probes to the GM model in the near future at the LHC, including the di-Higgs productions and several exotic scalar production channels.

Cornell potential in generalized soft wall holographic model

We derive and analyze the confinement potential of the Cornell type within the framework of the generalized soft wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the ‘linear plus Coulomb’ confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This result indicates the key role of the vacuum scalar sector in the formation of the confinement potential. As a by-product the overall consistency of our holographic description of confinement potential seems to confirm the glueball nature of the scalar meson f 0(1500).

Vector boson scattering from the lattice

We study vector-boson scattering of the physical, gauge-invariant states in a reduced standard-model setup on the lattice for various parameter sets. To this end, the phase shift in the scalar channel is determined using a L\"uscher-type analysis. The results can be readily interpreted in terms of the Higgs properties and a reunitarized Fr\"ohlich-Morchio-Strocchi analysis at Born level. The only deviation appears for a Higgs mass below the elastic threshold, where we find a negative scattering length indicative of the bound-state nature of the physical scalar degree of freedom. We assess the possible implications for an experimental detection of the effect.

Gaudin models and multipoint conformal blocks III: comb channel coordinates and OPE factorisation

We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratios that are well adapted to perform projections onto all intermediate primary fields. More concretely, our new set of cross ratios includes three for each intermediate mixed symmetry tensor exchange. These variables are designed such that the associated power series expansion coincides with the sum over descendants. The leading term of this expansion is argued to factorise into a product of lower point blocks. We establish this remarkable factorisation property by studying the limiting behaviour of the Gaudin Hamiltonians that are used to characterise multipoint conformal blocks. For six points we can map the eigenvalue equations for the limiting Gaudin differential operators to Casimir equations of spinning four-point blocks.

Gravitational quasinormal modes for Lifshitz black branes

We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by ωshear ∼ −i k4 and ωsound ∼ −i k2, while in the Einstein-Proca model they take the more conventional form ωshear ∼ −i k2 and ωsound ∼ k —the proportionality constants depend on the dynamical exponent and the appropriate factors of temperature. Through the holographic duality, this calculation provides information about the relaxation of the momentum and energy flux operators in a putative dual Lifshitz field theory. Comparing with the dispersion relations obtained directly by considering Lifshitz hydrodynamics suggest that the mass density of the equilibrium state in the Einstein-Maxwell-Dilaton model is infinite.