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DOE OSTI2024

Cosmological implications of Kalb-Ramond-like particles

The Kalb-Ramond field is an antisymmetric, rank-two tensor field which most notably appears in the context of string theory, but has largely been unexplored in the context of cosmology. In this work, motivated by the Kalb-Ramond field in string theory, and antisymmetric tensor fields that emerge in effective field theories ranging from particle physics to condensed matter, we study the primordial production of interacting massive Kalb-Ramond-like-particles (KRLPs). KRLPs contain features of both dark photon and axion models, which can be appreciated via their duality properties. While the massless non-interacting KRLP is dual to a pseudoscalar, and the massive non-interacting KRLP is dual to a pseudovector, the interacting massive KRLP can be distinguished from its scalar and vector counterparts. We study early-universe production of KRLPs via the freeze-in mechanism, considering a ‘dark photon-like’ interaction, an ‘axion-like’ interaction, and a ‘Higgs portal’ interaction, as well as production via cosmological gravitational particle production. We find that as a dark matter candidate, KRLPs can be produced by all of the above mechanisms and account for the relic density of dark matter today for a wide range of masses. Finally, we comment on the potential to obtain both warm and cold dark matter subcomponents, and speculate on observational and experimental prospects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics

We introduce a framework called Heavy Quarkonium Quantum Dynamics (HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution. Using HQQD we compute large sets of real-time solutions to the Schrödinger equation using a realistic in-medium complex-valued potential. We sample 2 million quarkonia wave packet trajectories and evolve them through the QGP using HQQD to obtain their survival probabilities. The computation is performed using three different HQQD model parameter sets in order to estimate our systematic uncertainty. After taking into account final state feed down we compare our results to existing experimental data for the suppression and elliptic flow of bottomonium states and find that HQQD predictions are good agreement with available data for R AA as a function of N part and p T collected at \( \sqrt{s_{\mathrm{NN}}} \) = 5 . 02 TeV. In the case of v 2 for the various states, we find that the path-length dependence of ϒ(1 s ) suppression results in quite small v 2 for ϒ(1 s ). Our prediction for the integrated elliptic flow for ϒ(1 s ) in the 10 – 90% centrality class, which now includes an estimate of the systematic error, is v 2 [ϒ(1 s )] = 0 . 003 ± 0 . 0007 ± \( {}_{0.0013}^{0.0006} \) . We also find that, due to their increased suppression, excited bottomonium states have a larger elliptic flow. Based on this observation we make predictions for v 2 [ϒ(2 s )] and v 2 [ϒ(3 s )] as a function of centrality and transverse momentum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Towards universal unfolding of detector effects in high-energy physics using denoising diffusion probabilistic models

Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability, flexibility, and dependence on simulations. We introduce a novel approach to multidimensional object-wise unfolding using conditional Denoising Diffusion Probabilistic Models (cDDPM). Our method utilizes the cDDPM for a non-iterative, flexible posterior sampling approach, incorporating distribution moments as conditioning information, which exhibits a strong inductive bias that allows it to generalize to unseen physics processes without explicitly assuming the underlying distribution. Our results highlight the potential of this method as a step towards a "universal" unfolding tool that reduces dependence on truth-level assumptions, while enabling the unfolding of a wide range of measured distributions with improved adaptability and accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations

The charge-conjugation and parity-reversal (CP) symmetry of fundamental particles is a symmetry between matter and antimatter. Violation of this CP symmetry was first observed in 1964, and CP violation in the weak interactions of quarks was soon established. Sakharov proposed that CP violation is necessary to explain the observed imbalance of matter and antimatter abundance in the Universe. Yet, CP violation in quarks is too small to support this explanation. So far, CP violation has not been observed in non-quark elementary particle systems. It has been shown that CP violation in leptons could generate the matter–antimatter disparity through a process called leptogenesis. Leptonic mixing, which appears in the standard model’s charged current interactions, provides a potential source of CP violation through a complex phase δ CP , which is required by some theoretical models of leptogenesis. This CP violation can be measured in muon neutrino to electron neutrino oscillations and the corresponding antineutrino oscillations, which are experimentally accessible using accelerator-produced beams as established by the Tokai-to-Kamioka (T2K) and NOvA experiments. Until now, the value of δ CP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δ CP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3σ). The 3σ confidence interval for δ CP , which is cyclic and repeats every 2π, is [-3.41, -0.03] for the so-called normal mass ordering and [-2.54, -0.32] for the inverted mass ordering. Our findings indicate CP violation in leptons and our method enables sensitive searches for matter–antimatter asymmetry in neutrino oscillations using accelerator-produced neutrino beams. Future measurements with larger datasets will test whether leptonic CP violation is larger than the CP violation in quarks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

SHAPER: can you hear the shape of a jet?

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover’s Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A Continuous Galactic Line Source of Axions: The Remarkable Case of 23 Na

Here, we argue that $^{23}$Na is a potentially significant source of galactic axions. For temperatures $\gtrsim 7 \times 10^8$K -- characteristic of carbon burning in the massive progenitors of supernovae and ONeMg white dwarfs -- the 440 keV first excited state of $^{23}$Na is thermally populated, with its repeated decays pumping stellar energy into escaping axions. Odd-A nuclear abundances are typically very low in high-temperature stellar environments (or absent entirely due to burn-up). $^{23}$Na is an exception: $\approx 0.1 M_\odot$ of the isotope is synthesized during carbon burning then maintained at $\approx 10^9$K for times ranging up to $6 \times 10^4$y. Using MESA simulations, a galactic model, and sampling over progenitor masses, locations, and evolutionary stages, we find a continuous flux at earth of $\langle ϕ_a \rangle \approx 22$/cm$^2$s for $g^\mathrm{eff}_{aNN} = 10^{-9}$. Some fraction of these axions convert to photons as they propagate through the galactic magnetic field, producing a distinctive 440 keV line $γ$ ray detectable by all-sky detectors like the Compton Spectrometer and Imager (COSI). Assuming a 1$μ$G galactic magnetic field and a sufficiently light axion mass, we find that COSI will be able to probe $| g_{aNN}^\mathrm{eff} g_{a γγ} | \gtrsim1.8 \times 10^{-22}$ GeV$^{-1}$ at $3σ$ after two years of surveying.

Dark matter↗
DOE OSTI2024

Pion gravitational form factors in the QCD instanton vacuum. I

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q 2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

AI for nuclear physics: the EXCLAIM project

An overview of the recent activity of the newly funded EXCLusives with AI and Machine learning (EXCLAIM) collaboration is presented. The main goal of the collaboration is to develop a framework to implement AI and machine learning techniques in problems emerging from the phenomenology of high energy exclusive scattering processes from nucleons and nuclei, maximizing the information that can be extracted from various sets of experimental data, while implementing theoretical constraints from lattice QCD. A specific perspective embraced by EXCLAIM is to use the methods of theoretical physics to understand the working of ML, beyond its standardized applications to physics analyses which most often rely on industrially provided tools, in an automated way.

Analysis and statistical methods↗
DOE OSTI2025

Thermodynamics of continuous spin photons

Special relativity allows massless particles to have states of different integer (or half-integer) helicities that mix under boosts, much like the spin states of a massive particle. Such massless particles are known as “continuous spin” particles (CSPs), a term coined by Wigner, and they are notable for their infinite tower of spin polarizations. The mixing under boosts is controlled by a spin scale 𝜌 with units of momentum. Normally, we assume 𝜌 = 0. The interactions of CSPs are known to satisfy certain simple properties, one of which is that the 𝜌 → 0 limit generically recovers familiar interactions of massless scalars, photons, or gravitons, with all other polarizations decoupling in this limit. Thus, one can ask if the photon of the Standard Model is a CSP at small but nonzero 𝜌. One concern about this possibility—originally raised by Wigner—is that the infinite tower of polarizations could pose problems for thermodynamics. To address this question, we study the thermal evolution of a CSP photon gas coupled to isothermal matter, across CSP helicity modes and phase space. We find that the structure of the interactions dictated by Lorentz symmetry implies well-behaved thermodynamics. When the CSP photon’s interactions with charged matter are turned on, the primary ℎ =±1 helicity modes thermalize quickly, while the other modes require increasingly long time scales to thermalize, set by powers of 𝑇/𝜌. In familiar thermal systems, the CSP photon behaves like the QED photon with small 𝜌- and time-dependent corrections to its effective relativistic degrees of freedom. Sizable departures from familiar thermal behavior arise at energy scales comparable to 𝜌 and could have testable experimental consequences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

New physics particles mixing with mesons: Production in the fragmentation chain

A class of extensions to the Standard Model adds hypothetical long-lived particles (LLPs) that have mass- or kinetic-mixing with neutral mesons, such as pions or rho mesons. The mixing can contribute significantly to the production of LLPs at proton accelerator experiments, and no consistent description of these production modes exists in the literature. In this paper, we develop a framework for studying different LLPs—dark photons, vector mediators coupled to the baryon current, and axionlike particles with different coupling patterns. In particular, we implement the production mechanisms in PYTHIA 8, study how the overall flux and kinematic distributions depend on the LLP’s mass, and compare various subprocesses where the mixing contributes—proton bremsstrahlung, meson decay, and production in the fragmentation chain. We find that our new description of LLP production predicts an integrated flux that differs from current approaches by one to two orders of magnitude, and highlight the unavoidable theoretical uncertainties coming from poor knowledge of the properties of heavy mesons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

The cosmological moduli problem and naturalness

Nowadays, the cosmological moduli problem (CMP) comes in three parts: 1. potential violation of Big-Bang nucleosynthesis (BBN) constraints from late decaying moduli fields, 2. the moduli-induced gravitino problem wherein gravitinos are overproduced and their decays violate BBN or dark matter overproduction bounds and 3. the moduli-induced lightest SUSY particle (LSP) overproduction problem. Also, the CMP may be regarded as either a problem or else a solution to scenarios with dark matter over- or under-production. We examine the cosmological moduli problem and its connection to electroweak naturalness. We calculate the various two-body decay widths of a light modulus field into MSSM particles and gravitinos within general supersymmetric models. We include both phase space and mixing effects. We examine cases without and with helicity suppression of modulus decays to gravitinos (cases 1 & 2) and/or gauginos (cases A & B). For case B1, we evaluate regions of gravitino mass m 3/2 vs. modulus mass mΦ parameter space constrained by BBN, by overproduction of gravitinos and by overproduction of neutralino dark matter, along with connections to naturalness. For this case, essentially all of parameter space is excluded unless mΦ ≳ 2.5 × 10 3 TeV with mΦ< 2m 3/2 For a potentially most propitious case B2 with Φ decay to Higgs and matter turned off, then modulus branching fractions to SUSY and to gravitinos become highly suppressed at large m Φ . But since the modulus number density increases faster than the branching fractions decrease, there is still gross overproduction of neutralino dark matter. We also show that in this scenario the thermally produced gravitino problem is fixed by huge entropy dilution, but non-thermal gravitino production from moduli decay remains a huge problem unless it is kinematically suppressed with m Φ < 2m 3/2 . In a pedagogical appendix, we present detailed calculations of modulus field two-body decay widths.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

On the Prediction of Uniaxial Tensile Behavior Beyond the Yield Point of Wrought and Additively Manufactured Ti-6Al-4V

In this paper, phenomenological relationships are presented that permit the prediction of the plastic regime of stress–strain curves using a limited number of parameters. These relationships were obtained from both conventional (wrought + β annealed) and additively manufactured (i.e., “3D printed”) Ti-6Al-4V. Three different methods of additive manufacturing have been exploited to produce the materials, including large-volume electron beam additive manufacturing, large-volume laser hot wire additive manufacturing, and small-volume selective laser melting. The general fundamental expressions are independent not only of the additive manufacturing process, but also of a wide variety of post-deposition heat treatments, however the coefficients are specific to material states. Thus, this work demonstrates that it is possible to predict not only the ultimate tensile strength, but also the full true stress, true strain curves, if certain parameters of the material are known. In general, the prediction of ultimate tensile strength are within 5% of the experimentally measured values across all additive manufacturing variants and subsequent heat treatments. The absolute values of ultimate tensile strength range from ~ 910 MPa to ~ 1170 MPa for the single alloy Ti-6Al-4V. Data representing 113 explicit samples are included in this work.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The ABC of RPV: classification of R-parity violating signatures at the LHC for small couplings

We perform a classification of all potential supersymmetric R-parity violating signatures at the LHC to address the question: are existing bounds on supersymmetric models robust, or are there still signatures not covered by existing searches, allowing LHC scale supersymmetry to be hiding? We analyze all possible scenarios with one dominant RPV trilinear coupling at a time, allowing for arbitrary LSPs and mass spectra. We consider direct production of the LSP, as well as production via gauge-cascades, and find 6 different experimental signatures for the $LL\overline{E}$-case, 6 for the $LQ\overline{D}$-case, and 5 for the $\overline{U}$ $\overline{D}$ $\overline{D}$-case; together these provide complete coverage of the RPV-MSSM landscape. This set of signatures is confronted with the existing searches by ATLAS and CMS. We find all signatures have been covered at the LHC, although not at the sensitivity level needed to probe the direct production of all LSP types. For the case of a dominant $LL\overline{E}$-operator, we use CheckMATE to quantify the current lower bounds on the supersymmetric masses and find the limits to be comparable to or better than the R-parity conserving case. Our treatment can be easily extended to scenarios with more than one non-zero RPV coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction

Antimatter cosmic-rays are used to probe new phenomena in physics, including dark matter annihilation. Here, we use the cosmic-ray positron fraction spectrum by the Alpha Magnetic Spectrometer, to search for such an annihilation signal in the Galaxy. We focus on dark matter with mass between 5 and 120 GeV, producing high-energy electrons and positrons. In these cosmic-ray energies the interplay of multiple astrophysical sources and phenomena, makes this search highly sensitive to the underlying astrophysical background assumptions. We use a vast public library of astrophysical models for the cosmic-ray positron fraction background, to derive robust upper limits on the dark matter's annihilation cross section for a number of annihilation channels. This library accounts for different types of cosmic-ray sources and uncertainties on their distribution in space and time. Also, it accounts for uncertainties on those sources' output, their injected into the interstellar medium cosmic-ray spectra and for uncertainties on cosmic-ray propagation. For any given dark matter particle mass and annihilation channel, upper limits on the annihilation cross section are given by bands that stretch a full order of magnitude in its value. Our work provides weaker limits compared to earlier results, that are however robust to all the relevant astrophysical uncertainties. Between 5 and 15 GeV, we find indications for a possible excess flux of cosmic-ray electrons and positrons. That excess is found for most, but not all of our astrophysical background parameter space, and its significance can vary appreciably. Further scrutiny is necessary to improve the understanding of these lower energy cosmic rays. Finally, we note that even if an excess signal is found in these energies, the current background uncertainties do not allow us to accurately deduce its underlying particle properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space Telescope

The Nancy Grace Roman Space Telescope will conduct a High Latitude Spectroscopic Survey (HLSS) over a large volume at high redshift, using the near-IR grism (1.0–1.93 μm, R = 435–865) and the 0.28 deg 2 wide-field camera. We present a reference HLSS that maps 2000 deg 2 and achieves an emission-line flux limit of 10 -16 erg s -1 cm -2 at 6.5σ, requiring ~0.6 yr of observing time. We summarize the flowdown of the Roman science objectives to the science and technical requirements of the HLSS. We construct a mock redshift survey over the full HLSS volume by applying a semianalytic galaxy formation model to a cosmological N-body simulation and use this mock survey to create pixel-level simulations of 4 deg 2 of HLSS grism spectroscopy. We find that the reference HLSS would measure ~10 million H α galaxy redshifts that densely map large-scale structure at z = 1–2 and 2 million [O III] galaxy redshifts that sparsely map structures at z = 2–3. We forecast the performance of this survey for measurements of the cosmic expansion history with baryon acoustic oscillations and the growth of large-scale structure with redshift-space distortions. We also study possible deviations from the reference design and find that a deep HLSS at f line > 7 × 10 -17 erg s -1 cm -2 over 4000 deg 2 (requiring ~1.5 yr of observing time) provides the most compelling stand-alone constraints on dark energy from Roman alone. This provides a useful reference for future optimizations. The reference survey, simulated data sets, and forecasts presented here will inform community decisions on the final scope and design of the Roman HLSS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Beam-dump ceiling and its experimental implications: The case of a portable experiment

We generalize the nature of the so-called beam-dump “ceiling” beyond which the improvement on the sensitivity reach in the search for fast-decaying mediators dramatically slows down, and we point out its experimental implications that motivate tabletop-sized beam-dump experiments for the search. Light (bosonic) mediators are well-motivated new-physics particles, as they can appear in dark-sector portal scenarios and models to explain various laboratory-based anomalies. Due to their low mass and feebly interacting nature, beam-dump-type experiments, utilizing high-intensity particle beams, can play a crucial role in probing the parameter space of such visibly decaying mediators—in particular, the “prompt decay” region, where the mediators feature relatively large coupling and mass. We present a general and semianalytic proof that the ceiling effectively arises in the prompt-decay region of an experiment and show its insensitivity to data statistics, background estimates, and systematic uncertainties, considering a concrete example, the search for axion-like particles interacting with ordinary photons at three benchmark beam facilities: PIP-II at FNAL, and SPS and LHC-dump at CERN. We then identify optimal criteria to perform a cost-effective and short-term experiment to reach the ceiling, demonstrating that very short-baseline compact experiments enable access to the parameter space unreachable thus far.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Dark Matter searches with photons at the LHC

We unveil blind spot regions in dark matter (DM) direct detection (DMDD), for weakly interacting massive particles with a mass around a few hundred GeV that may reveal interesting photon signals at the LHC. We explore a scenario where the DM primarily originates from the singlet sector within the Z 3 -symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM). A novel DMDD spin-independent blind spot condition is revealed for singlino-dominated DM, in cases where the mass parameters of the higgsino and the singlino-dominated lightest supersymmetric particle (LSP) exhibit opposite relative signs (i.e., κ < 0), emphasizing the role of nearby bino and higgsino-like states in tempering the singlino-dominated LSP. Additionally, proximate bino and/or higgsino states can act as co-annihilation partner(s) for singlino-dominated DM, ensuring agreement with the observed relic abundance of DM. Remarkably, in scenarios involving singlino-higgsino co-annihilation, higgsino-like neutralinos can distinctly favor radiative decay modes into the singlino-dominated LSP and a photon, as opposed to decays into leptons/hadrons. In exploring this region of parameter space within the singlino-higgsino compressed scenario, we study the signal associated with at least one relatively soft photon alongside a lepton, accompanied by substantial missing transverse energy (E T ) and a hard initial state radiation jet at the LHC. In the context of singlino-bino co-annihilation, the bino state, as the next-to-LSP, exhibits significant radiative decay into a soft photon and the LSP, enabling the possible exploration at the LHC through the triggering of this soft photon alongside large E T and relatively hard leptons/jets resulting from the decay of heavier higgsino-like states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Mixing effects on spectroscopy and partonic observables of heavy mesons with logarithmic confining potential in a light-front quark model

Using the variational principle, we systematically investigate the mass spectra and wave functions of both 1⁢𝑆 and 2⁢𝑆 state heavy pseudoscalar (𝑃) and vector (𝑉) mesons within the light-front quark model. This approach incorporates a Coulomb plus logarithmic confinement potential to accurately describe the constituent quark and antiquark dynamics. Additionally, spin hyperfine interactions are introduced perturbatively to compute the masses of pseudoscalar and vector mesons. The present analyses of the 1⁢𝑆 and 2⁢𝑆 states require the consideration of mixing between them to account for empirical constraints. These constraints include the mass gap Δ⁢𝑀 𝑃 >Δ⁢𝑀 𝑉 , where Δ⁢𝑀 𝑃⁡(𝑉) =𝑀$^{2⁢𝑆}_{𝑃⁡(𝑉)}$−𝑀$^{1⁢𝑆}_{𝑃⁡(𝑉)}$ and the hierarchy of the decay constants 𝑓 1⁢𝑆 >𝑓 2⁢𝑆 . We find the optimal value of the mixing angle to be 𝜃 =1⁢8°, significantly enhancing the consistency between our spectroscopic predictions and the experimental data compiled by the Particle Data Group. Furthermore, based on the predicted mass, the newly observed resonance 𝐵 𝐽⁡ (5840) could be assigned as a 2 1⁢ 𝑆 0 state in the 𝐵 meson family. The study also reports various pertinent observables, including twist-two distribution amplitudes, electromagnetic form factors, charge radii, 𝜉 moments, and transition form factors that are found to be consistent with both available lattice simulations and experimental data. In addition, our predicted branching ratios for the channels of 𝐵 + →𝜏 + ⁢𝜈 𝜏 as well as rare decays of 𝐵 0 and 𝐵$^0_𝑠$ appear in accordance with experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗