The standard model of the universe, $\lambda \mathrm{CDM}$, is based on the Friedmann-Lemaître-Robertson-Walker metric with a flat three-dimensional coordinate space and the Friedmann equations Navas et al. [Phys. Rev. D 110, 030001 (2024).]. The cosmological constant $\lambda$ provides the cancellation of the matter field contributions in the flat (Minkowski) space, as was proposed long ago in 1967 by Zeldovich for the first time to our knowledge Zeldovich [JETP Lett. 6, 316 (1967)]; see also Krasinski and Zeldovich [Sov. Phys. Usp. 11, 381 (1968)]. The dynamical dark energy appears on the surface of the vacuum energy of matter fields at the flat (Minkowski) space. Within the Standard Model, the gluon Yang-Mills (YM) fields are playing a specific role since the properties of their vacuum, where there is the presence of the gluon condensate, provide the nonperturbative vacuum energy. It is natural to apply the successful instanton liquid model of the QCD vacuum and its lowest excitations. Our aim is to calculate the contribution of gluon YM fields to the dark energy density. We find that the universe metric is generating the QCD vacuum excitation, which gives the contribution to the dark energy density. But this one may hardly play a central role in the dynamics of the universe, since its timescale is too small. We also find the equation-of-state parameters $w_0=-1,w_a=0$ in accordance with $\lambda \mathrm{CDM}$, while the newest data, analyzed at Shajib and Frieman [Phys. Rev. D 112, 063508 (2025).], give them at least in the range $-0.91<w_0<-0.73,-1.05<w_a<-0.65$. They are requesting a contribution from an ultralight scalar such as an axion, or from YM field topological configurations with the nontrivial holonomy due to the deviation from a pure de Sitter state Van Waerbeke and Zhitnitsky [DESI results and dark energy from QCD topological sectors, arXiv:2506.14182.].

We present a reanalysis of 17 gravitational wave events detected with Advanced LIGO and Advanced Virgo in their first three observing runs, using the new IMRPhenomTEHM model—a phenomenological time-domain multipolar waveform model for aligned-spin black hole binaries in elliptical orbits with two eccentric parameters: eccentricity and mean anomaly. We also analyze all events with the underlying quasicircular model IMRPhenomTHM to study the impact of including eccentricity and compare the eccentric and quasicircular binary hypotheses. The high computational efficiency of IMRPhenomTEHM enables us to explore the impact of two different eccentricity priors—uniform and log-uniform—as well as different sampler and data settings. We find evidence for eccentricity in two publicly available LIGO-Virgo-KAGRA events, GW200129 and GW200208_22, with Bayes factors favoring the eccentric hypothesis over the quasicircular aligned-spin scenario: ${\log }_{10}{\mathcal{B}}_{\mathrm{E}/\mathrm{QC}}\in [1.30_{-0.15}^{+0.15},5.14_{-0.15}^{+0.15}]$ and ${\log }_{10}{\mathcal{B}}_{\mathrm{E}/\mathrm{QC}}\in [0.49_{-0.08}^{+0.08},1.14_{-0.08}^{+0.08}]$, respectively. Additionally, the two high-mass events GW190701 and GW190929 exhibit potential eccentric features. For all four events, we conduct further analyses to study the impact of different sampler settings. We also investigate waveform systematics by exploring the support for spin precession using IMRPhenomTPHM and NRSur7dq4, offering new insights into the formation channels of detected binaries. Our results highlight the importance of considering eccentric waveform models in future observing runs, alongside precessing models, as they can help mitigate potential biases in parameter estimation studies. This will be particularly relevant with the expected increase in the diversity of the binary black hole population with new detectors.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling $A(\varphi )$ and chameleon/Vainshtein screening, we map cosmological responses $\{\mu (z,k),\mathrm{\Sigma }(z,k)\}$ inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials ${\mathrm{\Phi }}_N$. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly—an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with $|\gamma -1|\sim \mathrm{few}\times {10}^{-6}$, an AU-scale Yukawa tail, or a narrowband ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS)—triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization $\{V(\varphi ),A(\varphi )\}$. In a guardrail branch, Solar-System tests enforce universal constraints (EEP; PPN parameters $\gamma$, $\beta$; and $\dot{G}/G$) and close unscreened or weakly screened corners indicated by cosmology. Under realistic near-term conditions we forecast, per conjunction, $|\gamma -1|\lesssim (2-5)\times {10}^{-6}$ (Ka-/X-band or optical Shapiro), ${\eta }_{\mathrm{EEP}}\sim (1-10)\times {10}^{-17}$ (drag-free AIS), $|\dot{G}/G|\sim (3-5)\times {10}^{-15}\mathrm{y}{\mathrm{r}}^{-1}$ [sub-mm-class lunar laser ranging (LLR)], a uniform $\simeq 2\times$ tightening of AU-scale Yukawa/DM-density bounds, and $(3-10)\times$ improved ULDM-coupling reach from clock networks. For a conformal benchmark, ${\mu }_{\mathrm{lin},0}=0.10$ implies $\chi \simeq \sqrt{{\mu }_{\mathrm{lin},0}/2}$ and a Sun thin shell $\mathrm{\Delta }R/R\lesssim (1/3\chi )\sqrt{|\gamma -1|/2}=2.4\times {10}^{-3}$ at $|\gamma -1|=5\times {10}^{-6}$; Vainshtein screening at 1 AU yields $|\gamma -1|\lesssim {10}^{-11}$, naturally below near-term reach. We recommend a cost-effective $\mathrm{guardrail}+\mathrm{discovery}$ portfolio with explicit triggers for escalation to dedicated missions.

Strong gravitational lensing is a powerful cosmological probe, providing a direct tool to unveil the properties of dark matter (DM) on subgalactic scales. In particular, flux-ratio anomalies in quadruply imaged quasars (“quads”) can reveal the presence of dark substructure, such that population-level statistics can be used to constrain the particle nature of DM. Current methods, however, rely on globally parametrized models (“macromodels”) of the lens mass distribution, which impose rigid physical assumptions on the deflection field. Given the high stakes, it is important to develop complementary methods that do not require the assumption of a macromodel. One promising avenue consists of modeling the resolved emission from the quasar host galaxy (lensed arcs) using a local lensing formalism like the curved arc basis (CAB) description. This method effectively imposes minimal priors on the mass distribution within the lens galaxy and thus will provide conservative error estimates on the inferred DM properties. In this paper, we test the ability of CAB models to predict flux ratios from mock imaging data. We find that the CAB model-predicted flux ratios accurately reproduce the expected values, with a typical precision of $\sim 3\%–5\%$. While a macromodel-based approach yields smaller uncertainties, as expected, the CAB method permits a more flexible, local description of the deflection field, thus being more robust to angular structure in the main deflector mass profile, in particular avoiding false-positive detections of flux-ratio anomalies that can arise with overly simplistic parametrizations. On the other hand, by injecting individual DM halos near quasar images, we demonstrate that CAB models do not absorb the local lensing perturbations from DM substructure, and can therefore distinguish flux-ratio anomalies caused by DM substructure from other sources of small-scale perturbation. We conclude that CAB lens models can be used to infer DM properties from flux-ratio anomaly statistics with minimal assumptions, complementing the traditional macromodel-based approach.

The equation of state of dense matter remains a central challenge in astrophysics and high-energy physics, particularly at supranuclear densities where exotic degrees of freedom like hyperons or deconfined quarks are expected to appear. Neutron stars provide a unique natural laboratory to probe this regime. In this work, we present EVA–01, a novel equation of state that provides a unified description of dense matter by incorporating both hadron and quark degrees of freedom within a single relativistic mean-field Lagrangian, from which the equation of state is derived at finite temperature. The model extends the density-dependent formalism by introducing a Polyakov-loop-inspired scalar field to dynamically govern the hadron-quark phase transition, following the approach of chiral mean-field models. The resulting model is consistent with a wide range of theoretical and observational constraints, including those from chiral effective field theory, massive pulsars, gravitational-wave events, and NICER data. We analyze its thermodynamic properties by constructing the QCD phase diagram, identifying the deconfinement, chiral, and nuclear liquid-gas transitions. As a first application, we model the evolution of protoneutron stars using isentropic snapshots and explore the implications of the slow stable hybrid star hypothesis. Our findings establish EVA–01 as a robust and versatile framework for exploring dense matter, bridging the gap between microphysical models and multimessenger astrophysical observations.

Gravitational-wave detectors use state-of-the-art quantum technologies to reduce the noise induced by vacuum fluctuations, via injection of squeezed states of light. Future detectors, such as Einstein Telescope, may require the use of two filter cavities or a three-mirror coupled filter cavity to achieve a complex rotation of the squeezing ellipse, in order to reduce the quantum noise over the whole detector bandwidth. In this work, we compare the theoretical feasibility and performances of these two optical layouts and their resilience with respect to different degradation sources (optical losses, mismatching, locking precision), analytically and numerically. We extend previous analysis on squeezing degradation and find that the coupled cavity scheme provides similar or better performances than the two-cavity option, in terms of resilience with respect to imperfections and optical losses. We further highlight the role of mode-mismatch phases in limiting squeezing. Finally, we propose a possible two-step implementation scheme for Einstein Telescope using a single filter cavity that can be possibly upgraded into a coupled filter cavity.

Inspired by the significant virtual contributions of the subprocesses $D^{*}/B^{*}\to D\pi$ and $\rho \to \omega \pi /K\overline{K}$ in the three-body hadronic $B$ meson decays, we study the off-shell effects of the resonance $K^{*}$ decaying into the $K^{*}\pi$ or $K\rho$ system in the decays $B\to K^{*}\pi h$ and $B\to K\rho h$ (with $h=\pi ,K$) within the perturbative QCD approach. The strong coupling constants $g_{K^{*}{K}^{*}\pi }$ and $g_{K^{*}K\rho }$ involved in this work are derived from the coupling constant $g_{\rho \omega \pi }$ under the flavor SU(3) symmetry. The $CP$ averaged branching fractions for the quasi-two-body decays $B\to K^{*}[\to K^{*}\pi ]h$ and $B\to K^{*}[\to K\rho ]h$ are predicted to be on the order of ${10}^{-9}$ to ${10}^{-7}$ in this study. And the branching fractions for the decays $B\to K^{*}[\to K\rho ]h$ are found to be around half of the corresponding results for the $B\to K^{*}[\to K^{*}\pi ]h$ channels, mainly due to the phase space difference between the $K\rho$ and $K^{*}\pi$ pairs originating from the intermediate state $K^{*}$. Experimental data for the $K^{*}$ decaying into the final states $K^{*}\pi$ and $K\rho$ in the $B$ meson decays is expected to be obtained by the LHCb and Belle-II experiments in the near future.

We calculate the collisional energy loss and momentum diffusion coefficients of heavy quarks traversing a hot and dense QCD medium at finite quark chemical potential, $\mu \ne 0$. The analysis is performed within an extended soft-hard factorization model that consistently incorporates the $\mu$-dependence of the Debye screening mass $M_D(\mu )$ and of the fermionic thermal distribution functions. Both the energy loss and the diffusion coefficients are found to increase with $\mu$, with the enhancement being most pronounced at low temperatures where the chemical potential effects dominate the medium response. To elucidate the origin of this dependence, we derive analytic high-energy approximations in which the leading $\mu$-corrections appear as logarithmic terms: a soft logarithm $\sim {\mu }^2\ln (|t^{*}|/M_D^2)$ from $t$-channel scattering off thermal gluonic excitations, and a hard logarithm $\sim {\mu }^2\ln (E_{1}T/|t^{*}|)$ from scattering off thermal quarks. In the complete result the dependence on the intermediate separation scale $t^{*}$ cancels, as required. We also confirm the expected mass hierarchy $-dE/dz(\mathrm{charm})<-dE/dz(\mathrm{bottom})$ at fixed velocity. Our findings demonstrate that finite chemical potential plays a significant role in heavy-quark transport and must be included in theoretical descriptions of heavy-flavor dynamics in baryon-rich environments, such as those probed in the RHIC Beam Energy Scan, and at FAIR and NICA.

Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The $Z_{\mathcal{N}}$ QCD axion model reduces the QCD axion mass naturally, by invoking a discrete $Z_{\mathcal{N}}$ symmetry through which the axion field is coupled to $\mathcal{N}$ copies of the Standard Model. Before the QCD phase transition at temperature $T_{\mathrm{QCD}}$, the $Z_{\mathcal{N}}$ potential has a minimum at misalignment angle $\theta =\pi$. At $T_{\mathrm{QCD}}$, $\theta =\pi$ becomes a maximum; the axion potential becomes exponentially suppressed and develops $\mathcal{N}$ minima—only one of which actually solves the strong $CP$ problem. Before $T_{\mathrm{QCD}}$, $\theta$ relaxes toward $\pi$. After $T_{\mathrm{QCD}}$, the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the $Z_{\mathcal{N}}$ QCD axion using $\mathcal{C}$osmo$\mathcal{L}$attice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong $CP$ problem tends to diverge considerably from the naïve expectation of $1/\mathcal{N}$.

The $R^2$-Higgs inflation is one of the simplest yet best-fit models consistent with Planck data. The higher spectral index $n_s$ recently reported by the combined cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT), and Planck, along with baryonic acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI), disfavors the single-field-like regime of $R^2$-Higgs inflation at approximately $2\sigma$. Following a doubly covariant formalism, we show that the $R^2$-Higgs inflation, when modified by a dimension-six $R^3$ term, can account for the high $n_s$ reported by $\mathrm{CMB}+\mathrm{BAO}$. In this regard, we find that preheating may play a pivotal role. We also show that if the nonminimal coupling between the Ricci scalar $R$ and the Higgs field is $\mathcal{O}(10)$, then preheating via the production of Higgs quanta may help explain the reported observations.

We present a novel application of a qubit-coupled phonon detector to search for new physics, e.g., ultralight dark matter (DM) and high-frequency gravitational waves. The detector, motivated by recent advances in quantum acoustics, is composed of superconducting transmon qubits coupled to high-overtone bulk acoustic resonators ($h\mathrm{BARs}$) and operates in the $\mathrm{GHz}-10\mathrm{GHz}$ frequency range. New physics can excite $\mathcal{O}(10\mathrm{\mu }\mathrm{eV})$ phonons within the $h\mathrm{BAR}$, which are then converted to qubit excitations via a transducer. We detail the design, operation, backgrounds, and expected sensitivity of a prototype detector, as well as a next-generation detector optimized for new physics signals. We find that a future detector can complement current haloscope experiments in the search for both dark photon DM and high-frequency gravitational waves. Lastly, we comment on such a detector’s ability to operate as a $\mathcal{O}(10\mathrm{\mu }\mathrm{eV})$ athermal phonon sensor for sub-GeV DM detection.

We propose an explanation for the recently reported ultrahigh-energy neutrino signal at KM3NeT, which shows no clear association with known astrophysical sources. While decaying dark matter in the Galactic Center is a natural candidate, the observed arrival direction strongly suggests an extragalactic origin. We introduce a multicomponent dark matter scenario in which the components are part of a supermultiplet, with supersymmetry ensuring a nearly degenerate mass spectrum among the fields with different spins. In this setup, a cosmologically long-lived fermionic state decays into a slightly lighter bosonic dark matter state, producing a boosted neutrino spectrum with energy $E_{\nu }\sim 100\mathrm{PeV}$, determined by the mass difference. The heavy-to-light decay occurs at a cosmological redshift of $z\sim \mathrm{a}\mathrm{few}$ or higher, leading to an isotropic directional distribution of the signal.

We investigate the search for doubly charged Higgs bosons in the Georgi-Machacek (GM) model at same-sign lepton colliders. The dominant production mode is vector boson fusion, through which the particle is singly produced and decays into a pair of same-sign $W$ bosons if the triplet vacuum expectation value is sufficiently large, as allowed in the GM model. Considering the leptonic decays of the $W$ bosons, we discuss the discovery reach of the signal and a method to extract the mass of the doubly charged Higgs boson. It is impossible to construct the transverse mass of the decay product to obtain the mass because of the neutrinos radiated from the initial-state leptons. Alternatively, we propose to make use of the invariant mass of the same-sign leptons. We perform ${\chi }^2$ fitting using the analytical formula for the invariant mass distribution and demonstrate that this approach is effective in extracting the information on the mass. We also compare the process with pair production processes at the opposite-sign lepton colliders.

Interference effects in effective field theory (EFT) analyses can significantly distort sensitivity expectations, leaving subtle yet distinct signatures in the reconstruction of final states crucial for limit setting around Standard Model predictions. Using the specific example of four-fermion operators in top-quark pair production at the Large Hadron Collider (LHC), we provide a detailed quantitative assessment of these resonance distortions. We explore how continuum four-fermion interactions affect the resonance shapes, creating potential tensions between the high-statistics resonance regions and rare, high momentum-transfer continuum excesses. Our findings indicate that, although four-fermion interactions do modify the on-shell region comparably to continuum enhancements, current experimental strategies at the high-luminosity LHC are unlikely to capture these subtle interference-induced distortions. Nonetheless, such effects could become critical for precision analyses at future lepton colliders, such as the FCC-ee. Our work underscores the importance of resonance-shape measurements as complementary probes in global EFT approaches, guiding robust and self-consistent experimental strategies in ongoing and future high-energy physics programs.

NuMI Off-axis ${\nu }_e$ Appearance (NOvA) experiment is an ongoing long-baseline neutrino oscillation experiment. The primary channels of interest are the ${\nu }_e$, ${\overline{\nu }}_e$ appearance, ${\nu }_{\mu }$, ${\overline{\nu }}_{\mu }$ disappearance channels analyzed in the energy window $1<E_{\nu }<4\mathrm{GeV}$. However, NOvA far detector sees nontrivial high-energy ${\nu }_e$, ${\overline{\nu }}_e$ events in the energy range $4<E_{\nu }<20\mathrm{GeV}$. These high-energy events provide us with an opportunity to investigate the subleading new physics scenarios. In this context, we study the sensitivity of the NOvA experiment to constrain the nonstandard interaction (NSI) parameters and environmental decoherence parameters. We observe that by including high energy events ($\mathrm{signal}+\text{background}$) the degeneracy around ${\epsilon }_{e\tau }\sim 1.6$ can be removed throughout the ${\delta }_{CP}$ and ${\delta }_{e\tau }$ range. Further, we examine the role of signal versus beam background events in removing this degeneracy. In addition, we constrain the decoherence parameter $\mathrm{\Gamma }$ considering events from $1<E_{\nu }<20\mathrm{GeV}$. Later, assuming the presence of decoherence in nature we obtain the allowed regions in ${\theta }_{23}$ and ${\delta }_{CP}$ plane.

Within the framework of the generalized linear sigma model, a comprehensive analysis of scalar and pseudoscalar glueballs and their mixing with mesons is presented. The Lagrangian of the model contains two chiral nonets, a quark-antiquark type and a two-quark two-antiquark type. The pseudoscalar and scalar glueballs are introduced through their connections with the axial and the trace anomalies of QCD, respectively. It is found that in order to satisfy the axial anomaly and at the same time accurately generate all seven eta masses, it is necessary to include at least two pseudoscalar glueballs, a physical one and an unphysical one that gets integrated out and yields an effective instanton-type term which is needed in generation of the eta masses. At the leading order, which corresponds to keeping effective terms in the Lagrangian that contain no more than eight underlying quarks and antiquarks, the mass spectrum of the model is worked out and shown to be in complete agreement with experiment. The quark and glue contents of the isosinglet scalars below 2 GeV, and of the isosinglet pseudoscalars up to around 2.2 GeV, are analyzed in detail and their correlations with the scalar glueball condensate are examined. Decay widths of isosinglet scalars as well as different self-consistencies within this framework are used to probe the glueball condensate and thereby estimate the quark and glue contents of these states. In the pseudoscalar sector, the state that is dominantly made of glue is clearly a state with mass above 2 GeV. In the scalar sector, the identification of glue contents is less certain and in principle the three isosinglets in the 1.5–2.0 GeV can contain substantial glue. These glue contents are determined as functions of the scalar glueball condensate which is the key quantity in this analysis.

We revisit the calculation of exclusive $J/\psi$ production in electron-proton scattering within the QCD dipole model, employing a refined description of the proton in terms of gluonic hot spots in the dilute regime. In contrast to earlier studies, we incorporate key missing elements; the event-by-event fluctuations in both the number of hot spots and their local saturation scales, as well as the first relativistic corrections to the $J/\psi$ wave function. We perform a Bayesian analysis to constrain the model parameters using HERA data. These enhancements significantly improve the agreement with HERA data. Saturation scale fluctuations are found to be more important than fluctuations in the number of hot spots. Including the first relativistic correction is found to be important, especially in order to describe the observed power-law behavior in the incoherent cross section at large $t$.

We investigate charmed hybrid baryons using the QCD sum rule method within the framework of heavy quark effective theory. We construct 28 interpolating currents for charmed hybrid baryons, seven of which are employed in QCD sum rule analyses of 19 states with quark-gluon configurations $qqcg$, $qscg$, and $sscg$ ($q=u/d$). The masses of the lowest-lying charmed hybrid baryons in the $SU(3)$ flavor ${\mathbf{6}}_F$ representation are calculated to be $M_{{\mathrm{\Sigma }}_{cg}(1/2^{+})}=3.36_{-0.26}^{+0.27}\mathrm{GeV}$, $M_{{\mathrm{\Xi }}_{cg}^{\prime }(1/2^{+})}=3.59\pm 0.20\mathrm{GeV}$, and $M_{{\mathrm{\Omega }}_{cg}(1/2^{+})}=3.82\pm 0.21\mathrm{GeV}$. We propose that future experiments search for these states via their $P$-wave decay channels $N{D}^{(*)}$, $\mathrm{\Lambda }{D}^{(*)}$, and $\mathrm{\Xi }{D}^{(*)}$, respectively. Such investigations would provide valuable insight into the role of gluonic excitations in hadron structure.

The approximate SACOT-$\chi$ scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions $F_2$ and $F_L$. We extend this approach to the charged current case (also including $F_3$), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code apfel++ which provides fast numerical evaluations over a wide kinematic range; this addition to the apfel++ code is publicly available, with details provided in the Appendix. This SACOT-$\chi$ implementation enables detailed numerical insights on the mass dependence of the structure functions and cross sections in the $(x,Q^2)$-plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target $\nu \mathrm{DIS}$ experiments (NuTeV, CCFR, and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the $\nu \mathrm{DIS}$ experiments reveal a surprisingly strong dependence on the mass effects, offering valuable insights that may help resolve long-standing challenges in accurately describing these datasets.

Gravitational form factors (GFFs) of hadrons encode essential information about the internal distributions of mass, spin, pressure, and shear among their quark and gluon constituents. We compute the quark and gluon GFFs of the proton using a fully relativistic, nonperturbative framework based on a light-front quantized Hamiltonian with quantum chromodynamics (QCD) input. This allows us to quantify the impact of a dynamical gluon on the proton’s mechanical properties, such as pressure and shear distributions. Our predictions agree well with recent lattice QCD results and experimental extractions. We also determine the proton’s mass and mechanical radii and address the long-standing puzzle of its mass decomposition. At the scale ${\mu }^2=4{\mathrm{GeV}}^2$, we find that quark energy, gluon field energy, the quark condensate, and the QCD trace anomaly contribute 31.5%, 34.7%, 11.3%, and 22.5%, respectively, which are consistent with lattice QCD findings.