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It has previously been demonstrated that the mesonic fields in chiral Lagrangians can be related to the quark-level operators of QCD sum-rules via energy-independent (constant) scale factor matrices constrained by chiral symmetry. This leads to universal scale factors for each type of chiral nonet related to quark-antiquark ($q\bar q$) operators and four-quark ($qq\bar q\bar q$) operators. Motivated by these successful demonstrations of scale-factor universality for the $K_0^*$ isodoublet and $a_0$ isotriplet scalar mesons, a revised Gaussian QCD sum-rule methodology is developed that enables the extension to higher-dimensional isospin sectors, including the possibility of mixing with glueball components. Moreover, to extract non-perturbative information about a resonance stemming from the final state interactions of its decay products, a background-resonance interference approximation is developed and shown to provide an excellent description of both $\pi K$ scattering amplitude data and $\pi\eta$ scattering calculations. This background-resonance interference approximation inspires new resonance models as ingredients in the scale-factor analysis connecting chiral Lagrangians and QCD Gaussian sum-rules. Using the revised Gaussian QCD sum-rule methodology, key properties of the scale factors are examined for the $K_0^*$ isodoublet and $a_0$ isotriplet scalar mesons for a sequence of increasingly sophisticated resonance models. Gaussian sum-rules are demonstrated to have sufficient resolution to distinguish between different resonance models, and it is shown that the background-resonance interference approximation not only describes $\{\pi K,\pi\eta\}$ scattering, but leads to the best universality and energy-independence properties of the scale factors., Comment: 26 pages, 18 figures, 5 tables

We improve the determination of the mass and coupling of the $2^{++}$ tensor di-gluonium by using relativistic QCD Laplace sum rules (LSR). In so doing, we evaluate the next-to-leading order (NLO) corrections to the perturbative (PT) and $\langle \alpha_s G^2 \rangle$ condensate and the lowest order (LO) $\langle G^3 \rangle$ contributions to the $2^{++}$ di-gluonium two-point correlator. Within a vacuum saturation estimate ($k_G=1$) of the dimension-eight gluon condensates, we obtain: $M_{T}=3028(287)\mbox{MeV}$ and the renormalization group invariant (RGI) coupling $\hat{f}_T=224(33)\mbox{MeV}$. Assuming that the factorization hypothesis can be violated, we study the effect of the violation factor $k_G$ on the results and obtain: $M_T=3188(337)\mbox{MeV}$ and $\hat{f}_T=245(32)\mbox{MeV}$ for $k_G=(3\pm 2)$. Our estimation does not favour the interpretation of the observed $f_2(2010)$, $f_2(2300)$ and $f_2(2340)$ as pure glueball state., Comment: Talk given at the 14th International Conference in High-Energy Physics - HEPMAD24 (21-26th October 2024, Antananarivo-Madagascar)

Within the method of parity-projected QCD sum rules, we study the mass spectra of light hybrid baryons with $I(J^{P})=1/2(1/2^{\pm}), 3/2(1/2^{\pm}), 1/2(3/2^{\pm}), 3/2(3/2^{\pm})$ by constructing the local $qqqg$ interpolating currents. We calculate the correlation functions up to dimension eight condensates at the leading order of $\alpha_{s}$. The stable QCD Lapalce sum rules can be established for the positive-parity $N_{1/2^+}, \Delta_{3/2^+}, \Delta_{1/2^+}$ and negative-parity $N_{1/2^-}, N_{3/2^-}, \Delta_{1/2^-}$ channels to extract their mass spectra. The lowest-lying hybrid baryons are predicted to be the negative-parity $N_{1/2^-}$ state around 2.28 GeV and $\Delta_{1/2^-}$ state around 2.64 GeV. These hybrid baryons mainly decay into conventional baryon plus meson final states. We propose to search for the light hybrid baryons through the $\chi_{cJ}/\Upsilon$ decays via the three-gluon emission mechanism in BESIII and BelleII experiments. Our studies of the light hybrid baryons will be useful for understanding the excited baryon spectrum and the behavior of gluonic degrees of freedom in QCD., Comment: 6 pages, 5 figures

This study establishes bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_\mu^{\mathrm{HVP,LO}}$, $a_\mu = (g-2)_\mu/2$) by using H\"older's inequality and related inequalities in Finite-Energy QCD sum rules. Considering contributions from light quarks ($u,d,s$) up to five-loop order in perturbation theory within the chiral limit, leading-order light-quark mass corrections, next-to-leading order for dimension-four QCD condensates, and leading-order for dimension-six QCD condensates, the study finds QCD lower and upper bounds as $\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,$., Comment: 7 pages, 2 figures, 3 tables. Proceedings article for QCD24: 27th High-Energy Physics International Conference in Quantum Chromodynamis

We apply the method of QCD sum rules to study the $q c \bar q \bar c$ tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$, and extract the mass of the lowest-lying state to be ${4.49^{+0.45}_{-0.41}}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematic analysis of these interpolating currents indicates that: a) this state readily decays into the $P$-wave $[\rho J/\psi] / [\omega J/\psi ]$ channel but not into the $ [\rho \chi_{c2}]/[\omega \chi_{c2}]/[J/\psi f_2(1270)]$ channels, and b) it readily decays into the $[D^* \bar D_2^*]$ channel but not into the $P$-wave $[D^* \bar D^*]$ channel., Comment: 13 pages, 4 figures, revised version to be published in PRD

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_\mu^{\mathrm{HVP,LO}}$, $a_\mu=\left(g-2\right)_\mu/2$) are determined by imposing H\"older inequalities and related inequality constraints on systems of Finite-Energy QCD sum-rules. This novel methodology is complementary to lattice QCD and data-driven approaches to determining $a_\mu^{\mathrm{HVP,LO}}$. For the light-quark ($u,d,s$) contributions up to five-loop order in perturbation theory in the chiral limit, LO in light-quark mass corrections, next-to-leading order in dimension-four QCD condensates, and to LO in dimension-six QCD condensates, we find that $\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,$, bridging the range between lattice QCD and data-driven values., Comment: 17 pages, 4 figures. v2 contains extended analysis and discussion

Finite-temperature quantum field theory provides the foundation for many important phenomena in the Standard Model and extensions, including phase transitions, baryogenesis, and gravitational waves. Methods are developed to enable application of pySecDec (a Python-language-based package designed for numerical calculation of dimensionally-regulated loop integrals) to numerically evaluate finite-temperature loop integrals in the imaginary time (Matsubara) formalism. These methods consist of two main elements: an inverse Wick rotation that converts a finite-temperature loop integral into a form applicable to pySecDec, and asymptotic techniques to regulate and accelerate convergence of the Matsubara frequency summations. Numerical pySecDec evaluation of finite-temperature, two-point and three-point, one-loop topologies for scalar fields is used to illustrate and validate these new methodologies. Advantages of these finite-temperature pySecDec numerical methods are illustrated by the inclusion of multiple mass and external momentum scales., Comment: 16 pages, 9 figures

The vector-like quark model is one of the extensions of the standard model (SM) of particle physics. The simplest version of this model introduces a vector-like singlet quark which can mix with SM quarks and give rise to new contributions to the flavor-changing decays of the Higgs boson. In this work we first present a systematic analysis of the branching ratios of the decays $H\rightarrow b\bar{s}, b\bar{d}$ at leading order in the standard model. Our results show that it is challenging to observe these two modes because of their small branching ratios. Then augmenting the SM with a vector-like singlet top quark, assuming the top partner only mixes with the top quark, complete one-loop contributions are taken into account in the amplitudes. Further results indicate that the branching ratios of the decays $H\rightarrow b\bar{s}, b\bar{d}$ are sensitive to the mass of the top partner $M_{T}$ and the mixing effects characterized by $\sin\theta_{L}$. By tuning the values of $M_{T}$ and $\sin\theta_{L}$, the branching ratios may rise to a level accessible to LHC experiments. Combined with the branching ratios obtained from a probabilistic model, the allowed areas in the $M_{T}-\sin\theta_{L}$ plane are displayed. Tagging efficiencies and feasibility for detecting $H\rightarrow b\bar{s}$ are specifically discussed and we conclude that with large statistics it is promising to discover the $H\rightarrow b\bar{s}$ decay at the LHC., Comment: 34 pages, 8 figures, second revised

We evaluate the next-to-leading (NLO) corrections to the perturbative (PT) and $< \alpha_s G^2>$ condensate and the LO constant term of the $< G^3 > $ contributions to the $2^{++}$ tensor di-gluonium two-point correlator. Using these results into the inverse Laplace transform sum rules (LSR) moments and their ratio, we estimate the mass and coupling of the lowest ground state. We obtain\,: $M_T=3028(287)$ MeV and the renormalization group invariant (RGI) coupling $\hat f_T=224(33)$ MeV within a vacuum saturation estimate of the $D=8$ dimension gluon condensates ($k_G=1$). We study the effect of $k_G$ on the result and find: $M_T=3188(337)$ MeV and $\hat f_T$=245(32) MeV for $k_G=(3\pm 2)$. Our result does not favour the pure gluonia/glueball nature of the observed $f_2(2010,2300,2340)$ states., Comment: 7 pages, 9 figures, 1 Table

QCD Laplace sum-rules are used to examine the constituent mass spectrum of $J^P\in\{0^+,1^+\}$ heavy-light [Qq] diquarks with $Q\in\{c,b\}$ and $q\in\{u,d,s\}$. As in previous sum-rule studies, the negative parity $J^P\in\{0^-, 1^-\}$ [Qq] diquark mass predictions do not stabilize, so the sum-rule analysis focuses on positive parity [Qq] diquarks. Doubly-strange $J^P=1^{+}$ [ss] diquarks are also examined, but the resulting sum rules do not stabilize. Hence there is no sum-rule evidence for $J^P=1^{+}$ [ss] diquark states, aiding the interpretation of sum-rule analyses of fully-strange tetraquark states. The SU(3) flavour splitting effects for [Qq] diquarks are obtained by calculating QCD correlation functions of $J^P\in\{0^+,1^+\}$ diquark composite operators up to next-to-leading order in perturbation theory, leading-order in the strange quark mass, and in the chiral limit for non-strange (u,d) quarks with an isospin-symmetric vacuum $<\bar nn>=<\bar uu>=<\bar dd>$. Apart from the strange quark mass parameter $m_s$, the strange quark condensate parameter $\kappa=<\bar ss>/<\bar nn>$ has an important impact on SU(3) flavour splittings. A Laplace sum-rule analysis methodology is developed for the mass difference $M_{[Qs]}-M_{[Qn]}$ between the strange and non-strange heavy-light diquarks to reduce the theoretical uncertainties from all other QCD input parameters. The mass splitting is found to decrease with increasing $\kappa$, providing an upper bound on $\kappa$ where the $M_{[Qs]}-M_{[Qn]}$ mass hierarchy reverses. In the typical QCD sum-rule range $0.56<\kappa< 0.74$, $55~MeV < M_{[cs]}-M_{[cn]} < 100~MeV$ and $75~MeV < M_{[bs]}-M_{[bn]}< 150~MeV$, with a slight tendency for larger splittings for the $J^P=1^+$ channels. These constituent mass splitting results are discussed in comparison with values used in constituent diquark models for tetraquark and pentaquark hadronic states., Comment: 30 pages, 19 figures, 7 tables. v2 contains extended discussion

We have studied the strong decay properties of the recently observed $T^a_{c\bar s0}(2900)^{++/0}$ by considering it as a $cu\bar{d}\bar{s}/cd\bar{u}\bar{s}$ fully open-flavor tetraquark state with $I(J^P)=1(0^+)$. In the framework of QCD sum rules, we have calculated the three-point correlation functions of the two-body strong decay processes $T^a_{c\bar s0}(2900)^{++}\rightarrow D_s^+\pi^+$, $D^+K^+, D_s^{\ast +}\rho^+$ and $D_{s1}^+\pi^+$. The full width of $T^a_{c\bar s0}(2900)^{++/0}$ is obtained as $161.7\pm94.8$ MeV, which is consistent with the experimental observation. We predict the relative branching ratios as $\Gamma (T\rightarrow D_s\pi):\Gamma(T\rightarrow DK):\Gamma (T\rightarrow D_s^{\ast} \rho):\Gamma (T\rightarrow D_{s1}\pi)\approx1.00:1.10:0.04:0.43$, implying that the main decay modes of $T^a_{c\bar s0}(2900)^{++/0}$ state are $D_s\pi$ and $DK$ channels in our calculations. However, the $P$-wave decay mode $D_{s1}\pi$ is also comparable and important by including the uncertainties. To further identify the nature of $T^a_{c\bar s0}(2900)^{++/0}$, we suggest confirming them in the $DK$ and $D_{s}\pi$ final states, and measuring the above ratios in future experiments., Comment: 9 pages, 7 figures

QCD sum-rule studies have been useful to understand and get an insight on the structure of exotic states, such as tetraquark systems. Moreover, the majority of these studies are performed only at leading-order (LO) within the light tetraquarks systems picture, overlooking the effects of higher order corrections, thus motivating our analysis. Our study focused on the effects of next-to-leading order (NLO) contributions to the mass estimates of the lightest tetraquark state ($J^{PC} = 0^{++}$), the so-called $\sigma$ or $f_{0}(500)$, using ratios of QCD Laplace sum-rules. A variety of different models were used, which included multiple resonances and width effects, resulting in a final mass prediction of $0.52\,\text{GeV}< m_{\sigma}< 0.77\,\text{GeV}$. Even though the ratios of sum-rules demonstrated some insensitivity under superficially large NLO contributions, they added the beneficial feature of canceling the dependence on the anomalous dimension. Our findings were in good agreement with patterns found in Chiral Lagrangian studies regarding the four-quark structure of the $\sigma$ state, including the relative coupling strengths within the multiple resonance analysis.

In this talk, we briefly report the investigations of the mass spectra for the $cc\bar c\bar c, bb\bar b\bar b$, $bc\bar b\bar c$ and $cc\bar b\bar b$ tetraquark states by using the QCD moment sum rule method. The calculations for the fully-charm $cc\bar c\bar c$ tetraquarks have been successfully predicted the existence of di-$J/\psi$ resonances including $X(6900)$ in LHCb's observation. The quantum numbers for these resonance structures are also suggested. More efforts are still needed in both theoretical and experimental aspects to study the properties of these fully-heavy tetraquark states. They may be observed at facilities such as LHCb, CMS and RHIC in the future., Comment: Presentation at QCD 21: the 24th International Conference on Quantum Chromodynamics, held at Montpellier in July 5-9, 2021

We calculated next-to-leading-order (NLO) QCD perturbative contributions to a $J^{PC}=0^{+-}$, $d u\bar d\bar u$ tetraquark (diquark-antidiquark) correlator in the chiral limit of massless $u$ and $d$ quarks. At NLO, there are four quark self-energy diagrams and six gluon-exchange diagrams. Nonlocal divergences were cancelled using diagrammatic renormalization. Dimensionally regularized integrals were numerically computed using pySecDec. The combination of pySecDec with diagrammatic renormalization establishes a valuable new methodology for NLO calculations of QCD correlation functions. Compared to leading-order (LO) perturbation theory, we found that NLO perturbation theory is significant. To quantify the impact of NLO perturbation theory on physical predictions, we computed NLO perturbative contributions to QCD Laplace, Gaussian, and finite-energy sum rules. Using QCD sum rules, we determined upper and lower bounds on the $0^{+-}$, $d u\bar d\bar u$ tetraquark ground-state mass, $M$: at NLO in perturbation theory, we found $2.2~\text{GeV}\lesssim M\leq 4.2~\text{GeV}$ whereas, at LO, we found $2.4~\text{GeV}\lesssim M\leq 4.6~\text{GeV}$. This mass range suggests the possibility of mixing between $0^{+-}$, light-quark (i.e., $u$ and $d$ quarks) hybrid and $d u\bar d\bar u$ tetraquark states. Taking into account uncertainties in QCD parameters, we found no evidence for a $0^{+-}$, $d u\bar d\bar u$ tetraquark under 1.9 GeV., Comment: 22 pages, 13 figures. Updated version contains additional discussion

In QCD sum-rule methods, the fundamental field-theoretical quantities are correlation functions of composite operators that serve as hadronic interpolating fields. One of the challenges of loop corrections to QCD correlation functions in conventional approaches is the renormalization-induced mixing of composite operators. This involves a multi-step process of first renormalizing the operators, and then calculating the correlation functions in this mixed basis. This process becomes increasingly complicated as the number of operators mixed under renormalization increases, a situation that is exacerbated as the operator mass dimension increases in important physical systems such as tetraquarks, pentaquarks, and hybrids. Diagrammatic renormalization provides an alternative to the conventional operator renormalization approach. Diagrammatic renormalization methods are outlined and applied to a variety of QCD sum-rule examples of increasing complexity. The results are benchmarked, and the diagrammatic method is contrasted with the conventional operator mixing approach. Advantages and conceptual interpretations of the diagrammatic renormalization approach are outlined and technical subtleties are explored., Comment: 19 pages, 10 eps figures. V4 corrects typos and contains new material in Section 5 (Appendix)

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar ($J^{PC}=0^{++}$) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions $0.52\,\text{GeV}< m_{\sigma}< 0.77\,\text{GeV}$ for the lightest scalar-isoscalar $\sigma$ state are in good agreement with the four-quark interpretation of the $f_0(500)$, and the relative coupling strengths of the $f_{0}(980)$ and $f_0(500)$ to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the $\sigma$ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians., Comment: 14 pages, 8 figures. v2 contains extended analysis/discussion and additional references

Fronts are regions of transition from one state to another in a medium. They are present in many areas of science and applied mathematics, and modelling them and their evolution is often an effective way of treating the underlying phenomena responsible for them. In this paper, we propose a new approach to modelling front propagation, which characterises the evolution of structures surrounding radiative sources. This approach is generic and has a wide range of applications, particularly when dealing with the propagation of phase or state transitions in media surrounding radiation emitting objects. As an illustration, we show an application in modelling the propagation of ionisation fronts around early stars during the cosmological Epoch of Reionisation (EoR) and show that the results are consistent with those of existing equations but provide much richer sources of information., Comment: 10 pages, 4 figures

We study the bispectrum of large-scale structure in the EFTofLSS including corrections up to two-loop. We derive an analytic result for the double-hard limit of the two-loop correction, and show that the UV-sensitivity can be absorbed by the same four EFT operators that renormalize the one-loop bispectrum. For the single-hard region, we employ a simplified treatment, introducing one extra EFT parameter. We compare our results to N-body simulations, and show that going from one- to two-loop extends the wavenumber range with percent-level agreement from $k \simeq 0.08$ to $0.15~h/\mathrm{Mpc}$., Comment: 4 pages, 2 figures. Contribution to the 2022 Cosmology session of the 56th Rencontres de Moriond

The bispectrum is the leading non-Gaussian statistic in large-scale structure, carrying valuable information on cosmology that is complementary to the power spectrum. To access this information, we need to model the bispectrum in the weakly non-linear regime. In this work we present the first two-loop, i.e., next-to-next-to-leading order perturbative description of the bispectrum within an effective field theory (EFT) framework. Using an analytic expansion of the perturbative kernels up to $F_6$ we derive a renormalized bispectrum that is demonstrated to be independent of the UV cutoff. We show that the EFT parameters associated with the four independent second-order EFT operators known from the one-loop bispectrum are sufficient to absorb the UV sensitivity of the two-loop contributions in the double-hard region. In addition, we employ a simplified treatment of the single-hard region, introducing one extra EFT parameter at two-loop order. We compare our results to N-body simulations using the realization-based grid-PT method and find good agreement within the expected range, as well as consistent values for the EFT parameters. The two-loop terms start to become relevant at $k\approx 0.07h~\mathrm{Mpc}^{-1}$. The range of wavenumbers with percent-level agreement, independently of the shape, extends from $0.08h~\mathrm{Mpc}^{-1}$ to $0.15h~\mathrm{Mpc}^{-1}$ when going from one to two loops at $z=0$. In addition, we quantify the impact of using exact instead of Einstein-de-Sitter kernels for the one-loop bispectrum, and discuss in how far their impact can be absorbed into a shift of the EFT parameters., Comment: 34 pages, 17 figures

We study $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of $J^{PC}=1^{++}$, $1^{--}$, $1^{-+}$ states. By calculating the two-point mixed correlation functions of $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ currents, and we estimate the mass and coupling constants of the corresponding `"physical state" that couples to both $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ currents. Our results suggest that $1^{++}$ states are more likely mixing from $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ components, while for $1^{--}$ and $1^{-+}$ states, there is less mixing between $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$. Our results suggest the $Y$ series of states have more complicated components., Comment: 14 pages,3 figs, 7 tables

Correlations between the strange quark mass, strange quark condensate $\langle \bar s s\rangle$, and the kaon partially conserved axial current (PCAC) relation are developed. The key dimensionless and renormalization-group invariant quantities in these correlations are the ratio of the strange to non-strange quark mass $r_m=m_s/m_q$, the condensate ratio $r_c=\langle \bar s s\rangle/\langle \bar q q\rangle$, and the kaon PCAC deviation parameter $r_p=-m_s\langle \bar s s+\bar q q\rangle/2f_K^2m_K^2$. The correlations define a self-consistent trajectory in the $\{r_m,r_c,r_p\}$ parameter space constraining strange quark parameters that can be used to assess the compatibility of different predictions of these parameters. Combining the constraint with Particle Data Group (PDG) values of $r_m$ results in $\{r_c,r_p\}$ constraint trajectories that are used to asses the self-consistency of various theoretical determinations of $\{r_c,r_p\}$. The most precise determinations of $r_c$ and $r_p$ are shown to be mutually consistent with the constraint trajectories and provide improved bounds on $r_p$. In general, the constraint trajectories combined with $r_c$ determinations tend to provide more accurate bounds on $r_p$ than direct determinations. The $\{r_c,r_p\}$ correlations provide a natural identification of a self-consistent set of strange quark mass and strange quark condensate parameters., Comment: 9 pages, 6 figures, 1 table. Typo (factor of 1/2 in eq. (1)) corrected from PRD version

Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fields and quark operators., Comment: 5 pages. Proceedings article for QCD20: 23rd International Conference in Quantum Chromodynamics

The Coleman-Weinberg (CW) renormalization scheme for renormalization-group improvement of the effective potential is particularly valuable for CW symmetry-breaking mechanisms (including the challenging case of models with multiple scalar fields). CW mechanism is typically studied using models with classical scale invariance which not only provide a possibility for an alternative symmetry breaking mechanism but also partially address the gauge hierarchies through dimensional transmutation. As outlined in our discussion section, when the couplings are not large, models with CW symmetry-breaking mechanisms have also been shown to naturally provide the strong first-order phase transition necessary for stochastic gravitational wave signals. A full understanding of the CW-MS scheme transformation of couplings thus becomes important in the era of gravitational wave detection and precision coupling measurements. A generalized Coleman-Weinberg (GCW) renormalization scheme is formulated and methods for transforming scalar self-couplings between the GCW and MS (minimal-subtraction) renormalization schemes are developed. Scalar $\lambda\Phi^4$ theory with global $O(4)$ symmetry is explicitly studied up to six-loop order to explore the magnitude of this scheme transformation effect on the couplings. The dynamical rescaling of renormalization scales between the GCW and MS schemes can lead to significant (order of 10\%) differences in the coupling at any order, and consequently GCW-MS scheme transformation effects must be considered within precision determinations of scalar couplings in extensions of the Standard Model., Comment: 12 pages, 5 figures. V2 has additional figures, extended discussion, and additional references

Scale factor matrices relating mesonic fields in chiral Lagrangians and quark-level operators of QCD sum-rules are shown to be constrained by chiral symmetry, resulting in universal scale factors for each chiral nonet. Built upon this interplay between chiral Lagrangians and QCD sum-rules, the scale factors relating the $a_0$ isotriplet scalar mesons to their underlying quark composite field were recently determined. It is shown that the same technique when applied to $K_0^*$ isodoublet scalars reproduces the same scale factors, confirming the universality property and further validating this connection between chiral Lagrangians and QCD sum-rules which can have nontrivial impacts on our understanding of the low-energy QCD, in general, and the physics of scalar mesons in particular., Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:1909.07243

Properties of the scale-factor matrices forming a bridge between the mesonic fields of chiral Lagrangians and quark-level structures of QCD sum-rules are reviewed. The scale-factor matrices combined with mixing angles provide a physical projection of a QCD correlation function matrix that disentangles the mesonic states. This methodology is illustrated for the isotriplet $a_0(980)$-$a_0(1450)$ system, and the scale factors are determined from the combined inputs of QCD sum-rules and chiral Lagrangians. The resulting scale factors are shown to be in good agreement with the vacuum expectation values in the chiral Lagrangian framework. The sensitivity of the scale factors on the gluon condensate QCD sum-rule parameter is explored., Comment: 5 pages. Proceedings article for QCD19: 22nd International Conference in Quantum Chromodynamics

We study mixing between conventional and hybrid mesons in vector and axial vector charmonium using QCD Laplace sum-rules. We compute meson-hybrid cross correlators within the operator product expansion, taking into account condensate contributions up to and including those of dimension-six as well as composite operator renormalization-induced diagrams. Using measured masses of charmonium-like states as input, we probe known resonances for nonzero coupling to both conventional and hybrid meson currents, a signal for meson-hybrid mixing., Comment: 4 pages, 4 figures, proceedings article from Flavor Physics and CP Violation Conference, Victoria, BC, 2019

Constituent mass predictions for axial vector (i.e., $J^P=1^+$) $cc$ and $bb$ colour antitriplet diquarks are generated using QCD Laplace sum-rules. We calculate the diquark correlator within the operator product expansion to NLO, including terms proportional to the four- and six-dimensional gluon and six-dimensional quark condensates. The sum-rules analyses stabilize, and we find that the mass of the $cc$ diquark is 3.51~GeV and the mass of the $bb$ diquark is 8.67~GeV. Using these diquark masses as inputs, we calculate several tetraquark masses within the Type-II diquark-antidiquark tetraquark model., Comment: Updated analysis, discussion and references

QCD Gaussian sum-rules are used to explore the vector ($J^{PC}=1^{--}$) strangeonium hybrid interpretation of the $Y(2175)$. Using a two-resonance model consisting of the $Y(2175)$ and an additional resonance, we find that the relative resonance strength of the $Y(2175)$ in the Gaussian sum-rules is less than 5\% that of a heavier 2.9 GeV state. This small relative strength presents a challenge to a dominantly-hybrid interpretation of the $Y(2175)$., Comment: 9 pages, 3 figures

We study $\bar qq$-hybrid mixing for the light vector mesons and $\bar qq$-glueball mixing for the light scalar mesons in Monte-Carlo based QCD Laplace sum rules. By calculating the two-point correlation function of a vector $\bar q\gamma_\mu q$ (scalar $\bar q q$) current and a hybrid (glueball) current we are able to estimate the mass and the decay constants of the corresponding mixed "physical state" that couples to both currents. Our results do not support strong quark/gluonic mixing for either the $1^{--}$ or the $0^{++}$ states., Comment: 18 pages, 7 figures

We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the H\"older inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV., Comment: 19 pages, 7 figures. Additional analysis and discussion included

We explore conventional meson-hybrid mixing in $J^{PC}=1^{++}$ heavy quarkonium using QCD Laplace sum-rules. We calculate the cross-correlator between a heavy conventional meson current and heavy hybrid current within the operator product expansion, including terms proportional to the four- and six-dimensional gluon condensates and the six-dimensional quark condensate. Using experimentally determined hadron masses, we construct models of the $1^{++}$ charmonium and bottomonium mass spectra. These models are used to investigate which resonances couple to both currents and thus exhibit conventional meson-hybrid mixing. In the charmonium sector, we find almost no conventional meson-hybrid mixing in the $\chi_{c1}(1P)$, minimal mixing in the $X(3872)$, and significant mixing in both the $X(4140)$ and $X(4274)$. In the bottomonium sector, we find minimal conventional meson-hybrid mixing in the $\chi_{b1}(1P)$ and significant mixing in both the $\chi_{b1}(2P)$ and $\chi_{b1}(3P)$., Comment: Updated citations and added figures in latest version

We study the mass spectra for the $cc\bar c\bar c$ and $bb\bar b\bar b$ tetraquark states by developing a moment sum rule method. Our results show that the $bb\bar b\bar b$ tetraquarks lie below the threshold of $\eta_b(1S)\eta_b(1S)$. They are probably stable and very narrow. The masses for the doubly hidden-charm states $cc\bar c\bar c$ are higher than the spontaneous dissociation thresholds of two charmonium mesons. We suggest to search for such states in the $J/\psi J/\psi$ and $\eta_c(1S)\eta_c(1S)$ channels., Comment: 8 pages, 2 figures. More references added. Conference proceedings for 6th International Conference on New Frontiers in Physics (ICNFP 2017), Crete, Greece, 17-29 Aug, 2017

We calculate the complete form of the dimension-8 condensate contributions in the two-point correlator of the ($1^{-+}$,$0^{++}$) light hybrid current considering the operator mixing under renormalization. We find the inclusion these higher power corrections as well as the update of $\langle g^3G^3\rangle$ increase the QCD sum rule mass prediction for the $1^{-+}$ light hybrid. The obtained conservative mass range 1.72--2.60 GeV does not favor the $\pi_1(1400)$ and the $\pi_1(1600)$ to be pure hybrid states and suggests the $\pi_1(2015)$ observed by E852 is more likely to have much of a hybrid constituent. We also study the $b_1\pi$ and $\rho\pi$ decay patterns of the $1^{-+}$ light hybrid with light-cone QCD sum rules. We obtain a relatively large partial decay width of the $b_1\pi$ mode, which is consistent with the predictions from the flux tube models and lattice QCD. More interestingly, using the tensor interpolating current we find the partial decay width of the $\rho\pi$ mode is small due to the absence of the leading twist contribution in the light-cone expansion of the correlation function., Comment: 5 pages, 2 tables, 1 figure. Proceedings article for the 20th High-Energy Physics International Conference in Quantum Chromodynamics (QCD17) in Montpellier, France July 3-7 2017

We present QCD Laplace sum-rule predictions of ground state masses of heavy-light open-flavour hybrid mesons. Having computed leading-order diagonal correlation functions, including up to dimension six gluon condensate contributions, we extract hybrid mass predictions for all $J^P \in \{0^\pm, 1^\pm\}$, and explore possible mixing effects with conventional meson states. Similarities are found in the mass hierarchy in both charm and bottom systems with some exceptions that are discussed., Comment: 6 pages, 8 tables, 2 figures. Proceedings article for the 20th High-Energy Physics International Conference in Quantum Chromodynamics (QCD17) in Montpellier, France July 3-7 2017

We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/\psi$ and a $\approx4.3$ GeV resonance. In the bottomonium sector, we find that the $\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon(3S)$, and $\Upsilon(4S)$ all exhibit mixing., Comment: QCD-17 conference proceedings article

We construct asymptotically safe extensions of the Standard Model by adding gauged vector-like fermions. Using large number-of-flavour techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling can achieve an interacting ultraviolet fixed point., Comment: 5 pages, 3 figures, typos fixed

We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the $J/\psi$ and a 4.3~GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the $\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon(3S)$, and $\Upsilon(4S)$., Comment: Updated version includes extended analysis

We have studied the mass spectra of the hidden-charm/bottom $qc\bar q\bar c$, $sc\bar s\bar c$ and $qb\bar q\bar b$, $sb\bar s\bar b$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$ in the framework of QCD sum rules. We construct ten scalar and four tensor interpolating currents in a systematic way and calculate the mass spectra for these tetraquark states. The $X^\ast(3860)$ may be either an isoscalar tetraquark state or $\chi_{c0}(2P)$. If the $X^\ast(3860)$ is a tetraquark candidate, our results prefer the $0^{++}$ option over the $2^{++}$ one. The $X(4160)$ may be classified as either the scalar or tensor $qc\bar q\bar c$ tetraquark state while the $X(3915)$ favors a $0^{++}$ $qc\bar q\bar c$ or $sc\bar s\bar c$ tetraquark assignment over the tensor one. The $X(4350)$ can not be interpreted as a $sc\bar s\bar c$ tetraquark with either $J^{PC}=0^{++}$ or $2^{++}$., Comment: 15 pages, 4 figures, 5 tables, suggestions and comments welcome

We determine the phase diagram of complete asymptotically free SU($N_c$) gauge theories featuring $N_s$ complex scalars and $N_f$ Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly we discover that the complete asymptotically free conditions guarantee that the infrared dynamics displays long distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the theory and summarising the possible patterns of radiative symmetry breaking. These theories are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the Standard Model., Comment: 37 pages, 16 figures, including several appendices

We provide comprehensive investigations for the mass spectrum of exotic open-flavor charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar b$, $qq\bar q\bar b$ tetraquark states with various spin-parity assignments $J^P=0^+, 1^+, 2^+$ and $0^-, 1^-$ in the framework of QCD sum rules. In the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents using the color-antisymmetric scalar and axial-vector diquark fields. The stable mass sum rules are established in reasonable parameter working ranges, which are used to give reliable mass predictions for these tetraquark states. We obtain the mass spectra for the open-flavor charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar b$, $qq\bar q\bar b$ tetraquark states with various spin-parity quantum numbers. In addition, we suggest searching for exotic doubly-charged tetraquarks, such as $[sd][\bar u\bar c]\to D_s^{(\ast)-}\pi^-$ in future experiments at facilities such as BESIII, BelleII, PANDA, LHCb and CMS, etc., Comment: 19 pages, 4 figures, 5 tables, accepted by Phys. Rev. D (in press)

In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous H\"older-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $\sigma$ and $f_0(980)$, we obtain a prediction for light quark mass $m_q(2\,\textrm{GeV})$ = $\frac{1}{2}(m_u(2\,\textrm{GeV})$ + $m_d(2\,\textrm{GeV}))$ = $4.7^{+0.8}_{-0.7}\,\textrm{MeV}$, which is consistent with the PDG (Particle Data Group) value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $\sigma$ and $f_0(980)$ at 2 GeV, which are approximately $0.64-0.83$ GeV and $0.40-0.48$ GeV respectively., Comment: 9 pages, 1 figure, accepted for publication in PRD

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H\"older-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum.Therefore an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the $\rho$ meson channel with re-examination and inclusion of $\alpha_s$ corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels., Comment: 12 pages, 8 figures, accepted for publication in Chinese Physics C

This article provides the calculation of an effective vertex function between a nucleon and a $Z^\prime$ boson that couples preferentially to either the top quark or the third generation of fermions, for the purpose of calculating vector-portal dark matter nuclear recoil cross sections. Mixing effects between the new gauge group $U(1)^\prime$ and the Standard Model hypercharge group $U(1)_Y$ are taken into account. Contributions to the $U(1)^\prime$ nucleon current from heavy quarks are quantified using the heavy quark expansion. Also taken into account are contributions from the 1-loop $Z^\prime$-gluon interactions and mixing-induced contributions from the light quarks in the nucleon. We find that, for reasonable values of the $U(1)^\prime$ gauge parameter, contributions from the light quarks dominate despite being mixing-suppressed. It is shown that this holds for most models even if mixing effects do not appear at tree level. Contributions from the heavy quarks and gluons are suppressed by $1/m_Q^2$ and possibly also by momentum in the low momentum transfer limits relevant for dark matter direct detection. We discuss under which conditions the subdominant terms become relevant., Comment: 10 pages

We consider a conformal complex singlet extension of the Standard Model with a Higgs portal interaction. Two different scenarios depending on whether the global U(1) symmetry is broken or not have been studied. In the unbroken phase, the decay of the complex singlet is protected by the global U(1) symmetry which leads to an ideal cold dark matter candidate. In the broken phase, we are able to provide a second Higgs at $554\,\rm{GeV}$. In addition, gauging the global U(1) symmetry, we can construct an asymptotically safe U(1)' leptophobic model. We combine the notion of asymptotic safety with conformal symmetry and use the renormalization group equations as a bridge to connect UV boundary conditions and Electroweak/ TeV scale physics. We also provide a detailed example to show that these boundary conditions will lead to phenomenological signatures such as diboson excesses which could be tested at the LHC., Comment: 4 pages, 2 figures, Contribution to the proceedings of the 38th International Conference of High Energy Physics (ICHEP), Chicago, Aug. 3-10, 2016

Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed. We present selected QCD sum rule results from a full range of quantum numbers for open-flavour hybrid mesons with heavy valence quark content, including non-perturbative condensate contributions up to six-dimensions., Comment: Formatted from poster presented at 38th International Conference on High Energy Physics, 3-10 August 2016, Chicago, USA. 4 pages, 1 table and 2 figures. Submitted for publication in Proceedings of Science as PoS(ICHEP2016)849. Original poster attached

We work with a UV conformal U(1)' extension of the Standard Model, motivated by the hierarchy problem and recent collider anomalies. This model admits fermionic vector portal WIMP dark matter charged under the U(1)' gauge group. The asymptotically safe boundary conditions can be used to fix the coupling parameters, which allows the observed thermal relic abundance to constrain the mass of the dark matter particle. This highly restricts the parameter space, allowing strong predictions to be made. The parameter space of several UV conformal U(1)' scenarios will be explored, and both bounds and possible signals from direct and indirect detection observation methods will be discussed., Comment: 4 pages, 2 figures, Contribution to the proceedings of the 38th International Conference of High Energy Physics (ICHEP), Chicago, Aug. 3-10, 2016

We study the exotic $J^{PC}=0^{--}$ four-quark states in Laplace sum rules (LSR) and finite energy sum rules (FESR). We use the vector tetraquark-like currents as interpolating currents in the correlator, from which the $1^{+-}$ states are also studied. In the mass extraction, we use the standard stability criterion with respect to the Borel parameters and the QCD continuum thresholds and consider the effect of the violation of factorization in estimating the high dimensional condensates as a source of uncertainties. The obtained mass prediction $1.66\pm0.14$ GeV is much lower than the previous sum rule predictions obtained using the scalar currents. Our result favours the four-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$ decay. We also discuss the possible decay patterns of these exotic four-quark states., Comment: 10 pages, 8 figures. Comments and suggestions are welcome

We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid's constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract hybrid mass predictions for all $J^P\in\{0^{\pm},\,1^{\pm}\}$, as well as explore possible mixing effects with conventional quark-antiquark mesons. Within theoretical uncertainties, our results are consistent with a degeneracy between the heavy-nonstrange and heavy-strange hybrids in all $J^P$ channels. We find a similar mass hierarchy of $1^+$, $1^{-}$, and $0^+$ states (a $1^{+}$ state lighter than essentially degenerate $1^{-}$ and $0^{+}$ states) in both the charm and bottom sectors, and discuss an interpretation for the $0^-$ states. If conventional meson mixing is present the effect is an increase in the hybrid mass prediction, and we estimate an upper bound on this effect., Comment: 24 pages, 8 figures. Mass predictions updated from previous version to reflect corrected sign error in sum rule analysis. Mixing analysis and examination of higher weight sum-rules added. To be published in JHEP

We study the $\rho\pi$ and $b_1\pi$ decay modes of the $1^{-+}$ light hybrid state within the framework of light-cone QCD sum rules. We use both the tensor current $\bar\psi\sigma_{\mu\nu}\psi$ and the derivative current $\bar{\psi}\overleftrightarrow{D}_\mu\gamma_5\psi$ as interpolating currents to calculate the partial decay width of the $b_1\pi$ decay mode. Comparing the sum rules obtained by using different currents, we obtain $\Gamma(\pi_1\to b_1\pi)$ = 8--23, 32--86 and 52--151\,MeV for $m_{1^{-+}}$ = 1.6, 1.8 and 2.0\,GeV respectively, which favour the results from the flux tube models and lattice simulations. We also use the tensor current to study the $\rho\pi$ decay mode, and although an extended stability criterion is needed, our results suggest a small partial decay width., Comment: 12 pages, 7 figures, minor texts have been corrected

We develop a moment QCD sum rule method augmented by fundamental inequalities to study the existence of exotic doubly hidden-charm/bottom tetraquark states made of four heavy quarks. Using the compact diquark-antidiquark configuration, we calculate the mass spectra of these tetraquark states. There are 18 hidden-charm $cc\bar c\bar c$ tetraquark currents with $J^{PC} = 0^{++}$, $0^{-+}$, $0^{--}$, $1^{++}$, $1^{+-}$, $1^{-+}$, $1^{--}$, and $2^{++}$. We use them to perform QCD sum rule analyses, and the obtained masses are all higher than the spontaneous dissociation thresholds of two charmonium mesons, which are thus their dominant decay modes. The masses of the corresponding hidden-bottom $bb\bar b\bar b$ tetraquarks are all below or very close to the thresholds of the $\Upsilon(1S)\Upsilon(1S)$ and $\eta_b(1S)\eta_b(1S)$, except one current of $J^{PC}=0^{++}$. Hence, we suggest to search for the doubly hidden-charm states in the $J/\psi J/\psi$ and $\eta_c(1S)\eta_c(1S)$ channels., Comment: 5 pages, 3 figures and 2 tables. published in PLB