High-energy Expansion Research Articles

Low energy limit from high energy expansion in mass gapped theory

We present a method to extract the low energy behavior of physical observables from their high energy expansions, systematically calculable via the operator product expansion (OPE), in asymptotically free and mass-gapped theories. By applying the inverse Laplace transform to correlation functions, their analytic structure is modified such that low-energy information connects with high energy expansions. Furthermore, this transformation alleviates the renormalon problem, enabling a more straightforward application of the OPE compared to the OPE before the transformation. We demonstrate that the low energy limit of correlation functions can be accurately extracted using the OPE in the two dimensional O(N) nonlinear σ model, serving as a first testing ground.

Virtual QCD corrections to gg → ZZ: top-quark loops from a transverse-momentum expansion

We present the virtual corrections due to the top-quark loops for the process gg → ZZ at next-to-leading order in QCD. The associated two-loop box diagrams are computed using a small-transverse-momentum expansion. Our results are then merged with those available in the complementary energy region, obtained via a high-energy expansion, in order to provide an analytic result that is valid in the whole phase space. The results presented allow for an efficient modelling of the signal-background interference as well as the irreducible background in off-shell Higgs production.

Energy Management Strategy for Distributed Photovoltaic 5G Base Station DC Microgrid Integrated with the CF-P&O-INC MPPT Algorithm

With its technical advantages of high speed, low latency, and broad connectivity, fifth-generation mobile communication technology has brought about unprecedented development in numerous vertical application scenarios. However, the high energy consumption and expansion difficulties of 5G infrastructure have become the main obstacles restricting its widespread application. Therefore, aiming to optimize the energy utilization efficiency of 5G base stations, a novel distributed photovoltaic 5G base station DC microgrid structure and an energy management strategy based on the Curve Fitting–Perturb and Observe–Incremental Conductance (CF-P&O-INC) Maximum Power Point Tracking (MPPT) algorithm from the perspectives of energy and information flows are proposed. Simulation results show that the proposed MPPT algorithm can increase the efficiency to 99.95% and 99.82% under uniform irradiation and partial shading, respectively. Under the proposed strategy, when the base station load changes drastically, the voltage fluctuation of the DC bus is less than 1.875%, and returns to a steady state within 0.07s, alleviating the high energy consumption of 5G base stations effectively and achieving coordinated optimization management of various types of energy in multi-source power supply systems.

High-Energy Behavior of Scattering Amplitudes in Theories with Purely Virtual Particles

We study a class of renormalizable quantum field theories with purely virtual particles that exhibits nonrenormalizable behavior in the high-energy limit of scattering cross sections, which grow as powers of the center-of-mass energy squared and seems to violate unitarity bounds. We point out that the problem should be viewed as a violation of perturbativity, instead of unitarity, and show that the resummation of self energies fixes the issue. As an explicit example, we consider a class of O(N) theories at the leading order in the large-N expansion and show that the different quantization prescription of purely virtual particles takes care of the nonrenormalizable behavior, making the resummed cross sections to decrease at high energies and the amplitudes to satisfy the unitarity bounds. We compare the results to the case of theories with ghosts, where the resummation cannot change the behavior of cross sections due to certain cancellations in the high-energy expansion of the self energies. These results are particularly relevant for quantum gravity.

Pseudo and quasi quark PDF in the BFKL approximation

I examine the high-energy behavior of the Ioffe-time distribution for the quark bi-local space-like separated operator using the high-energy operator product expansion. These findings have significant implications for lattice calculations, which require extrapolation for large Ioffe-time values. I perform an explicit Fourier transform for both the pseudo-PDF and quasi-PDF, and investigate their behavior within the first two leading twist contributions.I show that the quark pseudo-PDF captures the BFKL resummation (resummation of all twists) and exhibits a rising behavior for small xB values, while the quasi-PDF presents a different behavior. I demonstrate that an appropriate small-xB behavior cannot be achieved solely through DGLAP dynamics, emphasizing the importance of all-twist resummation. This study provides valuable insights into quark non-local operators’ high-energy behavior and the limitations of lattice calculations in this context.

Application of New High-Energy Expansion Agent in Coal Mine Roadway Excavation

A new energy material, a high-energy expansion agent (HEEA), was proposed for the harsh engineering environment of a mine. A safety test and field engineering test were carried out. The results showed that the mechanical sensitivity of the HEEA was extremely low, and no combustion and explosion occurred in multiple impact and friction tests. Meanwhile, the HEEA only burns in open spaces without detonation. Through field experiments, the HEEA can achieve a good blasting effect, providing strong support for its promotion in low-disturbance environmental engineering applications.

Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes.

We study the mechanism of topological mass generation for 3-dimensional Chern-Simons gauge theories and propose a brand-new topological equivalence theorem to connect scattering amplitudes of the physical gauge boson states to that of the transverse states under high-energy expansion. We prove a general energy cancelation mechanism for N-point physical gauge boson amplitudes, which predicts large cancelations of E4 - L → E(4 - L) - N at any L-loop level (L ⩾ 0). We extend the double-copy approach to construct massive graviton amplitudes and to study their structures. We newly uncovered a series of strikingly large energy cancelations E12 → E1 of the tree-level 4-graviton scattering amplitude under high-energy expansion and establish a new correspondence between the 2 energy cancelations in the topologically massive Yang-Mills gauge theory and the topologically massive gravity theory. We further study the scattering amplitudes of Chern-Simons gauge bosons and gravitons in the nonrelativistic limit.

Study on Physicochemical Properties and Rock-Cracking Mechanism of High-Energy Expansion Agent

Aiming at the shortcomings of the current rock-breaking technology, a new type of high-energy expansion agent for energetic materials based on combustion-to-detonation was developed. By characterizing the basic physical and chemical properties of the high-energy expansion agent (HEEA) such as morphology, particle size distribution, and pyrolysis characteristics, the work performance of different types of high-energy expansion agents was analyzed in combination with the energy characteristics. The results showed that the relationship between the expansion work done by the gas to the outside world was WHEEA-I > WHEEA-II > WHEEA-III under the same quality of HEEA combustion. The damage effect of high-temperature and high-pressure gas cracking specimens generated by deflagration of HEEA was obvious, having the rule that the disturbance damage of rock caused by low heat and high gas specific volume was smaller, and the damage degree of rock caused by high heat and low gas specific volume was larger. The mechanism of HEEA combustion and detonation in confined space is revealed, which provides a theoretical basis for the application of HEEA-cracked rock.

ZH production in gluon fusion at NLO in QCD

We present fully differential next-to-leading order results for Higgs production in association with a Z boson in gluon fusion. Our two-loop virtual contributions are evaluated numerically using sector decomposition, including full top-quark mass effects, and supplemented at high pT by an analytic high-energy expansion to order {m}_Z^4,{m}_H^4,{m}_t^{32} . Using the expanded results we also present a study of the top-quark mass scheme uncertainty at large pT.

Winter (or [formula omitted]-shell) model at small and intermediate volumes

We consider Winter (or δ-shell) model at finite volume, describing a small resonating cavity weakly coupled to a large one, for small and intermediate volumes (lengths). By defining N as the ratio of the length of the large cavity over the small one, we study the symmetric case N=1, in which the two cavities actually have the same length, as well as the cases N=2,3,4.By increasing N in the above range, the transition from a simple quantum oscillating system to a system having a resonance spectrum is investigated. We find that each resonant state is represented, at finite volume, by a cluster of states, each one resonating in a specific coupling region, centered around a state resonating at very small couplings.We derive high-energy expansions for the particle momenta in the above N cases, which (approximately) resum their perturbative series to all orders in the coupling among the cavities. These new expansions converge rather quickly with the order, provide, surprisingly, a uniform approximation in the coupling and also work, again surprisingly, at low energies.We construct a first resummation scheme having a clear physical picture, which is based on a function-series expansion, as well as a second scheme based on a recursion equation. The two schemes coincide at leading order, while they differ from next-to-leading order on. In particular, the recursive scheme realizes an approximate resummation of the function-series expansion generated within the first scheme.

Gluon fusion production at NLO: merging the transverse momentum and the high-energy expansions

The virtual corrections to gg → HH and gg → ZH are analytically evaluated combining an expansion in the small transverse momentum of the final particles with an expansion valid at high energies. The two expansion methods describe complementary regions of the phase space and we merge their results, extending the range of validity of both expansions using Padé approximants. We show that this approach can reproduce the available numerical results retaining the exact top quark mass dependence with an accuracy below the 1% level. Our results allow a fast and flexible evaluation of the virtual corrections of the considered processes. Furthermore, they are available in different renormalisation schemes of the top quark mass.

Structure of Kaluza-Klein graviton scattering amplitudes from the gravitational equivalence theorem and double copy

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_\xi$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy

We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive. Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom. We formulate the mechanism of topological mass-generation at S-matrix level. For this, we propose and prove a Topological Equivalence Theorem (TET) which connects the N-point scattering amplitude of the gauge boson’s physical polarization states ( {A}_{mathrm{P}}^a ) to that of the transverse polarization states ( {A}_{mathrm{T}}^a ) under high energy expansion. We present a general 3d power counting method on the leading energy dependence of the scattering amplitudes in both topologically massive Yang-Mills (TMYM) and topologically massive gravity (TMG) theories. With these, we uncover a general energy cancellation mechanism for N -gauge boson scattering amplitudes which predicts the cancellation E4→ E4−N at tree level. Then, we compute the 4-gauge boson amplitudes of {A}_{mathrm{P}}^a -states and {A}_{mathrm{T}}^a -states, with which we explicitly demonstrate the TET and establish such energy cancellations for N = 4. We further extend the double-copy approach to reconstruct the massive 4-graviton amplitude of TMG from the massive 4-gauge boson amplitude of TMYM. With these, we uncover striking large energy cancellations in the 4-graviton amplitude: E12→ E1, and establish its correspondence to the leading energy cancellation E4→ E0in the 4-gauge boson amplitude of TMYM.

Efficient computation of two-loop amplitudes for Higgs boson pair production

We present a precise and efficient computation of the two-loop amplitudes entering the Higgs boson pair production process via gluon fusion. Our approach is based on the small-Higgs-mass expansion while keeping the full dependence on the top quark mass and other kinematic invariants. We compare our results to the up-to-date predictions based on a combination of sector decomposition and high-energy expansion. We find that our method provides precision numeric predictions in the entire phase space, while at the same time is highly efficient as the computation can be easily performed on a normal desktop or laptop computer. Our method is valuable for practical phenomenological studies of the Higgs boson pair production process, and can also be applied to other similar processes.

High-energy operator product expansion at sub-eikonal level

The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

Virtual corrections to gg \u2192 ZH in the high-energy and large-mt limits

We compute the next-to-leading order virtual corrections to the partonic cross-section of the process gg → ZH, in the high-energy and large-mt limits. We use Padé approximants to increase the radius of convergence of the high-energy expansion in {m}_t^2/s , {m}_t^2/t and {m}_t^2/u and show that precise results can be obtained down to energies which are fairly close to the top quark pair threshold. We present results both for the form factors and the next-to-leading order virtual cross-section.

Semiclassical p-branes in hyperbolic space

The one-loop effects to the Dirac action of p-branes in a hyperbolic background from the path integral and the solution of the Wheeler–DeWitt equation are analysed. The objective of comparing the equivalent quantization procedures is to study in detail the validity of the semiclassical approximation and divergences associated to one-loop corrections. This is in line with a bottom-up approach to holographic Wilson loops. We employ the heat kernel regularization method for both quantization procedures and we study in great detail one-loop corrections to geodesics in a two-dimensional hyperbolic space and semi-spheres in a three-dimensional hyperbolic space. We show that the divergences, given by the high energy expansion of the heat kernel, can be classified by their compatibility with the semiclassical approximation and geometric nature.

Goldstone equivalence and high energy electroweak physics

The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective $W$ Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.

Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD

We determine the three-loop form factor parameterising the amplitude for the production of an off-shell Higgs boson in gluon fusion in QCD with a single massive quark. The result is obtained via a numerical solution of a system of differential equation for the occurring master integrals. The solution is also used to determine the high-energy and threshold expansions of the form factor. Our findings may be used for the evaluation of virtual corrections generated by top-quark and b-quark loops in Higgs boson hadroproduction cross sections at next-to-next-to-leading order.

Gg \u2192 Z Z: analytic two-loop results for the low- and high-energy regions

We compute next-to-leading order virtual two-loop corrections to the process gg → Z Z in the low- and high-energy limits, considering the contributions with virtual top quarks. Analytic results for all 20 form factors are presented including expansion terms up to 1/{m}_t^{12} and {m}_t^{32} . We use a Padé approximation procedure to extend the radius of convergence of the high-energy expansion and apply this approach to the finite virtual next-to-leading order corrections.