Dimensional Regulator Research Articles

One-loop QCD helicity amplitudes for pp → toverline{t}j to O(ε2)

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to O(ε2) in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.

Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair

The associated production of a Higgs boson and a top-quark pair is important for probing the Yukawa coupling of the top quark, and calls for better theoretical modeling. In this paper, we calculate the two-loop infrared divergences in toverline{t}H production at hadron colliders. To do that we compute the one-loop amplitudes to higher orders in the dimensional regulator ϵ. Numeric results for the infrared poles are given as a reference at several representative phase-space points. The result in this work serves as a part of the ongoing efforts towards the toverline{t}H cross sections at the next-to-next-to-leading order.

FAPbI3 Perovskite Solar Cells: From Film Morphology Regulation to Device Optimization

Organic–inorganic hybrid perovskite solar cells (PSCs) have attracted great attentions due to their rapid increase of power conversion efficiency (PCE). Although the highest PCE of PSCs (25.7%) has been achieved via using formamidinium lead iodide (FAPbI3) with a suitable bandgap, there is still a lack of systematic analysis on FAPbI3‐based PSCs toward high stability and high efficiency. Herein, the progress in FAPbI3 films and achievements in their high‐efficiency and long‐term stability PSCs are comprehensively reviewed. First, the progress from the aspects of morphology, defect, dimension, and strain for FAPbI3 film optimization is summarized and then the development of FAPbI3 PSCs in both efficiency and stability is discussed. Then, the methods to improve the FAPbI3 film quality by morphology control, defect passivation, dimensional regulation, and strain engineering, as well as strategies to optimize the device structure and interface layers, which are critical to promote device stability and efficiency, are evaluated. Finally, the outlook and strategies for realizing commercialized FAPbI3 PSCs with high efficiency and long lifetime are discussed.

Magnetic MXene/PAMAM Composites with Flexible Dimensional Regulation for Highly Effective Enrichment of Phosphopeptides

Magnetic MXene/PAMAM Composites with Flexible Dimensional Regulation for Highly Effective Enrichment of Phosphopeptides

Novel 1d/3d Ceo2/G-C3n4 Catalysts for Photodegradation of Ciprofloxacin Under Visible Light Via Dimensional Regulation and Heterostructure Construction

Novel 1d/3d Ceo2/G-C3n4 Catalysts for Photodegradation of Ciprofloxacin Under Visible Light Via Dimensional Regulation and Heterostructure Construction

Sunrise integrals with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms

We consider a set of two-loop sunrise master integrals with two different internal masses at pseudo-threshold kinematics and we solve it in terms of elliptic polylogarithms to all orders of the dimensional regulator.

DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions

DiffExp is a Mathematica package for integrating families of Feynman integrals order-by-order in the dimensional regulator from their systems of differential equations, in terms of one-dimensional series expansions along lines in phase-space, which are truncated at a given order in the line parameter. DiffExp is based on the series expansion strategies that were explored in recent literature for the computation of families of Feynman integrals relevant for Higgs plus jet production with full heavy quark mass dependence at next-to-leading order. The main contribution of this paper, and its associated package, is to provide a public implementation of these series expansion methods, which works for any family of integrals for which the user provides a set of differential equations and boundary conditions (and for which the program is not computationally constrained). The main functions of the DiffExp package are discussed, and its use is illustrated by applying it to the three loop equal-mass and unequal-mass banana graph families. Program summaryProgram title: DiffExpCPC Library link to program files:https://doi.org/10.17632/j43fkg8vjt.1Developer's repository link:https://gitlab.com/hiddingm/diffexpLicensing provisions: GPLv3Programming language: Mathematica (Wolfram Language)Nature of problem: Obtaining high-precision numerical results for families of Feynman integrals in dimensional regularization, at arbitrary points in phase-space and in an efficient manner, from the system of differential equations satisfied by the integrals and a set of suitable boundary conditions.Solution method: The program provides a public implementation of the integration strategy outlined in Ref. [1]. A line is taken from a given boundary point to a point in phase-space at which numerical results are desired. The line is subdivided into multiple segments, and along each line segment the differential equations are solved in terms of one-dimensional series expansions with a radius of convergence that covers the respective line segment, and up to high order in the line parameter. Boundary conditions are transported by matching results along neighboring line segments. Branch points are crossed by analytically continuing logarithms and square roots that appear in the series expansions. By evaluating the series solutions of the last line segment at the endpoint, the desired numerical results are obtained.Additional comments including restrictions and unusual features: Depending on the complexity of the differential equations of the integrals, the package is limited by CPU speed and/or memory. The prefactors of the Feynman integrals in the basis of master integrals for which the differential equations are given, should only contain rational functions and/or square roots. Fine-tuning of the configuration options may be required for families involving sectors with a large numbers of coupled integrals. Reference[1]F. Moriello, J. High Energy Phys. 2020 (2020) 150. arXiv:1907.13234, https://doi.org/10.1007/JHEP01(2020)150.

Dimensional structure regulation of organic–inorganic hybrid perovskite and its application in thin film transistors

The effects of dimensional structure on the properties of lead iodide perovskite (C8H9NH3)2(CH3NH3) n−1Pb n I3n+1 were investigated. Furthermore, perovskite thin films with different dimensionalities were applied as the channel layer of thin film transistors (TFT). The electrical performance and stability of TFT devices were significantly improved through the regulation of dimensional microstructure of the perovskites. As a result, the quasi-2D (n = 6) perovskite TFTs achieved a field-effect mobility (μ FE) of 3.90 cm2 V−1 s−1, with 104 on-off current ratio and −1.85 V threshold voltage, which can be maintained well after 4 days without degradation at 30% ambient humidity. Moreover, the electrical performance of the TFTs based on Pure-2D and Quasi-2D perovskite also exhibited a good bias stability.

Pentagon integrals to arbitrary order in the dimensional regulator

We analytically calculate one-loop five-point Master Integrals, pentagon integrals, with up to one off-shell leg to arbitrary order in the dimensional regulator in d = 4−2\U0001d716 space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the Mathematica package HypExp. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.

Leading-color two-loop QCD corrections for three-photon production at hadron colliders

We compute the two-loop helicity amplitudes for the production of three photons at hadron colliders in QCD at leading-color. Using the two-loop numerical unitarity method coupled with analytic reconstruction techniques, we obtain the decomposition of the two-loop amplitudes in terms of master integrals in analytic form. These expressions are valid to all orders in the dimensional regulator. We use them to compute the two-loop finite remainders, which are given in a form that can be efficiently evaluated across the whole physical phase space. We further package these results in a public code which assembles the helicity-summed squared two-loop remainders, whose numerical stability across phase-space is demonstrated. This is the first time that a five-point two-loop process is publicly available for immediate phenomenological applications.

Modeling and Control of Islanded DC Microgrid Clusters With Hierarchical Event-Triggered Consensus Algorithm

This paper proposes a distributed hierarchical control framework for energy storage systems (ESSs) in DC microgrid clusters, which achieves voltage regulation and current sharing for ESSs in each microgrid as well as the whole microgrid cluster. The primary control stage adopts a droop controller which only requires local information while the secondary control stage provides correction terms for ESSs within microgrids. The tertiary control stage samples the pinned ESSs in different microgrids with low sampling rate to provide the voltage setpoint, which ensures global current sharing among microgrid cluster. The corresponding multilayered event-triggered consensus algorithm for clusters is proposed to reduce the communication cost generated by operation of the distributed controller. Both the control framework and the consensus algorithm can be extended for satisfying higher dimensional regulation needs. The controller is validated in a DC microgrid cluster through simulation under different scenarios, and the results illustrate the effectiveness of the proposed controller.

Genetic Complexity of the Human Genome in Health and Disease: Basic Concepts

Determination of the DNA sequence of the human genome, revealing extensive genetic variation, and the mapping of the genes and the various regulatory elements of genome function within the genomic DNA, has revolutionized the way we view the states of health and disease in our time. Genetic complexity of the genome is manifested on different levels. The first level refers to the expression of protein coding genes, as regulated by their individual promoter in linear proximity. The next level of genetic complexity involves long distance action by far away enhancers, interacting with promoters through DNA looping. This 3- dimensional (3D) regulation is further developing by chromosome folding into the so called transcription factories, for fully physiological expression. Chromosome folding, mediated by specific genetic elements - insulators - is adding to the genetic complexity by facilitating movements of chromatin of specific genomic regions - the so-called topologically associated domains (TAD) in support of transcription and other cellular functions. Further genetic complexity has emerged with the finding that over 75% of the genome is transcribed and except of the coding genes, a plethora of RNA transcripts are produced - the non-coding RNA - that has important regulatory roles in the gene expression context. The great variation of genome sequence and regulatory elements of the genome architecture are exploited in studies of genome-wide association with disease, in the framework of Precision Medicine and in general of Genomic Medicine.

Two dimensional nanomaterials-enabled smart light regulation technologies: Recent advances and developments

For a long time, human beings have been yearning for free regulation of light waves. But it is limited by poor performances of the natural materials. The emergence of two-dimensional(2D) synthetic nanomaterials greatly promotes the developments of light control technologies, which has dramatically improved the ability of human beings to control light. People can realize flexible regulation of the propagation speed or propagation direction of light wave in material, optical response and frequency, polarization state of light wave based on a series of novel photoelectric properties of 2D synthetic nanomaterials. So, 2D nanomaterials enabled light control technologies have become a research hotspot in recent years. In this review, we summarize the various technologies realized by 2D materials and introduce the related applications. We further analyze, compare these technologies. This review is aimed to give a generalized knowledge of 2D nanomaterials-enabled smart light regulation technologies and their current devices applications, and thus inspiring the exploration and development of other kinds of new light regulation devices and various novel applications. The challenges and the prospects of the future, especially the application of artificial intelligence (AI) in research and development of 2D materials, are also given.

Quark mass effects in two-loop Higgs amplitudes

We provide two two-loop amplitudes relevant for precision Higgs physics. The first is the two-loop amplitude for Higgs boson production through gluon fusion with exact dependence on the top quark mass up to squared order in the dimensional regulator ε. The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit. Both amplitudes are computed by finding canonical bases of master integrals, which we evaluate explicitly in terms of harmonic polylogarithms. We obtain the bare, renormalized and IR-subtracted amplitude and provide the results in terms of building blocks suitable for changing renormalization schemes.

Threshold factorization of the Drell-Yan process at next-to-leading power

We present a factorization theorem valid near the kinematic threshold z={Q}^2/hat{s}to 1 of the partonic Drell-Yan process qoverline{q}to {gamma}^{ast }+X for general subleading powers in the (1 − z) expansion. We then consider the specific case of next-to-leading power. We discuss the emergence of collinear functions, which are a key ingredient to factorization starting at next-to-leading power. We calculate the relevant collinear functions at mathcal{O}left({alpha}_sright) by employing an operator matching equation and we compare our results to the expansion-by- regions computation up to the next-to-next-to-leading order, finding agreement. Factorization holds only before the dimensional regulator is removed, due to a divergent convolution when the collinear and soft functions are first expanded around d = 4 before the convolution is performed. This demonstrates an issue for threshold resummation beyond the leading-logarithmic accuracy at next-to-leading power.

Constructing d-log integrands and computing master integrals for three-loop four-particle scattering

We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the dimensional regulator up to 8th power, with coefficients expressed in terms of harmonic polylogarithms. As a basis of master integrals we choose integrals with integrands that only have logarithmic poles — called dlog forms. This choice greatly facilitates the subsequent computation via the method of differential equations. We detail how this basis is obtained via an improved algorithm originally developed by one of the authors. We provide a public implementation of this algorithm. We explain how the algorithm is naturally applied in the context of unitarity. In addition, we classify our dlog forms according to their soft and collinear properties.

Fermion traces without evanescence

We outline the evaluation of $n$-dimensional fermion traces ($n\in\mathbb{N}$) built by products of Dirac-$\gamma$ matrices suitable for a uniform dimensional continuation. Such a continuation is needed for calculations employing a dimensional regulator whenever intrinsically integer dimensional tensors yield non-vanishing contributions. A prime example for such a tensor is given by $\gamma_5$ for $n=4$. The main difference between Dimensional Regularization (DREG) and a Dimensionally Continued Regularization (DCREG) is that DCREG does not attempt to lift the algebra to continuous $d$ dimensions ($d\in\mathbb{R}$). As a consequence one has to properly deal with evanescent structures in order to ensure the uniform application of the regulator. In basic steps we identify evanescent structures in fermion traces and show that their proper treatment is crucial for example when calculating the $VVA$ anomaly in four dimensions. We checked that the performed considerations enable the evaluation of Standard Model (SM) $Z$-factors within DCREG up to including three loops.

Transverse parton distribution and fragmentation functions at NNLO: the gluon case

We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through mathcal{O} (ϵ2) in dimensional regulator. We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the mathcal{N} = 1 super-Yang-Mills theory. The TMDFFs are used to calculate the two-loop gluon jet function for the energy-energy correlator in Higgs gluonic decay in the back-to-back limit.

Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon mathcal{N} = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf = 2Nc for gauge group SU(Nc). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in mathcal{N} = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.

Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator

We compute all helicity amplitudes for four particle scattering in massless QCD with nf fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, we consider all possible configurations of external quarks and gluons. We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N3LO) calculations. The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically. We present our findings in the conventional dimensional regularisation and in the t’Hooft-Veltman schemes.