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At least 505 records · Page 28

Search for the NΔ resonance in the 𝛾𝑑 → 𝑑𝜋 +𝜋 − reaction

A dibaryon which is an object with baryon number B = 2 has been studied for a long time. Dyson and Xuong classified non-strangeness dibaryon states based on SU(6) symmetries in 1960?s. In the framework, the deuteron is classified as one of the sextet states of dibaryons. Although dibaryon have been an interesting subject of research for a long time, most of the experimental studies up to the early 2000?s were unsuccessful. The CELCIUS/WASA collaboration reported this state via the double-pionic fusion reaction (?= ! 3c0c0) in 2009. Thereafter, the WASA-at-COSY collaboration revealed properties of the isoscaler resonance state via the ?= ! 3c0c0 reaction in 2011. The dibaryon resonance state with isospin ? = 0 and spin ( = 3 thought to be a ?03 which was predicted by Dyson and Xuong at 2.35 GeV?22 with a configuration of ??. The reported mass and width of that state were 2?37 GeV?22 and 0?07 GeV?22, espectively. The mass was ?0?08 GeV?22 smaller than that of 2?, the width was narrower than that of single ?. This surprising result made dibaryon study come back into the limelight. ?12 is one of the dibaryon states classified by Dyson and Xuong with isospin ? = 1, spin ( = 2. This state can be regarded as an s-wave #? resonance. ?12 is an interesting state from the point of view of the possibilities of existence as an internal structure of ?03 and contribution to many-body effects in nuclei. Though there were some experimental clues and theoretical studies of this state, it was unclear whether the obtained experimental results represented a real resonance or not due to the difficulty of separation from kinematical effects. Very recently, the FOREST group at Tohoku University reported a photoproduced isovector dibaryon state at mass of 2.14 GeV?22 in the 3c0 invariant mass spectra of the W3 ! 3c0c0 reaction. The most probable ?% configuration was 2¸ although they didn?t exclude the possibility of ?% = 1¸ or 3?. They separated the dibaryon production process from conventional pion production process for the first time using angular distribution of deuteron. We investigated the W3 ! 3c¸c? reaction for study of a possible #? dibaryon state using a deuterium target at the Research Center for Electron Photon Science, Tohoku University, Japan. In the experiment, ?3 ? 1012 tagged photon beam at energies ranging from 0.8 to 1.1 GeV was impinged to the liquid deuterium target (?520 mg?cm2) and the charged particles in the final state: deuteron, c¸, and c?, were detected by a magnetic spectrometer with a large solid angle named NKS2. NKS2 had capabilities of reconstructing momentum of charged particles, multi-track analysis, and ??c separation. We performed two different analyses named 2-track analysis and 3-track analysis. The 2-track (3-track) analysis was for events in which two (three) particles of 3c¸c? in the final state, including deuteron, were detected by NKS2. In the 3-track and 2-track analysis, ?2000? ?15000 events were identified as the W3 ! 3c¸c? reaction events, respectively. The 2-track analysis with higher statistics was mainly used to derive the cross sections, and the 3-track analysis was used to check the consistency of the 2-track analysis. In this thesis, we have shown the total cross section, the differential cross sections of the W3 ! 3c¸c? reaction in the region of jC j ¡ 0?15 GeV2. This is the world?s first measurement of this reaction in this energy region. Dibaryon resonance structures were observed below the #? threshold in the differential cross section of the invariant mass of 3c?. The mass and width of the structure were consistent with these of ?12 measured by the W3 ! 3c0c0 reaction. The mechanism of the production process was discussed based on the angular distribution of emitted deuteron.

Toyama, Yuichi↗

Application of a Chemical Index to Aerosol Mass Spectrometry: Delta Plots and Functional Group Distributions

A better understanding of the chemical properties of organic aerosol (OA) particles will improve our ability to characterize their sources and predict their lifetime. The high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) is widely used to measure OA in real time using thermal vaporization followed by electron ionization (EI). EI creates fragment ions that can be assigned to functional groups using delta analysis, a method of classifying mass spectra according to the presence of different chemically related ion series. In this study, we demonstrate the application of delta analysis to characterize molecular structures using a new visualization method. We also use delta analysis to quantify the functional group distribution with an average absolute error of ∼5–6% for individual standard molecules, comparable to the error observed for OA mixtures from biomass and coal combustion fit with Fourier transform infrared spectroscopy. Finally, we apply delta functional group analysis to AMS positive matrix factorization (PMF) factors across seven different field campaigns and find a similar composition across the more oxidized factors with about 55% acid and 26% alcohol groups. The analysis method described here can be applied to any HR-ToF-AMS data set to provide quantitative relative functional group distributions for OA mixtures.

aerosol↗

DIRECT DETECTION OF COMPLEX ORGANIC PRODUCTS IN ULTRAVIOLET (Lyα) AND ELECTRON-IRRADIATED ASTROPHYSICAL AND COMETARY ICE ANALOGS USING TWO-STEP LASER ABLATION AND IONIZATION MASS SPECTROMETRY

As discovery of complex molecules and ions in our solar system and the interstellar medium has proliferated, several groups have turned to laboratory experiments in an effort to simulate and understand these chemical processes. So far only infrared (IR) and ultraviolet (UV) spectroscopy has been able to directly probe these reactions in ices in their native, low-temperature states. Here we report for the first time results using a complementary technique that harnesses two-step two-color laser ablation and ionization to measure mass spectra of energetically processed astrophysical and cometary ice analogs directly without warming the ices—a method for hands-off in situ ice analysis. Electron bombardment and UV irradiation of H{sub 2}O, CH{sub 3}OH, and NH{sub 3} ices at 5 K and 70 K led to complex irradiation products, including HCO, CH{sub 3}CO, formamide, acetamide, methyl formate, and HCN. Many of these species, whose assignment was also strengthened by isotope labeling studies and correlate with IR-based spectroscopic studies of similar irradiated ices, are important ingredients for the building blocks of life. Some of them have been detected previously via astronomical observations in the interstellar medium and in cometary comae. Other species such as CH{sub 3}CO (acetyl) are yet to be detected in astrophysical ices or interstellar medium. Our studies suggest that electron and UV photon processing of astrophysical ice analogs leads to extensive chemistry even in the coldest reaches of space, and lend support to the theory of comet-impact-induced delivery of complex organics to the inner solar system.

79 ASTRONOMY AND ASTROPHYSICS↗

A review on recent machine learning applications for imaging mass spectrometry studies

Imaging mass spectrometry (IMS) is a powerful analytical technique widely used in biology, chemistry, and materials science fields that continue to expand. IMS provides a qualitative compositional analysis and spatial mapping with high chemical specificity. The spatial mapping information can be 2D or 3D depending on the analysis technique employed. Due to the combination of complex mass spectra coupled with spatial information, large high-dimensional datasets (hyperspectral) are often produced. Therefore, the use of automated computational methods for an exploratory analysis is highly beneficial. The fast-paced development of artificial intelligence (AI) and machine learning (ML) tools has received significant attention in recent years. These tools, in principle, can enable the unification of data collection and analysis into a single pipeline to make sampling and analysis decisions on the go. There are various ML approaches that have been applied to IMS data over the last decade. Here, in this review, we discuss recent examples of the common unsupervised (principal component analysis, non-negative matrix factorization, k-means clustering, uniform manifold approximation and projection), supervised (random forest, logistic regression, XGboost, support vector machine), and other methods applied to various IMS datasets in the past five years. The information from this review will be useful for specialists from both IMS and ML fields since it summarizes current and representative studies of computational ML-based exploratory methods for IMS.

47 OTHER INSTRUMENTATION↗

Identification and quantification of lignin monomers and oligomers from reductive catalytic fractionation of pine wood with GC × GC – FID/MS

Thorough lignin characterization is vital to understand the physicochemical properties of lignin and to evaluate lignocellulose biorefinery processes. In this study, an in-depth characterization of lignin oil, obtained from reductive catalytic fractionation (RCF) of pine wood, was performed with quantitative GC × GC – FID analysis and qualitative GC × GC – MS. By utilizing high-temperature resistant column sets in the GC × GC system and by applying a derivatization step, unambiguous detection of lignin monomers, dimers, and trimers is enabled. In addition to confirm the identity of eleven monomers, corresponding to 34 wt% of the RCF lignin oil, thirty-six dimers (16 wt%) and twenty-one trimers (7 wt%) were comprehensively identified by analysis of their mass spectra and quantified by a FID, encompassing the identity of an additional 23 wt% of the RCF lignin oil. The proposed structures reveal the interlinkages present in the dimeric and trimeric oligomers, containing β-5, β-1, β–β, 5–5, and a minor fraction of β-O-4 and 4-O-5 bonds. Furthermore, aliphatic end-units in the dimeric and trimeric molecules were identified, consisting of various substituents at the C4 position, that have been previously observed in the RCF-derived lignin monomers. To reduce complexity for analysis, the RCF oil was separated into six fractions, prior to analysis. The structural motifs (inter-unit linkages and end-units) that are found in the different fractions vary significantly, such that the lignin fractions extracted in more polar solvents contained higher molecular weight fragments and more hydroxyl containing structural motifs. Additionally, the identified structures of individual dimer and trimer molecules by GC × GC align well with and further complement the recent findings from 1 H– 13 C HSQC NMR spectroscopy, demonstrating complementarity between both 2D techniques to obtain a holistic view on both the molecular structures and the distribution of bonds and end-units in RCF oil. The combination of these two techniques provides a powerful tool for future RCF and other lignin depolymerization research.

09 BIOMASS FUELS↗

Inspection of next-generation EUV resists with nano-projectile secondary ion mass spectrometry

There is a rapidly growing need for new materials for extreme ultraviolet (EUV) lithography, which incorporate high EUV absorbing elements. Hybrid resists, which are a combination of inorganic and organic moieties, are promising as they offer both high EUV sensitivity and high etch resistance. However, there is a glaring lack of methods to examine the uniformity of these important materials at the nanoscale. We examine the capabilities of nano-projectile secondary ion mass spectrometry (NP-SIMS) to investigate hybrid resists. NP-SIMS is a mass spectrometry-based technique with high lateral resolution. Using NP-SIMS, a surface is probed stochastically with a suite of individual projectiles, 10 6 to 10 7 in total, separated in time and space. Examining these individual mass spectra allows for nanoscale investigation of the uniformity of the surface. We evaluated the performance of NP-SIMS using samples of poly(methyl methacrylate) (PMMA) infiltrated with varying amounts of InO x via vapor-phase infiltration (VPI), an organic–inorganic hybridization method derived from atomic layer deposition. Here, we found that NP-SIMS measurements contained abundant characteristic ions related to both the PMMA and infiltrated In. The intensity of In atomic ions increased linearly with the number of infiltration cycles; however, the uniformity of In and PMMA varied with the number of infiltration cycles. After one cycle, we found that both the PMMA and In were relatively inhomogeneous. The homogeneity improved with subsequent infiltration cycles. In addition, NP-SIMS measurements contained characteristic ions related to the infiltration reaction and provided insights into the VPI mechanism. Overall, the results show that NP-SIMS is capable of examining both the inorganic and organic moieties in a hybrid resist and will be an important method for understanding the performance of these materials for use in EUV lithography.

36 MATERIALS SCIENCE↗

Photoionization mass spectrometric measurements of initial reaction pathways in low-temperature oxidation of 2,5-dimethylhexane

The product formation from R + O 2 reactions relevant to low-temperature autoignition chemistry was studied for 2,5-dimethylhexane, a symmetrically branched octane isomer, at 550 and 650 K using Cl-atom initiated oxidation and multiplexed photoionization mass spectrometry (MPIMS). The interpretation of time- and photon-energy-resolved mass spectra led to three specific results important to characterizing the initial oxidation steps: (1) quantified isomer-resolved branching ratios for HO 2 + alkene channels; (2) 2,2,5,5-tetramethyltetrahydrofuran is formed in substantial yield from addition of O 2 to tertiary 2,5-dimethylhex-2-yl followed by isomerization of the resulting ROO adduct to tertiary hydroperoxyalkyl (QOOH) and exhibits a positive dependence on temperature over the range covered leading to a higher flux relative to aggregate cyclic ether yield. The higher relative flux is explained by a 1,5-hydrogen atom shift reaction that converts the initial primary alkyl radical (2,5-dimethylhex-1-yl) to the tertiary alkyl radical 2,5-dimethylhex-2-yl, providing an additional source of tertiary alkyl radicals. Furthermore, quantum-chemical and master-equation calculations of the unimolecular decomposition of the primary alkyl radical reveal that isomerization to the tertiary alkyl radical is the most favorable pathway, and is favored over O 2 -addition at 650 K under the conditions herein. The isomerization pathway to tertiary alkyl radicals therefore contributes an additional mechanism to 2,2,5,5-tetramethyltetrahydrofuran formation; (3) carbonyl species (acetone, propanal, and methylpropanal) consistent with β-scission of QOOH radicals were formed in significant yield, indicating unimolecular QOOH decomposition into carbonyl + alkene + OH.

2,2,5,5-tetramethyl-tetrahydrofuran↗

Extending the Southern Shore of the Island of Inversion to F 28

Detailed spectroscopy of the neutron-unbound nucleus 28 F has been performed for the first time following proton/neutron removal from 29 Ne/ 29 F beams at energies around 230 MeV / nucleon . The invariant-mass spectra were reconstructed for both the 27 F(*) + n and 26 F(*) + 2n coincidences and revealed a series of well-defined resonances. A near-threshold state was observed in both reactions and is identified as the 28 F ground state, with S n ( 28 F) = -199(6) keV, while analysis of the 2n decay channel allowed a considerably improved S n ( 27 F) = 162(60) keV to be deduced. Comparison with shell-model predictions and eikonal-model reaction calculations have allowed spin-parity assignments to be proposed for some of the lower-lying levels of 28 F. Importantly, in the case of the ground state, the reconstructed 27 F + n momentum distribution following neutron removal from 29 F indicates that it arises mainly from the 1p 3/2 neutron intruder configuration. Finally, this demonstrates that the island of inversion around N = 20 includes 28 F, and most probably 29 F, and suggests that 28 O is not doubly magic.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Proteomics Analysis of Human Contaminant Proteins

Complete characterization of unknowns via proteomics remains challenging. There exist regions of mass spectrometry-based proteomics data where empirical measurements are not attributed to peptides, and/or sequenced peptides from mass spectra are not attributed to any source. These uncharacterized regions are known as the “dark” proteome. Many proteomics tools rely on some a priori knowledge of sample composition; few tools allow for investigation of unknowns without relying on composition assumptions. Further, the potential low abundance of minor traces in these uncharacterized regions can make elucidation of the “dark” proteome challenging. Herein, we describe the development and evaluation of approaches to study the “dark” proteome and move towards an untargeted approach for more complete characterization, namely by studying minor human protein traces in non-human samples and combining that approach with non-human source organism identification without relying on assumptions. Human protein markers, in the form of genetically variant peptides, have been extensively examined in a variety of human matrices, including blood, plasma, and hair, but have yet to be investigated in non-human samples, such as cell cultures, as human contaminant traces. Genetically variant peptides are those that are found in proteins carrying single nucleotide polymorphisms. In this work, we aimed to (1) investigate the feasibility of detecting human contaminant genetically variant peptides (GVPs) in a diverse set of non-human organisms using public proteomics data and a computational pipeline, as well as to (2) develop a combined capability for untargeted source organism characterization and GVP detection. To our knowledge, this is the first report of applying these approaches towards a more complete proteomic characterization of unknowns. We successfully demonstrate the feasibility of broad human contaminant GVP detection in proteomics data, develop a better understanding of GVP detectability, characterize the sample-to-sample variability in GVP detection, and identify a core set of GVPs that can potentially be used as markers indicative of the human contaminant traces portion of the “dark” proteome. Further, we developed and evaluated a combined pipeline, MARLOWE-GVP, that enables both untargeted source organism characterization and GVP detection. We show high accuracy of correct source organism characterization and high degree of similarity of human contaminant GVP detection compared to the conventional approach. Success on both these efforts have allowed us to advance our understanding and characterization of the “dark” proteome.

59 BASIC BIOLOGICAL SCIENCES↗

Characterization of Gas-Phase Native(-like) Proteins Using Structures for Lossless Ion Manipulations

High-resolution mobility-based ion separations in Structures for Lossless Ion Manipulations (SLIM) have been useful for ion mobility separations for a variety of molecular classes in the gas phase. Here, in this study, we present multipass SLIM separations for gas-phase proteins in their near-native state exhibiting charge-state-dependent arrival time distributions using carbonic anhydrase (29 kDa), alcohol dehydrogenase (148 kDa), and apo-transferrin (79 kDa). The experimental CCS values were obtained from calibration curves for the arrival times of Agilent Tune Mix ions. For multipass separations, the ATDs were converted to CCS values by deconvoluting the multipass arrival times into accurate single-pass values amenable to the single-pass calibration curves. Mass spectra of carbonic anhydrase (CA) showed three different charge states (z = 9+ to 11+). Their corresponding mobility peaks were baseline-separated by using 8-m single-pass separations. When compared to the corresponding drift tube ion mobility (DTIMS) measurements, the CCS values obtained from DTIMS and SLIM were in agreement within experimental error. Single-pass analysis of alcohol dehydrogenase (ADH) exhibits three predominant charge states (z = 23+ to 25+) with mobility overlap between adjacent charge states. The mobility peak resolution for ADH improved with multipass separations (up to 24-m path length). In addition, CCS distributions obtained for charge states z = 16+ to 18+ of apo-transferrin reveal a transition from a compact unimodal form (z = 18+ and 19+) to broader multimodal CCS distributions for z = 16+. For apo-transferrin, 40-m multipass separations were performed allowing for complete isolation of the selected mobility range corresponding to z = 17+, leading to selective isolation of a narrow arrival time window. The extended mobility separations provided minimal alterations to the structure of the proteins, and the experimentally derived CCS values showed minimal change as a function of the separation time or number of passes. Mobility-based ion separations for native-like proteins, using SLIM, open opportunities for native-IMS applications as well as other manipulations enabled by SLIM-like mobility-selective isolation and collection.

charge state distribution↗

SIMS analysis of high-performance accelerator niobium

Niobium is used to fabricate superconducting radio frequency accelerator modules because of its high critical temperature, high critical magnetic field, and easy formability. Recent experiments have shown a very significant improvement in performance (over 100%) after a high-temperature bake at 1400 degrees C for 3h. SIMS analysis of this material showed the oxygen profile was significantly deeper than the native oxide with a shape that is indicative of diffusion. Positive secondary ion mass spectra showed the presence of Ti with a depth profile similar to that of O. It is suspected that Ti is associated with the performance improvement. The source of Ti contamination in the anneal furnace has been identified, and a new furnace was constructed without Ti. Initial results from the new furnace do not show the yield improvement. Further analyses should determine the relationship of Ti to cavity performance.

Maheshwari, P.↗

Scalar-induced neutrinoless double beta decay in SU(5)

We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay (0νββ) within the SU(5) Grand Unified Theory framework, extended suitably to include neutrino mass. In such a minimal realistic SU(5) setup for fermion masses, the scalar contributions to 0νββ are extremely suppressed as a consequence of the proton decay bound. We circumvent this problem by imposing a discrete Z 3 symmetry. However, the scalar contributions to 0νββ remain suppressed in this SU(5) x Z 3 model due to the neutrino mass constraint. We find that the 0νββ contribution can be enhanced by extending the scalar sector with an additional 15-dimensional scalar representation with suitable Z 3 charge. Such an extension not only yields realistic fermion mass spectra but also leads to experimentally testable predictions in upcoming ton-scale 0νββ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to ∼ 10 10 GeV.

Baryon/Lepton Number Violation↗

Search for nonresonant new physics signals in high-mass dilepton events produced in association with b-tagged jets in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for nonresonant new physics phenomena in high-mass dilepton events produced in association with b-tagged jets is performed using proton-proton collision data collected in 2016–2018 by the CMS experiment at the CERN LHC, at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb −1 . The analysis considers two effective field theory models with dimension-six operators; involving four-fermion contact interactions between two leptons (ℓℓ, electrons or muons) and b or s quarks (bbℓℓ and bsℓℓ). Two lepton flavor combinations (ee and μμ) are required and events are classified as having 0, 1, or ≥2 b-tagged jets in the final state. No significant excess is observed over the standard model backgrounds. Upper limits are set on the production cross section of the new physics signals. These translate into lower limits on the energy scale Λ of 6.9 to 9.0 TeV in the bbℓℓ model, depending on model parameters, and on the ratio of energy scale and effective coupling, Λ/g*, of 2.0 to 2.6 TeV in the bsℓℓ model. Lepton flavor universality is also tested by comparing the dielectron (ee) and dimuon (μμ) mass spectra for different b-tagged jet multiplicities. No significant deviation from the standard model expectation of unity is observed.

Beyond Standard Model↗

A cornucopia of AdS5 vacua

We report on a systematic search for AdS 5 vacua corresponding to critical points of the potential in the five-dimensional $$ \mathcal{N} $$ N = 8 SO(6) gauged supergravity. By employing Google’s TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non- supersymmetric AdS 5 vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the $$ \mathcal{N} $$ N = 8 supergravity with respect to discrete subgroups of the S(O(6) × GL(2 , R)) symmetry of the potential. In par- ticular, we discuss in detail a $$ {\mathrm{\mathbb{Z}}}_2^3 $$ Z 2 3 -invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a $$ {\mathrm{\mathbb{Z}}}_2^2 $$ Z 2 2 -invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a Z 2 -invariant subspace spanned by 22 scalar fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Search for resonant and nonresonant new phenomena in high-mass dilepton final states at $\sqrt{s}$ = 13 TeV

A search is presented for physics beyond the standard model (SM) using electron or muon pairs with high invariant mass. A data set of proton-proton collisions collected by the CMS experiment at the LHC at √s = 13 TeV from 2016 to 2018 corresponding to a total integrated luminosity of up to 140 fb -1 is analyzed. No significant deviation is observed with respect to the SM background expectations. Upper limits are presented on the ratio of the product of the production cross section and the branching fraction to dileptons of a new narrow resonance to that of the Z boson. These provide the most stringent lower limits to date on the masses for various spin-1 particles, spin-2 gravitons in the Randall-Sundrum model, as well as spin-1 mediators between the SM and dark matter particles. Lower limits on the ultraviolet cutoff parameter are set both for four-fermion contact interactions and for the Arkani-Hamed, Dimopoulos, and Dvali model with large extra dimensions. Lepton flavor universality is tested at the TeV scale for the first time by comparing the dimuon and dielectron mass spectra. No significant deviation from the SM expectation of unity is observed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Disorder and mimesis at hadron colliders

We discuss how systems with a large number of degrees of freedom and disorder in their mass matrix can play a role in particle physics. We derive results on their mass spectra using, where applicable, QFT techniques. We study concrete realizations of these scenarios in the context of the LHC and HL-LHC, showing that collider events with a large number of soft b-quark jets can be common. Such final states can hide these models from current searches at the LHC. This motivates the ongoing effort aimed at lowering trigger thresholds and expanding data scouting.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dark matter, sparticle spectroscopy and muon (g - 2) in SU(4) c × SU(2) L × SU(2) R

We explore the sparticle mass spectra including LSP dark matter within the framework of supersymmetric SU(4) c × SU(2) L × SU(2) R (422) models, taking into account the constraints from extensive LHC and cold dark matter searches. The soft supersymmetry-breaking parameters at MGUT can be non-universal, but consistent with the 422 symmetry. We identify a variety of coannihilation scenarios compatible with LSP dark matter, and study the implications for future supersymmetry searches and the ongoing muon g-2 experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Building bases of loop integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all ‘leading-(transcendental-)weight’ contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory — for generic helicities and arbitrary multiplicity.

1/NExpansion↗