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DOE OSTI2023

Depth profiling and standardization from the back side of a sample for accurate analyses: Emphasis on quantifying low‐fluence, shallow implants in diamond‐like carbon

Rationale Back‐side thinning of wafers is used to eliminate issues with transient sputtering when analyzing near‐surface element distributions. Precise and accurate calibrated implants are created by including a standard reference material during the implantation. Combining these methods allows accurate analysis of low‐fluence, shallow features even if matrix effects are a concern. Methods Implanted Na (<2.0 × 10 11 ions/cm 2 , peaking <50 nm) in diamond‐like carbon (DLC) film on silicon (solar wind returned by NASA's Genesis mission) was prepared for measurement as follows. Implanted surfaces of samples were epoxied to wafers and back‐side‐thinned using physical or chemical methods. Thinned samples were then implanted with reference ions for accurate quantification of the solar wind implant. Analyses used a CAMECA IMS 7f‐GEO SIMS in depth‐profiling mode. Results Back‐side‐implanted reference ions reduced the need to change sample mounts or stage position and could be spatially separated from the solar wind implant even when measuring monoisotopic ions. Matrix effects in DLC were mitigated and the need to find an identical piece of DLC for a reference implant was eliminated. Accuracy was only limited by the back‐side technique itself. Conclusions Combining back‐side depth profiling with back‐side‐implanted internal standards aides quantification of shallow mono‐ and polyisotopic implants. This technique helps mitigate matrix effects and keeps measurement conditions consistent. Depth profile acquisition times are longer, but if sample matrices are homogeneous, procedural changes can decrease measurement times.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Charged Hole‐Transporting Materials Based on Imidazolium for Defect Passivation in Inverted Perovskite Solar Cells

The hole‐transporting material (HTM) in perovskite solar cells (PSCs) provides an ideal interface with the perovskite layer for hole collection while influencing the perovskite crystalline structure and morphology. This article presents SIM and DIM, two new dopant‐free imidazolium‐based HTMs with charged units accompanied by counter ions that show the potential to function as ionic HTMs and ionic liquid additives and help improve the efficiency and stability of inverted PSCs. DIM‐based PSCs demonstrates exceptional performance with a high‐power conversion efficiency of 19.15%, attributed to improved passivation of perovskite interface defects. Furthermore, these new imidazolium salt‐based HTMs can be manufactured economically, making them a viable option for mass production and PSC commercialization.

Tingare, Yogesh S.↗

DOE OSTI2026

Impact of Salt Chemistry and Interlayer Architecture on Solid Electrolyte Interphase Composition and Performance

Reversible lithium metal anodes require interphases that are chemically stable, mechanically robust, and compatible with scalable processing. Here, we use slot-die-coated, salt-rich PEO interlayers to design SEI nanolayers on Cu current collectors and isolate how salt anion chemistry controls interphase composition and lithium plating/stripping behavior in architectures relevant to Li plating and anode-free cells. Mesoscale modeling shows that dendrite initiation at SEI defects is governed by a tradeoff among interphase thickness, ionic conductivity, and stiffness through defect-driven current focusing, motivating controlled formation from thin precursor layers. Using UHV-transferred XPS and ToF-SIMS depth profiling after controlled Li deposition, we find that fluorinated sulfonylimide salts (LiTFSI, LiFSI) form mixed inorganic/organic interphases containing LiF and PEO-derived alkoxides, with LiFSI producing a more LiF-dominant Li-facing surface than LiTFSI under identical conditions. In contrast, LiNO 3 -containing interlayers yield a comparatively thick nitrate-derived interphase that reduces upon Li contact to an N-rich inorganic layer (Li–N/N 3− , LiN x O y ). In Cu| |Li cells, these designed interlayers reduce interfacial resistance and improve Coulombic efficiency (CE) and critical current density (CCD) relative to uncoated controls, with LiFSI- and LiNO 3 -based interlayers providing the highest CE/CCD. Overall, the results demonstrate a manufacturing-relevant approach to engineer SEI nanolayers by salt chemistry, providing pathways to improve reversible lithium metal anodes while reducing reliance on LiTFSI.

anion chemistry↗

DOE OSTI2026

Charged loops at the cosmological collider with chemical potential

Cosmological collider physics allows the detection of heavy particles at inflationary scales through their imprints on primordial non-Gaussianities. We study the chemical potential mechanism applied to a pair of charged scalars. We analytically evaluate the resulting one-loop contribution to the bispectrum, using the spectral decomposition. In this way we are able to determine the parametric dependencies for both the signal and the background. We show that a signal strength ${f}_{\text{NL}}\sim \mathcal{O}(0.01)$ can be obtained within theoretical control, potentially reachable by 21 cm tomography. As an application we consider the colored Higgs bosons in SU(5) supersymmetric orbifold grand unification with masses M ≲ 10$^{15}$ GeV.

Bodas, Arushi [Chicago U., EFI; Fermilab] (ORCID:0↗

DOE OSTI2020

The Higgs trilinear coupling and the scale of new physics

We consider modifications of the Higgs potential due to new physics at high energy scales. These upset delicate cancellations predicted by the Standard Model for processes involving Higgs bosons and longitudinal gauge bosons, and lead to a breakdown of the theory at high energies. We focus on modifications of the Higgs trilinear coupling and use the violation of tree-level unitarity as an estimate of the scale where the theory breaks down. We obtain a completely model-independent bound of $ \underset{\sim }{<} $ 13 TeV for an order-1 modification of the trilinear. We argue that this bound can be saturated only in fine-tuned models, and the scale of new physics is likely to be much lower. The most stringent bounds are obtained from amplitudes involving multiparticle states that are not conventional scattering states. Our results show that a future determination of the Higgs cubic coupling can point to a well-defined scale of new physics that can be targeted and explored at future colliders.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Differential cross-section measurements of Higgs boson production in the H → τ + τ - decay channel in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

Differential measurements of Higgs boson production in the τ-lepton-pair decay channel are presented in the gluon fusion, vector-boson fusion (VBF), VH and $t\overline{t}H$ associated production modes, with particular focus on the VBF production mode. The data used to perform the measurements correspond to 140 fb -1 of proton-proton collisions collected by the ATLAS experiment at the LHC. Two methods are used to perform the measurements: the Simplified Template Cross-Section (STXS) approach and an Unfolded Fiducial Differential measurement considering only the VBF phase space. For the STXS measurement, events are categorized by their production mode and kinematic properties such as the Higgs boson’s transverse momentum (${p}_{\textrm{T}}^{\textrm{H}}$ ), the number of jets produced in association with the Higgs boson, or the invariant mass of the two leading jets (mjj). For the VBF production mode, the ratio of the measured cross-section to the Standard Model prediction for m jj > 1.5 TeV and ${p}_{\textrm{T}}^{\textrm{H}}$ > 200 GeV (${p}_{\textrm{T}}^{\textrm{H}}$ < 200 GeV) is ${1.29}_{-0.34}^{+0.39}$ (${0.12}_{-0.33}^{+0.34}$ ). This is the first VBF measurement for the higher-${p}_{\textrm{T}}^{\textrm{H}}$ criteria, and the most precise for the lower-${p}_{\textrm{T}}^{\textrm{H}}$ criteria. The fiducial cross-section measurements, which only consider the kinematic properties of the event, are performed as functions of variables characterizing the VBF topology, such as the signed ΔΦ jj between the two leading jets. The measurements have a precision of 30%–50% and agree well with the Standard Model predictions. These results are interpreted in the SMEFT framework, and place the strongest constraints to date on the CP-odd Wilson coefficient ${c}_{H\overset{\sim }{W}}$ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Heavy Higgs as a portal to the supersymmetric electroweak sector

The electroweak sector of the Minimal Supersymmetric Standard Model (MSSM) - neutralinos, charginos and sleptons - remains relatively weakly constrained at the LHC due in part to the small production cross sections of these particles. In this paper, we study the prospects of searching for decays of heavy Higgs bosons into these superpartners at the high luminosity LHC. In addition to the kinematic handles offered by the presence of a resonant particle in the production chain, heavy Higgs decays can be the dominant production modes of these superpartners, making it possible to extend coverage to otherwise inaccessible regions of the supersymmetry and heavy Higgs parameter space. We illustrate our ideas with detailed collider analyses of two specific topologies: We propose search strategies for heavy Higgs decay to a pair of neutralinos, which can probe heavy Higgs bosons up to 1 TeV in the intermediate tan $\beta (\sim 2-8)$ region, where standard heavy Higgs searches have no reach. Similarly, we show that targeted searches for heavy Higgs decays into staus can probe stau masses up to several hundred GeV. We also provide a general overview of additional decay channels that might be accessible at the high luminosity LHC. This motivates a broader program for LHC heavy Higgs searches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Search for supersymmetry in final states with two or three soft leptons and missing transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A search for supersymmetry in events with two or three low-momentum leptons and missing transverse momentum is performed. The search uses proton-proton collisions at $\sqrt{s}$ = 13 TeV collected in the three-year period 2016–2018 by the CMS experiment at the LHC and corresponding to an integrated luminosity of up to 137 fb -1 . The data are found to be in agreement with expectations from standard model processes. The results are interpreted in terms of electroweakino and top squark pair production with a small mass difference between the produced supersymmetric particles and the lightest neutralino. For the electroweakino interpretation, two simplified models are used, a wino-bino model and a higgsino model. Exclusion limits at 95% confidence level are set on $^{\sim0}_{χ2}/^{\sim±}_{χ1}$ masses up to 275 GeV for a mass difference of 10 GeV in the wino-bino case, and up to 205(150) GeV for a mass difference of 7.5 (3) GeV in the higgsino case. The results for the higgsino are further interpreted using a phenomenological minimal supersymmetric standard model, excluding the higgsino mass parameter μ up to 180 GeV with the bino mass parameter M 1 at 800 GeV. In the top squark interpretation, exclusion limits are set at top squark masses up to 540 GeV for four-body top squark decays and up to 480 GeV for chargino-mediated decays with a mass difference of 30 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

b - τ Yukawa unification in SUSY SU(5) with mirage mediation: LHC and dark matter implications

We consider a class of b - τ Yukawa unified Supersymmetric (SUSY) SU(5) GUTs, in which the asymptotic gaugino M 1,2,3 masses are generated through the mirage mediated supersymmetry breaking, which is a combination of the gravity and anomaly mediation. Due to the contributions from the anomaly contribution, M 3 is always lighter than M 1 and M 2 , and consequently for the range of asymptotic masses considered, the gluino mass $ {m}_{\tilde{g}} $ at low scale is bounded from above at about 4 TeV. We realize two different regions, in one of which the MSSM μ -term is less than about 3 TeV. This region yields a stop mass up to 5 TeV, and the stop mass is nearly degenerate with the LSP neutralino for mass around 0.8 to 1.7 TeV. A stau mass can be realized up to about 5 TeV, and the stau mass is approximately degenerate with the LSP neutralino for mass around 2 to 3 TeV. In addition, an A-funnel solution with $ {m}_A\approx 2{m}_{{\tilde{\chi}}_1^0} $ and $ {m}_{{\tilde{\chi}}_1^0}\sim 700-900 $ GeV is realized. These three cases yield LSP dark matter abundance in accordance with observations. A second region, on the other hand, arises for $ {m}_{\tilde{g}}\lesssim 1.1{m}_{{\tilde{\chi}}_1^0} $ . The μ -term is rather large (≳20 TeV), and the LSP neutralino is a bino-wino mixture. The gluino mass (~ 0 . 8-1 . 2 TeV) is nearly degenerate with the LSP neutralino mass and hence, the gluino-neutralino coannihilation processes play a role in reducing the relic abundance of LSP neutralino down to ranges allowed by the current WMAP measurements. The two regions above can be distinguished through the direct detection experiments. The first region with relatively low μ values yields Higgsino-like DM, whose scattering on the nucleus typically has a large cross-section. We find that such solutions are still allowed by the current results from the LUX experiment, and they will be severely tested by the LUX-Zeplin (LZ) experiment. The second region contains bino-wino DM whose scattering cross-section is relatively low. These solutions are harder to rule out in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Dark photon dark matter in the presence of inhomogeneous structure

Dark photon dark matter will resonantly convert into visible photons when the dark photon mass is equal to the plasma frequency of the ambient medium. In cosmological contexts, this transition leads to an extremely efficient, albeit short-lived, heating of the surrounding gas. Existing work in this field has been predominantly focused on understanding the implications of these resonant transitions in the limit that the plasma frequency of the Universe can be treated as being perfectly homogeneous, \ie neglecting inhomogeneities in the electron number density. In this work we focus on the implications of heating from dark photon dark matter in the presence of inhomogeneous structure (which is particularly relevant for dark photons with masses in the range $10^{-15} \, {\rm eV} \, \lesssim m_{A^\prime} \lesssim 10^{-12}$ eV), emphasizing both the importance of inhomogeneous energy injection, as well as the sensitivity of cosmological observations to the inhomogeneities themselves. More specifically, we derive modified constraints on dark photon dark matter from the Ly-$\alpha$ forest, and show that the presence of inhomogeneities allows one to extend constraints to masses outside of the range that would be obtainable in the homogeneous limit, while only slightly relaxing their strength. We then project sensitivity for near-future cosmological surveys that are hoping to measure the 21cm transition in neutral hydrogen prior to reionization, and demonstrate that these experiments will be extremely useful in improving sensitivity to masses near $\sim 10^{-14}$ eV, potentially by several orders of magnitude. Finally, we discuss implications for reionization, early star formation, and late-time $y$-type spectral distortions, and show that probes which are inherently sensitive to the inhomogeneous state of the Universe could resolve signatures unique to the light dark photon dark matter scenario, and thus offer a fantastic potential for a positive detection.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Higgs Parity, strong CP and dark matter

An exact spacetime parity replicates the $SU(2) \times U(1)$ electroweak interaction, the Higgs boson $H$, and the matter of the Standard Model. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken at scale $v' = \left\langle{H'} \right\rangle \gg \left\langle{H}\right\rangle$, yielding the Standard Model below $v'$ with a quartic coupling that essentially vanishes at $v'$: $\lambda_{SM}(v') \sim 10^{-3}$. The strong CP problem is solved as Higgs parity forces the masses of mirror quarks and ordinary quarks to have opposite phases. Dark matter is composed of mirror electrons, $e'$, stabilized by unbroken mirror electromagnetism. These interact with Standard Model particles via kinetic mixing between the photon and the mirror photon, which arises at four-loop level and is a firm prediction of the theory. Physics below $v'$, including the mass and interaction of $e'$ dark matter, is described by $\textit{one fewer parameter}$ than in the Standard Model. The allowed range of $m_{e'}$ is determined by uncertainties in $(\alpha_s, m_t, m_h)$, so that future precision measurements of these will be correlated with the direct detection rate of $e'$ dark matter, which, together with the neutron electric dipole moment, will probe the entire parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Optimizing energetic light dark matter searches in dark matter and neutrino experiments

Neutrino and dark matter experiments with large-volume ($ \underset{\sim }{>} $,2 1 ton) detectors can provide excellent sensitivity to signals induced by energetic light dark matter coming from the present universe. Taking boosted dark matter as a concrete example of energetic light dark matter, we scrutinize two representative search channels, electron scattering and proton scattering including deep inelastic scattering processes, in the context of elastic and inelastic boosted dark matter, in a completely detector-independent manner. In this work, a dark gauge boson is adopted as the particle to mediate the interactions between the Standard Model particles and boosted dark matter. We find that the signal sensitivity of the two channels highly depends on the (mass-)parameter region to probe, so search strategies and channels should be designed sensibly especially at the earlier stage of experiments. In particular, the contribution from the boosted-dark-matter-initiated deep inelastic scattering can be subleading (important) compared to the quasi-elastic proton scattering, if the mass of the mediator is below (above) $ \mathcal{O} $(GeV). We demonstrate how to practically perform searches and relevant analyses, employing example detectors such as DarkSide-20k, DUNE, Hyper-Kamiokande, and DeepCore, with their respective detector specifications taken into consideration. For other potential detectors we provide a summary table, collecting relevant information, from which similar studies can be fulfilled readily.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

A search for the decays of stopped long-lived particles at $ \sqrt{\mathrm{s}} $ = 13 TeV with the ATLAS detector

A search for long-lived particles, which have come to rest within the ATLAS detector, is presented. The subsequent decays of these particles can produce high-momentum jets, resulting in large out-of-time energy deposits in the ATLAS calorimeters. These de- cays are detected using data collected during periods in the LHC bunch structure when collisions are absent. The analysed dataset is composed of events from proton-proton collisions produced by the Large Hadron Collider at a centre-of-mass energy of s = 13 TeV and recorded by the ATLAS experiment during 2017 and 2018. The dataset used for this search corresponds to a total live time of 579 hours. The results of this search are used to derive lower limits on the mass of gluino R -hadrons, assuming a branching fraction $ \mathcal{B}\left(\overset{\sim }{g}\to q\overline{q}{\chi}_1^0\right) $ B g ~ → q q ¯ χ 1 0 = 100%, with masses of up to 1 . 4 TeV excluded for gluino lifetimes of 10 - 5 to 10 3 s.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Dark radiation and superheavy dark matter from black hole domination

If even a relatively small number of black holes were created in the early universe, they will constitute an increasingly large fraction of the total energy density as space expands. It is thus well-motivated to consider scenarios in which the early universe included an era in which primordial black holes dominated the total energy density. Within this context, we consider Hawking radiation as a mechanism to produce both dark radiation and dark matter. If the early universe included a black hole dominated era, we find that Hawking radiation will produce dark radiation at a level $\Delta N_{\rm eff} \sim 0.03-0.2$ for each light and decoupled species of spin 0, 1/2, or 1. This range is well suited to relax the tension among late and early-time Hubble determinations, and is within the reach of upcoming CMB experiments. The dark matter could additionally originate as Hawking radiation in a black hole dominated early universe, although such dark matter candidates must be very heavy ($m_{\rm DM} >10^{11}$ GeV) if they are to avoid exceeding the measured abundance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Helicity at small x: oscillations generated by bringing back the quarks

We construct a numerical solution of the recently-derived large-N c &N f small-x helicity evolution equations with the aim to establish the small-x asymptotics of the quark helicity distribution beyond the large-N c limit explored previously in the same framework. (Here N c and N f are the numbers of quark colors and flavors.) While the large-N c helicity evolution involves gluons only, the large-N c &N f evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of x. Our numerical results in the large-N c &N f limit lead to the x-dependence of the flavor-singlet quark helicity distribution which is well-approximated by $$ {\left.\Delta \Sigma \left(x,{Q}^2\right)\right|}_{\mathrm{large}\hbox{-} {N}_c\&{N}_f}\sim {\left(\frac{1}{x}\right)}^{\alpha_h^q}\cos \left[{\omega}_q\ln \left(\frac{1}{x}\right)+{\varphi}_q\right]. $$. The power $α^{q}_{h}$ exhibits a weak N f -dependence, and, for all Nf values considered, remains very close to $α^{q}_{h}$(N f =0)=$\left(4/\sqrt{3}\right)\sqrt{\alpha_s{N}_c/\left(2\pi \right)}$ obtained earlier in the large-N c limit. The novel oscillation frequency ω q and phase shift φ q depend more strongly on the number of flavors N f (with ω q = 0 in the pure-glue large-N c limit). The typical period of oscillations for ΔΣ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with x seen in the strange quark helicity distribution extracted from the data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Luminous signals of inelastic dark matter in large detectors

In this work, we study luminous dark matter signals in models with inelastic scattering. Dark matter $\chi_1$ that scatters inelastically off elements in the Earth is kicked into an excited state $\chi_2$ that can subsequently decay into a monoenergetic photon inside a detector. The photon signal exhibits large sidereal-daily modulation due to the daily rotation of the Earth and anisotropies in the problem: the dark matter wind comes from the direction of Cygnus due to the Sun's motion relative to the galaxy, and the rock overburden is anisotropic, as is the dark matter scattering angle. This allows outstanding separation of signal from backgrounds. We investigate the sensitivity of two classes of large underground detectors to this modulating photon line signal: large liquid scintillator neutrino experiments, including Borexino and JUNO, and the proposed large gaseous scintillator directional detection experiment CYGNUS. Borexino's (JUNO's) sensitivity exceeds the bounds from xenon experiments on inelastic nuclear recoil for mass splittings $\delta \gtrsim 240 (180)$ keV, and is the only probe of inelastic dark matter for ${350 \text{ keV} \lesssim \delta \lesssim 600 \text{ keV}}$. CYGNUS's sensitivity is at least comparable to xenon experiments with $\sim 10 \; {\rm m}^3$ volume detector for $\delta \lesssim 150$ keV, and could be substantially better with larger volumes and improved background rejection. Such improvements lead to the unusual situation that the inelastic signal becomes the superior way to search for dark matter even if the elastic and inelastic scattering cross sections are comparable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Freezing in, heating up, and freezing out: predictive nonthermal dark matter and low-mass direct detection

Freeze-in dark matter (DM) mediated by a light ($\ll$ keV) weakly-coupled dark-photon is an important benchmark for the emerging low-mass direct detection program. Since this is one of the only predictive, detectable freeze-in models, we investigate how robustly such testability extends to other scenarios. For concreteness, we perform a detailed study of models in which DM couples to a light scalar mediator and acquires a freeze-in abundance through Higgs-mediator mixing. Unlike dark-photons, whose thermal properties weaken stellar cooling bounds, the scalar coupling to Standard Model (SM) particles is subject to strong astrophysical constraints, which severely limit the fraction of DM that can be produced via freeze-in. While it seems naively possible to compensate for this reduction by increasing the mediator-DM coupling, sufficiently large values eventually thermalize the dark sector with itself and yield efficient DM annihilation to mediators, which depletes the freeze-in population; only a small window of DM candidate masses near the $\sim$ GeV scale can accommodate the total observed abundance. Since many qualitatively similar issues arise for other light mediators, we find it generically difficult to realize a viable freeze-in scenario in which production arises only from renormalizable interactions with SM particles. Furthermore, we also comment on several model variations that may evade these conclusions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge C T , we clarify the properties of stress tensor composite primary operators of minimal twist, [ T m ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle$, where ${\mathcal{O}}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $\left\langle TT{\mathcal{O}}_L\right\rangle$, the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle$ is modified at large C T if $\left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to ${\mathcal{O}}_L $ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin- ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗