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A patient's digital twin is a computational model that describes the evolution of their health over time. Digital twins have the potential to revolutionize medicine by enabling individual-level computer simulations of human health, which can be used to conduct more efficient clinical trials or to recommend personalized treatment options. Due to the overwhelming complexity of human biology, machine learning approaches that leverage large datasets of historical patients' longitudinal health records to generate patients' digital twins are more tractable than potential mechanistic models. In this manuscript, we describe a neural network architecture that can learn conditional generative models of clinical trajectories, which we call Digital Twin Generators (DTGs), that can create digital twins of individual patients. We show that the same neural network architecture can be trained to generate accurate digital twins for patients across 13 different indications simply by changing the training set and tuning hyperparameters. By introducing a general purpose architecture, we aim to unlock the ability to scale machine learning approaches to larger datasets and across more indications so that a digital twin could be created for any patient in the world.

Randomized controlled trials (RCTs) with binary primary endpoints introduce novel challenges for inferring the causal effects of treatments. The most significant challenge is non-collapsibility, in which the conditional odds ratio estimand under covariate adjustment differs from the unconditional estimand in the logistic regression analysis of RCT data. This issue gives rise to apparent paradoxes, such as the variance of the estimator for the conditional odds ratio from a covariate-adjusted model being greater than the variance of the estimator from the unadjusted model. We address this challenge in the context of adjustment based on predictions of control outcomes from generative artificial intelligence (AI) algorithms, which are referred to as prognostic scores. We demonstrate that prognostic score adjustment in logistic regression increases the power of the Wald test for the conditional odds ratio under a fixed sample size, or alternatively reduces the necessary sample size to achieve a desired power, compared to the unadjusted analysis. We derive formulae for prospective calculations of the power gain and sample size reduction that can result from adjustment for the prognostic score. Furthermore, we utilize g-computation to expand the scope of prognostic score adjustment to inferences on the marginal risk difference, relative risk, and odds ratio estimands. We demonstrate the validity of our formulae via extensive simulation studies that encompass different types of logistic regression model specifications. Our simulation studies also indicate how prognostic score adjustment can reduce the variance of g-computation estimators for the marginal estimands while maintaining frequentist properties such as asymptotic unbiasedness and Type I error rate control. Our methodology can ultimately enable more definitive and conclusive analyses for RCTs with binary primary endpoints., Comment: 27 pages, 1 figure, 9 tables

A crucial task for a randomized controlled trial (RCT) is to specify a statistical method that can yield an efficient estimator and powerful test for the treatment effect. A novel and effective strategy to obtain efficient and powerful treatment effect inferences is to incorporate predictions from generative artificial intelligence (AI) algorithms into covariate adjustment for the regression analysis of a RCT. Training a generative AI algorithm on historical control data enables one to construct a digital twin generator (DTG) for RCT participants, which utilizes a participant's baseline covariates to generate a probability distribution for their potential control outcome. Summaries of the probability distribution from the DTG are highly predictive of the trial outcome, and adjusting for these features via regression can thus improve the quality of treatment effect inferences, while satisfying regulatory guidelines on statistical analyses, for a RCT. However, a critical assumption in this strategy is homoskedasticity, or constant variance of the outcome conditional on the covariates. In the case of heteroskedasticity, existing covariate adjustment methods yield inefficient estimators and underpowered tests. We propose to address heteroskedasticity via a weighted prognostic covariate adjustment methodology (Weighted PROCOVA) that adjusts for both the mean and variance of the regression model using information obtained from the DTG. We prove that our method yields unbiased treatment effect estimators, and demonstrate via comprehensive simulation studies and case studies from Alzheimer's disease that it can reduce the variance of the treatment effect estimator, maintain the Type I error rate, and increase the power of the test for the treatment effect from 80% to 85%~90% when the variances from the DTG can explain 5%~10% of the variation in the RCT participants' outcomes., Comment: 49 pages, 6 figures, 12 tables

Alzheimer's Disease (AD) is a neurodegenerative disease that affects subjects in a broad range of severity and is assessed in clinical trials with multiple cognitive and functional instruments. As clinical trials in AD increasingly focus on earlier stages of the disease, especially Mild Cognitive Impairment (MCI), the ability to model subject outcomes across the disease spectrum is extremely important. We use unsupervised machine learning models called Conditional Restricted Boltzmann Machines (CRBMs) to create Digital Twins of AD subjects. Digital Twins are simulated clinical records that share baseline data with actual subjects and comprehensively model their outcomes under standard-of-care. The CRBMs are trained on a large set of records from subjects in observational studies and the placebo arms of clinical trials across the AD spectrum. These data exhibit a challenging, but common, patchwork of measured and missing observations across subjects in the dataset, and we present a novel model architecture designed to learn effectively from it. We evaluate performance against a held-out test dataset and show how Digital Twins simultaneously capture the progression of a number of key endpoints in clinical trials across a broad spectrum of disease severity, including MCI and mild-to-moderate AD.

Multiple Sclerosis (MS) is a neurodegenerative disorder characterized by a complex set of clinical assessments. We use an unsupervised machine learning model called a Conditional Restricted Boltzmann Machine (CRBM) to learn the relationships between covariates commonly used to characterize subjects and their disease progression in MS clinical trials. A CRBM is capable of generating digital twins, which are simulated subjects having the same baseline data as actual subjects. Digital twins allow for subject-level statistical analyses of disease progression. The CRBM is trained using data from 2395 subjects enrolled in the placebo arms of clinical trials across the three primary subtypes of MS. We discuss how CRBMs are trained and show that digital twins generated by the model are statistically indistinguishable from their actual subject counterparts along a number of measures.

Most approaches to machine learning from electronic health data can only predict a single endpoint. Here, we present an alternative that uses unsupervised deep learning to simulate detailed patient trajectories. We use data comprising 18-month trajectories of 44 clinical variables from 1908 patients with Mild Cognitive Impairment or Alzheimer's Disease to train a model for personalized forecasting of disease progression. We simulate synthetic patient data including the evolution of each sub-component of cognitive exams, laboratory tests, and their associations with baseline clinical characteristics, generating both predictions and their confidence intervals. Our unsupervised model predicts changes in total ADAS-Cog scores with the same accuracy as specifically trained supervised models and identifies sub-components associated with word recall as predictive of progression. The ability to simultaneously simulate dozens of patient characteristics is a crucial step towards personalized medicine for Alzheimer's Disease.

Restricted Boltzmann Machines (RBMs) are a class of generative neural network that are typically trained to maximize a log-likelihood objective function. We argue that likelihood-based training strategies may fail because the objective does not sufficiently penalize models that place a high probability in regions where the training data distribution has low probability. To overcome this problem, we introduce Boltzmann Encoded Adversarial Machines (BEAMs). A BEAM is an RBM trained against an adversary that uses the hidden layer activations of the RBM to discriminate between the training data and the probability distribution generated by the model. We present experiments demonstrating that BEAMs outperform RBMs and GANs on multiple benchmarks.

Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant. In this paper we propose a method, which we call the $\sigma\text{-improved}$ scheme, to resolve this issue. It consists of two steps: (i) include higher-order terms in the spectrum to improve the agreement with the cumulant central value, and (ii) employ profile scales that encode correlations between different points to give robust uncertainty estimates for the integrated spectrum. We provide a generic algorithm for determining such profile scales, and show the application to the thrust distribution in $e^+e^-$ collisions at NLL$'$+NLO and NNLL$'$+NNLO., Comment: 8 pages, 8 figures

We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in Standard Perturbation Theory (SPT), and using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. We compare the non-Gaussian part of the one-loop covariance computed with both SPT and EFT of LSS to two separate simulations. In one simulation, we find that the one-loop prediction from SPT reproduces the simulation well to $k_i + k_j \sim$ 0.25 h/Mpc, while in the other simulation we find a substantial improvement of EFT of LSS (with one free parameter) over SPT, more than doubling the range of $k$ where the theory accurately reproduces the simulation. The disagreement between these two simulations points to unaccounted for systematics, highlighting the need for improved numerical and analytic understanding of the covariance., Comment: v2 - 10+9 pages, 6 figures; minor changes + data analysis and conclusions updated. Version accepted for publication in PRD

We present results for Drell-Yan production from the GENEVA Monte-Carlo framework. We combine the fully-differential NNLO calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by PYTHIA8. The 0-jettiness resummation is carried out to NNLL', which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of perturbative uncertainties. In this way, inclusive observables are correct to NNLO, up to small power corrections in the resolution cutoff. Furthermore, the perturbative accuracy of 0-jet-like resummation variables is significantly improved beyond the parton shower approximation. We provide comparisons with LHC measurements of Drell-Yan production at 7 TeV from ATLAS, CMS, and LHCb. As already observed in $e^+e^-$ collisions, for resummation-sensitive observables, the agreement with data is noticeably improved by using a lower value of $\alpha_s(M_Z) = 0.1135$., Comment: 26 pages, 20 figures

We present a subtraction method utilizing the N-jettiness observable, Tau_N, to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular contributions of N-jet cross sections for Tau_N -> 0, and uses these to construct suitable Tau_N-subtractions. The construction is systematic and economic, due to being based on a physical observable. The resulting NNLO calculation is fully differential and in a form directly suitable for combining with resummation and parton showers. We explain in detail the application to processes with an arbitrary number of massless partons at lepton and hadron colliders together with the required external inputs in the form of QCD amplitudes and lower-order calculations. We provide explicit expressions for the Tau_N-subtractions at NLO and NNLO. The required ingredients are fully known at NLO, and at NNLO for processes with two external QCD partons. The remaining NNLO ingredient for three or more external partons can be obtained numerically with existing NNLO techniques. As an example, we employ our method to obtain the NNLO rapidity spectrum for Drell-Yan and gluon-fusion Higgs production. We discuss aspects of numerical accuracy and convergence and the practical implementation. We also discuss and comment on possible extensions, such as more-differential subtractions, necessary steps for going to N3LO, and the treatment of massive quarks., Comment: 51 pages, 10 figures, v2: journal version

In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of "jets without jets". In this paper, we perform the first analytic studies of fractional jet multiplicity $\tilde{N}_{\rm jet}$ in the context of $e^+e^-$ collisions. We use fixed-order QCD to understand the $\tilde{N}_{\rm jet}$ cross section at order $\alpha_s^2$, and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The $\tilde{N}_{\rm jet}$ observable does not satisfy ordinary soft-collinear factorization, and the $\tilde{N}_{\rm jet}$ cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of $\tilde{N}_{\rm jet}$ at hadron colliders like the LHC., Comment: 45 pages, 11 figures, 2 tables; v2: expanded discussion of non-additivity, v3: journal version

We present a new tagger which aims at identifying partially reconstructed objects, in which only some of the constituents are collected in a single jet. As an example, we focus on top decays in which either part of the hadronically decaying W or the b jet is soft or falls outside of the top jet cone. We construct an observable to identify remnant substructure from the decay and employ aggressive jet grooming to reject QCD backgrounds. The tagger is complementary to existing ones and works well in the intermediate boost regime where jet substructure techniques usually fail. It is anticipated that a similar tagger can be used to identify non-QCD hadronic jets, such as those expected from hidden valleys., Comment: 6 pages, 4 figures

The energy dependence of the electroweak gauge couplings has not been measured above the weak scale. We propose that percent-level measurements of the energy dependence of $\alpha_{1,2}$ can be performed now at the LHC and at future higher energy hadron colliders. These measurements can be used to set limits on new particles with electroweak quantum numbers without relying on any assumptions about their decay properties. The shape of the high invariant mass spectrum of Drell-Yan, $p p \rightarrow Z^*/\gamma^* \rightarrow \ell^+ \ell^-$, constrains $\alpha_{1,2}(Q)$, and the shape of the high transverse mass distribution of $p p \rightarrow W^* \rightarrow \ell \nu$ constrains $\alpha_{2}(Q)$. We use existing data to perform the first fits to $\alpha_{1,2}$ above the weak scale. Percent-level measurements are possible because of high precision in theoretical predictions and existing experimental measurements. We show that the LHC already has the reach to improve upon electroweak precision tests for new particles that dominantly couple through their electroweak charges. The 14 TeV LHC is sensitive to the predicted Standard Model (SM) running of $\alpha_2$, and can show that $\alpha_2$ decreases with energy at $2-3 \sigma$ significance. A future 100 TeV proton-proton collider will have significant reach to measure running weak couplings, with sensitivity to the SM running of $\alpha_2$ at $4-5 \sigma$ and sensitivity to winos with masses up to $\sim$ 1.3 TeV at $2\sigma$., Comment: 34 pages + appendices; v2: references and minor changes to text added, version to appear in JHEP

We compare methods to resum logarithms in event shape distributions as they have been used in perturbative QCD directly and in effective field theory. We demonstrate that they are equivalent. In showing this equivalence, we are able to put standard soft-collinear effective theory (SCET) formulae for cross sections in momentum space into a novel form more directly comparable with standard QCD formulae, and endow the QCD formulae with dependence on separated hard, jet, and soft scales, providing potential ways to improve estimates of theoretical uncertainty. We show how to compute cross sections in momentum space to keep them as accurate as the corresponding expressions in Laplace space. In particular, we point out that that care is required in truncating differential distributions at N$^k$LL accuracy to ensure they match the accuracy of the corresponding cumulant or Laplace transform. We explain how to avoid such mismatches at N$^k$LL accuracy, and observe why they can also be avoided by working to N$^k$LL$'$ accuracy., Comment: 65 pages plus Appendices, 8 figures, uses JHEP style. v2: improved clarity, added references, clarified that potential mismatches in accuracy of distribution vs. cumulant/Laplace transform exist at unprimed but not primed orders. v3: added references, footnote in Sec. 3.5 on earlier related results, minor corrections, version published in JHEP

Experimental analyses often use jet binning to distinguish between different kinematic regimes and separate contributions from background processes. To accurately model theoretical uncertainties in these measurements, a consistent description of the jet bins is required. We present a complete framework for the combination of resummed results for production processes in different exclusive jet bins, focusing on Higgs production in gluon fusion as an example. We extend the resummation of the Higgs + 1-jet cross section into the challenging low transverse momentum region, lowering the uncertainties considerably. We provide combined predictions with resummation for cross sections in the Higgs + 0-jet and Higgs + 1-jet bins, and give an improved theory covariance matrix for use in experimental studies. We estimate that the relevant theoretical uncertainties on the signal strength in the Higgs to WW analysis are reduced by nearly a factor of 2 compared to the current value., Comment: 26 pages, 4 figures

Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, a dependence that is poorly controlled due to the non-global nature of the clustering. At jet radii of experimental interest, the leading order (LO) clustering effects are numerically significant, but the higher order effects are currently unknown. We rectify this situation by calculating the most important part of the next-to-leading order (NLO) clustering logarithms of R for any 0-jet process, which enter as $O(\alpha_s^3)$ corrections to the cross section. The calculation blends subtraction methods for NLO calculations with factorization properties of QCD and soft-collinear effective theory (SCET). We compare the size of the known LO and new NLO clustering logarithms and find that the impact of the NLO terms on the 0-jet cross section in Higgs production is small. This brings clustering effects under better control and may be used to improve uncertainty estimates on cross sections with a jet veto., Comment: 39 pages, 5 figures. v2: journal version. v3: added missing term in calculation, conclusions unchanged

We present a general method to match fully differential next-to-next-to-leading (NNLO) calculations to parton shower programs. We discuss in detail the perturbative accuracy criteria a complete NNLO+PS matching has to satisfy. Our method is based on consistently improving a given NNLO calculation with the leading-logarithmic (LL) resummation in a chosen jet resolution variable. The resulting NNLO$+$LL calculation is cast in the form of an event generator for physical events that can be directly interfaced with a parton shower routine, and we give an explicit construction of the input "Monte Carlo cross sections" satisfying all required criteria. We also show how other proposed approaches naturally arise as special cases in our method., Comment: 53 pages, 3 figures

We present predictions for Higgs production via gluon fusion with a p_T veto on jets and with the resummation of jet-veto logarithms at NNLL'+$NNLO order. These results incorporate explicit O(alphas^2) calculations of soft and beam functions, which include the dominant dependence on the jet radius R. In particular the NNLL' order accounts for the correct boundary conditions for the N3LL resummation, for which the only unknown ingredients are higher-order anomalous dimensions. We use scale variations in a factorization theorem in both rapidity and virtuality space to estimate the perturbative uncertainties, accounting for both higher fixed-order corrections as well as higher-order towers of jet-p_T logarithms. This formalism also predicts the correlations in the theory uncertainty between the exclusive 0-jet and inclusive 1-jet bins. At the values of R used experimentally, there are important corrections due to jet algorithm clustering that include logarithms of R. Although we do not sum logarithms of R, we do include an explicit contribution in our uncertainty estimate to account for higher-order jet clustering logarithms. Precision predictions for this H+0-jet cross section and its theoretical uncertainty are an integral part of Higgs analyses that employ jet binning., Comment: 24 pages, 11 figures

We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA8) to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolution scales. Results for e+e- -> jets compared to LEP data and for Drell-Yan production are presented., Comment: 4 pages, 3 figures. To appear in the proceedings of the 48th Rencontres de Moriond (QCD and High Energy Interactions), La Thuile, Italy, March 9-16, 2013

We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e+e and pp collisions. We present first results of the implementation in the GENEVA Monte Carlo framework, where we employ N-jettiness as the jet resolution variable, combining its next-to-next-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and PYTHIA8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e+e- -> jets, taking alpha_s(mZ) = 0.1135 from fits to LEP thrust data, together with the PYTHIA8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables., Comment: 64 pages, 14 figures; v2: plot in Fig. 5 and Refs. added, journal version

Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that can be used to veto jets in hadronic collisions. We consider two inclusive variables, the scalar sum over pT and beam thrust, and two corresponding exclusive variables based on jet algorithms, namely the largest pT and largest beam thrust of a jet. The inclusive variables can, in principle, be resummed to higher orders. We show that for the jet-based variables, there are dual effects due to clustering in the jet algorithm for both large and small jet radius R that make a complete resummation at or beyond next-to-leading logarithmic order (NLL) challenging. For R~1, the clustering of soft and collinear emissions gives O(1) contributions starting at next-to-next-to-leading logarithmic order that are not reproduced by an all-orders soft-collinear factorization formula and therefore are not automatically resummed by it. For R<<1, clustering induces logarithms of R that contribute at NLL in the exponent of the cross section, which cannot be resummed with currently available methods. We explicitly compute the leading jet clustering effects at two loops and comment on their numerical size., Comment: 13 pages + appendices, 3 figures; v2: explained agreement with Ref. [14]; v3: journal version; v4: corrected error in Appendix B, which changes the results for independent emissions for the Taucut case in Eqs. (48), (49), (50). Conclusions remain unchanged

Clustering algorithms build jets though the iterative application of single particle and pairwise metrics. This leads to phase space constraints that are extremely complicated beyond the lowest orders in perturbation theory, and in practice they must be implemented numerically. This complication presents a significant barrier to gaining an analytic understanding of the perturbative structure of jet cross sections. We present a novel framework to express the jet algorithm's phase space constraints as a function of clustered groups of particles, which are the possible outcomes of the algorithm. This approach highlights the analytic properties of jet observables, rather than the explicit constraints on individual final state momenta, which can be unwieldy at higher orders. We derive the form of the n-particle phase space constraints for a jet algorithm with any measurement. We provide an expression for the measurement that makes clustering effects manifest and relates them to constraints from clustering at lower orders. The utility of this framework is demonstrated by using it to understand clustering effects for a large class of jet shape observables in the soft/collinear limit. We apply this framework to isolate divergences and analyze the logarithmic structure of the Abelian terms in the soft function, providing the all-orders form of these terms and showing that corrections from clustering start at next-to-leading logarithmic order in the exponent of the cross section., Comment: 29 pages, 7 figures. v2: fixed typos in enumerated clustering maps, figure 6

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution, and we show that new clustering effects contributing at NLL likely arise at each order. Therefore we find that it is unlikely that clustering logs can be resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at two loops for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that previously identified logarithms from clustering effects can be naturally thought of as a class of non-global logarithms (NGLs), which have traditionally been tied to non-Abelian correlations in soft gluon emission., Comment: 22 pages + appendices, 8 figures

Factorization underpins our ability to make predictions at the LHC, both in Monte Carlo simulations and direct calculations. An improved theoretical understanding of jet substructure can lead to calculations that can confront data and validate the Monte Carlo description of jets. We derive constraints on jet substructure algorithms from factorization, focusing on the broad class of jet observables where the soft and collinear dynamics of QCD dominate. A necessary condition for factorization is that the phase space constraints on soft and collinear dynamics for a given observable are independent of each other. This condition allows us to use a simple power counting analysis to place strong constraints on the form of jet substructure methods that can factorize. We illustrate this approach by considering four substructure algorithms, the mass-drop filter Higgs tagger, pruning, trimming, and N-subjettiness. We find that factorization constrains the scaling of parameters in all of the substructure algorithms, and that the generic declustering and filtering techniques do not factorize. However, we determine simple modifications that can be made to allow for factorization., Comment: 22 pages, 10 figures

We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto \Lambda due to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form \alpha_s^2 \ln^2(\Lambda/m_{1,2}) or \alpha_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambridge-Aachen algorithms. In addition to determining the full algorithmic and R dependence of the leading NGLs, we derive new relations among their coefficients. We also derive to all orders in \alpha_s a factorized form for the soft function S(k_L,k_R,\Lambda) in the cross section \sigma(m_1,m_2,\Lambda) in which dependence on each of the global logs of \mu/k_L, \mu/k_R and \mu/\Lambda determined by the renormalization group are separated from one another and from the non-global logs. The same kind of soft function, its associated non-global structure, and the algorithmic dependence we derive here will also arise in exclusive jet cross sections at hadron colliders, and must be understood and brought under control to achieve precise theoretical predictions., Comment: 19 pages, 10 figures. v2: minor edits, additional discussion in Introduction. v3: version published in JHEP

Multijet cross sections at the LHC and Tevatron are sensitive to several distinct kinematic energy scales. When measuring the dijet invariant mass m_jj between two signal jets produced in association with other jets or weak bosons, m_jj will typically be much smaller than the total partonic center-of-mass energy Q, but larger than the individual jet masses m, such that there can be a hierarchy of scales m << m_jj << Q. This situation arises in many new-physics analyses at the LHC, where the invariant mass between jets is used to gain access to the masses of new-physics particles in a decay chain. At present, the logarithms arising from such a hierarchy of kinematic scales can only be summed at the leading-logarithmic level provided by parton-shower programs. We construct an effective field theory, SCET+, which is an extension of soft-collinear effective theory that applies to this situation of hierarchical jets. It allows for a rigorous separation of different scales in a multiscale soft function and for a systematic resummation of logarithms of both m_jj/Q and m/Q. As an explicit example, we consider the invariant mass spectrum of the two closest jets in e+e- -> 3 jets. We also give the generalization to pp -> N jets plus leptons relevant for the LHC., Comment: 37 pages, 6 figures; v2: journal version

High energy scattering processes involving jets generically involve matrix elements of light- like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on terms not determined by its renormalization group evolution that have a non-separable dependence on these masses. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete O({\alpha}_s^2) soft function for dijet production in both position and momentum space., Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the hard regime. v3: minor typos corrected, version published in JHEP. v4: typos in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main result, numerical results, or conclusions

We consider searching for light sterile fermions and new forces by using long baseline oscillations of neutrinos and antineutrinos. A new light sterile state and/or a new force can lead to apparent CPT violation in muon neutrino and antineutrino oscillations. As an example, we present an economical model of neutrino masses containing a sterile neutrino. The potential from the Standard Model neutral current gives rise to a difference between the disappearance probabilities of neutrinos and antineutrinos, when mixing with a light sterile neutrino is considered. The addition of a B-L interaction adds coherently to the neutrino current potential and increases the difference between neutrino and antineutrino disappearance. We find that this model can improve the fit to the results of MINOS for both neutrinos and antineutrinos, without any CPT violation, and that the regions of parameter space which improve the fit are within experimental constraints., Comment: 8 pages, 3 figures, added comment about CDHS, added references

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar., Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections. v3: Journal version. Introductory sections significantly reorganized for clarity, classification of logarithmic accuracy clarified, results for non-Mercedes-Benz configurations added

We demonstrate the consistency at the next-to-leading-logarithmic (NLL) level of a factorization theorem based on Soft-Collinear Effective Theory (SCET) for jet shapes in e+e- collisions. We consider measuring jet observables in exclusive multijet final states defined with cone and k_T-type jet algorithms. Consistency of the factorization theorem requires that the renormalization group evolution of hard, jet, and soft functions is such that the physical cross-section is independent of the factorization scale mu. The anomalous dimensions of the various factorized pieces, however, depend on the color representation of jets, choice of jet observable, the number of jets whose shapes are measured, and the jet algorithm, making it highly nontrivial to satisfy the consistency condition. We demonstrate the intricate cancellations between anomalous dimensions that occur at the NLL level, so that, up to power corrections that we identify, our factorization of the jet shape distributions is consistent for any number of quark and gluon jets, for any number of jets whose shapes are measured or unmeasured, for any angular size R of the jets, and for any of the algorithms we consider. Corrections to these results are suppressed by the SCET expansion parameter lambda (the ratio of soft to collinear or collinear to hard scales) and in the jet separation measure 1/t^2 = tan^2(R/2)/tan^2(psi/2), where psi is the angular separation between jets. Our results can be used to calculate a wide variety of jet observables in multijet final states to NLL accuracy., Comment: 8 pages, 1 figure, uses elsarticle.cls; v2: minor edits, added references

We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide angle radiation, improves the mass resolution of jets reconstructing a heavy particle decay, and decreases the QCD background. We show that pruning provides significant improvements over unpruned jets in identifying top quarks and W bosons and separating them from a QCD background, and may be useful in a search for heavy particles., Comment: 33 pages, 42 figures

We present a generic method for improving the effectiveness of heavy particle searches in hadronic channels at the Large Hadron Collider. By selectively removing, or pruning, protojets from the substructure provided by a k_T-style jet algorithm, we improve the mass resolution for heavy decays and decrease the QCD background. We show that the protojets removed are typical of soft radiation and underlying event contributions, and atypical of accurately reconstructed heavy particles., Comment: 4 pages, 3 figures; 5 pages, provide definition of h_T, correct description of making cells massless; IR safe definition for parameter D_cut, more complete references, comparisons to matched QCD jet samples, slightly changed figures; correct references