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We demonstrate the recently proposed nucleon energy-energy correlator (NEEC) f_{EEC}(x,θ) can unveil the gluon saturation in the small-x regime in eA collisions. The novelty of this probe is that it is fully inclusive just like the deep-inelastic scattering (DIS), with no requirements of jets or hadrons but still provides an evident portal to the small-x dynamics through the shape of the θ distribution. We find that the saturation prediction is significantly different from the expectation of the collinear factorization.

We present an operator-based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-next-to-leading logarithm (NNLL) matched to fixed order at the LHC. Our results constitute the first NNLL resummation for a dijet event shape observable at a hadron collider, and the first analytic result for a hadron collider dijet soft function at NNLO. We anticipate that the theoretical simplicity of the TEEC observable will make it indispensable for precision studies of QCD at the LHC, and as a playground for theoretical studies of factorization and its violation.

Abstract : We continue the study of power corrections for N -jettiness subtractions by analytically computing the complete next-to-leading power corrections at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s for colorsinglet production. This includes all nonlogarithmic terms and all partonic channels for Drell-Yan and gluon-fusion Higgs production. These terms are important to further improve the numerical performance of the subtractions, and to better understand the structure of power corrections beyond their leading logarithms, in particular their universality. We emphasize the importance of computing the power corrections differential in both the invariant mass, Q, and rapidity, Y, of the color-singlet system, which is necessary to account for the rapidity dependence in the subtractions. This also clarifies apparent disagreements in the literature. Performing a detailed numerical study, we find excellent agreement of our analytic results with a previous numerical extraction.

Abstract We continue the study of power corrections for N -jettiness subtractions by analytically computing the complete next-to-leading power corrections at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s for colorsinglet production. This includes all nonlogarithmic terms and all partonic channels for Drell-Yan and gluon-fusion Higgs production. These terms are important to further improve the numerical performance of the subtractions, and to better understand the structure of power corrections beyond their leading logarithms, in particular their universality. We emphasize the importance of computing the power corrections differential in both the invariant mass, Q, and rapidity, Y, of the color-singlet system, which is necessary to account for the rapidity dependence in the subtractions. This also clarifies apparent disagreements in the literature. Performing a detailed numerical study, we find excellent agreement of our analytic results with a previous numerical extraction.

Abstract : We derive an operator based factorization theorem for the energy-energy correlation (EEC) observable in the back-to-back region, allowing the cross section to be written as a convolution of hard, jet and soft functions. We prove the equivalence of the soft functions for the EEC and color singlet transverse-momentum resummation to all-loop order, and give their analytic result to three-loops. Large logarithms appearing in the perturbative expansion of the EEC can be resummed to all orders using renormalization group evolution. We give analytic results for all required anomalous dimensions to three-loop order, providing the first example of a transverse-momentum (recoil) sensitive e + e − event shape whose anomalous dimensions are known at this order. The EEC can now be computed to next-to-next-to-next-to-leading logarithm matched to next-to-next-to-leading order, making it a prime candidate for precision QCD studies and extractions of the strong coupling constant. We anticipate that our factorization theorem will also be crucial for understanding non-perturbative power corrections for the EEC, and their relationship to those appearing in other observables.

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N3LO) in QCD. The N3LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction z. We resum such logarithmic terms to the third order in the expansion of αs. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments. [ABSTRACT FROM AUTHOR]

We study the single soft-gluon current at two loops with two energetic partons in massless perturbative QCD, which describes, for example, the soft limit of the two-loop amplitude for gg → Hg. The results are presented as Laurent expansions in ϵ in D = 4 − 2 ϵ spacetime dimension. We calculate the expansion to order ϵ2 analytically, which is a necessary ingredient for Higgs production at hadron colliders at next-to-next-to-next-to-leading order in the soft-virtual approximation. We also give two-loop results of the single soft-gluon current in $ \mathcal{N}=4 $ Super-Yang-Mills theory, and find that it has uniform transcendentality. By iteration relation of splitting amplitudes, our calculations can determine the three-loop single soft-gluon current to order ϵ0 in $ \mathcal{N}=4 $ Super-Yang-Mills theory in the limit of large Nc. [ABSTRACT FROM AUTHOR]

We calculate the coefficients of the leading non-global logarithms for the hemispheremass distribution analytically at 3, 4, and 5 loops at large Nc. We confirm that the integrand derived with the strong-energy-ordering approximation and fixed-order iteration of the Banfi-Marchesini-Syme (BMS) equation agree. Our calculation exploits a hidden PSL(2, R) symmetry associated with the jet directions, apparent in the BMS equation after a stereographic projection to the Poincar´e disk. The required integrals have an iterated form, leading to functions of uniform transcendentality. This allows us to extract the coefficients, and some functional dependence on the jet directions, by computing the symbols and coproducts of appropriate expressions involving classical and Goncharov polylogarithms. Convergence of the series to a numerical solution of the BMS equation is also discussed., Physics

A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level, and all the global logarithms at next-to-next-to-leading logarithmic level. A key step in the derivation is the factorization of the soft function into pieces associated with single scales and a remainder which contains nonglobal structure. This step, which is standard in traditional resummation, is implemented in effective field theory which is then used to resum the large logarithms using the renormalization group in a systematically improvable manner., Physics

We investigate the exclusive jet mass distribution in e+e− events, defined with a veto on the out-of-jet radiation, at two-loop order. In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region. When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order. The result is in excellent agreement with full QCD. The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale. The result clarifies the structure of the potentially large logarithms (both global and nonglobal) which arise in jet observables for the first time at this order. Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms. This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables., Physics

We introduce the concept of the nucleon energy correlators, a set of novel objects that encode the microscopic details of a nucleon, such as the parton angular distribution in a nucleon, the collinear splitting to all orders, as well as the internal transverse dynamics of the nucleon. The nucleon energy correlators complement the conventional nucleon or nucleus tomography, but without introducing the nonperturbative fragmentation functions or the jet clustering algorithms. We demonstrate how the nucleon energy correlators can be measured in the lepton-nucleon deep inelastic scattering. The predicted distributions display a fascinating phase transition between the perturbative and nonperturbative regime. In the perturbative phase, a polar angle version of the Bjorken scaling behavior is predicted. We discuss its possible applications and expect it to aggrandize the physics content at the electron ion colliders with a far-forward detector.

Jets of hadrons produced at high-energy colliders provide experimental access to the dynamics of asymptotically free quarks and gluons and their confinement into hadrons. In this Letter, we show that the high energies of the Large Hadron Collider (LHC), together with the exceptional resolution of its detectors, allow multipoint correlation functions of energy flow operators to be directly measured within jets for the first time. Using Open Data from the CMS experiment, we show that reformulating jet substructure in terms of these correlators provides new ways of probing the dynamics of QCD jets, which enables direct imaging of the confining transition to free hadrons as well as precision measurements of the scaling properties and interactions of quarks and gluons. This opens a new era in our understanding of jet substructure and illustrates the immense unexploited potential of high-quality LHC data sets for elucidating the dynamics of QCD.

Collider experiments often exploit information about the quantum numbers of final state hadrons to maximize their sensitivity, with applications ranging from the use of tracking information (electric charge) for precision jet substructure measurements, to flavor tagging for nucleon structure studies. For such measurements, perturbative calculations in terms of quarks and gluons are insufficient, and nonperturbative track functions describing the energy fraction of a quark or gluon converted into a subset of hadrons (e.g., charged hadrons) must be incorporated. Unlike fragmentation functions, track functions describe correlations between hadrons and therefore satisfy complicated nonlinear evolution equations whose structure has so far eluded calculation beyond the leading order. In this Letter, we develop an understanding of track functions and their interplay with energy flow observables beyond the leading order, allowing them to be used in state-of-the-art perturbative calculations for the first time. We identify a shift symmetry in the evolution of their moments that fixes their structure, and we explicitly compute the evolution of the first three moments at next-to-leading order, allowing for the description of up to three-point energy correlations. We then calculate the two-point energy correlator on charged particles at O(α_{s}^{2}), illustrating explicitly that infrared singularities in perturbation theory are absorbed by moments of the track functions and also highlighting how these moments seamlessly interplay with modern techniques for perturbative calculations. Our results extend the boundaries of traditional perturbative QCD, enabling precision perturbative predictions for energy flow observables sensitive to the quantum numbers of hadronic states.

We compute for the first time the lepton-pair rapidity distribution in the photon-mediated Drell-Yan process to next-to-next-to-next-to-leading order in QCD. The calculation is based on the q_{T}-subtraction method, suitably extended to this order for quark-antiquark initiated Born processes. Our results display sizeable QCD corrections at next-to-next-to-next-to-leading order over the full rapidity region and provide a fully independent confirmation of the recent results for the total Drell-Yan cross section at this order.

The emerging cleavage under target and tagment (CUT&Tag) technology uses Tn5 transposase to cleavage near the DNA binding site of target protein and study the generated DNA fragments by the next-generation sequencing. It can quickly identify protein-DNA interactions, which greatly simplifies the experimental process of ChIP-Seq. After CUT&Tag tagment reaction, DNA recovery or other post-processing is required to perform library construction PCR. Different recovery methods have significant impact respectively. By establishing Streptavidin beads recovery CUT&Tag(srCUT&Tag), we can quickly and conveniently complete the product recovery of CUT&Tag. We carried out CUT&Tag assay of H3K4me3, RNA Polymerase II (RNA polymerase II, RNAPII), transcription factor CTCF and HMGA1 in K562 cells with different recovery methods, including ethanol precipitation, fragment separation magnetic beads (SPRI) Magnetic bead recovery, direct PCR method, as well as our srCUT&Tag recovery method. The results show that among the CUT&Tag results of four different targets, the SPRI magnetic bead recovery and our srCUT&Tag methods have higher recovery efficiency than the direct PCR method and ethanol precipitation method. All CUT&Tag results showed that the recovery of SPRI magnetic beads would lose most of the product fragments less than 150 bp. In the recovery of CTCF and HMGA1, direct PCR lost most of the fragments larger than 300 bp and has significant difference from result of other recovery method. This enables srCUT&Tag to provide more real and higher-resolution information than other recovery method. In summary, the newly established srCUT&Tag recovery method can improve the efficiency of CUT&Tag library construction and obtain better data quality compared with the existing CUT&Tag product recovery method, providing a better technical choice for epigenetics research.

Collimated sprays of hadrons, called jets, are an emergent phenomenon of quantum chromodynamics (QCD) at collider experiments, whose detailed internal structure encodes valuable information about the interactions of high energy quarks and gluons and their confinement into color-neutral hadrons. The flow of energy within jets is characterized by correlation functions of energy flow operators, with the three-point correlator being the first correlator with nontrivial shape dependence, playing a special role in unraveling the dynamics of QCD. In this Letter, we initiate a study of the three-point energy correlator to all orders in the strong coupling constant, in the limit where two of the detectors are squeezed together. We show that, by rotating the two squeezed detectors with respect to the third by an angle ϕ, a cos(2ϕ) dependence arising from the quantum interference between intermediate virtual gluons with +/- helicity is imprinted on the detector. This can be regarded as a double slit experiment performed with jet substructure, and it provides a direct probe of the ultimately quantum nature of the substructure of jets and of transverse spin physics in QCD. To facilitate our all-orders analysis, we adopt the operator product expansion (OPE) for light-ray operators in conformal field theory and develop it in QCD. Our application of the light-ray OPE in real world QCD establishes it as a powerful theoretical tool with broad applications for the study of jet substructure.