arXiv subjects

Hua Xing Zhu

Publications and source records attributed to Hua Xing Zhu.

At least 73 records · Page 4Linked to original sources

arXiv2021

Quantum Interference in Jet Substructure from Spinning Gluons

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 non-trivial shape dependence, playing a special role in unravelling 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.

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arXiv2020

Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO

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 (N$^3$LO) in QCD. The N$^3$LO 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 $α_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

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arXiv2020

Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results

Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in $\mathcal{N}=4$ super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In $\mathcal{N}=4$, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.

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arXiv2020

Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation

We introduce an infinite set of jet substructure observables, derived as projections of $N$-point energy correlators, that are both convenient for experimental studies and maintain remarkable analytic properties derived from their representations in terms of a finite number of light ray operators. We show that these observables can be computed using tracking or charge information with a simple reweighting by integer moments of non-perturbative track or fragmentation functions. Our results for the projected $N$-point correlators are analytic functions of $N$, allowing us to derive resummed results to next-to-leading logarithmic accuracy for all $N$. We analytically continue our results to non-integer values of $N$ and define a corresponding analytic continuation of the observable, which we term a $ν$-correlator, that can be measured on jets of hadrons at the LHC. This enables observables that probe the leading twist collinear dynamics of jets to be placed into a single analytic family, which we hope will lead to new insights into jet substructure.

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arXiv2020

Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD

It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not analytic function of external momenta. However, splitting functions can be constructed from square of (generalized) splitting amplitudes. We establish the rule of analytic continuation for splitting amplitudes, and use them to determine the analytic continuation of certain holomorphic and anti-holomorphic part of splitting functions and transverse-momentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We also propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops.

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arXiv2020

Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of non-standard Feynman integrals with rapidity divergence. We introduce a set of generalized Integration-By-Parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.

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arXiv2020

The Soft Quark Sudakov

There has been recent interest in understanding the all loop structure of the subleading power soft and collinear limits, with the goal of achieving a systematic resummation of subleading power infrared logarithms. Most of this work has focused on subleading power corrections to soft gluon emission, whose form is strongly constrained by symmetries. In this paper we initiate a study of the all loop structure of soft fermion emission. In $\mathcal{N}=1$ QCD we perform an operator based factorization and resummation of the associated infrared logarithms, and prove that they exponentiate into a Sudakov due to their relation to soft gluon emission. We verify this result through explicit calculation to $\mathcal{O}(α_s^3)$. We show that in QCD, this simple Sudakov exponentiation is violated by endpoint contributions proportional to $(C_A-C_F)^n$ which contribute at leading logarithmic order. Combining our $\mathcal{N}=1$ result and our calculation of the endpoint contributions to $\mathcal{O}(α_s^3)$, we conjecture a result for the soft quark Sudakov in QCD, a new all orders function first appearing at subleading power, and give evidence for its universality. Our result, which is expressed in terms of combinations of cusp anomalous dimensions in different color representations, takes an intriguingly simple form and also exhibits interesting similarities to results for large-x logarithms in the off diagonal splitting functions.

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arXiv2020

Differential Distributions for t-channel Single Top-Quark Production and Decay at Next-to-Next-to-Leading Order in QCD

We present a detailed phenomenological study of the next-to-next-to-leading order (NNLO) QCD corrections for $t$-channel single top (anti-)quark production and its semi-leptonic decay at the CERN Large Hadron Collider (LHC). We find the NNLO corrections for the total inclusive rates at the LHC with different center of mass energies are generally smaller than the NLO corrections, indicative of improved convergence. However, they can be large for differential distributions, reaching a level of $10\%$ or more in certain regions of the transverse momentum distributions of the top (anti-)quark and the pseudo-rapidity distributions of the leading jet in the event. In all cases the perturbative hard scale uncertainties are greatly reduced after the NNLO corrections are included. We also show a comparison of the normalized parton-level distributions to recent data from the 8 TeV measurement of the ATLAS Collaboration. The NNLO corrections tend to shift the theoretical predictions closer to the measured transverse momentum distribution of the top (anti)-quark. Importantly, for the LHC at 13 TeV, we present NNLO cross sections in a fiducial volume with decays of the top quark included.

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arXiv2019

Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case

We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the ${\cal N}=1$ super-Yang-Mills theory. The TMDFFs are used to calculate the two-loop gluon jet function for the energy-energy correlator in Higgs gluonic decay in the back-to-back limit.

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arXiv2019

Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case

We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to $\mathcal{O}(ε^2)$ in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N$^3$LL resummation.

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arXiv2019

Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays

The energy-energy correlation (EEC) function in $e^+e^-$ annihilation is currently the only QCD event shape observable for which we know the full analytic result at the next-to-leading order (NLO). In this work we calculate the EEC observable for gluon initiated Higgs decay analytically at NLO in the Higgs Effective Field Theory (HEFT) framework and provide the full results expressed in terms of classical polylogarithms, including the asymptotic behavior in the collinear and back-to-back limits. This observable can be, in principle, measured at the future $e^+e^-$ colliders such as CEPC, ILC, FCC-ee or CLIC. It provides an interesting opportunity to simultaneously probe our understanding of the strong and Higgs sectors and can be used for the determinations of the strong coupling.

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arXiv2019

First Subleading Power Resummation for Event Shapes

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables $τ$ at subleading power in the $τ\ll 1$ expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call $θ$-jet and $θ$-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in $α_s$, and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for $H\to gg$ in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to ${\cal O}(α_s^3)$. Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the $θ$-soft and $θ$-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.

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arXiv2019

The Collinear Limit of the Energy-Energy Correlator

The energy-energy-correlator (EEC) observable in $e^+e^-$ annihilation measures the energy deposited in two detectors as a function of the angle between the detectors. The collinear limit, where the angle between the two detectors approaches zero, is of particular interest for describing the substructure of jets produced at hadron colliders as well as in $e^+e^-$ annihilation. We derive a factorization formula for the leading power asymptotic behavior in the collinear limit of a generic quantum field theory, which allows for the resummation of logarithmically enhanced terms to all orders by renormalization group evolution. The relevant anomalous dimensions are expressed in terms of the timelike data of the theory, in particular the moments of the timelike splitting functions, which are known to high perturbative orders. We relate the small angle and back-to-back limits to each other via the total cross section and an integral over intermediate angles. This relation provides us with the initial conditions for quark and gluon jet functions at order $α_s^2$. In QCD and in $\mathcal{N}=1$ super-Yang-Mills theory, we then perform the resummation to next-to-next-to-leading logarithm, improving previous calculations by two perturbative orders. We highlight the important role played by the non-vanishing $β$ function in these theories, which while subdominant for Higgs decays to gluons, dominates the behavior of the EEC in the collinear limit for $e^+e^-$ annihilation, and in $\mathcal{N}=1$ super-Yang-Mills theory. In conformally invariant $\mathcal{N}=4$ super-Yang-Mills theory, reciprocity between timelike and spacelike evolution can be used to express our factorization formula as a power law with exponent equal to the spacelike twist-two spin-three anomalous dimensions, thus providing a connection between timelike and spacelike approaches.

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arXiv2019

Subleading Power Rapidity Divergences and Power Corrections for $q_T$

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum ($q_T$) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-$x$ logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding $\overline{\rm MS}$-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the $q_T$ spectrum for color-singlet production, for which we compute the complete $q_T^2/Q^2$ suppressed power corrections at $\mathcal{O}(α_s)$, including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

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arXiv2019

Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation

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.

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arXiv2019

The Transverse Energy-Energy Correlator in the Back-to-Back Limit

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.

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arXiv2018

Power Corrections for N-Jettiness Subtractions at ${\cal O}(α_s)$

We continue the study of power corrections for $N$-jettiness subtractions by analytically computing the complete next-to-leading power corrections at $\cal{O}(α_s)$ for color-singlet 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.

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arXiv2018

Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum

The transverse momentum ($p_T$) distribution of Higgs bosons at hadron colliders enables a detailed probe of its production dynamics and is a key ingredient to precision studies of Higgs boson properties, but receives very large QCD corrections. We obtain a precision prediction for the $p_T$ spectrum by matching second-order (NNLO) QCD corrections at large $p_T$ with resummation of third-order logarithmic (N$^3$LL) corrections at small $p_T$. We achieve significantly improved results for $p_T< 35\,{\rm GeV}$ with perturbative uncertainties $\lesssim \pm 6\%$, and thus a convergent perturbative series for all values of $p_T$.

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