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We present the first complete next-to-next-to-next-to-leading-order calculation of the matching coefficients that link unpolarized flavor non-singlet parton distribution functions with lattice QCD computable correlation functions. By using this high-order result, we notice a reduction in theoretical uncertainties compared to relying solely on previously known lower-order matching coefficients. Furthermore, based on this result we have extracted the three-loop unpolarized flavor non-singlet splitting function, which is in agreement with the state-of-the-art result. Due to the simplicity of our method, it has the potential to advance the calculation of splitting functions to the desired four-loop order., Comment: 12 pages, 2 figures

In this article, we present the package Blade as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain integration-by-parts system, allowing for strictly block-by-block solutions. This results in faster evaluations and reduced resource consumption. We elucidate the algorithms involved in obtaining the block-triangular form along with their implementations. Additionally, we introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Our benchmarks for various state-of-the-art problems demonstrate that Blade is remarkably competitive among existing reduction tools. Furthermore, the Blade package offers several distinctive features, including support for complex kinematic variables or masses, user-defined Feynman prescriptions for each propagator, and general integrands., Comment: 20 pages, 8 figures, 10 tables

We propose to measure the energy correlator in quarkonium production, which tracks the energy deposited in the calorimeter $\chi$-angular distance away from the identified quarkonium. The observable eliminates the need for jets while sustaining the perturbative predictive power. Analyzing the power correction to the energy correlator, we demonstrate the novel observable supplies a unique gateway to probing the hadronization, especially when $\cos\chi\gtrsim 0$ in the quarkonium rest frame where the perturbative emissions are depleted due to the dead-cone effects. We expect the quarkonium energy correlator to add a new dimension to quarkonium studies., Comment: 7 pages, 4 figures + supplemental materials (3 pages), reorganized the text to enhance clarity and incorporated theoretical uncertainties, references updated

We study the mass spectra of hidden-charm tetraquark systems with quantum numbers $(I^G)J^P=(1^+)1^+$ using QCD sum rules. The analysis incorporates the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the operator product expansions, with particular attention to operator mixing effects due to renormalization group evolution. For the $\bar{d}c\bar{c}u$ system, the masses of two mixed operators, $J_{1,5}^{\text{Mixed}}$ and $J_{2,6}^{\text{Mixed}}$, are determined to be $3.89^{+0.18}_{-0.12}$ GeV and $4.03^{+0.06}_{-0.07}$ GeV, respectively, closely matching those of $Z_c$(3900) and $Z_c(4020)$. Similarly, for the $\bar{s}c\bar{c}u$ states, the masses of $J_{1,5}^{\text{Mixed}}$ and $J_{2,6}^{\text{Mixed}}$ are found to be $4.02^{+0.17}_{-0.09}$ GeV and $4.21^{+0.08}_{-0.07}$ GeV, respectively, in close proximity to $Z_{cs}$(3983)/$Z_{cs}$(4000) and $Z_{cs}$(4220), consistent with the expectation that they are the partners of $Z_c$(3900) and $Z_c$(4020). Our results highlight the crucial role of operator mixing, an inevitable effect in a complete NLO calculation, in achieving a robust phenomenological description for the tetraquark system., Comment: 49 pages, 32 fugures. version accepted for publication in JHEP. arXiv admin note: substantial text overlap with arXiv:2201.11714

We present the results for the complete next-to-leading order electroweak corrections to $pp \to HH$ at the Large Hadron Collider, focusing on the dominant gluon-gluon fusion process. While the corrections at the total cross-section level are approximately $-4\%$, those near the energy of $HH$ production threshold exceed $+15\%$, and corrections at the high-energy region are around $-10\%$, leading to a shape distortion for the differential distributions. Our findings substantially diminish the theoretical uncertainties associated with this pivotal process, providing valuable input for understanding the shape of the Higgs boson potential upon comparison with experimental measurements., Comment: 7 pages, 4 figures, version published in PRL

Although Feynman integrals in general cannot be expressed as well-studied special functions, they can be calculated systematically and efficiently using the \texttt{AMFlow} method in combination with differential equations in the kinematic space. Therefore, it is constructive to define Feynman integrals as a new class of special functions (or transcedental numbers if there is no kinematic variable). Several crucial avenues for further exploration in this direction are outlined., Comment: 4 pages, 1 figure, published version

Inflation with Weyl scaling symmetry provides a viable scenario that can generate both the nearly scaling invariant primordial density fluctuation and a dark matter candidate. Here we point out that, in additional to the primordial gravitational waves (GWs) from quantum fluctuations, the production of high-frequency GWs from preheating in such inflation models can provide an another probe of the inflationary dynamics. We conduct both linear analytical analysis and nonlinear numerical lattice simulation in a typical model. We find that significant stochastic GWs can be produced and the frequency band is located around $10^8$ Hz $\sim$ $10^9$ Hz, which might be probed by future resonance-cavity experiments., Comment: 21 pages, 6 figures

We perform a high-precision computation of the three-loop three-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM. Both the leading-color and non-leading-color form factors are expanded in terms of simple integrals. We compute the complete set of integrals at a special kinematic point with very high precision using $\mathtt{AMFlow}$. The high-precision leading-color result enables us to obtain the analytic form of a numerical constant in the three-loop BDS ansatz, which is previously known only numerically. The high-precision values of the non-leading-color finite remainder as well as all integrals are also presented, which can be valuable for future use., Comment: 6 pages, 25 pages of appendix; v2: appendix modified, published version

We present the first complete high-precision QCD corrections to the inclusive decay width $\mathrm{\Gamma}_t$, the $W$-helicity fractions $f_{\mathrm{L,R,0}}$ and semi-inclusive distributions for the top-quark decay process $t \rightarrow b + W^+ + X_{\mathrm{\tiny QCD}}$ at NNNLO in the strong coupling constant $\alpha_s$. In particular, the pure NNNLO QCD correction decreases the $\mathrm{\Gamma}_t$ by about $0.8\%$ of the previous NNLO result at the top-quark pole mass scale, exceeding the error estimated by the usual scale-variation prescription. After taking into account all sources of errors, we get $\mathrm{\Gamma}_t = 1.3148^{+0.003}_{-0.005} + 0.027\,(m_t - 172.69)\,\text{GeV} $, the error of which meets the request by future colliders. On the other hand, the NNNLO QCD effects on $f_{\mathrm{L,R,0}}$ are found to be much smaller, at the level of one per-mille for the dominating $f_{0}$, predestining them to act as precision observables for the top-quark decay process., Comment: 7 pages, 3 figures

Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and solving differential equations of these generating functions, we are able to derive a system of reduction rules that effectively reduce any associated Feynman integrals to their bases. We illustrate this method through various examples and observe its potential value in numerous scenarios., Comment: 11 pages, 4 figures, references added

It was found that, using nonrelativistic QCD factorization, the predicted $\chi_{cJ}$ hadroproduction cross section at large $p_T$ can be negative. The negative cross sections originate from terms proportional to plus function in ${^{3}\hspace{-0.6mm}P_{J}^{[1]}}$ channels, which are remnants of the infrared subtraction in matching the ${^{3}\hspace{-0.6mm}P_{J}^{[1]}}$ short-distance coefficients. In this article, we find that the above terms can be factorized into the nonperturbative ${^{3}\hspace{-0.6mm}S_{1}^{[8]}}$ soft gluon distribution function in the soft gluon factorization (SGF) framework. Therefore, the problem can be naturally resolved in SGF. With an appropriate choice of nonperturbative parameters, the SGF can indeed give positive predictions for $\chi_{cJ}$ production rates within the whole $p_T$ region. The production of $\psi(2S)$ is also discussed, and there is no negative cross section problem., Comment: 15 pages, 8 figures

We compute the complete two-loop electroweak corrections to the Higgsstralung process $e^+e^-\rightarrow HZ$ at the future Higgs factory. The Feynman integrals involved in the computation are decomposed into linear combinations of a minimal set of master integrals taking advantage of the recent developments of integral reduction techniques. The master integrals are then evaluated by differential equations with boundary conditions provided by the auxiliary mass flow method. Our final result for given $\sqrt{s}$ is expressed as a piecewise function defined by several deeply expanded power series, which has high precision and can be further manipulated efficiently. Our calculation presents the first complete two-loop electroweak corrections for processes with four external particles., Comment: 5 pages, 2 figures. arXiv admin note: text overlap with arXiv:2209.14259

We compute the total cross-section and invariant mass distribution for heavy-quark pair production in $e^+e^-$ annihilation at the next-to-next-to-next-to-leading order in QCD. The obtained results are expressed as piecewise functions defined by several deeply expanded power series, facilitating a rapid numerical evaluation. Utilizing top-pair production at a collision energy of 500 GeV as a benchmark, we observe a correction of approximately $0.1\%$ for the total cross-section and around $10\%$ for the majority of the invariant mass distribution range. These results play a crucial role in significantly reducing theoretical uncertainty: the scale dependence has been diminished to $0.06\%$ for the total cross-section and to $5\%$ for the invariant mass distribution. This reduction of uncertainty meets the stringent requirements of future lepton colliders., Comment: 7 pages, 5 figures; invariant mass distribution for heavy-quark pair added; version published at PRL

We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up to 5 loops are given to verify this observation. As a byproduct, we get a powerful method to calculate perturbative corrections in quantum field theory., Comment: 6 pages, 1 figure, version to be published in PRL

We proposed a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass flow method. The key of the recipe is to introduce a quadratic term for each linear propagator and then using differential equations to get rid of their effects. As an application, we calculated all master integrals of vacuum integrals containing a gauge link up to four loops, and we checked the results by nontrivial dimensional recurrence relations., Comment: We found a typographical error in our previous code, and thus numerical results in Eq. (30) and the ancillary file are updated

We study the mass spectra of $\bar{Q}Q\bar{Q}Q\ (Q=c,b)$ systems in QCD sum rules with the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Instead of meson-meson or diquark-antidiquark currents, we use diagonalized currents under operator renormalization. We find that differing from conventional mesons $\bar qq$ and baryons $qqq$, a unique feature of the multiquark systems like $\bar{Q}Q\bar{Q}Q$ is the operator mixing or color configuration mixing induced by NLO corrections, which is crucial to understand the color structure of the states. Our numerical results show that the NLO corrections are very important for the $\bar{Q}Q\bar{Q}Q$ system, because they not only give significant contributions but also reduce the scheme and scale dependence and make Borel platform more distinct, especially for the $\bar{b}b\bar{b}b$ in the $\overline{\rm{MS}}$ scheme. We use currents that have good perturbation convergence in our phenomenological analysis. With the $\overline{\rm{MS}}$ scheme, we get three $J^{PC}=0^{++}$ states, with masses $6.35^{+0.20}_{-0.17}$ GeV, $6.56^{+0.18}_{-0.20}$ GeV and $6.95^{+0.21}_{-0.31}$ GeV, respectively. The first two seem to agree with the broad structure around $6.2\sim6.8$ GeV measured by the LHCb collaboration in the $J/\psi J/\psi$ spectrum, and the third seems to agree with the narrow resonance $X(6900)$. For the $2^{++}$ states we find one with mass $7.03^{+0.22}_{-0.26}$ GeV, which is also close to that of $X(6900)$, and another one around $7.25^{+0.21}_{-0.35}$ GeV, which has good scale dependence but slightly large scheme dependence., Comment: 60 pages, 53 figures, nonrelativistic (NR) reductions of some operators are illustrated

AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter and their results can be obtained by constructing and solving differential systems with respect to this parameter, in an automatic way. The usage of this package is described in detail through an explicit example of double-box family involved in two-loop $t\bar{t}$ hadroproduction., Comment: published version with 30 pages, 4 figures and 1 table

We have studied color-octet contributions for $J/\psi$ inclusive production at B factories, i.e., $e^+e^-\to J/\psi(^3P_J^{[8]},^1S_0^{[8]}) + X_{\mathrm{non}-c\bar c}$, using the soft gluon factorization (SGF) approach, in which the $J/\psi$ energy spectrum is expressed in a form of perturbatively calculable short-distance hard parts convoluted with one-dimensional soft gluon distributions (SGDs). The series of velocity corrections originated from kinematic effect can be naturally resummed in this approach. Short-distance hard parts have been calculated analytically to next-to-leading order in $\alpha_s$. Renormalization group equations for SGDs have been derived and solved, which resums Sudakov logarithms originated from soft gluon emissions. Our final result gives a upper bound for color-octet matrix elements consistent with that extracted from hadron colliders. This may relieve the well-known universality problem in the NRQCD factorization. As a comparison, we also analytically calculated short-distance hard parts in the NRQCD factorization, with Sudakov logarithms resummed by using soft collinear effective theory. The comparison shows that velocity corrections from kinematic effect, which have been resummed in SGF, are significant for phenomenological study. Furthermore, it is found that Sudakov logarithms originated from soft gluon emissions are very important, while it is not the case for Sudakov logarithms originated from jet function. Therefore, the partial Sudakov resummation in SGF has already captured the main physics., Comment: 35 pages, 5 figures, published version

In this paper, we review the current status of the phenomenological study of quarkonium production in high energy collisions. After a brief introduction of several important models and effective field theories for quarkonium production, we discuss the comparisons between theoretical predictions and experimental measurements.

With a key improvement, the auxiliary mass flow method is now able to compute Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it to compute some integrals involved in two-loop electroweak corrections to $e^+e^-\to HZ$, two-loop QCD corrections to $3j$, $W/Z/H+2j$, $t\bar{t}H$ and $4j$ production at hadron colliders, and three-loop QCD corrections to $t\bar{t}$ production at hadron colliders, all of which are crucial for precision frontier in collider physics in the following decade. Our results are important building blocks and benchmarks for future studies of these processes., Comment: 7 pages, 4 figures, published version

We study the triply heavy baryons $\Omega_{QQQ}$ $(Q=c, b)$ in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the $\Omega_{QQQ}$. This is because the NLO not only results in a large correction, but also reduces the parameter dependence, making the Borel platform more distinct, especially for the $\Omega_{bbb}$ in the $\overline{\rm{MS}}$ scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ($\bar {MS}$ and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be $4.53^{+0.26}_{-0.11}$ GeV for $\Omega_{ccc}$ and $14.27^{+0.33}_{-0.32}$ GeV for $\Omega_{bbb}$, where the results are obtained at $\mu=M_B$ with errors including those from the variation of the renormalization scale $\mu$ in the range $(0.8-1.2) M_B$. A careful study of the $\mu$ dependence in a wide range is further performed, which shows that the LO results are very sensitive to the choice of $\mu$ whereas the NLO results are considerably better. In addition to the $\mu=M_B$ result, a more stable value, (4.75-4.80) GeV, for the $\Omega_{ccc}$ mass is found in the range of $\mu=(1.2-2.0) M_B$, which should be viewed as a more relevant prediction in our NLO approach because of $\mu$ dependence., Comment: An auxiliary file added showing calculations of NLO amplitudes; More discussions added on renormalization scale dependence. 12 pages, 6 figures, 5 tables. to be published in Chinese Physics C

We study the fragmentation function of the gluon to color-octet $^3S_1$ heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet $^3S_1$ soft gluon distribution (SGD). The short distance hard part is calculated to next-to-leading order in $\alpha_s$ and a renormalization group equation for the SGD is derived. By solving the renormalization group equation, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study., Comment: 38 pages, 8 figures

The next-to-leading order (NLO) ($\mathcal{O}(\alpha_s^3)$) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ${^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}$ states are calculated within the NRQCD factorization. We use integration-by-parts reduction and differential equations to semi-analytically calculate fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through matching procedure, infrared-safe short distance coefficients and $\mathcal{O}(\alpha_s^2)$ perturbative NRQCD matrix elements $\langle{\mathcal O}^{{^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}}({^{3}\hspace{-0.6mm}S_{1}^{[8]}})\rangle_{\mathrm{NLO}}$ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones., Comment: 19 pages, 6 figures. arXiv admin note: text overlap with arXiv:1810.07656

We extend the nonrelativistic QCD framework to explore the nature of the newly discovered di-$J/\psi$ resonances. Assuming them as either molecule-like states or tetraquarks, we calculated their hadroproduction cross sections at the LHC. We find that the observed resonances are most likely spin-2 particles, and there should exist their spin-0 counterparts near these resonances. The ratio of production cross sections of the observed resonances to the latent spin-0 ones are also presented, which might help to distinguish molecule-like states from tetraquarks.

We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals involving also phase-space integration. Flow of the auxiliary mass from the boundary ($\infty$) to the physical point ($0^+$) is obtained by numerically solving differential equations with respective to the auxiliary mass. For problems with two or more kinematical invariants, the AMF method can be combined with traditional differential equation method by providing systematical boundary conditions and highly nontrivial self-consistent check. The method is described in detail with a pedagogical example of $e^+e^-\rightarrow \gamma^* \rightarrow t\bar{t}+X$ at NNLO. We show that the AMF method can systematically and efficiently calculate integrals to high precision., Comment: 14 pages, 4 figures

We present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor non-singlet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients for corresponding quasi-PDFs and pseudo-PDFs. Our method of calculations can be readily generalized to evaluate the matching coefficients for sea-quark and gluon correlation functions, putting the program to extract partonic structure of hadrons from lattice QCD calculations to be comparable with and complementary to that from experimental measurements., Comment: 14 pages, 2 figures; analytical matching coefficients for quark correlation functions, quasi-PDFs and pseudo-PDFs added; version to be published in PRL

We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that for any given process these two factorization theories are either both valid or both violated. We use two methods to achieve this conclusion. In the first method, we apply the two factorization theories to the physical process $J/\psi \to e^+e^-$. Our explicit calculation shows that both SGF and NRQCD can correctly reproduce low energy physics of full QCD, and thus the two factorizations are equivalent. In the second method, by using equations of motion we successfully deduce SGF from NRQCD effective field theory. By identifying SGF with NRQCD factorization, we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relations as a by product. Comparing with the NRQCD factorization, the advantage of SGF is that it resums the series of relativistic corrections originated from kinematic effects to all powers, which gives rise to a better convergence in relativistic expansion., Comment: 15 pages, 1 figure

We extract the pion valence quark distribution $q^\pi_{\rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^\pi_{\rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\rm v}^{\pi}(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data., Comment: Published version, Physical Review D

We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals., Comment: 8 pages, 2 figures, version published at Chin.Phys.C

In this paper, we study the application of the recently proposed soft gluon factorization (SGF) to exclusive quarkonium production or decay. We find that in the nonrelativistic QCD factorization framework there are too many nonperturbative parameters. Thanks to the factorization of kinematical physics from dynamical physics, the SGF significantly reduces the number of nonperturbative parameters. Therefore, the SGF can improve our predictive power of exclusive quarkonium production or decay. By applying to $\eta_c+\gamma$ production at B-factories, our result is the closest one to data among all theoretical calculations., Comment: 13 pages, 1 figure, version published in JHEP

By combining NRQCD factorization and collinear factorization, we compute a series of relativistic corrections for $J/\psi$ hadroproduction to all orders in $v^2$ at large $p_T$ limit. The $v^2$ expansion converges well for all channels. We find that the ratio of relativistic correction term to the corresponding leading term is independent of kinematic variables for any channel, which generalizes the proportional relations found in previous works to all orders., Comment: 24 pages, 2 figures

High order calculation at semi-hard scale is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize rapidity divergences in the CGC factorization, which makes higher order calculation rigorous and straight forward. By applying this method to single hadron production in pA collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading order (NLO) result to have a smaller theoretical uncertainty comparing with LO result, which makes high order calculation in CGC factorization to be useful. As a byproduct, the negativity problem found in literature can also be overcome in our framework by a proper choosing of factorization scale., Comment: 10 pages, 3 figures, published version

We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in ${^{1}\hspace{-0.6mm}S_{0}^{[1]}}$ or ${^{1}\hspace{-0.6mm}S_{0}^{[8]}}$ state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of $z$ (light-cone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of $z$, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. $\eta_c$ and $J/\psi$) production at the LHC., Comment: 28 pages, 9 figures

We compute the $J/\psi$ polarization observables $\lambda_\theta$, $\lambda_\phi$, $\lambda_{\theta\phi}$ in a Color Glass Condensate (CGC) + nonrelativistic QCQ (NRQCD) formalism that includes contributions from both color singlet and color octet intermediate states. Our results are compared to low $p_T$ data on $J/\psi$ polarization from the LHCb and ALICE experiments on proton-proton collisions at center-of-mass energies of $\sqrt{s}=7$ TeV and 8 TeV. Our CGC+NRQCD computation provides a better description of data for $p_T \leq 15$ GeV relative to extant next-to-leading (NLO) calculations within the collinear factorization framework. These results suggest that higher order computations in the CGC+NRQCD framework have the potential to greatly improve the accuracy of extracted values of the NRQCD universal long distance matrix elements., Comment: 26 pages, 8 figures, accepted for publication in JHEP

Extracting parton distribution functions (PDFs) from lattice QCD calculation of quasi-PDFs has been actively pursued in recent years. We extend our proof of the multiplicative renormalizability of quasi-quark operators in Ref. [1] to quasi-gluon operators, and demonstrated that quasi-gluon operators could be multiplicatively renormalized to all orders in perturbation theory, without mixing with other operators. We find that using a gauge-invariant UV regulator is essential for achieving this proof. With the multiplicative renormalizability of both quasi-quark and quasi-gluon operators, and QCD collinear factorization of hadronic matrix elements of there operators into PDFs, extracting PDFs from lattice QCD calculated hadronic matrix elements of quasi-parton operators could have a solid theoretical foundation., Comment: 7 pages, 4 figures

We discuss the production of $D$-mesons and $J/\psi$ in high multiplicity proton-proton and proton-nucleus collisions within the Color-Glass-Condensate (CGC) framework. We demonstrate that the modification of the LHC data on $D$ and $J/\psi$ yields in high multiplicity events relative to minimum bias events arise from a significant enhancement of the gluon saturation scales of the corresponding rare parton configurations in the colliding protons and nuclei. For a given event multiplicity, we predict these relative yields to be energy independent from $\sqrt{s}=200$ GeV at RHIC to the highest LHC energies., Comment: 4 pages 3 figures, proceedings of Quark Matter 2018, Venice, Italy, May 13-19 2018

Heavy flavor measurements in high multiplicity proton-proton and proton-nucleus collisions at collider energies enable unique insights into their production and hadronization mechanism because experimental and theoretical uncertainties cancel in ratios of their cross-sections relative to minimum bias events. We explore such event engineering using the Color Glass Condensate (CGC) effective field theory to compute short distance charmonium cross-sections. The CGC is combined with heavy-quark fragmentation functions to compute $D$-meson cross-sections; for the $J/\psi$, hadronization is described employing Nonrelativistic QCD (NRQCD) and an Improved Color Evaporation model. Excellent agreement is found between the CGC computations and the LHC heavy flavor data in high multiplicity events. Event engineering in this CGC+NRQCD framework reveals a very rapid growth in the fragmentation of the $^3S_1^{[8]}$ state in rare events relative to minimum bias events., Comment: 13 pages, 11 figures. v2: title changed, Figs.1,2 modified, Fig.4 added, further discussion expanded, version accepted for publication in PRD

By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore conceptually translates the problem of computing Feynman integrals to the problem of performing analytical continuations. As an application of the new representation, we use it to construct a novel reduction method for multi-loop Feynman integrals, which is expected to be more efficient than known integration-by-parts reduction method. Using the new method, we successfully reduced all complicated two-loop integrals in $gg\to HH$ process and $gg\to ggg$ process., Comment: Version published in PRD (Rapid Communication)

We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals., Comment: references added, version published in PLB

Following our previous proposal [1], we construct a class of good "lattice cross sections" (LCSs), from which we could study partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that proposed functions for lattice QCD calculation of PDFs in the literature are special cases of these good LCSs., Comment: 6 pages, 1 figure, version accepted by Physical Review Letters