Search

We consider conformal transitions arising from the merging of IR and UV fixed points, expected to occur in QCD with a large enough number of flavors. We study the smoothness of physical quantities across this transition, being mostly determined by the logarithmic breaking of conformal invariance. We investigate this explicitly using holography where approaching the conformal transition either from outside or inside the conformal window (perturbed by a mass term) is characterized by the same dynamics. The mass of spin-1 mesons and Fπ are shown to be continuous across the transition, as well as the dilaton mass. This implies that the lightness of the dilaton cannot be a consequence of the spontaneous breaking of scale invariance when leaving the conformal window. Our analysis suggests that the light scalar observed in QCD lattice simulations is a q q ¯ meson that becomes light since the q q ¯ -operator dimension reaches its minimal value. [ABSTRACT FROM AUTHOR]

We study the small-mass asymptotic behavior of so-called angular integrals, appearing in phase-space calculations in perturbative quantum field theory. For this purpose we utilize the strategy of expansion by regions, which is a universal method both for multiloop Feynman integrals and various parametric integrals. To apply the technique to angular integrals, we convert them into suitable parametric integral representations, which are accessible to existing automation tools. We use the code asy.m to reveal regions contributing to the asymptotic expansion of angular integrals. To evaluate the contributions of these regions in an epsilon expansion we apply the method of Mellin-Barnes representation. Our approach is checked against existing results on angular integrals revealing a connection between contributing regions and angular integrals constructed from an algebraic decomposition. We explicitly calculate the previously unknown asymptotics for angular integrals with three and four denominators and formulate a conjecture for the leading asymptotics and the pole part for a general number of denominators and masses. [ABSTRACT FROM AUTHOR]

We revisit the hadronization and decay of excited heavy mesons and heavy baryons in Herwig 7 general-purpose event-generator, following four distinct steps: (i) Passing through the polarisation of heavy hadrons at the end of parton shower through the application of heavy quark effective theory (HQET), where the emergence of a spin-flavour symmetry allows for the determination of the polarisations of the excited heavy mesons and heavy baryons from the helicity states of the light and heavy quarks. (ii) Improving the strong and radiative decay modes of the excited heavy mesons, where in the absence of conclusive experimental data on many of the decays, one needs to rely on HQET symmetries to determine the favoured decay modes, widths and branching ratios. (iii) Re-examination of the production rates of heavy hadrons using all available experimental data sources and (iv) performing a general tune for Herwig’s free parameters to reflect the implemented changes. We compare our predictions against existing experimental data in the presence/absence of the newly implemented updates. These improvements will be available with Herwig-7.3.0 public release. [ABSTRACT FROM AUTHOR]

We compute the leading logarithmic power corrections at next-to-next-to-next-to-leading order for 0-jettiness subtractions for Drell-Yan and Higgs production in gluon fusion differential in both the invariant mass and rapidity of the color singlet. We review how to disentangle these power corrections from those arising from the presence of fiducial and isolation cuts by using Projection-to-Born improved slicing. Our results include all the channels contributing at leading logarithmic order for these processes, including the off-diagonal channels that receive contributions from soft quark emission. We study the numerical impact of the power corrections for Drell-Yan and Higgs production and find it to become negligible compared to the size of the N3LO corrections only below τcut ~ 10−5. We estimate that in a fully differential calculation at N3LO combining the Projection-to-Born improved slicing method and our results for the leading logarithmic power corrections may allow for keeping the slicing uncertainties under control already with τcut ≲ 10−3, marking a significant improvement in efficiency for these methods. These results constitute a crucial ingredient for fully differential N3LO calculations based on the N-jettiness subtraction scheme. [ABSTRACT FROM AUTHOR]

X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MS ¯ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MS ¯ -renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O(αS) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B − B ¯ mixing. [ABSTRACT FROM AUTHOR]

Abstract Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an S-wave fully-charmed tetraquark, denoted as T 4c . The charm-to-T 4c fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in α s expansion. The LDMEs are approximated using the T 4c four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-T 4c fragmentation function, we predict the T 4c production rate at high transverse momentum p T regime in colliders. Both the differential distribution over p T and the integrated cross sections are predicted at the LHC. The cross sections for T 4c states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for T 4c event production at the LHC. Additionally, we estimate for the photoproduction of T 4c in electron-proton (ep) collisions. It is observed that the cross sections for these processes are moderate at the HERA and EIC, and relatively small at the EicC. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at ep colliders is somewhat challenging.

Abstract Using chiral effective field theory, we predict that there must be isovector charmonium-like D D ¯ ∗ $$ D{\overline{D}}^{\ast } $$ hadronic molecules with J PC = 1++ denoted as W c1. The inputs are the properties of the X(3872), including its mass and the ratio of its branching fractions of decays into J/ψρ 0 and J/ψω. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the X(3872) as well as its spin partners. They should show up as either a mild cusp or dip at the D D ¯ ∗ $$ D{\overline{D}}^{\ast } $$ thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the X(3872) is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the X(3872) signal dominates over that from the W c 1 0 $$ {W}_{c1}^0 $$ . The pole positions are 3881.2 − 0.0 + 0.8 $$ {3881.2}_{-0.0}^{+0.8} $$ − i 1.6 − 0.9 + 0.7 $$ i{1.6}_{-0.9}^{+0.7} $$ MeV for W c 1 0 $$ {W}_{c1}^0 $$ on the fourth Riemann sheet of the D 0 D ¯ ∗ 0 $$ {D}^0{\overline{D}}^{\ast 0} $$ -D + D ∗− coupled-channel system, and 3866.9 − 7.7 + 4.6 $$ {3866.9}_{-7.7}^{+4.6} $$ − i(0.07 ± 0.01) MeV for W c 1 ± $$ {W}_{c1}^{\pm } $$ on the second Riemann sheet of the D D ¯ ∗ ± $$ {\left(D{\overline{D}}^{\ast}\right)}^{\pm } $$ single-channel system. The findings imply that the peak in the J/ψπ + π − invariant mass distribution is not purely from the X(3872) but contains contributions from W c 1 0 $$ {W}_{c1}^0 $$ predicted here. The states should have isovector heavy quark spin partners with J PC = 0++, 2++ and 1+−, with the last one corresponding to Z c . We suggest to search for the charged 0++, 1++ and 2++ states in J/ψπ ± π 0.

Abstract We study the small-mass asymptotic behavior of so-called angular integrals, appearing in phase-space calculations in perturbative quantum field theory. For this purpose we utilize the strategy of expansion by regions, which is a universal method both for multiloop Feynman integrals and various parametric integrals. To apply the technique to angular integrals, we convert them into suitable parametric integral representations, which are accessible to existing automation tools. We use the code asy.m to reveal regions contributing to the asymptotic expansion of angular integrals. To evaluate the contributions of these regions in an epsilon expansion we apply the method of Mellin-Barnes representation. Our approach is checked against existing results on angular integrals revealing a connection between contributing regions and angular integrals constructed from an algebraic decomposition. We explicitly calculate the previously unknown asymptotics for angular integrals with three and four denominators and formulate a conjecture for the leading asymptotics and the pole part for a general number of denominators and masses.

Abstract Chiral perturbation theory systematically describes the low energy dynamics of meson and baryons using nonlinear Nambu-Goldstone fields. Using the Young tensor technique, we construct the pure mesonic effective operators up to p 8-order, one-to-one corresponding to contact amplitudes with the on-shell Adler zero condition. The off-shell external sources, non-vanishing under equation-of-motion conditions, are also added to the operator bases. We also show the invariant tensor bases using the Young tableau is equivalent to the trace bases with Cayley-Hamilton relations. Separated into different CP eigenstates, at O p 8 $$ \mathcal{O}\left({p}^8\right) $$ we obtain the operator lists of the 567 C+P+ operators, 483 C+P- operators, 376 C-P+ operators, and 408 C-P- operators for SU(2) case, while there are 1959 C+P+ operators, 1809 C+P- operators, 1520 C-P+ operators, and 1594 C-P- operators for SU(3) case, consistent with results using the Hilbert series.

Abstract We consider conformal transitions arising from the merging of IR and UV fixed points, expected to occur in QCD with a large enough number of flavors. We study the smoothness of physical quantities across this transition, being mostly determined by the logarithmic breaking of conformal invariance. We investigate this explicitly using holography where approaching the conformal transition either from outside or inside the conformal window (perturbed by a mass term) is characterized by the same dynamics. The mass of spin-1 mesons and F π are shown to be continuous across the transition, as well as the dilaton mass. This implies that the lightness of the dilaton cannot be a consequence of the spontaneous breaking of scale invariance when leaving the conformal window. Our analysis suggests that the light scalar observed in QCD lattice simulations is a q q ¯ $$ q\overline{q} $$ meson that becomes light since the q q ¯ $$ q\overline{q} $$ -operator dimension reaches its minimal value.

Abstract Predicting the rate for μ → e conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for μ → e conversion in nuclei, including 40,48Ca, 48,50Ti, and 27Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for μ → e conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general μ → e conversion rates with quantified uncertainties.

Abstract The two-particle finite-volume scattering formalism derived by Lüscher and generalized in many subsequent works does not hold for energies far enough below the two-particle threshold to reach the nearest left-hand cut. The breakdown of the formalism is signaled by the fact that a real scattering amplitude is predicted in a regime where it should be complex. In this work, we address this limitation by deriving an extended formalism that includes the nearest branch cut, arising from single particle exchange. We focus on two-nucleon (NN → NN) scattering, for which the cut arises from pion exchange, but give expressions for any system with a single channel of identical particles. The new result takes the form of a modified quantization condition that can be used to constrain an intermediate K-matrix in which the cut is removed. In a second step, integral equations, also derived in this work, must be used to convert the K-matrix to the physical scattering amplitude. We also show how the new formalism reduces to the standard approach when the N → Nπ coupling is set to zero.

Abstract The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of Glauber phases. Building on the formalism of [1], it is shown that the leading terms in this series for large N c can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large-N c methods might also be helpful to study other aspects of non-global logarithms at hadron colliders, and to combine our analytic results with amplitude-level parton showers.

Abstract A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

Abstract We revisit the hadronization and decay of excited heavy mesons and heavy baryons in Herwig 7 general-purpose event-generator, following four distinct steps: (i) Passing through the polarisation of heavy hadrons at the end of parton shower through the application of heavy quark effective theory (HQET), where the emergence of a spin-flavour symmetry allows for the determination of the polarisations of the excited heavy mesons and heavy baryons from the helicity states of the light and heavy quarks. (ii) Improving the strong and radiative decay modes of the excited heavy mesons, where in the absence of conclusive experimental data on many of the decays, one needs to rely on HQET symmetries to determine the favoured decay modes, widths and branching ratios. (iii) Re-examination of the production rates of heavy hadrons using all available experimental data sources and (iv) performing a general tune for Herwig’s free parameters to reflect the implemented changes. We compare our predictions against existing experimental data in the presence/absence of the newly implemented updates. These improvements will be available with Herwig-7.3.0 public release.

Abstract We compute the leading logarithmic power corrections at next-to-next-to-next-to-leading order for 0-jettiness subtractions for Drell-Yan and Higgs production in gluon fusion differential in both the invariant mass and rapidity of the color singlet. We review how to disentangle these power corrections from those arising from the presence of fiducial and isolation cuts by using Projection-to-Born improved slicing. Our results include all the channels contributing at leading logarithmic order for these processes, including the off-diagonal channels that receive contributions from soft quark emission. We study the numerical impact of the power corrections for Drell-Yan and Higgs production and find it to become negligible compared to the size of the N3LO corrections only below τ cut ~ 10−5. We estimate that in a fully differential calculation at N3LO combining the Projection-to-Born improved slicing method and our results for the leading logarithmic power corrections may allow for keeping the slicing uncertainties under control already with τ cut ≲ 10−3, marking a significant improvement in efficiency for these methods. These results constitute a crucial ingredient for fully differential N3LO calculations based on the N-jettiness subtraction scheme.

Abstract X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MS ¯ $$ \overline{\textrm{MS}} $$ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MS ¯ $$ \overline{\textrm{MS}} $$ -renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O(α S ) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B − B ¯ $$ \overline{B} $$ mixing.

Abstract We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at next-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding O $$ \mathcal{O} $$ (10%) effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region.

Abstract We reanalyze the origin of the large transverse logarithms associated with the QCD one loop β function coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders in α s in the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrix S(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.

Abstract We study χ cJ → VV decays using the QCD effective field theory approach. The helicity suppressed decay amplitudes are also considered. The colour-singlet contributions of these amplitudes suffer from the endpoint singularities, it is shown that they can be absorbed into renormalisation of the nonfactorisable colour-octet matrix element. The latter can be associated with the colour-octet component of the charmonium wave function. The heavy quark spin symmetry makes it possible to establish the relationships between colour-octet matrix elements for different states χ cJ up to higher order corrections in small velocity v. This allows us to estimate the polarisation parameters for χ c2 → VV using data for χ c0,1 → VV. This analysis is carried out for the available data on the χ cJ → ϕϕ decays.

Abstract We compute the N-jettiness soft function in hadronic collisions to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an extension of the SoftSERVE framework to soft functions that involve an arbitrary number of lightlike Wilson lines. We present numerical results for 1-jettiness and 2-jettiness, and illustrate that our formalism carries over to a generic number of jets by calculating a few benchmark points for 3-jettiness. We also perform a detailed analytic study of the asymptotic behaviour of the soft-function coefficients at the edges of phase space, where one of the jets becomes collinear to another jet or beam direction, and comment on previous calculations of the N-jettiness soft function.

Abstract The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at O α s $$ \mathcal{O}\left({\alpha}_s\right) $$ .

Abstract Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

Abstract We extend the local infrared-divergence subtraction formalism, originally proposed by Frixione, Kunszt and Signer (FKS), to calculate short-distance (differential) cross section for any inclusive process involving a quarkonium particle in non-relativistic QCD (NRQCD) factorisation at next-to-leading order (NLO) accuracy in the strong coupling constant α s . The new formulas are generally applicable to the production of an S- or P-wave quarkonium state in association with any number of elementary particles. The main new ingredients derived in this paper are the local and integrated soft counterterms for the colour-singlet and colour-octet P-wave bound states. It, therefore, paves the way to the automation of the NLO calculations for heavy quarkonium inclusive and associated production processes.

Abstract We compute the gluon beam function for jet-veto resummation to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an automated framework that was previously used for the computation of the respective quark beam function, and which we significantly extended for the present calculation. In particular, the perturbative matching kernels are directly calculated in momentum space, without the need to perform an additional Mellin transform. We present results for both gluon and quark-initiated processes, which we cross-checked with an independent semi-analytical method that exploits the similarity of the beam functions to the more familiar case of transverse-momentum resummation. Our computation is relevant for jet-veto resummations at NNLL′ accuracy.

Abstract We present a comprehensive investigation of leading-twist lightcone distribution amplitudes (LCDAs) and quasi distribution amplitudes (quasi-DAs) for light octet and decuplet baryons within large momentum effective theory. In LaMET, LCDAs can be factorized in terms of a hard kernel and quasi-DAs that are defined as spatial correlators and calculable on Lattice QCD. To renormalize quasi-DAs and eliminate the singular terms ln( μ 2 z i 2 $$ {\mu}^2{z}_i^2 $$ ) in them, which undermine the efficacy in perturbative expansion, we adopt a hybrid renormalization scheme that combines the self-renormalization and ratio scheme. Through self-renormalization, we eliminate UV divergences and linear divergences at large spatial separations in quasi distribution amplitudes without introducing additional nonperturbative effects. By taking a ratio with respect to the zero-momentum matrix element, we effectively remove UV divergences at small spatial separations. Under the hybrid renormalization scheme, we calculate the hard kernels up to one-loop accuracy. It turns out that only four different hard kernels are needed for all leading-twist LCDAs of octet and decuplet baryons. These results are crucial for the lattice-based exploration of the LCDAs of a light baryon from the first principle of QCD.

Abstract Off-lightcone Wilson-line operators are constructed using local operators connected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For instance, space-like Wilson-line operators play a crucial role in determining quasi-distribution functions (quasi-PDFs), while time-like Wilson-line operators are essential for understanding quarkonium decay and production within the potential non-relativistic QCD (pNRQCD) framework. In this work, we establish a systematic approach for calculating the matching from the gradient-flow scheme to the MS ¯ $$ \overline{\textrm{MS}} $$ scheme in the limit of small flow time for off-lightcone Wilson-line operators. By employing the one-dimensional auxiliary-field formalism, we simplify the matching procedure, reducing it to the matching of local current operators. We provide one-loop level matching coefficients for these local current operators. For the case of hadronic matrix element related to the quark quasi-PDFs, we show at one-loop level that the finite flow time effect is very small as long as the flow radius is smaller than the physical distance z, which is usually satisfied in lattice gradient flow computations. Applications include lattice gradient flow computations of quark/gluon quasi-PDFs, gluonic correlators related to quarkonium decay and production in pNRQCD, and spin-dependent potentials in terms of chromoelectric and chromomagnetic field insertions into a Wilson loop.

Abstract We present the leading order coupling of double-heavy hadrons to heavy hadron pairs in Born-Oppenheimer effective field theory. We obtain the expressions for the contribution of heavy hadron pairs to the masses and widths of double-heavy hadrons. We apply our result for the specific case of the coupling of the lowest lying heavy hybrids and D s ∗ D ¯ s ∗ B s ∗ B ¯ s ∗ $$ {D}_{(s)}^{\left(\ast \right)}{\overline{D}}_{(s)}^{\left(\ast \right)}\left({B}_{(s)}^{\left(\ast \right)}{\overline{B}}_{(s)}^{\left(\ast \right)}\right) $$ obtaining a set of selection rules for the decays. We build a model for the coupling potential and compute the corresponding decay widths and the contributions to the mass of the heavy hybrids. We compare our results with the experimental exotic quarkonium spectrum and discuss the most likely experimental candidates for quarkonium hybrids.

Abstract We present numerical solutions in a one-dimensional setting of quantum master equations that have been recently derived. We focus on the dynamics of a single heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in the so-called quantum Brownian regime where the temperature of the plasma is large in comparison with the spacing between the energy levels of the Q Q ¯ $$ Q\overline{Q} $$ system. The one-dimensional potential used in the calculations has been adjusted so as to produce numbers that are relevant for the phenomenology of the charmonium. The equations are solved using different initial states and medium configurations. Various temperature regimes are studied and the effects of screening and collisions thoroughly analyzed. Technical features of the equations are analyzed. The contributions of the different operators that control the evolution are discussed as a function of the temperature. Some phenomenological consequences are addressed.

Abstract We present an improved calculation of the light element abundances in the framework of Big Bang nucleosynthesis as a function of the Higgs vacuum expectation value v. We compare the methods of our calculation to previous literature including the recently published work of Burns et al. [1]. The PDG result for the 4He abundance can be explained within 2σ by −0.014 ≤ δv/v ≤ 0.026, for deuterium we find the constraint −0.005 ≤ δv/v ≤ −0.001. These bounds are more stringent than what was found earlier.

Abstract Within the nonrelativistic QCD (NRQCD) framework, we complete the three-loop calculations of the NRQCD renormalization constants and the matching coefficients, for the heavy flavor-changing temporal vector, spatial-spatial tensor, spatial-temporal axial-tensor currents, which are coupled to the P-wave c b ¯ $$ c\overline{b} $$ mesons. We further study the ten decay constants for the c b ¯ $$ c\overline{b} $$ mesons (B c , B c ∗ $$ {B}_c^{\ast } $$ , B c 0 ∗ $$ {B}_{c0}^{\ast } $$ , B c1) coupled with the ten heavy flavor-changing currents involving (pseudo-)scalar, (axial-)vector and (axial-)tensor up to the next-to-next-to-next-to-leading order (N3LO) of α s . We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N3LO perturbative QCD results for the six ratios of decay constants have good convergence and weak scale-dependence. We finally predict the hierarchical relationship among the ten decay constants for the c b ¯ $$ c\overline{b} $$ mesons coupled with the ten currents.

Abstract The magnetic moment yields an excellent framework to explore the inner structure of particles determined by the quark-gluon dynamics of QCD, as it is the leading-order response of a bound system to a weak external magnetic field. Motivated by this, in this study, the magnetic moments of possible axial-vector T bc u ¯ u ¯ $$ {T}_{bc\overline{u}\overline{u}} $$ , T bc d ¯ d ¯ $$ {T}_{bc\overline{d}\overline{d}} $$ , and T bc u ¯ d ¯ $$ {T}_{bc\overline{u}\overline{d}} $$ tetraquarks are obtained with the help of light-cone QCD sum rules. For this purpose, we assume that these states are represented as a diquark-antidiquark picture with different structures and interpolating currents. The magnetic moment results derived using different diquark-antidiquark configurations differ substantially from each other. This can be translated into more than one tetraquark state with the same quantum number and quark content yet possessing different magnetic moments. From the numerical results obtained, we have concluded that the magnetic moments of the T bc states can project their inner structure, which can be used for their quantum numbers and quark-gluon organization. The contribution of individual quarks to the magnetic moments is also analyzed for completeness. We hope that our predictions of the magnetic moments of the T bc tetraquarks, together with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these interesting tetraquarks, may be valuable in the search for these states in future experiments and in unraveling the internal structure of these tetraquarks.

Abstract The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order.

Abstract We calculate directly in position space the one-loop renormalization kernels of the soft operators O γ and O g that appear in the soft-quark contributions to, respectively, the subleading-power γγ → h and gg → h form factors mediated by the b-quark. We present an IR/rapidity divergence-free definition for O g and demonstrate that with a correspondent definition of the collinear function, a consistent factorization theorem is recovered. Using conformal symmetry techniques, we establish a relation between the evolution kernels of the leading-twist heavy-light light-ray operator, whose matrix element defines the B-meson light-cone distribution amplitude (LCDA), and O γ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of O γ to the two-loop level. We construct an ansatz for the kernel of O g at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant.

Abstract We investigate the gravitational form factors (GFFs) of the nucleon and the baryon octet, decomposed into their flavor components, utilizing a pion mean-field approach grounded in the large N c limit of Quantum Chromodynamics (QCD). Our focus is on the contributions from the twist-2 operators to the flavor-triplet and octet GFFs, and we decompose the mass, angular momentum, and D-term form factors of the nucleon into their respective flavors. The strange quark contributions are found to be relatively mild for the mass and angular momentum form factors, while providing significant corrections to the D-term form factor. In the course of examining the flavor decomposition of the GFFs, we uncover that the effects of twist-4 operators play a crucial role. While the gluonic contributions are suppressed by the packing fraction of the instanton vacuum in the twist-2 case, contributions from twist-4 operators are of order unity, necessitating its explicit consideration.

Abstract Processes involving only massless or massive quarks at tree-level get corrections from massive (lighter, heavier, or equal-mass) secondary quarks starting at two-loop order, generated by a virtual gluon splitting into a massive quark anti-quark pair. One convenient approach to compute such two-loop corrections is starting with the one-loop diagram considering the virtual gluon massive. Carrying out a dispersive integral with a suitable kernel over the gluon mass yields the desired two-loop result. On the other hand, the Mellin-Barnes representation can be used to compute the expansion of Feynman integrals in powers of a small parameter. In this article we show how to combine these two ideas to obtain the corresponding expansions for large and small secondary quark masses to arbitrarily high orders in a straightforward manner. Furthermore, the convergence radius of both expansions can be shown to overlap, being each series rapidly convergent. The advantage of our method is that the Mellin representation is obtained directly for the full matrix element from the same one-loop computation one needs in large-β 0 computations, therefore many existing results can be recycled. With minimal modifications, the strategy can be applied to compute the expansion of the one-loop correction coming from a massive gauge boson. We apply this method to a plethora of examples, in particular those relevant for factorized cross sections involving massless and massive jets, recovering known results and obtaining new ones. Another bonus of our approach is that, postponing the Mellin inversion, one can obtain the small- and large-mas expansions for the RG-evolved jet functions. In many cases, the series can be summed up yielding closed expressions.

Abstract I look at the renormalization of the medium structure function and a medium induced jet function in a factorized cross section for jet substructure observables in Heavy Ion collisions. This is based on the formalism developed in [1], which uses an Open quantum system approach combined with the Effective Field Theory (EFT) for forward scattering to derive a factorization formula for jet observables which work as hard probes of a long lived dilute Quark Gluon Plasma (QGP) medium. I show that the universal medium structure function that captures the observable independent physics of the QGP has both rapidity and UV anomalous dimensions that appear due to medium induced Bremsstrahlung. The resulting Renormalization Group (RG) equations correspond to the BFKL equation and the running of the QCD coupling respectively. I present the first results for the numerical impact of resummation using these RG equations on the mean free path of the jet in the medium. I also briefly discuss the prospects of extending this formalism for a short lived dense medium.

Abstract We study multifield extensions of Reggeon Field Theory (also equivalent to Directed Percolation model) at criticality in the perturbative ϵ-expansion below the upper critical dimension D c = 4 at one loop, for the special case when all fields have the same scale (anomalous) dimensions. Analyzing all the fixed points of the renormalization group flow for N = 2 flavors and some for N = 3, we find scale invariant solutions which are characterized by specific emergent global symmetries of the interacting potential. We also study two infinite families as a function of N having ℤ N and S N+1 symmetries.

Abstract We revisit the Next-to-Leading Order (two-loop) contributions to the Anomalous Dimensions of ∆F = 1 four-quark operators in QCD. We devise a test for anomalous dimensions, that we regard as of general interest, and by means of which we detect a problem in the results available in the literature. Deconstructing the steps leading to the available result, we identify the source of the problem, which is related to the operator known as Q 11. We show how to fix the problem and provide the corrected anomalous dimensions. With the insight of our findings, we propose an alternative approach to the one used in the literature which does not suffer from the identified disease, and which confirms our corrected results. We assess the numerical impact of our corrections, which happens to be in the ballpark of 5% in certain entries of the evolution matrix. Our results are important for the correct resummation of Next-to-Leading Logarithms in analyses of physics beyond the Standard Model in ∆F = 1 processes, such as the decays of Kaons and B-mesons.

Abstract In this paper, we present an algorithm to construct the q T distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability and usefulness of our algorithm, we calculate the N2LP corrections for Higgs hadroproduction for the first time. We observe that our approximate N2LP-accurate q T spectra replicate the asymptotic behaviour of the full QCD calculation to a much better degree than the previously available results, both within the q T → 0 limit and in the large-q T domain for all the involved partonic processes. While playing a minor role at larger transverse momenta, we show that the newly incorporated boundary contribution plays a vital role in the q T → 0 limit, where any subleading power accuracy would be lost without them. In particular, our N2LP-accurate q T expansion can approximate the exact q T distribution up to q T ≈ 30 GeV at the percent level for rapidities |Y H | ≲ 3.

Off-lightcone Wilson-line operators are constructed using local operators connected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For instance, space-like Wilson-line operators play a crucial role in determining quasi-distribution functions (quasi-PDFs), while time-like Wilson-line operators are essential for understanding quarkonium decay and production within the potential non-relativistic QCD (pNRQCD) framework. In this work, we establish a systematic approach for calculating the matching from the gradient-flow scheme to the MS ¯ scheme in the limit of small flow time for off-lightcone Wilson-line operators. By employing the one-dimensional auxiliary-field formalism, we simplify the matching procedure, reducing it to the matching of local current operators. We provide one-loop level matching coefficients for these local current operators. For the case of hadronic matrix element related to the quark quasi-PDFs, we show at one-loop level that the finite flow time effect is very small as long as the flow radius is smaller than the physical distance z, which is usually satisfied in lattice gradient flow computations. Applications include lattice gradient flow computations of quark/gluon quasi-PDFs, gluonic correlators related to quarkonium decay and production in pNRQCD, and spin-dependent potentials in terms of chromoelectric and chromomagnetic field insertions into a Wilson loop. [ABSTRACT FROM AUTHOR]

We present the leading order coupling of double-heavy hadrons to heavy hadron pairs in Born-Oppenheimer effective field theory. We obtain the expressions for the contribution of heavy hadron pairs to the masses and widths of double-heavy hadrons. We apply our result for the specific case of the coupling of the lowest lying heavy hybrids and D s ∗ D ¯ s ∗ B s ∗ B ¯ s ∗ obtaining a set of selection rules for the decays. We build a model for the coupling potential and compute the corresponding decay widths and the contributions to the mass of the heavy hybrids. We compare our results with the experimental exotic quarkonium spectrum and discuss the most likely experimental candidates for quarkonium hybrids. [ABSTRACT FROM AUTHOR]

We present an improved calculation of the light element abundances in the framework of Big Bang nucleosynthesis as a function of the Higgs vacuum expectation value v. We compare the methods of our calculation to previous literature including the recently published work of Burns et al. [1]. The PDG result for the 4He abundance can be explained within 2σ by −0.014 ≤ δv/v ≤ 0.026, for deuterium we find the constraint −0.005 ≤ δv/v ≤ −0.001. These bounds are more stringent than what was found earlier. [ABSTRACT FROM AUTHOR]

We present numerical solutions in a one-dimensional setting of quantum master equations that have been recently derived. We focus on the dynamics of a single heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in the so-called quantum Brownian regime where the temperature of the plasma is large in comparison with the spacing between the energy levels of the Q Q ¯ system. The one-dimensional potential used in the calculations has been adjusted so as to produce numbers that are relevant for the phenomenology of the charmonium. The equations are solved using different initial states and medium configurations. Various temperature regimes are studied and the effects of screening and collisions thoroughly analyzed. Technical features of the equations are analyzed. The contributions of the different operators that control the evolution are discussed as a function of the temperature. Some phenomenological consequences are addressed. [ABSTRACT FROM AUTHOR]

Within the nonrelativistic QCD (NRQCD) framework, we complete the three-loop calculations of the NRQCD renormalization constants and the matching coefficients, for the heavy flavor-changing temporal vector, spatial-spatial tensor, spatial-temporal axial-tensor currents, which are coupled to the P-wave c b ¯ mesons. We further study the ten decay constants for the c b ¯ mesons (Bc, B c ∗ , B c 0 ∗ , Bc1) coupled with the ten heavy flavor-changing currents involving (pseudo-)scalar, (axial-)vector and (axial-)tensor up to the next-to-next-to-next-to-leading order (N3LO) of αs. We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N3LO perturbative QCD results for the six ratios of decay constants have good convergence and weak scale-dependence. We finally predict the hierarchical relationship among the ten decay constants for the c b ¯ mesons coupled with the ten currents. [ABSTRACT FROM AUTHOR]

The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order. [ABSTRACT FROM AUTHOR]

The magnetic moment yields an excellent framework to explore the inner structure of particles determined by the quark-gluon dynamics of QCD, as it is the leading-order response of a bound system to a weak external magnetic field. Motivated by this, in this study, the magnetic moments of possible axial-vector T bc u ¯ u ¯ , T bc d ¯ d ¯ , and T bc u ¯ d ¯ tetraquarks are obtained with the help of light-cone QCD sum rules. For this purpose, we assume that these states are represented as a diquark-antidiquark picture with different structures and interpolating currents. The magnetic moment results derived using different diquark-antidiquark configurations differ substantially from each other. This can be translated into more than one tetraquark state with the same quantum number and quark content yet possessing different magnetic moments. From the numerical results obtained, we have concluded that the magnetic moments of the Tbc states can project their inner structure, which can be used for their quantum numbers and quark-gluon organization. The contribution of individual quarks to the magnetic moments is also analyzed for completeness. We hope that our predictions of the magnetic moments of the Tbc tetraquarks, together with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these interesting tetraquarks, may be valuable in the search for these states in future experiments and in unraveling the internal structure of these tetraquarks. [ABSTRACT FROM AUTHOR]

We calculate directly in position space the one-loop renormalization kernels of the soft operators Oγ and Og that appear in the soft-quark contributions to, respectively, the subleading-power γγ → h and gg → h form factors mediated by the b-quark. We present an IR/rapidity divergence-free definition for Og and demonstrate that with a correspondent definition of the collinear function, a consistent factorization theorem is recovered. Using conformal symmetry techniques, we establish a relation between the evolution kernels of the leading-twist heavy-light light-ray operator, whose matrix element defines the B-meson light-cone distribution amplitude (LCDA), and Oγ to all orders in perturbation theory. Application of this relation allows us to bootstrap the kernel of Oγ to the two-loop level. We construct an ansatz for the kernel of Og at higher orders. We test this ansatz against the consistency requirement at two-loop and find they differ only by a particular constant. [ABSTRACT FROM AUTHOR]

We investigate the gravitational form factors (GFFs) of the nucleon and the baryon octet, decomposed into their flavor components, utilizing a pion mean-field approach grounded in the large Nc limit of Quantum Chromodynamics (QCD). Our focus is on the contributions from the twist-2 operators to the flavor-triplet and octet GFFs, and we decompose the mass, angular momentum, and D-term form factors of the nucleon into their respective flavors. The strange quark contributions are found to be relatively mild for the mass and angular momentum form factors, while providing significant corrections to the D-term form factor. In the course of examining the flavor decomposition of the GFFs, we uncover that the effects of twist-4 operators play a crucial role. While the gluonic contributions are suppressed by the packing fraction of the instanton vacuum in the twist-2 case, contributions from twist-4 operators are of order unity, necessitating its explicit consideration. [ABSTRACT FROM AUTHOR]

Processes involving only massless or massive quarks at tree-level get corrections from massive (lighter, heavier, or equal-mass) secondary quarks starting at two-loop order, generated by a virtual gluon splitting into a massive quark anti-quark pair. One convenient approach to compute such two-loop corrections is starting with the one-loop diagram considering the virtual gluon massive. Carrying out a dispersive integral with a suitable kernel over the gluon mass yields the desired two-loop result. On the other hand, the Mellin-Barnes representation can be used to compute the expansion of Feynman integrals in powers of a small parameter. In this article we show how to combine these two ideas to obtain the corresponding expansions for large and small secondary quark masses to arbitrarily high orders in a straightforward manner. Furthermore, the convergence radius of both expansions can be shown to overlap, being each series rapidly convergent. The advantage of our method is that the Mellin representation is obtained directly for the full matrix element from the same one-loop computation one needs in large-β0 computations, therefore many existing results can be recycled. With minimal modifications, the strategy can be applied to compute the expansion of the one-loop correction coming from a massive gauge boson. We apply this method to a plethora of examples, in particular those relevant for factorized cross sections involving massless and massive jets, recovering known results and obtaining new ones. Another bonus of our approach is that, postponing the Mellin inversion, one can obtain the small- and large-mas expansions for the RG-evolved jet functions. In many cases, the series can be summed up yielding closed expressions. [ABSTRACT FROM AUTHOR]