Variable Flavor Number Scheme Research Articles

Fully charmed tetraquarks from LHC to FCC: natural stability from fragmentation

We investigate the inclusive production of fully charmed tetraquarks, T4c(0++)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}(0^{++})$$\\end{document} or T4c(2++)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}(2^{++})$$\\end{document} radial excitations, in high-energy proton collisions. We build our study upon the collinear fragmentation of a single parton in a variable-flavor number scheme, suited to describe the tetraquark formation mechanism from moderate to large transverse-momentum regimes. To this extent, we derive a novel set of DGLAP-evolving collinear fragmentation functions, named TQ4Q1.0 determinations. They encode initial-scale inputs corresponding to both gluon and heavy-quark fragmentation channels, defined within the context of quark-potential and spin-physics inspired models, respectively. We work within the NLL/NLO+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NLO}^+$$\\end{document} hybrid factorization and make use of the JETHAD numeric interface along with the symJETHAD symbolic calculation plugin. With these tools, we provide predictions for high-energy observables sensitive to T4c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}$$\\end{document} plus jet emissions at center-of-mass energies ranging from 14 TeV at the LHC to the 100 TeV nominal energy of the FCC.

Next-to-next-to-leading order evolution of polarized parton densities in the Larin scheme

In many calculations involving polarized twist-2 parton densities to higher order in the strong coupling constant one uses the Larin scheme to describe chiral effects in dimensional regularization. Upon forming observables, the scheme dependence cancels. Still one needs a corresponding regularization scheme to compute the contributing building blocks, like massless and massive Wilson coefficients, as well as the massive three-loop operator matrix elements used in the variable flavor number scheme. These are matched to the evolved parton distribution functions in the Larin scheme. Starting with suitable input distributions we provide the solution of scale evolution of the different polarized parton distribution functions in Bjorken x space for a wide range of virtualities Q2 in the Larin scheme, at next-to-leading, at next-to-next-to-leading order for the first time. We also illustrate the deviation between the parton distributions in the Larin and MS¯ schemes numerically. Published by the American Physical Society 2024

Tt¯bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}b\\overline{b} $$\\end{document} at NLO precision in a variable flavor number scheme

Top-quark pair production in association with two b-jets is computed at next-to-leading order QCD precision, including effects of the b-quark mass, and matched to a tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document}+jets simulation in a variable flavor number scheme. The Monte Carlo realization of this method, called fusing, consistently embeds the four-flavor calculation in a particle-level event generator. As a first phenomenological application, we present observables relevant to the data-driven estimation of irreducible backgrounds to tt¯H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}H $$\\end{document}-production.

Exotic Tetraquarks at the HL-LHC with JETHAD: A High-Energy Viewpoint

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the formation mechanism of a tetraquark state within the next-to-leading order perturbative QCD. This framework builds on the basis of a spin physics-inspired model, taken as a proxy for the lowest-scale input of the constituent heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation functions are consistently obtained via the above-threshold DGLAP evolution in a variable-flavor number scheme. We provide predictions for a series of differential distributions calculated by the hands of the JETHAD method, well-adapted to NLL/NLO+ hybrid-factorization studies, where the resummation of next-to-leading energy logarithms and beyond is included in the collinear picture. We provide corroborating evidence that high-energy observables sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair stability under radiative corrections, as well as MHOU studies. Our analysis constitutes a prime contact point between QCD resummations and the exotic matter.

Formula omitted]) polarized heavy flavor corrections to deep-inelastic scattering at Q2 ≫ m2

We calculate the quarkonic O(αs2) massive operator matrix elements ΔAQg(N),ΔAQqPS(N) and ΔAqq,QNS(N) for the twist–2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region Q2≫m2 to O(ε) in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region Q2≫m2 derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for g1(x,Q2) to O(αs2) for all but the power suppressed terms ∝(m2/Q2)k,k≥1. The results in momentum fraction z-space are also presented. We also discuss the small x effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two–mass variable flavor number scheme to O(ε).

The unpolarized and polarized single-mass three-loop heavy flavor operator matrix elements Agg,Q and ∆Agg,Q

We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, Agg,Q(x, μ2) and ∆Agg,Q(x, μ2), at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin N-space and iterated integrals over square root-valued alphabets in momentum fraction x-space. We derive the necessary analytic relations for the analytic continuation of these quantities from the even or odd Mellin moments into the complex plane, present analytic expressions in momentum fraction x-space and derive numerical results. The present results complete the gluon transition matrix elements both of the single- and double-mass variable flavor number scheme to three-loop order.

A massive variable flavour number scheme for the Drell-Yan process

The prediction of differential cross-sections in hadron-hadron scattering processes is typically performed in a scheme where the heavy-flavour quarks (c, b, tc,b,t) are treated either as massless or massive partons. In this work, a method to describe the production of colour-singlet processes which combines these two approaches is presented. The core idea is that the contribution from power corrections involving the heavy-quark mass can be numerically isolated from the rest of the massive computation. These power corrections can then be combined with a massless computation (where they are absent), enabling the construction of differential cross-section predictions in a massive variable flavour number scheme. As an example, the procedure is applied to the low-mass Drell-Yan process within the LHCb fiducial region, where predictions for the rapidity and transverse-momentum distributions of the lepton pair are provided. To validate the procedure, it is shown how the n_fnf-dependent coefficient of a massless computation can be recovered from the massless limit of the massive one. This feature is also used to differentially extract the massless N^3LON3LO coefficient of the Drell-Yan process in the gluon-fusion channel.

Bottom-flavored inclusive emissions in the variable-flavor number scheme: A high-energy analysis

We propose the inclusive semi-hard production, in proton-proton collisions, of two bottom-flavored hadrons, as well as of a single bottom-flavored hadron accompanied by a light jet, as novel channels for the manifestation of stabilization effects of the high-energy resummation under next-to-leading-order corrections. Our formalism relies on a hybrid high-energy and collinear factorization, where the BFKL resummation of leading and next-to-leading energy logarithms is used together with collinear factorization. We present results for cross sections and azimuthal correlations differential in rapidity, which are widely recognized as standard observables where to hunt for distinctive signals of the BFKL dynamics. We propose the study of double differential distributions in the transverse momenta of final-state particles as a common basis to investigate the interplay of different kinds of resummation mechanisms.

QCD analysis of pion fragmentation functions in the xFitter framework

We present the first open-source analysis of fragmentation functions (FFs) of charged pions (entitled IPM-xFitter) computed at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD using the xFitter framework. This study incorporates a comprehensive and up-to-date set of pion production data from single-inclusive annihilation (SIA) processes, as well as the most recent measurements of inclusive cross-sections of single pion by the BELLE collaboration. The determination of pion FFs along with their theoretical uncertainties is performed in the Zero-Mass Variable-Flavor Number Scheme (ZM-VFNS). We also present comparisons of our FFs set with recent fits from the literature. The resulting NLO and NNLO pion FFs provide valuable insights for applications in present and future high-energy analysis of pion final state processes.

Logarithmic contributions to the polarized O(αs3) asymptotic massive Wilson coefficients and operator matrix elements in deeply inelastic scattering

We compute the logarithmic contributions to the polarized massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the polarized massive operator matrix elements needed in the variable flavor number scheme. The calculation is performed in the Larin scheme. For the massive operator matrix elements $A_{qq,Q}^{(3),\rm PS}$ and $A_{qg,Q}^{(3),\rm S}$ the complete results are presented. The expressions are given in Mellin-$N$ space and in momentum fraction $z$-space.

Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme

In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the impact of target mass corrections and higher twist effects which are expected to be important in the region of large $x$ and intermediate-to-low $Q^2$. Our analysis is based on a publicly available open-source tool {\tt APFEL}, which has been modified to be applicable for our analysis of nuclear PDFs. Heavy quark contributions to nuclear DIS are considered within the framework of the {\tt FONLL} general-mass variable-flavor-number scheme. The most recent {\tt CT18} PDFs are used as baseline proton PDFs. The uncertainties of nuclear PDFs are determined using the standard Hessian approach. The results of our global QCD analysis are compared with existing nuclear PDF sets and with the fitted cross-sections, for which our set of nuclear PDFs provides a very good description.

The polarized transition matrix element Agq(N) of the variable flavor number scheme at [formula omitted

We calculate the polarized massive operator matrix element Agq(3)(N) to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable N both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at O(αs3). We also present the results in momentum fraction space.

J/ψ meson production in association with an open charm hadron at the LHC: A reappraisal

We critically (re)examine the associated production process of a $J/\psi$ meson plus an open charm hadron at the LHC in the proton-proton ($pp$) and proton-lead ($p{\rm Pb}$) collisions. Such a process is very intriguing in the sense of tailoring to explore the double parton structure of nucleons and to determine the geometry of partons in nuclei. In order to interpret the existing $pp$ data with the LHCb detector at the center-of-mass energy $\sqrt{s}=7$ TeV, we introduce two overlooked mechanisms for the double parton scattering (DPS) and single parton scattering (SPS) processes. Besides the conventional DPS mode, where the two mesons are produced almost independently in the two separate scattering subprocesses, we propose a novel DPS mechanism that the two constituent (heavy) quarks stemming from two hard scatterings can form into a composite particle, like the $J/\psi$ meson, during the hadronization phase. However, it turns out the corresponding contribution is small in $J/\psi+c\bar{c}$ hadroproduction. On the contrary, we point out that the resummation of the initial state logarithms due to gluon splitting into a charm quark pair is crucial to understand the LHCb measurement, which was overlooked in the literature. We perform a proper matching between the perturbative calculations in different initial-quark flavor number schemes, generically referring to the variable flavor number scheme. The new variable flavor number scheme calculation for the process strongly enhance the SPS cross sections, almost closing the discrepancies between theory and experiment. Finally, we present our predictions for the forthcoming LHCb measurement in $p{\rm Pb}$ collisions at $\sqrt{s_{NN}}=8.16$ TeV. Some interesting observables are exploited to set up the control regions of the DPS signal and to probe the impact-parameter dependent parton densities in lead.

Λc± production in pp collisions with a new fragmentation function

We study inclusive $\Lambda_c^{\pm}$-baryon production in $pp$ collisions in the general-mass variable-flavor number scheme and compare with data from the LHCb, ALICE and CMS collaborations. We perform a new fit of the $c \to \Lambda_c^+$ fragmentation function combining $e^+e^-$ data from OPAL and Belle. The agreement with LHC data is slightly worse compared with a calculation using an older fragmentation function, and the tension between different determinations of $\Lambda_c^{\pm}$ production cross sections from the LHC experimental collaborations is not resolved. The ratio of data for $\Lambda_c^+$-baryon and $D^0$-meson production seems to violate the universality of $c$-charm quark to $c$-hadron fragmentation.

The two-mass contribution to the three-loop polarized gluonic operator matrix element [formula omitted

We compute the two-mass contributions to the polarized massive operator matrix element Agg,Q(3) at third order in the strong coupling constant αs in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep–inelastic scattering in the asymptotic regime Q2≫mc2,mb2. The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in N-space and by iterated integrals involving square-root valued arguments in z space, as functions of the mass ratio. Numerical results are presented. New two–scale iterative integrals are calculated.

The three-loop single mass polarized pure singlet operator matrix element

We calculate the massive polarized three-loop pure singlet operator matrix element AQq(3),PS in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient HQq(3),PS in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provide analytic results in Mellin N and in x space and study the behaviour of this operator matrix element in the region of small and large values of the Bjorken variable x.

The three-loop polarized pure singlet operator matrix element with two different masses

We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the polarized structure function g1(x,Q2) at O(αs3) as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square–root valued letters.

Determination of contributions from residual light charged hadrons to inclusive charged hadrons from e+e- annihilation data

In this paper, we present an extraction of the contribution from the "{\it residual}" light charged hadrons to the inclusive unidentified light charged hadron fragmentation functions (FFs) at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. Considering the contributions from charged pion, kaon and (anti)proton FFs from recent {\tt NNFF1.0} analysis of charged hadron FFs, we determine the small but efficient {\it residual} charged hadron FFs from QCD analysis of all available single inclusive unidentified charged hadron data sets in electron-positron ($e^+ e^-$) annihilations. The zero-mass variable flavor number scheme (ZM-VFNS) has been applied to account the heavy flavor contributions. The obtained optimum set of {\it residual} charged hadron FFs is accompanied by the well-known Hessian technique to assess the uncertainties in the extraction of these new sets of FFs. It is shown that the {\it residual} contributions of charged hadron FFs have very important impact on the inclusive charged hadron FFs and substantially on the quality and the reliability of the QCD fit. Furthermore, this study shows that the {\it residual} contributions become also sizable for the case of heavy quark FFs as well as for the $c$- and $b$-tagged cross sections.

Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions

The current analysis aims to present the results of a QCD analysis of diffractive parton distribution functions (diffractive PDFs) at next-to-leading order (NLO) accuracy in perturbative QCD. In this new determination of diffractive PDFs, we use all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) datasets from H1 and ZEUS Collaborations at HERA including the most recent H1/ZEUS combined measurements. In this analysis, we consider the heavy quark contributions to the diffractive DIS in the so-called framework of {\tt FONLL} general mass variable flavor number scheme (GM-VFNS). The uncertainties on the diffractive PDFs are calculated using the standard "Hessian error propagation" which served to provide a more realistic estimate of the uncertainties. This analysis are enriched, for the first time, by including the nonperturbative higher twist (HT) effects in the calculation of diffractive DIS cross sections which are particularly important at large-$x$ and low $Q^{2}$ regions. Then, the stability and reliability of the extracted diffractive PDFs are investigated upon inclusion of HT effects. We discuss the novel aspects of the approach used in this QCD fit, namely, optimized and flexible parameterizations of diffractive PDFs, the inclusion of HT effects, and considering the recent H1/ZEUS combined dataset. Finally, we present the extracted diffractive PDFs with and without the presence of HT effects, and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted datasets. We show that the inclusion of HT effects in diffractive DIS can improve the description of the data which leads, in general, to a very good agreement between data and theory predictions.

Multijet merging in a variable flavor number scheme

We propose a novel technique for the combination of multi-jet merged simulations in the five-flavor scheme with calculations for the production of b-quark associated final states in the four-flavor scheme. We show the equivalence of our algorithm to the FONLL method at the fixed-order and logarithmic accuracy inherent to the matrix-element and parton-shower simulation employed in the multi-jet merging. As a first application we discuss Zbb production at the Large Hadron Collider.