Heavy Quark Mass Effects Research Articles

An FONLL prescription with coexisting flavor number PDFs

We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active flavors at a given scale and, thus, use coexisting PDFs with different active flavor number. This new prescription is perturbatively equivalent to the former but improves the implementation in two ways. First, it can be naturally generalized to account simultaneously for multiple heavy quark effects, such as charm and bottom effects, which can both be relevant at the same scale due to the small mass difference. Second, it can be trivially generalized to use at any fixed-order or collinear resummed accuracy, while previous prescriptions required ad-hoc expansions of the DGLAP evolution kernels for each coefficient. We supplement the paper with codes for the computation of deep inelastic scattering observables in this new prescription.

Heavy quark transverse momentum dependent fragmentation

In this paper, we investigate the heavy quark (HQ) mass effects on the transverse momentum dependent fragmentation function (TMDFF). We first calculate the one-loop TMDFF initiated by a heavy quark. We then investigate the HQ TMDFF in the limit where the transverse momentum, q⊥ is small compared to the heavy quark mass, q⊥ ≪ m and also in the opposite limit where q⊥ ≫ m. As applications of the HQ TMDFF, we study the HQ transverse momentum dependent jet fragmentation function, where the heavy quark fragments into a jet containing a heavy hadron, and we investigate a heavy hadron’s transverse momentum dependent distribution with respect to the thrust axis in e+e− collisions.

NLO QCD corrections to the ( γ*→QQ¯ )-Reggeon vertex

Next-to-leading order (NLO) QCD corrections to the ${\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}Q\overline{Q}$-Reggeon vertex are calculated, where $Q\overline{Q}$ denotes a heavy quark pair $c\overline{c}$ or $b\overline{b}$. The heavy quark mass effects on the photon impact factor are found to be significant, and hence may influence the results of high energy photon-photon scattering and heavy quark pair leptoproduction. In our NLO calculation, similar to the massless case, the ultraviolate (UV) divergences are fully renormalized in the standard procedure, while the infrared (IR) divergences are regulated by the parameter ${\ensuremath{\epsilon}}_{\mathrm{IR}}$ in dimensional regularization. For the process ${\ensuremath{\gamma}}^{*}+q\ensuremath{\rightarrow}Q\overline{Q}+q$, we calculate all NLO coefficients in terms of ${\ensuremath{\epsilon}}_{\mathrm{IR}}$, and find they are enhanced due to the heavy quark mass, as compared with the light quark case, and the enhancement factors increase rapidly as the quark mass increases. This might essentially indicate the quark mass effect, in spite of the absence of real corrections that are needed in a complete NLO calculation. Moreover, unlike the ${\ensuremath{\gamma}}^{*}$ to massless-quark-Reggeon vertex, the results in the present work may apply to the real photon case.

Charged lepton flavor violation associated with heavy quark production in deep inelastic lepton-nucleon scattering via scalar exchange

We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering ℓiN → ℓjq overline{q} X. Here ℓi and ℓj denote the initial and final leptons; N and X are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mass effects in the final lepton momentum distribution. We clarify the necessity of inclusion of the heavy quark mass to obtain reliable theory predictions for the CLFV signal searches in the deep-inelastic scattering.

Predictions for Z -Boson Production in Association with a b -Jet at O(αs3)

Precise predictions are provided for the production of a $\mathrm{Z}$-boson and a $\mathrm{b}$-jet in hadron-hadron collisions within the framework of perturbative QCD, at $\mathcal{O}(\alpha_s^3)$. To obtain these predictions we perform the first calculation of a hadronic scattering process involving the direct production of a flavoured-jet at next-to-next-to-leading order accuracy in massless QCD, and extend techniques to also account for the impact of finite heavy-quark mass effects. The predictions are compared to CMS data obtained in $\mathrm{pp}$ collisions at a centre-of-mass energy of $8~\mathrm{TeV}$, which are the most precise data from Run I of the LHC for this process, where a good description of the data is achieved. To allow this comparison we have performed an unfolding of the data, which overcomes the long-standing issue that the experimental and theoretical definitions of jet flavour are incompatible.

Nuclear parton distributions from lepton-nucleus scattering and the impact of an electron-ion collider

We present a first determination of the nuclear parton distribution functions (nPDF) based on the NNPDF methodology: nNNPDF1.0. This analysis is based on neutral-current deep-inelastic structure function data and is performed up to NNLO in QCD calculations with heavy quark mass effects. For the first time in the NNPDF fits, the chi ^2 minimization is achieved using stochastic gradient descent with reverse-mode automatic differentiation (backpropagation). We validate the robustness of the fitting methodology through closure tests, assess the perturbative stability of the resulting nPDFs, and compare them with other recent analyses. The nNNPDF1.0 distributions satisfy the boundary condition whereby the NNPDF3.1 proton PDF central values and uncertainties are reproduced at A=1, which introduces important constraints particularly for low-A nuclei. We also investigate the information that would be provided by an Electron-Ion Collider (EIC), finding that EIC measurements would significantly constrain the nPDFs down to xsimeq 5times 10^{-4}. Our results represent the first-ever nPDF determination obtained using a Monte Carlo methodology consistent with that of state-of-the-art proton PDF fits, and provide the foundation for a subsequent global nPDF analyses including also proton-nucleus data.

Light and heavy flavor dijet production and dijet mass modification in heavy ion collisions

Back-to-back light and heavy flavor dijet measurements are promising experimental channels to accurately study the physics of jet production and propagation in a dense QCD medium. They can provide new insights into the path length, color charge, and mass dependence of quark and gluon energy loss in the quark-gluon plasma produced in reactions of ultra-relativistic nuclei. To this end, we perform a comprehensive study of both light and heavy flavor dijet production in heavy ion collisions. We propose the modification of dijet invariant mass distributions in such reactions as a novel observable that shows enhanced sensitivity to the QGP transport properties and heavy quark mass effects on in-medium parton showers. This is achieved through the addition of the jet quenching effects on the individual jets as opposed to their subtraction. The latter drives the subtle effects on more conventional observables, such as the dijet momentum imbalance shifts, which we also calculate here. Results are presented in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for comparison to data at the Large Hadron Collider and in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV to guide the future sPHENIX program at the Relativistic Heavy Ion Collider.

Neutrino telescopes as QCD microscopes

We present state-of-the-art predictions for the ultra-high energy (UHE) neutrino-nucleus cross-sections in charged- and neutral-current scattering. The calculation is performed in the framework of collinear factorisation at NNLO, extended to include the resummation of small-x BFKL effects. Further improvements are made by accounting for the free-nucleon PDF constraints provided by D-meson data from LHCb and assessing the impact of nuclear corrections and heavy-quark mass effects, which are treated at NLO. The calculations presented here should play an important role in the interpretation of future data from neutrino telescopes such as IceCube and KM3NeT, and highlight the opportunities that astroparticle experiments offer to study the strong interactions.

Heavy quark mass effects in parton-to-kaon hadronization probabilities

We examine the relevance of the heavy quarks masses in the perturbative QCD description of hard interactions where charged kaons are produced in the final state. We extract a set of parton-to-kaon hadronization probabilities from a next to leading order QCD global analysis where a general mass variable flavor number scheme accounting for mass effects is implemented. We compare the results with those obtained in the massless approximation and also with those found in the case of final state pions. At variance with the very significant improvement found for the much more precise pion fragmentation phenomenology, the heavy quark mass dependent scheme improves mildly the overall description of current kaon production data. Nevertheless, we find a noticeable reduction in the charm-to-kaon hadronization probability.

Heavy quark jet fragmentation

In this paper we study the fragmentation of a parton into a jet containing a heavy quark. When heavy quarks are involved in a jet, the quark mass can lead to a numerically significant correction to the jet cross section and its substructure. With this motivation, we calculated the heavy quark mass effects to next-to-leading order in αs on the fragmentation functions to a jet (FFJs) and the jet fragmentation functions (JFFs), where the former describes fragmentation of parton into a jet and the latter describes fragmenting processes inside a jet. The finite size of the heavy quark mass does not change the ultraviolet behaviors, but it can give significant corrections to the finite contributions. When we take the zero mass limit, we find that the FFJs and the JFFs reproduce established results for massless partons. If we define the heavy quark jet as one that include at least one heavy (anti-)quark, the tagged heavy quark jet production is sensitive to the heavy quark mass and produces large logarithms of the mass. Taking advantage of the FFJs and JFFs, we formulate a factorization theorem for heavy quark jet production in order to resum these large logarithms systematically. As an application, we study inclusive b-jet production and show phenomenological implications due to keeping a non-zero quark mass.

Role of heavy quarks in light hadron fragmentation

We investigate the role of heavy quarks in the production of light flavored hadrons and in the determination of the corresponding non perturbative hadronization probabilities. We define a general mass variable flavor number scheme for fragmentation functions that accounts for heavy quark mass effects, and perform a global QCD analysis to an up-to-date data set including very precise Belle and BaBar results. We show that the mass dependent picture provides a much more accurate and consistent description of data.

Towards parton distributions with fitted charm

Modern parton distribution function fits require an accurate treatment of heavy quark mass effects. In this contribution, we discuss how the FONLL general-mass variable flavour number scheme can be extended to allow for the possibility of a fitted charm PDF. We present a first estimate of the impact of a fitted charm contribution in the FONLL structure functions, and we discuss the development towards including a fitted charm PDF in the NNPDF framework.

Charm in deep-inelastic scattering

We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions $F^c_2$, $F^c_L$ and $F^c_3$ to NNLO.

Heavy-quark mass effects in Higgs boson production at the LHC

We study the impact of heavy-quark masses in Higgs boson production through gluon fusion at the LHC. We extend previous computations of the fully differential cross section and of the transverse momentum spectrum of the Higgs boson by taking into account the finite top- and bottom-quark masses up to $ \mathcal{O}\left( {\alpha_{\mathrm{S}}^3} \right) $ . We also discuss the issues arising when the heavy-quark mass is much smaller than the Higgs mass. Our results are implemented in updated versions of the HNNLO and HRes numerical programs.

Heavy quark production in the Aivazis-Collins-Olness-Tung scheme at next-to-next-to-leading and next-to-next-to-next-to-leading order

We analyze the properties of the Aivazis-Collins-Olness-Tung (ACOT) scheme for heavy quark production and make use of the $\overline{\mathrm{MS}}$ massless results at next-to-next-to-leading order and ${\mathrm{N}}^{3}\mathrm{LO}$ for the structure functions ${F}_{2}$ and ${F}_{L}$ in neutral current deep-inelastic scattering to estimate the higher order corrections. For this purpose we decouple the heavy quark mass entering the phase space from the one entering the dynamics of the short distance cross section. We show numerically that the phase space mass is generally more important. Therefore, the dominant heavy quark mass effects at higher orders can be taken into account using the massless Wilson coefficients together with an appropriate slow-rescaling prescription implementing the phase space constraints. Combining the exact ACOT scheme at next-to-leading order with these expressions should provide a good approximation to the missing full calculation in the ACOT scheme at next-to-next-to-leading order and ${\mathrm{N}}^{3}\mathrm{LO}$.

Impact of heavy quark masses on parton distributions and LHC phenomenology

We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology including heavy quark mass effects: NNPDF2.1. In comparison to the previous NNPDF2.0 parton determination, the dataset is enlarged to include deep-inelastic charm structure function data. We implement the FONLL-A general-mass scheme in the FastKernel framework and assess its accuracy by comparison to the Les Houches heavy quark benchmarks. We discuss the impact on parton distributions of the treatment of the heavy quark masses, and we provide a determination of the uncertainty in the parton distributions due to uncertainty in the masses. We assess the impact of these uncertainties on LHC observables by providing parton sets with different values of the charm and bottom quark masses. Finally, we construct and discuss parton sets with a fixed number of flavors.

Resummation of large logarithms in the heavy-quark effects on the parton distributions inside the virtual photon

We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and discuss the property of the resummed heavy quark effects.

Heavy quark effects on parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD

We investigate the heavy quark mass effects on the parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD. Our formalism is based on the QCD-improved parton model described by the DGLAP evolution equation as well as on the operator product expansion supplemented by the mass-independent renormalization group method. We evaluate the various components of the parton distributions inside the virtual photon with the massive quark effects, which are included through the initial condition for the heavy quark distributions, or equivalently from the matrix element of the heavy quark operators. We discuss some features of our results for the heavy quark effects and their factorization-scheme dependence.

HPro: A NLO Monte-Carlo for Higgs production via gluon fusion with finite heavy quark masses

We compute fully differential next-to-leading order QCD cross-sections for Higgs boson production via gluon fusion in the Standard Model. We maintain the full dependence of the cross-sections on the top and bottom quark mass. We find that finite quark mass effects are important given the achieved precision of QCD predictions for gluon fusion. Our Monte-Carlo program, HPro, can correct existing NNLO fully differential calculations, which employ the approximation of an infinitely heavy top and a vanishing bottom quark Yukawa coupling, for heavy quark finite mass effects through NLO.

Heavy Quark Effects in the Virtual Photon Structure Functions

2 ,P 2 )a ndF γ L (x,Q 2 ,P 2 ) in the framework of the mass-independent renormalization group equation (RGE). We study a formalism in which the heavy quark mass effects are treated based on parton picture as well as on the operator product expansion (OPE), and perform the numerical evaluation of F γ eff (x,Q 2 ,P 2 ) to the next-leading order (NLO) in QCD. Subject Index: 165