Inclusive production of heavy-flavored hadrons at NLO in the GM-VFNS
Bernd A. Kniehl
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4 pages, 8 figures, to appear in the Proceedings of the XVI International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2008), 7-11 April 2008, University College London
We summarize recent progress in the theoretical description of heavy-flavored-hadron inclusive production at next-to-leading order in the general-mass variable-flavor-number scheme. Specifically, we discuss the influence of finite-mass effects on the determination D-meson fragmentation functions from a global fit to e^+e^- annihilation data and on the transverse-momentum distribution of B-meson hadroproduction. We also demonstrate that the fixed-flavor-number scheme, implemented with up-to-date parton density functions and strong-coupling constant, provides a surprisingly good description of B-meson data from run II at the Fermilab Tevatron.
I consider variations in the definition of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions, both at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO). I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. At both NLO and NNLO I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the distributions when a new MSTW-type global fit to data is performed for each GM-VFNS. At NLO the par…
We study the inclusive production of J/psi and psi(2S) mesons originating from the decays of bottom-flavored hadrons produced in p anti-p collisions at the Fermilab Tevatron and in pp collisions at the CERN LHC. We work at next-to-leading order in the general-mass variable-flavor-number scheme (GM-VFNS) implemented with nonperturbative fragmentation functions fitted to e^+e^- data of inclusive b-hadron production exploiting their universality. The three-momentum distributions of the charmonia used were extracted from B-decay data in the framework of nonrelativistic-QCD factorization. Comparing…
I consider variations in the definitions, at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO), of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions. I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the PDFs when a new MSTW2008-type global fit to data is performed for each GM-VFNS. At NLO the parton distributions, and predic…
We study the scaled-energy (x_B) distribution of bottom-flavored hadrons (B) inclusively produced in top-quark decays at next-to-leading order (NLO) in the general-mass variable-flavor-number scheme endowed with realistic, nonperturbative fragmentation functions that are obtained through a global fit to e^+e^- data from CERN LEP1 and SLAC SLC exploiting their universality and scaling violations. Specifically, we study the effects of gluon fragmentation and finite bottom-quark and B-hadron masses. We find the NLO corrections to be significant. Gluon fragmentation leads to an appreciable reducti…
We compare `fixed flavor number scheme' (FFNS) and `variable flavor number scheme' (VFNS) parton model predictions at high energy colliders. Based on our recent LO- and NLO-FFNS dynamical parton distributions, we generate radiatively two sets of VFNS parton distributions where also the heavy quark flavors h=c,b,t are considered as massless partons within the nucleon. By studying the role of these distributions in the production of heavy particles (h\bar{h}, t\bar{b}, hW^{+-}, Higgs--bosons, etc.) at high energy ep, p\bar{p} and pp colliders, we show that the VFNS predictions are compatible wit…
The Thorne-Roberts variable flavour number scheme (VFNS) for heavy quarks is presented in detail for the specific case of charged current DIS. As in neutral current DIS this provides a smooth extrapolation from the fixed flavour number scheme (FFNS) appropriate at low $Q^2$ to the zero-mass variable flavour number scheme (ZM-VFNS) appropriate as $Q^2 \to \infty$, and differs from alternative versions of a VFNS by the definition of the coefficient functions at each order, and the strict ordering of the expansion in $α_S$. However, there are subtle differences from the neutral current case which…
We consider the decay of a polarized top quark into a stable $W^+$ boson and charmed-flavored (D) or bottom-flavored (B) hadrons, via $t(\uparrow)\rightarrow W^++D/B+X$. We study the angular distribution of the scaled-energy of B/D-hadrons at next-to-leading order (NLO) considering the contribution of bottom and gluon fragmentations into the heavy mesons B and D. To obtain the energy spectrum of B/D-hadrons we present our analytical expressions for the parton-level differential decay widths of $t(\uparrow)\rightarrow b+W^+(+g)$ at NLO. Comparison of our predictions with data at the LHC enable …
We study the energy spectrum of the inclusive bottom-flavored mesons in top-quark decay into a charged-Higgs-boson and a massless bottom quark at next-to-leading order (NLO) in the two-Higgs-doublet model. To extract the result we work in the Zero-Mass Variable-Flavor-Number scheme(ZM-VFNs) using realistic nonperturbative fragmentation functions obtained through a global fit to $e^+e^-$ data from CERN LEP1 and SLAC SLC on the Z-boson resonance. We study both the contribution of the bottom-quark fragmentation and the gluon fragmentation to produce the bottom-flavored meson (B-Meson). We find th…
We present the results of a calculation of the perturbative QCD corrections for the semileptonic inclusive width of a heavy flavored meson. Within the Heavy Quark Expansion we analytically compute the QCD correction to the coefficient of power suppressed contribution of the chromo-magnetic operator in the limit of vanishing mass of the final state quark. The important phenomenological applications are decays of bottom mesons, and to the less extend, charmed mesons.
We determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2<1 GeV^2) by employing the "fixed flavor number factorization scheme" (FFNS). These are compared with "standard" NNLO distributions, generated at some fixed and higher resolution scale (Q_0^2>1 GeV^2). The NNLO corrections imply in both approaches an improved value of χ^2, typically χ^2_{NNLO} \sim 0.9χ^2_{NLO}. The dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both …
Next-to-leading order (NLO) QCD predictions for the production of heavy quarks in proton-proton collisions are presented within three different approaches to quark mass, resummation and fragmentation effects. In particular, new NLO and parton shower simulations with POWHEG are performed in the ALICE kinematic regime at three different centre-of-mass energies, including scale and parton density variations, in order to establish a reliable baseline for future detailed studies of heavy-quark suppression in heavy-ion collisions. Very good agreement of POWHEG is found with FONLL, in particular for …
The production of heavy-flavored hadron at the hadronic colliders provides a challenging opportunity to test the validity of pQCD predictions. There are two mechanisms for the $B^{(*)}_s$ hadroproduction, i.e. the gluon-gluon fusion mechanism via the subprocess $g+g\rightarrow B^{(*)}_s+b+\bar{s}$ and the extrinsic heavy quark mechanism via the subprocesses $g+\bar{b}\to B^{(*)}_s +\bar{s}$ and $g+s\to B^{(*)}_s +b$, both of which shall have sizable contributions in proper kinematic region. Different from the fixed-flavor-number scheme (FFNS) previously adopted in the literature, we study the …
We review one-particle inclusive production of heavy-flavored hadrons in a framework which resums the large collinear logarithms through the evolution of the FFs and PDFs and, at the same time, retains the full dependence on the heavy-quark mass without additional theoretical assumptions. The main focus is on the production of D^* mesons in deep inelastic electron--proton scattering at HERA. We show results, neglecting for the time being the heavy-quark mass terms, for deep inelastic D^* meson production at finite transverse momenta. Work to implement this process in the above mentioned massiv…
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-Ma…
We present our analytic results for the NLO corrections to the partial decay width $t\to H^+b$ followed by $b\to BX$ for nonzero b-quark mass ($m_b\neq 0$) in the Fixed-Flavor-Number scheme (FFNs). To make our predictions for the energy distribution of the outgoing bottom-flavored hadron (B-hadron) as a function of the normalized B-energy fraction $x_B$, we apply the General-Mass Variable-Flavor-Number scheme (GM-VFNs) in the two-Higgs-doublet model. To extract the results we use data from $e^+e^-$ machines in order to describe both the b-quark and the gluon hadronizations in top decay. We fin…
Charged Higgs bosons $H^\pm$ are predicted by some non-minimal Higgs scenarios, such as models containing Higgs triplets and two-Higgs-doublet models, so that the experimental observation of these bosons would indicate physics beyond the Standard Model. In the present work, we introduce a new channel to indirect search for the charged Higgses through the hadronic decay of polarized top quarks where a top quark decays into a charged Higgs $H^+$ and a bottom-flavored hadron $B$ via the hadronization process of the produced bottom quark, $t(\uparrow)\rightarrow H^++b(\to B+jet)$. To obtain the en…
We present {\tt GKG18-DPDFs}, a next-to-leading order (NLO) QCD analysis of diffractive parton distribution functions (diffractive PDFs) and their uncertainties. This is the first global set of diffractive PDFs determined within the {\tt xFitter} framework. This analysis is motivated by all available and most up-to-date data on inclusive diffractive deep inelastic scattering (diffractive DIS). Heavy quark contributions are considered within the framework of the Thorne-Roberts (TR) general mass variable flavor number scheme (GM-VFNS). We form a mutually consistent set of diffractive PDFs due to…
We present nonperturbative fragmentation functions (FFs) for bottom-flavored ($B$) hadrons both at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. They are determined by fitting all available experimental data of inclusive single $B$-hadron production in $e^+e^-$ annihilation, from the ALEPH, DELPHI, and OPAL Collaborations at CERN LEP1 and the SLD Collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using t…
We present a novel study on the inclusive production of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a test field of the high-energy QCD dynamics. The large transverse momenta at which the two final-state objects are detected permits us to perform an analysis in the spirit of the variable-flavor number scheme (VFNS), in which the cross section for the hadroproduction of a light parton is convoluted with a perturbative fragmentation function that describes the transition from a light quark to a heavy hadron. The quarkonium collinear fragmentation function is b…
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 se…
The goal of this study is to determine a set of diffractive parton distribution function (diffractive PDFs) from a QCD analysis of all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) data sets from HERA $ep$ collider, including the most recent H1 and ZUES combined inclusive diffractive cross section measurements. This extraction of diffractive PDFs, referred to as {\tt HK19-DPDF}, is performed at next-to-leading (NLO) and next-to-next-to-leading (NNLO) in perturbative QCD. This new determination of diffractive PDFs is based on the fracture functions methodology…
Analogous to NRQCD factorization for heavy quarkonium exclusive production, in this work we propose to employ the heavy-quark-effective-theory (HQET) factorization, which has been predominantly applied to account for exclusive $B$ decays, to study the exclusive production of the heavy-flavored mesons. We take $W\to B(D_s)+γ$ as a prototype process. The validity of the HQET factorization rests upon the presumed scale hierarchy: $m_W\sim m_b\gg Λ_{\rm QCD}$. Through an explicit analysis at next-to-leading order in $α_s$ yet at leading order in $1/m_b$, we verify that the decay form factors can i…
In this thesis we study the b-quark fragmentation in top decay as well as the effect of the threshold resummation on heavy quark production in charged-current DIS. To predict the spectrum of b-flavored hadrons in top decay, we calculate at NLO the QCD corrections for bottom production in top decay with the b-mass fully taken into account. Using the perturbative fragmentation function formalism we then resum with NLL accuracy large collinear logs of the ratio of bottom-to-top mass, which leads to an essential improvement of the result. Next we perform the threshold resummation for the coefficie…
We present our QCD analysis of the proton structure function $F_2^p(x,Q^2)$ to determine the parton distributions at the next-to-leading order (NLO). The heavy quark contributions to $F_2^i(x,Q^2)$, with $i$ = $c$, $b$ have been included in the framework of the `fixed flavour number scheme' (FFNS). The results obtained in the FFNS are compared with available results such as the general-mass variable-flavour-number scheme (GM-VFNS) and other prescriptions used in global fits of PDFs. In the present QCD analysis, we use a wide range of the inclusive neutral-current deep-inelastic-scattering (NC …
We calculate the ${\cal O}(α_s)$ radiative corrections to the spin dependent differential decay rates of the process $t\rightarrow b+W^+$. These are needed to study the angular distribution of the energy of hadrons produced in polarized top quark decays at next-to-leading order (NLO). In our previous work, we studied the angular distribution of the scaled-energy of bottom-flavored hadrons (B) from polarized top quark decays, using a specific helicity coordinate system where the top quark spin was measured relative to the bottom momentum (system~1). Here, we study the angular distribution of th…
A clear understanding of nuclear parton distribution functions (nPDFs) plays a crucial role in the interpretation of collider data taken at the Relativistic Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC) and in the near future at the Electron-Ion Collider (EIC). Even with the recent inclusions of vector boson and light meson production data, the uncertainty of the gluon PDF remains substantial and limits the interpretation of heavy ion collision data. To obtain new constraints on the nuclear gluon PDF, we extend our recent nCTEQ15WZ+SIH analysis to inclusive quarkonium and open hea…
