The fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson are derived up to QCD next-to-leading order (NLO). They are further computed numerically and presented in figures precisely. In order to reach a higher accuracy, we have also tried properly to apply them to estimating the $B_c$ and $B_c^*$ production at a $Z$-factory (an $e^+e^-$ collider running at the energy of the $Z$-boson pole).
We apply the method of perturbative fragmentation to study bottom fragmentation in top decay. We present the energy spectrum of b-quarks and b-flavoured hadrons in top decay
In the paper, we calculate the fragmentation functions for $c \to η_c$ and $b \to η_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{c \to η_c}(z,μ_F)$ and $D_{b \to η_b}(z,μ_F)$ up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and th…
In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium $J/Ψ$ or $Υ$. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. $μ_{F}=3 m_c$ for $c\to J/Ψ$ and $μ_{F}=3m_b$ for $b\to Υ$, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial applicati…
In this review, we discuss the results on the parton-to-pion fragmentation functions obtained in a combined NLO fit to data of single-inclusive hadron production in electron-positron annihilation, proton-proton collisions, and lepton-nucleon deep-inelastic scattering. A more complete discussion can be found in Ref. [1].
We present the first calculation at next-to-leading order (NLO) in $α_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction…
We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual …
In this document, we present the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An extended analysis of this work can be found in Ref.[1].
A combined analysis of both $e^+\,e^-$ (LEP, SLD) and $p\,p$ (RHIC-PHENIX and LHC-ALICE) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3) symmetry. The transverse momentum ($p_T$) and rapidity ($y$) dependence of the differential cross section for $ω$ and $ϕ$ mesons of the $p\,p$ data are also discussed. The input universal quark (valence and singlet) fragmentation functions at a starting scale of $Q_0^2=1.5$ GeV$^2$, after evolution, have values that are consistent with the earlier analysis for …
We calculate the fragmentation function for charm quark into J/psi at the QCD next-to-leading-order (NLO) and find that the produced J/psi is of larger momentum fraction than it is at the leading-order. Based on the fragmentation function and partonic processes calculated at the NLO, the transverse momentum distribution on J/psi hadroproduction associated with a charm c (or \bar{c}) jet are predicted. We find that the distribution is enhanced by a factor of 2.0--3.3 at the NLO as p_t increased from 10 GeV to 100 GeV and it is measurable at the LHC with charm tagger. The measurement at the LHC …
Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the ${}^1S_0^{(1,8)}$ components of a heavy quarkonium. Starting from the Collins and Soper's operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.
A detailed study of fragmentation of vector mesons at the next-to-leading order (NLO) is given for e^+ e^- scattering. A model with broken SU(3) symmetry uses three input fragmentation functions α(x, Q^2), β(x,Q^2) and γ(x,Q^2) and a strangeness suppression parameter λto describe all the light quark fragmentation functions for the entire vector meson octet. At a starting low energy scale of Q_0^2 = 1.5 GeV^2 for three light quarks (u, d, s) along with initial parameterization, the fragmentation functions are evolved through DGLAP evolution equations at NLO and the cross-section is calculated. …
The next-to-leading order (NLO) ($\mathcal{O}(α_s^3)$) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ${^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}$ states are calculated within the NRQCD factorization. We use integration-by-parts reduction and differential equations to semi-analytically calculate fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergence…
We have computed semi-inclusive spin asymmetries for proton and deuteron targets including next to leading order (NLO) QCD corrections and contributions coming from the target fragmentation region. These corrections have been estimated using NLO fragmentation functions, parton distributions and also a model for spin dependent fracture functions which is proposed here. We have found that NLO corrections are small but non-negligible in a scheme where gluons are polarised and that our estimate for target fragmentation effects does not modify significantly charged asymmetries but affects the so ca…
An NLO QCD analysis of the final HERMES data on pion multiplicities is presented and a new set of pion fragmentation functions is extracted from the best fit to the data. We have studied the so-called [x,z] and [Q^2,z] presentations of their data, as given by HERMES, which, in principle, should simply be two different ways of presenting the experimental data. We have based our extraction on an excellent fit to the [Q^2,z] presentation of the data. We also draw attention to what appears to be a problem with the [x,z] presentation of the HERMES data.
Recently, the {\it Belle} and {\it BABAR} Collaborations published the single-inclusive electron-positron annihilation data at the center of mass energies ($\sqrt{s}$) of $10.52$ GeV and $10.54$ GeV, respectively. These new data offer one the possibility to determine the nonperturbative initial conditions of fragmentation functions much more accurately. In our previous work \cite{Soleymaninia:2013cxa}, we extracted the fragmentation functions for $π^\pm$ and $K^\pm$ particles at next-to-leading order (NLO) including these new data, for the first time. These new data are in the regions of large…
For processes involving structure functions and/or fragmentation functions, arguments that there is a part that dominates the NLO corrections are briefly reviewed. The arguments are tested against more recent NLO and in particular NNLO calculations.
The QCD coupling alpha_s is determined from a combined analysis of experimental e+e- and e-p jet data confronted to theoretical predictions of the energy evolution of the parton-to-hadron fragmentation functions (FFs) moments --multiplicity, peak, width, skewness-- at low fractional hadron momentum z. The impact of approximate next-to-leading order (NLO*) corrections plus next-to-next-to-leading log (NNLL) resummations, compared to previous LO+NLL calculations, is discussed. A global fit of the full set of existing data, amounting to 360 FF moments at collision energies sqrt(s)~1--200 GeV, res…
We analyse the phenomenological consequences of target and current fragmentation contributions at next to leading order in semi-inclusive spin dependent deep inelastic scattering asymmetries.
We discuss preliminary results on medium-modified fragmentation functions obtained in a combined NLO fit to data on semi-inclusive deep inelastic scattering off nuclei and hadroproduction in deuteron-gold collisions.
We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in ${^{1}\hspace{-0.6mm}S_{0}^{[1]}}$ or ${^{1}\hspace{-0.6mm}S_{0}^{[8]}}$ state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of $z$ (light-cone momentum fract…
The concept of parton fragmentation in QCD hard scattering phenomenology as well as NLO pQCD analysis of fragmentation functions are outlined. Hadroproduction of pions of a few GeV pT is discussed through the example of recent measurements at \sqrt{S_{RHIC}}=200 GeV.
The transverse momentum ($p_t$) distributions of production and polarization for $J/ψ$ measured by CDF Collaboration are still challenging our understanding of the heavy quarkonium production mechanism even with recent significant theoretical progresses on the next-to-leading-order (NLO) QCD calculation. We suggest a new mechanism for $J/ψ$ production at hadron collider, $pp(\bar p)\to γ^{\ast}(J/ψ)+X$ with $J/ψ$ from a virtual photon $γ^{\ast}$ fragmentation. Our calculations show it's $p_t$ distribution at NLO will be larger than that of the conventional $J/ψ$ production from the color-singl…
We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large-$p_{\bot}$ hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.
The formulas directly connecting parton distribution functions (PDFs) and fragmentation functions (FFs) at the next to leading order (NLO) QCD with the same quantities at the leading order (LO) are derived. These formulas are universal, i.e. have the same form for all kinds of PDFs and FFs, differing only in the respective splitting functions entering there.
It is well-known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using the Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and…
A new analysis of the modification of the hadronization process in the nuclear medium for pions is presented. The effective description is condensed in a set of medium modified fragmentation functions (nFFs) obtained at next-to-leading order (NLO) accuracy. The study was made using the open-source tool xFitter, conveniently modified to incorporate semi-inclusive processes. Theoretical uncertainties for the nFFs are also provided.
We present new sets of fragmentation functions for protons and inclusive charged hadrons obtained in combined NLO QCD analyses of single-inclusive hadron production in electron-positron annihilation, proton-proton collisions, and deep-inelastic lepton-proton scattering. These analyses complement previous results for pion and kaon fragmentation functions with charge and flavor discrimination. The Lagrange multiplier technique is used to assess the uncertainties in the extraction of the new sets of fragmentation functions.
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…
A next-to-leading order (NLO) analysis of hadron-jet momentum correlations in p-p collisions at the LHC is carried out. We show that the inclusive charged hadron momentum distributions inside jets is a very sensitive observable which allows one to disentangle among various fragmentation function sets presently available. Correlations with identified hadrons (kaons, protons) are investigated as well.
Fragmentation functions for D mesons, based on the convolution of a perturbative part, related to the heavy quark perturbative showering, and a non-perturbative model for its hadronization into the meson, are used to describe D^* production in e^+e^- and ep collisions. The non-perturbative part is determined by fitting the e^+e^- data taken by ARGUS and OPAL at 10.6 and 91.2 GeV respectively. When fitting with a non perturbative Peterson fragmentation function and using next-to-leading evolution for the perturbative part, we find an epsilon parameter sensibly different from the one commonly us…
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 the NLO QCD corrections to diphoton plus jet production at hadron colliders. Our calculation includes contributions from the fragmentation of a hadronic jet into a highly energetic photon, and consequently allows the implementation of arbitrary infrared-safe photon isolation definitions. We compare different photon isolation criteria and perform a detailed study of the dependence of the diphoton plus jet cross section on the photon isolation parameters.
Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ($p_{\rm T}$) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $A+A$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $\hat{q}$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $p_{\rm T}$ hadron productions, we extract $\hat{q}$ quantitatively via a global fit to d…
We present an interface between the multipurpose NLO Monte Carlo tool MadGraph5_aMC@NLO and the automated one-loop amplitude generator GoSam. As a first application of this novel framework, we compute the NLO corrections to $pp \to t\bar{t}H$ and $pp \to t\bar{t}γγ$ matched to a parton shower. In the phenomenological analyses of these processes, we focus our attention on observables which are sensitive to the polarisation of the top quarks.
We use a recent O(alpha_s^2) calculation of the differential cross section for the production of heavy quarks in e+e- annihilation to compute a few moments of the heavy quark single-inclusive production cross section. We verify that, contrary to some recent claims, the leading and next-to-leading logarithmic terms in this cross section are correctly given by the standard NLO fragmentation function formalism for heavy quark production.
We review the main aspects of the fragmentation of bottom quarks in top quark decay. The NLO b-quark energy spectrum presents large mass logarithms ln(m_t^2/m_b^2), which can be resummed by the use of the approach of perturbative fragmentation functions. Large soft contributions in both coefficient function and initial condition of the perturbative fragmentation function have been resummed as well. Results on the energy distribution of b quarks and b-flavoured hadrons are finally presented in both x and moment spaces.
We study inclusive charged-hadron production in collisions of quasireal photons at NLO in perturbative QCD, using fragmentation functions recently extracted from PEP and LEP1 data. We superimpose the direct (DD), single-resolved (DR), and double-resolved (RR) gamma-gamma channels. First, we confront existing data taken by TASSO at PETRA and by MARK II at PEP with our NLO calculations. We also make comparisons with the neutral-kaon to charged-hadron ratio measured by MARK II. Then, we present NLO predictions for LEP2, a next-generation e+e- linear collider (NLC) in the TESLA design, and a Compt…
Within the NRQCD factorization framework, we compute the next-to-leading-order QCD corrections to the gluon fragmentation into the ${}^1S_0^{(1,8)}$ Fock components of a quarkonium, at the lowest order in velocity expansion. We follow the operator definition of the fragmentation function advanced by Collins and Soper. The key technique underpinning our calculation is the sector decomposition method widely used in the area of multi-loop computation. It is found that the NLO QCD corrections have significant effects, and qualitatively modify the profiles of the corresponding leading-order fragmen…
The inclusive spectra of charged particles measured at high transverse momenta ($p_T\gtrsim$2GeV/c) in proton-proton and proton-antiproton collisions in the range of center-of-mass energies $\sqrt{s}=200-7000$GeV are compared with next-to-leading order perturbative QCD calculations using seven recent sets of parton-to-hadron fragmentation functions (FFs). Accounting for the uncertainties in the scale choices and in the parton distribution functions, we find that most of the theoretical predictions tend to overpredict the measured LHC and Tevatron cross sections by up to a factor of two. We ide…
Inspired by the recent measurements of the $η_c$ meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into $η_c$, which constitutes the crucial nonperturbative elements to understand $η_c$ production at high $p_T$. Employing three distinct methods, we calculate the leading relativistic correction to the $g\toη_c$ fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the $c\to η_c$ fragmentation function. We also study the evolution behavior of these fragmentation functions wit…
We present a full off-shell NLO QCD calculation of $pp \rightarrow e^+ ν_e b μ^- \barν_μ\bar{b} b \bar{b} + X$. Results are obtained using the HELAC-NLO Monte Carlo framework. We discuss a comparison to previous results and to experimental measurements. We also investigate the contribution of the initial states involving $b$-quarks and we introduce two $b$-jet tagging schemes.
Fitting $Z^0$-pole data from ALEPH and SLD, and TPC data at a lower c.m.s.\ energy, we fix the boundary condition for NLO parton$\to$hadron (hadron$=π^\pm, K^\pm, \sum_h h^\pm$) fragmentation functions (FFs) at the low resolution scale of the radiative parton model of Glück, Reya and Vogt (GRV). Perturbative LO$\leftrightarrow$NLO stability is investigated. The emphasis of the fit is on information on the fragmentation process for individual light ($u,d,s$) and heavy ($c,b$) quark flavours where we comment on the factorization scheme for heavy quarks in $e^+e^-$ annihilations as compared to de…
We report on state-of-the-art theoretical predictions for $pp\to t\bar{t}b\bar{b}$ including full off-shell effects in the di-lepton decay channel at NLO QCD accuracy. We briefly discuss the impact of NLO QCD corrections on differential distributions and also asses theoretical uncertainties from scale and PDF dependence. Furthermore, we propose a simple kinematic reconstruction in order to distinguish $b$ jets originating from top-quark decays from arising from gluon splittings.
We present the next-to-leading order QCD corrections to the production of a photon pair in association with one or two jets. This class of processes constitutes an important background for Higgs physics at the LHC. For the one jet process we include photon fragmentation contributions and perform a comparison between different photon isolation criteria and various isolation parameters. The two jet calculation has been performed using a smooth cone isolation criterion. We find that the NLO QCD corrections are substantial and can lead to distortions of differential distributions.
We study single-hadron inclusive electroproduction in ep scattering at DESY HERA at next-to-leading order in the parton model of quantum chromodynamics endowed with non-perturbative fragmentation functions. Specifically, we consider charged-hadron production, with unspecified transverse momentum p_T, in the Breit frame and D^{*+-} production as a function of p_T, and perform comparisons with recent data from the H1 Collaboration.
We present a brief description of the determination of the two-loop spin-dependent time-like splitting functions relevant for the NLO evolution of polarized fragmentation functions. Our calculation based on the analytic continuation of the corresponding space-like results obtained within the light-cone gauge method proposed by Curci, Furmanski, and Petronzio. As an application we present an analysis of polarized Lambda production in e+e- and ep collisions.
The interpretation of Drell-Yan production in terms of the antiquark densities depends on NLO corrections. Besides the NLO corrections to the familiar annihilation $q\bar{q}\to γ^* \to l^+ l^-$, there is a substantial contribution from the QCD Compton subprocesses $gq \to qγ^* \to q l^+ l^-$ and $g\bar{q} \to qγ^* \to q l^+ l^-$. The beam and target dependence of the two classes of corrections is different. We discuss the impact of this difference on the determination of the $\bar{d}-\bar{u}$ asymmetry in the proton from the comparison of the $pp$ and $pn$ Drell-Yan production.
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 a parton shower which implements the DGLAP evolution of parton densities and fragmentation functions at next-to-leading order precision up to effects stemming from local four-momentum conservation. The Monte-Carlo simulation is based on including next-to-leading order collinear splitting functions in an existing parton shower and combining their soft enhanced contributions with the corresponding terms at leading order. Soft double counting is avoided by matching to the soft eikonal. Example results from two independent realizations of the algorithm, implemented in the two event gene…
With the QCD sum rules approach, we study the newly discovered doubly heavy baryon $Ξ_{cc}^{++}$. We analytically calculate the next-to-leading order (NLO) contribution to the perturbative part of $J^{P} = \frac{1}{2}^{+}$ baryon current with two identical heavy quarks, and then reanalyze the mass of $Ξ_{cc}^{++}$ at the NLO level. We find that the NLO correction significantly improves both scheme dependence and scale dependence, whereas it is hard to control these theoretical uncertainties at leading order. With the NLO contribution, the baryon mass is estimated to be $m_{Ξ_{cc}^{++}} = 3.66_…
The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $σ^{γ^*}_{T}$ and $σ^{γ^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the $q\bar{q}$ and the $q\bar{q}g$ Fock states in the photon are directly calculated, using earlier results for the $q\bar{q}$ light-front wave-functions at one loop inside a dressed virtual photon. Both the $q\bar{q}$ and the $q\bar{q}g$ contributions have UV divergences, which are shown to cancel each other, using…
