Nonperturbative Fragmentation Functions Research Articles

NNLO B-fragmentation fits and their application to toverline{t} production and decay at the LHC

In this work we derive three sets of non-perturbative fragmentation functions, with uncertainties, for B-hadrons, J/ψ’s and muons resulting from semileptonic B decays. All three sets are with next-to-next-to leading order accuracy and include next-to-next-to leading logarithmic soft gluon resummation. The novel feature of these new sets is that they are fully consistent with our formalism for next-to-next-to leading order (NNLO) calculations for final states with identified B, J/ψ or a μ. We employ the fragmentation functions derived in this work to make state of the art predictions for such final states in toverline{t} events at the LHC. A special emphasis is placed on observables sensitive to the top quark mass. The present work opens the door for many LHC applications, like, open B production or B production in association with bosons.

Nucleon Energy Correlators.

We introduce the concept of the nucleon energy correlators, a set of novel objects that encode the microscopic details of a nucleon, such as the parton angular distribution in a nucleon, the collinear splitting to all orders, as well as the internal transverse dynamics of the nucleon. The nucleon energy correlators complement the conventional nucleon or nucleus tomography, but without introducing the nonperturbative fragmentation functions or the jet clustering algorithms. We demonstrate how the nucleon energy correlators can be measured in the lepton-nucleon deep inelastic scattering. The predicted distributions display a fascinating phase transition between the perturbative and nonperturbative regime. In the perturbative phase, a polar angle version of the Bjorken scaling behavior is predicted. We discuss its possible applications and expect it to aggrandize the physics content at the electron ion colliders with a far-forward detector.

Λc+ fragmentation functions from pQCD approach and the Suzuki model

Through data analysis, we present new sets of nonperturbative fragmentation functions (FFs) for $\Lambda_c^+$ baryon both at leading and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the minimal subtraction factorization scheme with five massless quarks. The FFs are determined by fitting all available data of inclusive single $\Lambda_c^+$ baryon production in $e^+e^-$ annihilation taken by the OPAL Collaboration at CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties in the $\Lambda_c^+$ FFs as well as in the corresponding observables. In a completely different approach based on the Suzuki model, we will theoretically calculate the $\Lambda_c^+$ FF from charm quark and present our result at leading order perturbative QCD framework. A comparison confirms a good consistency between both approaches. We will also apply the $\Lambda_c^+$ FFs to make theoretical predictions for the energy distribution of $\Lambda_c^+$ produced through the top quark decay, to be measured at the CERN LHC.

NNLO charmed-meson fragmentation functions and their uncertainties in the presence of meson mass corrections

The main aim of this paper is to present new sets of non-perturbative fragmentation functions (FFs) for D^0 and D^+ mesons 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. This new determination of FFs is based on the QCD fit to the OPAL experimental data for hadron production in the electron-positron single-inclusive annihilation (SIA). We discuss in detail the novel aspects of the methodology used in our analysis and the validity of obtained FFs by comparing with previous works in literature which have been carried out up to NLO accuracy. We will also incorporate the effect of charmed meson mass corrections into our QCD analysis and discuss the improvements upon inclusion of these effects. The uncertainties in the extracted FFs as well as in the corresponding observables are estimated using the “Hessian” approach. For a typical application, we use our new FFs to make theoretical predictions for the energy distributions of charmed mesons inclusively produced through the decay of unpolarized top quarks, to be measured at the CERN LHC. As a result of this analysis, suggestions are discussed for possible future studies on the current topic to consider any theory improvements and other available experimental observables.

B -hadron fragmentation functions at next-to-next-to-leading order from a global analysis of e+e− annihilation data

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 the Hessian approach. We perform comparisons with available NLO sets of $B$-hadron FFs. We apply our new FFs to generate theoretical predictions for the energy distribution of $B$ hadrons produced through the decay of unpolarized or polarized top quarks, to be measured at the CERN LHC.

-baryon production in pp collisions in the general-mass variable-flavour-number scheme, and comparison with CMS and LHCb data

We calculate the next-to-leading-order cross section for the inclusive production of Λb baryons in pp collisions in the general-mass variable-flavor-number scheme. We use realistic evolved non-perturbative fragmentation functions obtained from fits to B-meson production in e+e− annihilation and compare our results for transverse-momentum and rapidity distributions with recent experimental data from the CMS and the LHCb collaborations at the CERN LHC. We find satisfactory agreement in general, with some indication for the need to modify the available fragmentation functions at larger values of the scale variable.

Hadron energy spectrum in polarized top-quark decays considering the effects of hadron and bottom quark masses

We present the analytical expressions for the next-to-leading order corrections to the partial decay width $t(\uparrow) \rightarrow bW^+$, followed by $b\rightarrow H_bX$, for nonzero b-quark mass ($m_b\neq 0$) in the fixed-flavor-number scheme (FFNs). To make the predictions for the energy distribution of outgoing hadrons $H_b$, as a function of the normalized $H_b$-energy fraction $x_H$, we apply the general-mass variable-flavor-number scheme (GM-VFNs) in a specific helicity coordinate system where the polarization of top quark is evaluated relative to the b-quark momentum. We also study the effects of gluon fragmentation and finite hadron mass on the hadron energy spectrum so that hadron masses are responsible for the low-$x_H$ threshold. In order to describe both the b-quark and the gluon hadronizations in top decays we apply realistic and nonperturbative fragmentation functions extracted through a global fit to $e^+e^-$ annihilation data from CERN LEP1 and SLAC SLC by relying on their universality and scaling violations.

Inclusive photoproduction of bottom quarks for low and medium pT in the general-mass variable-flavour-number scheme

We present predictions for b-quark production in photoproduction and compare with experimental data from HERA. Our theoretical predictions are obtained at next-to-leading-order in the general-mass variable-flavor-number scheme, an approach which takes into account the finite mass of the b quarks. We use realistic evolved nonperturbative fragmentation functions obtained from fits to e+e− data. We find in general good agreement of data with both the GM-VFNS and the FFNS calculations, while the more precise ZEUS data seem to prefer the GM-VFNS predictions.

Relative yield of heavy hadrons as a function of the transverse momentum in LHC experiments

It is shown that the dependence of ratio $f_s/f_d$ could be understood within the fragmentation approach. However, the validity of fragmentation model is questionable at low $p_T$, and contributions of nonfragmentation mechanisms are possible. It is demonstrated, that the precise measurements of $p_T$ dependence of $f_s/f_d$, $f_{\Lambda_b}/f_{B}$ and analogous values as function of $p_T$ can essentially improve our understanding of heavy hadron production.At large $p_T$ a plateau is expected in $f_s/f_d$ distribution. Contrary, a plateau is not expected in $f_{B_c}/f_{B}$ distribution on $p_T$.

Heavy quarkonium production at collider energies: Factorization and evolution

We present a factorization formalism for inclusive production of heavy quarkonia of large transverse momentum, $p_T$ at collider energies, including both leading power (LP) and next-to-leading power (NLP) behavior in $p_T$. We demonstrate that both LP and NLP contributions can be factorized in terms of perturbatively calculable short-distance partonic coefficient functions and universal non-perturbative fragmentation functions, and derive the evolution equations that are implied by the factorization. We identify projection operators for all channels of the factorized LP and NLP infrared safe short-distance partonic hard parts, and corresponding operator definitions of fragmentation functions. For the NLP, we focus on the contributions involving the production of a heavy quark pair, a necessary condition for producing a heavy quarkonium. We evaluate the first non-trivial order of evolution kernels for all relevant fragmentation functions, and discuss the role of NLP contributions.

Bottom-flavored hadrons from top-quark decay at next-to-leading order in the general-mass variable-flavor-number scheme

We study the scaled-energy (xB) 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 reduction in the partial decay width at low values of xB. Hadron masses are responsible for the low-xB threshold, while the bottom-quark mass is of minor importance. Neglecting the latter, we also study the doubly differential distribution d2Γ/(dxBdcosθ) of the partial width of the decay t→bW+→Bℓ+νℓ+X, where θ is the decay angle of the charged lepton in the W-boson rest frame.

Bmesons from top-quark decay in the presence of the charged Higgs boson in the zero-mass variable-flavor-number scheme

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 that the contribution of the gluon leads to an appreciable reduction in decay rate at low values of the B-meson energy. It means the NLO corrections are significant.

InclusiveB-meson production at the LHC in the general-mass variable-flavor-number scheme

We calculate the next-to-leading-order cross section for the inclusive production of B mesons in pp collisions in the general-mass variable-flavor-number scheme, an approach which takes into account the finite mass of the b quarks. We use realistic evolved non-perturbative fragmentation functions obtained from fits to e+e- data and compare results for the transverse-momentum and rapidity distributions at a center-of-mass energy of 7 TeV with recent data from the CMS Collaboration. We find good agreement, in particular at large values of pT.

Erratum: Quark fragmentation within an identified jet [Phys. Rev. D81, 074009 (2010)

We derive a factorization theorem that describes an energetic hadron h fragmenting from a jet produced by a parton i, where the jet invariant mass is measured. The analysis yields a "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass s, and on the energy fraction z of the fragmentation hadron. We show that G^h_i can be computed in terms of perturbatively calculable coefficients, J_{ij}(s,z/x), integrated against standard non-perturbative fragmentation functions, D_j^{h}(x). We also show that the sum over h of the integral over z of z G_i^h(s,z) is given by the standard inclusive jet function J_i(s) which is perturbatively calculable in QCD. We use Soft-Collinear Effective Theory and for simplicity carry out our derivation for a process with a single jet, B -> X h l nu, with invariant mass m_{X h}^2 >> Lambda_QCD^2. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h. We apply this rule to derive factorization theorems for B -> X K gamma which is the fragmentation to a Kaon in b -> s gamma, and for e^+e^- -> (dijets)+h with measured hemisphere dijet invariant masses.

Fragmentation production of charmed hadrons in electron-positron annihilation

The processes of D^{(*)}-mesons and \Lambda_c-baryons production in e^+e^--annihilation at 10.58 GeV and 91.18 GeV energies are concerned. At the 10.58 GeV energy the production of charmed particles via the B-mesons decays is also concerned. Scaling violation of the fragmentation functions is calculated at the NLL-accuracy. Nonperturbative fragmentation functions are retrieved from the experimental data of B-factories and are approximated by simple analytic expressions. It is proved, that the difference between nonperturbative fragmentation functions of mesons and baryons can be easily explained by quark counting.

Quark fragmentation within an identified jet

We derive a factorization theorem that describes an energetic hadron $h$ fragmenting from a jet produced by a parton $i$, where the jet invariant mass is measured. The analysis yields a ``fragmenting jet function'' ${\mathcal{G}}_{i}^{h}(s,z)$ that depends on the jet invariant mass $s$, and on the energy fraction $z$ of the fragmentation hadron. We show that ${\mathcal{G}}_{i}^{h}$ can be computed in terms of perturbatively calculable coefficients, ${\mathcal{J}}_{ij}(s,z/x)$, integrated against standard nonperturbative fragmentation functions, ${D}_{j}^{h}(x)$. We also show that $\ensuremath{\sum}_{h}\ensuremath{\int}dz{\mathcal{G}}_{i}^{h}(s,z)$ is given by the standard inclusive jet function ${J}_{i}(s)$ which is perturbatively calculable in QCD. We use soft collinear effective theory and for simplicity carry out our derivation for a process with a single jet, $\overline{B}\ensuremath{\rightarrow}Xh\ensuremath{\ell}\overline{\ensuremath{\nu}}$, with invariant mass ${m}_{Xh}^{2}\ensuremath{\gg}{\ensuremath{\Lambda}}_{\mathrm{QCD}}^{2}$. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function ${J}_{i}$ to be converted to a semi-inclusive process with a fragmenting hadron $h$. We apply this rule to derive factorization theorems for $\overline{B}\ensuremath{\rightarrow}XK\ensuremath{\gamma}$ which is the fragmentation to a Kaon in $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$, and for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}(\mathrm{\text{dijets}})+h$ with measured hemisphere dijet invariant masses.

Charmed-meson fragmentation functions with finite-mass corrections

We elaborate the inclusive production of single heavy-flavored hadrons in e + e − annihilation at next-to-leading order in the general-mass variable-flavor-number scheme. In this framework, we determine non-perturbative fragmentation functions for D 0 , D + , and D ∗ + mesons by fitting experimental data from the Belle, CLEO, ALEPH, and OPAL Collaborations, taking dominant electroweak corrections due to photonic initial-state radiation into account. We assess the significance of finite-mass effects through comparisons with a similar analysis in the zero-mass variable-flavor-number scheme. Under Belle and CLEO experimental conditions, charmed-hadron mass effects on the phase space turn out to be appreciable, while charm-quark mass effects on the partonic matrix elements are less important.

Finite-mass effects on inclusiveB-meson hadroproduction

We calculate the transverse-momentum (${p}_{T}$) distribution for the inclusive hadroproduction of $B$ mesons at intermediate values of ${p}_{T}$ at next-to-leading order (NLO) in a dedicated finite-mass scheme using realistic nonperturbative fragmentation functions that are obtained through a global fit to ${e}^{+}{e}^{\ensuremath{-}}$ data from CERN LEP1 and SLAC SLC exploiting their universality and scaling violations. We find that finite-mass effects moderately enhance the cross section, by about 20% at ${p}_{T}=2{m}_{b}$, and rapidly fade out with increasing value of ${p}_{T}$, so that the zero-mass prediction is reached. We also perform comparisons with recent $p\overline{p}$ data taken by the CDF Collaboration in run II at the Fermilab Tevatron and comment on the usefulness of the fixed-flavor-number scheme.

D0,D+,Ds+, andΛc+fragmentation functions from CERN LEP1

We present new sets of nonperturbative fragmentation functions for ${D}^{0}$, ${D}^{+}$, and ${D}_{s}^{+}$ mesons as well as for ${\ensuremath{\Lambda}}_{c}^{+}$ baryons, both at leading and next-to-leading order in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. They are determined by fitting data of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation taken by the OPAL Collaboration at CERN LEP1. We take the charm-quark fragmentation function to be of the form proposed by Peterson et al. and thus obtain new values of the ${ϵ}_{c}$ parameter, which are specific for our choice of factorization scheme.

InclusiveD*±production inpp¯collisions with massive charm quarks

We calculate the next-to-leading order cross section for the inclusive production of D^{*+-} mesons in p p-bar collisions as a function of the transverse momentum and the rapidity in two approaches using massive or massless charm quarks. For the inclusive cross section, we derive the massless limit from the massive theory. We find that this limit differs from the genuine massless version with MS-bar factorization by finite corrections. By adjusting subtraction terms, we establish a massive theory with MS-bar subtraction which approaches the massless theory with increasing transverse momentum. With these results and including the contributions due to the charm and anti-charm content of the proton and anti-proton, we calculate the inclusive D^{*+-} cross section in p p-bar collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the CDF Collaboration at the Fermilab Tevatron at center-of-mass energy root(S) = 1.96 TeV. We find reasonable, though not perfect, agreement with the measured cross sections.