Jet Functions Research Articles

NRQCD Confronts LHCb Data on Quarkonium Production within Jets.

We analyze the recent LHCb measurement of the distribution of the fraction of the transverse momentum, z(J/ψ), carried by the J/ψ within a jet. LHCb data are compared with analytic calculations using the fragmenting jet function (FJF) formalism for studying J/ψ in jets. Logarithms in the FJFs are resummed using Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We also convolve hard QCD partonic cross sections, showered with pythia, with leading order nonrelativistic quantum chromodynamics (NRQCD) fragmentation functions and obtain consistent results. Both approaches use madgraph to calculate the hard process that creates the jet initiating parton. These calculations give reasonable agreement with the z(J/ψ) distribution that was shown to be poorly described by default pythia simulations in the LHCb paper. We compare our predictions for the J/ψ distribution using various extractions of nonperturbative NRQCD long-distance matrix elements (LDMEs) in the literature. NRQCD calculations agree with LHCb data better than default pythia regardless of which fit to the LDMEs is used. LDMEs from fits that focus exclusively on high transverse momentum data from colliders are in good agreement with the LHCb measurement.

Factorization for substructures of boosted Higgs jets

We present a perturbative QCD factorization formula for substructures of an energetic Higgs jet, taking the energy profile resulting from the H→bb¯ decay as an example. The formula is written as a convolution of a hard Higgs decay kernel with two b-quark jet functions and a soft function that links the colors of the two b quarks. We derive an analytical expression to approximate the energy profile within a boosted Higgs jet, which significantly differs from those of ordinary QCD jets. This formalism also extends to boosted W and Z bosons in their hadronic decay modes, allowing an easy and efficient discrimination of fat jets produced from different processes.

Perturbative corrections to B \u2192 D form factors in QCD

We compute perturbative QCD corrections to B → D form factors at leading power in Λ/mb, at large hadronic recoil, from the light-cone sum rules (LCSR) with B-meson distribution amplitudes in HQET. QCD factorization for the vacuum-to-B-meson correlation function with an interpolating current for the D-meson is demonstrated explicitly at one loop with the power counting scheme {m}_csim mathcal{O}left(sqrt{Lambda {m}_b}right) . The jet functions encoding information of the hard-collinear dynamics in the above-mentioned correlation function are complicated by the appearance of an additional hard-collinear scale mc, compared to the counterparts entering the factorization formula of the vacuum-to-B-meson correction function for the construction of B → π from factors. Inspecting the next-to-leading-logarithmic sum rules for the form factors of B → Dℓν indicates that perturbative corrections to the hard-collinear functions are more profound than that for the hard functions, with the default theory inputs, in the physical kinematic region. We further compute the subleading power correction induced by the three-particle quark-gluon distribution amplitudes of the B-meson at tree level employing the background gluon field approach. The LCSR predictions for the semileptonic B → Dℓν form factors are then extrapolated to the entire kinematic region with the z-series parametrization. Phenomenological implications of our determinations for the form factors fBD+,0(q2) are explored by investigating the (differential) branching fractions and the R(D) ratio of B → Dℓν and by determining the CKM matrix element |Vcb| from the total decay rate of B → Dμνμ.

Radiative distortion of kinematic edges in cascade decays

Kinematic edges of cascade decays of new particles produced in high-energy collisions may provide important constraints on the involved particles' masses. For the exemplary case of gluino decay g˜→qq¯χ˜ into a pair of quarks and a neutralino through a squark resonance, we study the hadronic invariant mass distribution in the vicinity of the kinematic edge. We perform a next-to-leading order calculation in the strong coupling αs and the ratio of squark width and squark mass Γq˜/mq˜, based on a systematic expansion in Γq˜/mq˜. The separation into hard, collinear and soft contributions elucidates the process-dependent and universal features of distributions in the edge region, represented by on-shell decay matrix elements, universal jet functions and a soft function that depends on the resonance propagator and soft Wilson lines.

Inclusive production of small radius jets in heavy-ion collisions

We develop a new formalism to describe the inclusive production of small radius jets in heavy-ion collisions, which is consistent with jet calculations in the simpler proton–proton system. Only at next-to-leading order (NLO) and beyond, the jet radius parameter R and the jet algorithm dependence of the jet cross section can be studied and a meaningful comparison to experimental measurements is possible. We are able to consistently achieve NLO accuracy by making use of the recently developed semi-inclusive jet functions within Soft Collinear Effective Theory (SCET). In addition, single logarithms of the jet size parameter αsnlnn⁡R are resummed to next-to-leading logarithmic (NLLR) accuracy in proton–proton collisions. The medium modified semi-inclusive jet functions are obtained within the framework of SCET with Glauber gluons that describe the interaction of jets with the medium. We present numerical results for the suppression of inclusive jet cross sections in heavy ion collisions at the LHC and the formalism developed here can be extended directly to corresponding jet substructure observables.

Efficacy of a Novel Narrow Knife with Water Jet Function for Colorectal Endoscopic Submucosal Dissection.

Backgrounds With respect to the knife's design in colorectal endoscopic submucosal dissection (ESD), diameter, water jet function, and electric power are important because these relate to efficient dissection. In this study, we analyzed a novel, narrow ball tip-typed ESD knife with water jet function (Flush knife BT-S, diameter: 2.2 mm, length: 2000 mm, Fujifilm Co., Tokyo, Japan) compared to a regular diameter knife (Flush knife BT, diameter: 2.6 mm, length: 1800 mm). Methods In laboratory and clinical research, electric power, knife insertion time, vacuum/suction amount with knife in the endoscopic channel, and water jet function were analyzed. We used a knife 2.0 mm long for BT-S and BT knives. Results The BT-S showed faster mean knife insertion time (sec) and better vacuum amount (ml/min) compared to the BT (insertion time: 16.7 versus 21.6, p < 0.001, vacuum amount: 38.0 versus 14.0, p < 0.01). Additionally, the water jet function of the BT-S was not inferior. In 39 colorectal ESD cases in two institutions, there were mean 4.7 times (range: 1–28) of knife insertion. Suction under knife happened 59% (23/39) and suction of fluid could be done in 100%. Conclusions Our study showed that the narrow knife allows significantly faster knife insertion, better vacuum function, and effective clinical results.

バブル噴射機能を備えた浸漬型プリーツ濾材による粒子懸濁液の濾過特性

バブル噴射機能を備えた浸漬型プリーツ濾材による粒子懸濁液の濾過特性

Fragmentation of a jet with small radius

In this paper we consider the fragmentation of a parton into a jet with small jet radius $R$. Perturbatively, logarithms of $R$ can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we introduce the fragmentation function to a jet (FFJ), which describes the fragmentation of a parton into a jet. We discuss how these objects are related to the standard jet functions. Calculating the FFJ to next-to-leading order, we show that these objects satisfy the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, with a natural scale that depends upon $R$. By using the standard renormalization group evolution, we can therefore resum logarithms of $R$. We further use the soft-collinear effective theory to prove a factorization theorem where the FFJs naturally appear, for the fragmentation of a hadron within a jet with small $R$. Finally, we also show how this formalism can be used to resum the ratio of jet radii for a subjet to be emitted from within a fat jet.

Non-abelian factorisation for next-to-leading-power threshold logarithms

Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a non-abelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

Jet substructure using semi-inclusive jet functions in SCET

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron $h$ is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function ${\mathcal G}^h_i(z= \omega_J/\omega,z_h=\omega_h/\omega_J,\omega_J, R,\mu)$, which depends on the jet radius $R$ and the large light-cone momenta of the parton `$i$' initiating the jet ($\omega$), the jet ($\omega_J$), and the hadron $h$ ($\omega_h$). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at next-to-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function ${\mathcal G}_i^h(z,z_h, \omega_J, R,\mu)$ are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter $R$ up to next-to-leading logarithmic (NLL$_R$) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL$_R$ results for the hadron distribution inside the jet. We present numerical results for $pp\to(\mathrm{jet}\,h)X$ in the new framework, and find excellent agreement with existing LHC experimental data.

Transverse momentum dependent fragmenting jet functions with applications to quarkonium production

We introduce the transverse momentum dependent fragmenting jet function (TMDFJF), which appears in factorization theorems for cross sections for jets with an identified hadron. These are functions of $z$, the hadron's longitudinal momentum fraction, and transverse momentum, $\boldsymbol{\mathrm{p}}_{\perp}$, relative to the jet axis. In the framework of Soft-Collinear Effective Theory (SCET) we derive the TMDFJF from both a factorized SCET cross section and the TMD fragmentation function defined in the literature. The TMDFJFs are factorized into distinct collinear and soft-collinear modes by matching onto SCET$_+$. As TMD calculations contain rapidity divergences, both the renormalization group (RG) and rapidity renormalization group (RRG) must be used to provide resummed calculations with next-to-leading-logarithm prime (NLL') accuracy. We apply our formalism to the production of $J/\psi$ within jets initiated by gluons. In this case the TMDFJF can be calculated in terms of NRQCD (Non-relativistic quantum chromodynamics) fragmentation functions. We find that when the $J/\psi$ carries a significant fraction of the jet energy, the $p_T$ and $z$ distributions differ for different NRQCD production mechanisms. Another observable with discriminating power is the average angle that the $J/\psi$ makes with the jet axis.

The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production

We introduce a new kind of jet function: the semi-inclusive jet function $J_i(z, \omega_J, \mu)$, which describes how a parton $i$ is transformed into a jet with a jet radius $R$ and energy fraction $z = \omega_J/\omega$, with $\omega_J$ and $\omega$ being the large light-cone momentum component of the jet and the corresponding parton $i$ that initiates the jet, respectively. Within the framework of Soft Collinear Effective Theory (SCET) we calculate both $J_q(z, \omega_J, \mu)$ and $J_g(z, \omega_J, \mu)$ to the next-to-leading order (NLO) for cone and anti-k$_{\rm T}$ algorithms. We demonstrate that the renormalization group (RG) equations for $J_i(z, \omega_J, \mu)$ follow exactly the usual DGLAP evolution, which can be used to perform the $\ln R$ resummation for {\it inclusive} jet cross sections with a small jet radius $R$. We clarify the difference between our RG equations for $J_i(z, \omega_J, \mu)$ and those for the so-called unmeasured jet functions $J_i(\omega_J, \mu)$, widely used in SCET for {\it exclusive} jet production. Finally, we present applications of the new semi-inclusive jet functions to inclusive jet production in $e^+e^-$ and $pp$ collisions. We demonstrate that single inclusive jet production in these collisions shares the same short-distance hard functions as single inclusive hadron production, with only the fragmentation functions $D_i^h(z, \mu)$ replaced by $J_i(z, \omega_J, \mu)$. This can facilitate more efficient higher-order analytical computations of jet cross sections. We further match our $\ln R$ resummation at both LL$_{R}$ and NLL$_{R}$ to fixed NLO results and present the phenomenological implications for single inclusive jet production at the LHC.

P.1.l.004 - The correlation between perceived level of distress and physiological parameters in palliative cancer patients

We demonstrate the consistency at the next-to-leading-logarithmic (NLL) level of a factorization theorem based on Soft-Collinear Effective Theory (SCET) for jet shapes in e+e− collisions. We consider measuring jet observables in exclusive multijet final states defined with cone and kT-type jet algorithms. Consistency of the factorization theorem requires that the renormalization group evolution of hard, jet, and soft functions is such that the physical cross section is independent of the factorization scale μ. The anomalous dimensions of the various factorized pieces, however, depend on the color representation of jets, choice of jet observable, the number of jets whose shapes are measured, and the jet algorithm, making it highly nontrivial to satisfy the consistency condition. We demonstrate the intricate cancellations between anomalous dimensions that occur at the NLL level, so that, up to power corrections that we identify, our factorization of the jet shape distributions is consistent for any number of quark and gluon jets, for any number of jets whose shapes are measured or unmeasured, for any angular size R of the jets, and for any of the algorithms we consider. Corrections to these results are suppressed by the SCET expansion parameter λ (set by the ratio of the typical momentum in a jet transverse to the jet axis to the total jet energy) and in the jet separation measure 1/t2=tan2(R/2)/tan2(ψ/2), where ψ is the angular separation between jets. Our results can be used to calculate a wide variety of jet observables in multijet final states to NLL accuracy.

Factorization and dispersion relations for radiative leptonic B decay

Applying the dispersion approach we compute perturbative QCD corrections to the power suppressed soft contribution of $B \to \gamma \ell \nu$ at leading twist. QCD factorization for the $B \to \gamma^{\ast}$ form factors is demonstrated explicitly for the hard-collinear transverse polarized photon at one loop, with the aid of the method of regions. While the one-loop hard function is identical to the matching coefficient of the QCD weak current $\bar u \, \gamma_{\mu \perp} \, (1- \gamma_5) \, b$ in soft-collinear effective theory, the jet function from integrating out the hard-collinear fluctuations differs from the corresponding one entering the factorization formula of $B \to \gamma \ell \nu$. Furthermore, we evaluate the sub-leading power contribution to the $B \to \gamma$ form factors from the three-particle $B$-meson distribution amplitudes (DAs) at tree level. The soft contribution to the $B \to \gamma$ form factors from the three-particle $B$-meson DAs is shown to be of the same power compared with the corresponding hard correction, in contrast to the two-particle counterparts. Numerically the next-to-leading-order QCD correction to the soft two-particle contribution in $B \to \gamma$ form factors will induce an approximately $\left (10 \sim 20 \right) \%$ shift to the tree-level contribution at $\lambda_B(\mu_0)=354 \, {\rm MeV}$. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the $B \to \gamma$ form factors by an amount of $\left (10 \sim 30 \right) \%$ with the same value of $\lambda_B(\mu_0)$. Employing the phenomenological model of the three-particle $B$-meson DAs inspired by a QCD sum rule analysis, the three-particle contribution to the $B \to \gamma$ form factors is predicted to be of ${\cal O} (1 \%)$, at leading order in $\alpha_s$, with the default theory inputs.

Streamlining resummed QCD calculations using Monte Carlo integration

Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph, Alpgen or Sherpa. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution. These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including $e^+e^-$ two- and four-jet event shapes, $n$-jettiness and jet-mass related observables at hadron colliders. Attached code can be used to modify MadGraph to export the relevant leading-order hard functions and color structures for arbitrary processes.

Level set jet schemes for stiff advection equations: The semijet method

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.

Analytic and Monte Carlo studies of jets with heavy mesons and quarkonia

We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified hadron in a jet with angularity, \tau_a. The FJFs are convolutions of fragmentation functions (FFs), evolved to the jet energy scale, with perturbatively calculable matching coefficients. Renormalization group equations are used to provide resummed calculations with next-to-leading logarithm prime (NLL') accuracy. We apply this formalism to two-jet events in e^+ e^- collisions with B mesons in the jets, and three-jet events in which a J/\psi is produced in the gluon jet. In the case of B mesons, we use a phenomenological FF extracted from e^+ e^- collisions at the Z^0 pole evaluated at the scale \mu = m_b. For events with J/\psi, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix elements at the scale \mu =2 m_c. The z and \tau_a distributions from our NLL' calculations are compared with predictions from monte carlo event generators. While we find consistency between the predictions for B mesons and the J/\psi distributions in \tau_a, we find the z distributions for J/\psi differ significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs that gives good agreement with NLL' calculations of the z distributions.

Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory

The jet fragmentation function describes the longitudinal momentum distribution of hadrons inside a reconstructed jet. We study the jet fragmentation function in proton-proton collisions in the framework of soft-collinear effective theory (SCET). We find that, up to power corrections, the jet fragmentation function can be expressed as the ratio of the fragmenting jet function and the unmeasured jet function. Using renormalization group techniques, we are able to resum large logarithms of jet radii R in the perturbative expansion of the cross section. We use our theoretical formalism to describe the jet fragmentation functions for light hadron and heavy meson production measured at the Large Hadron Collider (LHC). Our calculations agree very well with the experimental data for the light hadron production. On the other hand, although our calculations for the heavy meson production inside jets are consistent with the PYTHIA simulation, they fail to describe the LHC data. We find that the jet fragmentation function for heavy meson production is very sensitive to the gluon-to-heavy-meson fragmentation function.

Jet shapes in dijet events at the LHC in SCET

We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e+e- collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k_T-type (anti-k_T, C/A, and k_T) algorithms and cone-type algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where non-global logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e+e- collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(\alpha_s). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p_T veto and rapidity cuts together with two tagged jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 \to 2 channels, we compute explicitly for the qq' \to qq' channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p_T^{\rm cut} dependence, and the dependence on the angularity parameter a.

Jet substructures of boosted polarized hadronic top quarks

We study jet substructures of a boosted polarized top quark, which undergoes the hadronic decay $t\to b u\bar d$, in the perturbative QCD framework, focusing on the energy profile and the differential energy profile. These substructures are factorized into the convolution of a hard top-quark decay kernel with a bottom-quark jet function and a $W$-boson jet function, where the latter is further factorized into the convolution of a hard $W$-boson decay kernel with two light-quark jet functions. Computing the hard kernels to leading order in QCD and including the resummation effect in the jet functions, we show that the differential jet energy profile is a useful observable for differentiating the helicity of a boosted hadronic top quark: a right-handed top jet exhibits quick descent of the differential energy profile with the inner test cone radius $r$, which is attributed to the $\mbox{V-A}$ structure of weak interaction and the dead-cone effect associated with the $W$-boson jet. The above helicity differentiation may help to reveal the chiral structure of physics beyond the Standard Model at high energies.