Universal Jet Research Articles

Subleading effects in soft-gluon emission at one-loop in massless QCD

We elucidate the structure of the next-to-leading-power soft-gluon expansion of arbitrary one-loop massless-QCD amplitudes. The expansion is given in terms of universal colour-, spin- and flavour-dependent operators acting on process-dependent gauge-invariant amplitudes. The result is proven using the method of expansion-by-regions and tested numerically on non-trivial processes with up to six partons. In principle, collinear-region contributions are expressed in terms of convolutions of universal jet operators and process-dependent amplitudes with two collinear partons. However, we evaluate these convolutions exactly for arbitrary processes. This is achieved by deriving an expression for the next-to-leading power expansion of tree-level amplitudes in the collinear limit, which is a novel result as well. Compared to previous studies, our analysis, besides being more general, yields simpler formulae that avoid derivatives of process-dependent amplitudes in the collinear limit.

The Structure of Gamma Ray Burst Jets

Due to relativistic bulk motion, the structure and orientation of gamma-ray burst (GRB) jets have a fundamental role in determining how they appear. The recent discovery of the GW170817 binary neutron star merger and the associated GRB boosted the interest in the modeling and search for signatures of the presence of a (possibly quasi-universal) jet structure in long and short GRBs. In this review, following a pedagogical approach, we summarize the history of GRB jet structure research over the last two decades, from the inception of the idea of a universal jet structure to the current understanding of the complex processes that shape the structure, which involves the central engine that powers the jet and the interaction of the latter with the progenitor vestige. We put some emphasis on the observable imprints of jet structure on prompt and afterglow emission and on the luminosity function, favoring intuitive reasoning over technical explanations.

Towards all-order factorization of QED amplitudes at next-to-leading power

We generalise the factorization of abelian gauge theory amplitudes to next-to-leading power (NLP) in a soft scale expansion, following a recent generalisation for Yukawa theory. From an all-order power counting analysis of leading and next-to-leading regions, we infer the factorized structure for both a parametrically small and zero fermion mass. This requires the introduction of new universal jet functions, for non-radiative and single-radiative QED amplitudes, which we compute at one-loop order. We show that our factorization formula reproduces the relevant regions in one- and two-loop scattering amplitudes, appropriately addressing endpoint divergences. It provides a description of virtual collinear modes and accounts for non-trivial hard-collinear interplay present beyond the one-loop level, making this a first step towards a complete all-order factorization framework for gauge-theory amplitudes at NLP.

The Jet Structure and the Intrinsic Luminosity Function of Short Gamma-Ray Bursts

Abstract The joint observation of GW170817 and GRB 170817A indicated that short gamma-ray bursts (SGRBs) can originate from binary neutron star mergers. Moreover, some SGRBs could be detected off axis, while the SGRB jets are highly structured. Then, by assuming a universal angular distribution of the jet emission for all SGRBs, we reproduce the flux and redshift distributions of the cosmological SGRBs detected by Swift and Fermi. For self-consistency, this angular distribution is simultaneously constrained by the luminosity and event rate of GRB 170817A. As a result, it is found that the universal jet structure of SGRBs could approximately have a two-Gaussian profile. Meanwhile, the intrinsic luminosity function (LF) of the on-axis emission of the jets can be simply described by a single power law with a low-luminosity exponential cutoff. The usually discovered broken-power-law apparent LF for relatively high luminosities can naturally result from the coupling of the intrinsic LF with the angular distribution of the jet emission, as the viewing angles to the SGRBs are arbitrarily distributed.

Two-loop massive quark jet functions in SCET

We calculate the O( {alpha}_s^2 ) corrections to the primary massive quark jet functions in Soft-Collinear Effective Theory (SCET). They are an important ingredient in factorized predictions for inclusive jet mass cross sections initiated by massive quarks emerging from a hard interaction with smooth quark mass dependence. Due to the effects coming from the secondary production of massive quark-antiquark pairs there are two options to define the SCET jet function, which we call universal and mass mode jet functions. They are related to whether or not a soft mass mode (zero) bin subtraction is applied for the secondary massive quark contributions and differ in particular concerning the infrared behavior for vanishing quark mass. We advocate that a useful alternative to the common zero-bin subtraction concept is to define the SCET jet functions through subtractions related to collinear-soft matrix elements. This avoids the need to impose additional power counting arguments as required for zero-bin subtractions. We demonstrate how the two SCET jet function definitions may be used in the context of two recently developed factorization approaches to treat secondary massive quark effects. We clarify the relation between these approaches and in which way they are equivalent. Our two-loop calculation involves interesting technical subtleties related to spurious rapidity divergences and infrared regularization in the presence of massive quarks.

First subleading power resummation for event shapes

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables τ at subleading power in the τ ≪ 1 expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call θ-jet and θ-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in αs, and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for H → gg in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to mathcal{O}left({alpha}_s^3right) . Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the θ-soft and θ-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.

Statistical state dynamics based theory for the formation and equilibration of Saturn's north polar jet

Coherent jets with most of the kinetic energy of the flow are common in atmospheric turbulence. In the gaseous planets these jets are maintained by incoherent turbulence excited by small-scale convection. Large-scale coherent waves are sometimes observed to coexist with the jets; a prominent example is Saturn's hexagonal North polar jet (NPJ). The mechanism responsible for forming and maintaining such a turbulent state remains elusive. The coherent planetary-scale component of the turbulence arises and is maintained by interaction with the incoherent small-scale turbulence component. Theoretical understanding of the dynamics of the jet/wave/turbulence coexistence regime is gained by employing a statistical state dynamics (SSD) model. Here, a second-order closure implementation of a two-layer beta-plane SSD is used to develop a theory that accounts for the structure and dynamics of the NPJ. Asymptotic analysis of the SSD equilibrium in the weak jet damping limit predicts a universal jet structure in agreement with NPJ observations. This asymptotic theory also predicts the wavenumber (six) of the prominent jet perturbation. Analysis with this model of the jet/wave/turbulence regime dynamics reveals that jet formation is controlled by the effective value of $\beta$; the required value of this parameter for correspondence with observation is obtained. As this is a robust prediction it is taken as an indirect observation of a deep poleward sloping stable layer beneath the NPJ. The slope required is obtained from observations of NPJ structure as is the small-scale turbulence excitation required to maintain the jet. The observed jet structure is then predicted by the theory as is the wave-six disturbance. This wave, which is identified with the least stable mode of the equilibrated jet, is shown to be primarily responsible for equilibrating the jet with the observed structure and amplitude.

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.

Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules

We compute radiative corrections to $\Lambda_b \to \Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with $\Lambda_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-$\Lambda_b$-baryon correlation function is justified at leading power in $\Lambda/m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at ${\cal O}(\alpha_s)$ shift the $\Lambda_b \to \Lambda$ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the $\Lambda_b \to \Lambda$ from factors we further investigate several decay observables in the electro-weak penguin $\Lambda_b \to \Lambda \, \ell^{+} \ell^{-}$ transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the $\Lambda_b \to \Lambda$ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.

Hadron fragmentation inside jets in hadronic collisions

We present an analytical next-to-leading order QCD calculation of the partonic cross sections for the process $pp\rightarrow ({\text{jet}} \,h)X$, for which a specific hadron is observed inside a fully reconstructed jet. In order to obtain the analytical results, we assume the jet to be relatively narrow. We show that the results can be cast into a simple and systematic form based on suitable universal jet functions for the process. We confirm the validity of our calculation by comparing to previous results in the literature for which the next-to-leading order cross section was treated entirely numerically by Monte-Carlo integration techniques. We present phenomenological results for experiments at the LHC and at RHIC. These suggest that $pp\rightarrow ({\text{jet}} \,h)X$ should enable very sensitive probes of fragmentation functions, especially of the one for gluons.

Gas-focused liquid microjets from a slit

We report an experimental study on a new arrangement of flow focusing that uses a slit aperture. The slit can achieve similar flow chocking function as a classic circular aperture to established gas flow pressure drop. Fundamentally, the jetting mechanism and quantitative behavior of slit flow focusing are very similar to the classic flow focusing because of the singularity nature of the jet despite the drastically different aperture shapes. After re-scaling the jet shape, the axial coordinate with the hydraulic diameter of the slit, the experimental data follow closely with the universal jet profile derived in Gañán-Calvo, Ferrera, and Montanero [“Universal size and shape of viscous capillary jets: Application to gas-focused microjets,” J. Fluid Mech. 670, 427-438 (2011)] based on circular aperture. Practically, the slit configuration expands the possibility of manipulating the jets. The two thin plates that form the slit aperture can also be used as electrodes to apply electrohydrodynamic excitation to the jet for controlled jet breakup with narrower droplet size distribution. In addition, the modest throughput of a single flow focused jet can be increased by operating a linear array of jets focused and excited by the same slit.

Synchrotron and inverse-Compton emission from blazar jets – IV. BL Lac type blazars and the physical basis for the blazar sequence

In this paper, we investigate the properties of a sample of six BL Lacs by fitting their spectra using our inhomogeneous jet model with an accelerating, magnetically dominated, parabolic base, which transitions to a slowly decelerating conical jet with a geometry based on observations of M87. Our model is able to fit very well to the simultaneous multiwavelength spectra of all the BL Lacs including radio observations. We find that the BL Lacs have lower jet powers and bulk Lorentz factors than the sample of Compton-dominant blazars investigated in Paper III, consistent with the blazar sequence. Excitingly, we find a correlation between the radius at which the jet first comes into equipartition and the jet power, in agreement with our prediction from Paper III. We interpret this result as one of two physical scenarios: a universal jet geometry which scales linearly with black hole mass or a dichotomy in Eddington accretion rates between flat-spectrum radio quasars (FSRQs) and BL Lacs. If we assume that the jet geometry of all blazars scales linearly with black hole mass, then we find a plausible range of masses (∼107–1010 M⊙). We find that the quiescent gamma-ray spectrum of Markarian 421 is best fitted by scattering of external cosmic microwave background photons. We are unable to fit the spectrum using synchrotron self-Compton emission due to strong gamma-ray absorption via pair production even using a compact, rapidly decelerating, jet with a very large bulk Lorentz factor (50), as has been suggested recently. This is because the ratio of synchrotron to inverse-Compton emission requires a high density of synchrotron photons to scatter which makes the region opaque to TeV gamma-rays even with large bulk Lorentz factors. Finally, we fit to the spectral energy distributions of the four high power high synchrotron peak frequency BL Lacs recently found by Padovani et al. We find that their high peak frequency emission is caused by high maximum electron energies whilst the rest of their jet properties are typical of relatively high power BL Lacs and consistent with our predictions.

Shape-function effects and split matching inB→Xsℓ+ℓ−

We derive the triply differential spectrum for the inclusive rare decay $B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ in the shape-function region, in which ${X}_{s}$ is jetlike with ${m}_{X}^{2}\ensuremath{\lesssim}{m}_{b}{\ensuremath{\Lambda}}_{\mathrm{QCD}}$. Experimental cuts make this a relevant region. The perturbative and nonperturbative parts of the matrix elements can be defined with the soft-collinear effective theory, which is used to incorporate ${\ensuremath{\alpha}}_{s}$ corrections consistently. We prove that, with a suitable power counting for the dilepton invariant mass, the same universal jet and shape functions appear as in $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ and $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays. Parts of the usual ${\ensuremath{\alpha}}_{s}({m}_{b})$ corrections go into the jet function at a lower scale, and parts go into the nonperturbative shape function. For $B\ensuremath{\rightarrow}{X}_{s}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$, the perturbative series in ${\ensuremath{\alpha}}_{s}$ are of a different character above and below $\ensuremath{\mu}={m}_{b}$. We introduce a ``split matching'' method that allows the series in these regions to be treated independently.

A Unified Jet Model of X‐Ray Flashes, X‐Ray–rich Gamma‐Ray Bursts, and Gamma‐Ray Bursts. I. Power‐Law–shaped Universal and Top‐Hat–shaped Variable Opening Angle Jet Models

HETE-2 has provided strong evidence that the properties of X-ray flashes (XRFs), X-ray-rich gamma-ray bursts (GRBs), and GRBs form a continuum, and therefore that these three kinds of bursts are the same phenomenon. A key feature found by HETE-2 is that the density of bursts is roughly constant per logarithmic interval in burst fluence SE and observed spectral peak energy E, and in isotropic-equivalent energy Eiso and spectral peak energy Epeak in the rest frame of the burst. In this paper, we explore a unified jet model of all three kinds of bursts, using population synthesis simulations of the bursts and detailed modeling of the instruments that detect them. We show that both a variable jet opening angle model in which the emissivity is a constant independent of the angle relative to the jet axis and a universal jet model in which the emissivity is a power-law function of the angle relative to the jet axis can explain the observed properties of GRBs reasonably well. However, if one tries to account for the properties of XRFs, X-ray-rich GRBs, and GRBs in a unified picture, the extra degree of freedom available in the variable jet opening angle model enables it to explain the observations reasonably well while the power-law universal jet model cannot. The variable jet opening angle model of XRFs, X-ray-rich GRBs, and GRBs implies that the energy Eγ radiated in gamma rays is ~100 times less than has been thought. The model also implies that most GRBs have very small jet opening angles (~half a degree). This suggests that magnetic fields may play an important role in GRB jets. It also implies that there are ~104-105 more bursts with very small jet opening angles for every burst that is observable. If this is the case, the rate of GRBs could be comparable to the rate of Type Ic core-collapse supernovae. These results show that XRFs may provide unique information about the structure of GRB jets, the rate of GRBs, and the nature of Type Ic supernovae.

Gamma‐Ray Burst Intensity Distributions

We use the lag-luminosity relation to calculate self-consistently the redshifts, apparent peak bolometric luminosities L_B, and isotropic energies E_iso for a large sample of BATSE gamma-ray bursts. We consider two different forms of the lag-luminosity relation; for both forms the median redshift for our burst database is 1.6. We model the resulting E_iso sample with power law and Gaussian probability distributions without redshift evolution, both of which are reasonable models. The power law model has an index of alpha_E=1.76+/-0.05 (95% confidence), where p(E_iso) propto E_iso^(-alpha_E). The simple universal jet profile model suggested but did not require alpha_E=2, and subsequent physically reasonable refinements to this model permit greater diversity in alpha_E, as well as deviations from a power law; therefore our observed E_iso probability distribution does not disprove the universal jet model.

Quasi-universal Gaussian Jets: A Unified Picture for Gamma-Ray Bursts and X-Ray Flashes

An observed correlation Ep ∝ (Eiso)1/2 extending from gamma-ray bursts (GRBs) to X-ray flashes (XRFs) poses problems both for a power-law universal jet model, in which the energy per solid angle decreases as the inverse square of the angle with respect to the jet axis, and for a conical jet model with a uniform energy density within the jet beam and a sharp energy cutoff at the jet edge. Here we show that the current GRB-XRF prompt emission/afterglow data can be understood in terms of a picture in which the GRB-XRF jets are quasi-universal and structured, with a Gaussian-like or similar structure, i.e., one where the jet has a characteristic angle, with a mild variation of energy inside and a rapid (e.g., exponential) decrease of energy outside of it. A Monte Carlo simulation shows that the current data is compatible with such a quasi-universal Gaussian jet with a typical opening angle of 5.7 deg and with a standard jet energy of about log(Ej/1 erg) = 51.1 ± 0.3. According to this model, the true-to-observed number ratio of the whole GRB-XRF population is about 14 with the current instrumental sensitivity.

Quark interactions and universal multihadron jets

The constituent approach to strong and electromagnetic hadron interactions requires weak coupling at large momentum transfer, to obtain scaling, and strong coupling at low momentum transfer, to permit quark confinement. Asymptotically free or weakly coupled hard interactions do not provide multiparticle production. Thus soft high-energy quark-quark interactions constitute a universal jet mechanism for multihadron production in soft and in hard hadron-hadron collisions, as well as in deep inelastic lepton-hadron scattering and in e+e− annihilation.