Virtual Amplitudes Research Articles

Beam spin asymmetry measurements of deeply virtual π0 production with CLAS12

The new experimental measurements of beam spin asymmetry were performed for the deeply virtual exclusive π0 production in a wide kinematic region with the photon virtualities Q2 up to 6.6 GeV2 and the Bjorken scaling variable xB in the valence regime. The data were collected by the CEBAF Large Acceptance Spectrometer (CLAS12) at Jefferson Lab with longitudinally polarized 10.6 GeV electrons scattered on an unpolarized liquid-hydrogen target. Sizable asymmetry values indicate a substantial contribution from transverse virtual photon amplitudes to the polarized structure functions. The interpretation of these measurements in terms of the Generalized Parton Distributions (GPDs) demonstrates their sensitivity to the chiral-odd GPD E¯T, which contains information on quark transverse spin densities in unpolarized and polarized nucleons and provides access to the nucleon's transverse anomalous magnetic moment. Additionally, the data were compared to a theoretical model based on a Regge formalism that was extended to the high photon virtualities.

Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD

In this work, we provide a comprehensive set of differential cross-section distributions for photon + di-jet production in proton-proton collisions with next-to-next-to-leading order precision in massless QCD. The event selection corresponds to recent measurements by the ATLAS collaboration. We observe an improved description of data in comparison to lower-order calculations in the case of observables that are expected to be well described by perturbation theory. The results also show better agreement with data than parton-shower-matched and multi-jet-merged predictions generated for the ATLAS analysis using the Sherpa Monte Carlo. A particular highlight of our study is the use of exact five-point two-loop virtual amplitudes. This is the first calculation of a complete two-to-three hadron-collider process at next-to-next-to-leading order in QCD that does not rely on the leading-colour approximation at two loops. We demonstrate, nevertheless, that the sub-leading-colour effects present in the infraredand ultraviolet-finite double-virtual contributions are negligible in view of the remaining scale uncertainties.

Mixed QCD-EW two-loop amplitudes for neutral current Drell-Yan production

We present the mixed QCD-EW two-loop virtual amplitudes for the neutral current Drell-Yan production. The evaluation of the two-loop amplitudes is one of the bottlenecks for the complete calculation of the NNLO mixed QCD-EW corrections. We present the computational details, especially the evaluation of all the relevant two-loop Feynman integrals using analytical and semi-analytical methods. We perform the subtraction of universal infrared singularities and present the numerical evaluation of the hard function.

Top-quark mass effects in H+jet and H+2 jets production

We present calculations of Higgs boson production via gluon-gluon fusion in association with one or two additional jets at next-to-leading order in QCD. The calculation of H+jet is exact in the treatment of the top-quark mass, whereas for the H+2 jets calculation the two-loop virtual amplitudes are approximated via a reweighting with leading-order mass effects, while keeping all top-quark mass effects in the real radiation contributions. For H+jet production, this study extends a previous calculation, revealing an error in the previous results. For total and differential cross sections, we present new results and compare the QCD corrections with the infinite top-mass limit, for which we find a strikingly good agreement if all amplitudes are rescaled by the leading-order mass dependence.

Updates to the one-loop provider NLOX

We describe the 1.2 update to NLOX, a computer program for calculations in high-energy particle physics. New features since the 1.0 release and other changes are described, along with usage documentation.

QED corrections in overline{B}to overline{K}{mathrm{ell}}^{+}{mathrm{ell}}^{-} at the double-differential level

We present a detailed analysis of QED corrections to overline{B}to overline{K}{mathrm{ell}}^{+}{mathrm{ell}}^{-} decays at the double-differential level. Cancellations of soft and collinear divergences are demonstrated analytically using the phase space slicing method. Whereas soft divergences are found to cancel at the differential level, the cancellation of the hard-collinear logs ln mℓ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution (q2), are sizeable and need to be treated with care when comparing with experiment. Virtual and real amplitudes are evaluated using an effective mesonic Lagrangian. Crucially, we show that going beyond this approximation does not introduce any further infrared sensitive terms. All analytic computations are performed for generic charges and are therefore adaptable to semileptonic decays such as overline{B}to Dmathrm{ell}overline{nu } .

NLOX, a one-loop provider for Standard Model processes

NLOX is a computer program for calculations in high-energy particle physics. It provides fully renormalized scattering matrix elements in the Standard Model of particle physics, up to one-loop accuracy for all possible coupling-power combinations in the strong and electroweak couplings, and for processes with up to six external particles. Program summaryProgram Title: NLOXProgram Files doi:http://dx.doi.org/10.17632/y7jth5hznv.1Licensing provisions: CC BY NC 3.0Programming language:C++. Fortran interface available, and Fortran compiler required for dependencies.Nature of problem: The computation of higher-order terms in the coupling expansion of Standard Model scattering amplitudes is required for precision studies in collider experiments. Techniques for computing the first corrections are well-known, and are now suited to automation. We wish to provide code that calculates virtual (one-loop) quantum chromodynamics and electroweak corrections for desired amplitudes using a package that automates the production of this code.Solution method: We use Python scripts and a computer algebra system, FORM, to reduce virtual amplitudes to C++ code and data based on Feynman rules of the Standard Model. The scripts perform a tensor decomposition of the one loop integral to reduce the amplitude to dependence on tensor integral coefficients. These coefficients are called at runtime by the provided library TRed, which performs tensor reduction into base (scalar) coefficients at runtime. The scripts identify repeated structures to be calculated once in the produced code for efficiency. The tensor reduction code is designed such that needed tensor coefficients need to be computed only once per evaluation of the desired amplitude, and are built recursively from other needed coefficients.Additional comments including restrictions and unusual features: The code-producing scripts are not provided in this release, only fixed libraries such as TRed and required interface code for pre-generated processes. Some processes are provided with this release, with others available upon request.

Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity

We construct Faddeev-Kulish states in QED and perturbative quantum gravity to subleading order in the soft momentum expansion and to first order in the coupling constant, using the charge conservation formula of asymptotic symmetries associated with the tree-level subleading soft theorems. We demonstrate that the emission and absorption of soft photons/gravitons in dressed amplitudes vanish. The fact that no additional soft radiation may be added to a dressed amplitude supports the claim that, in the dressed state formalism, the soft and hard sectors of scattering processes are correlated. We also show that the dressed virtual amplitudes are equivalent to the infrared-finite part of the traditional amplitudes constructed using Fock states. Since there is no real soft radiation in the asymptotic Hilbert space, the dressed state formalism gives the same cross sections as the Bloch-Nordsieck method.

A forward branching phase space generator for hadron colliders

In this paper we develop a projective phase space generator appropriate for hadron collider geometry. The generator integrates over bremsstrahlung events which project back to a single, fixed Born event. The projection is dictated by the experimental jet algorithm allowing for the forward branching phase space generator to integrate out the jet masses and initial state radiation. When integrating over the virtual and bremsstrahlung amplitudes this results in a single K-factor, assigning an event probability to each Born event. This K-factor is calculable as a perturbative expansion in the strong coupling constant.One can build observables from the Born kinematics, giving identical results to traditional observables as long as the observable does not depend on the infrared sensitive jet mass or initial state radiation.

Higgs boson pair production at NNLO with top quark mass effects

We consider QCD radiative corrections to Higgs boson pair production through gluon fusion in proton collisions. We combine the exact next-to-leading order (NLO) contribution, which features two-loop virtual amplitudes with the full dependence on the top quark mass Mt, with the next-to-next-to-leading order (NNLO) corrections computed in the large-Mt approximation. The latter are improved with different reweighting techniques in order to account for finite-Mt effects beyond NLO. Our reference NNLO result is obtained by combining one-loop double-real corrections with full Mt dependence with suitably reweighted real-virtual and double-virtual contributions evaluated in the large-Mt approximation. We present predictions for inclusive cross sections in pp collisions at sqrt{s} = 13, 14, 27 and 100 TeV and we discuss their uncertainties due to missing Mt effects. Our approximated NNLO corrections increase the NLO result by an amount ranging from +12% at sqrt{s}=13 TeV to +7% at sqrt{s}=100 TeV, and the residual uncertainty of the inclusive cross section from missing Mt effects is estimated to be at the few percent level. Our calculation is fully differential in the Higgs boson pair and the associated jet activity: we also present predictions for various differential distributions at sqrt{s}=14 and 100 TeV, and discuss the size of the missing Mt effects, which can be larger, especially in the tails of certain observables. Our results represent the most advanced perturbative prediction available to date for this process.

Polarized double-virtual amplitudes for heavy-quark pair production

We present the two-loop virtual amplitudes for heavy-quark pair production in light quark-antiquark annihilation and gluon fusion channels, including full spin and color dependence. We use expansions around kinematical limits and numerical integration to obtain results for the involved master integrals. From these, we determine the renormalised infrared finite remainders of the coefficients of amplitude decompositions in terms of color and spin structures. The remainders are given in form of numerical interpolation grids supported by expansions around the production threshold and the high energy limit. Finally, we provide the spin density matrix, which encodes the heavy-quark spin correlations and is sufficient for phenomenological applications. Our results are necessary for the derivation of top-quark pair production cross sections in hadron collisions in the narrow width approximation with next-to-next-to-leading order accuracy in QCD.

Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes

We propose a novel method for the treatment of top-quark mass effects in the production of H(∗), HH, HZ and ZZ final states in gluon fusion. We show that it is possible to reconstruct the full top-quark mass dependence of the virtual amplitudes from the corresponding large-mt expansion and the non-analytic part of the amplitude near the top-quark threshold ŝ = 4mt2 with a Padé ansatz. The reliability of our method is clearly demonstrated by a comparison with the recent NLO result for Higgs pair production with full top-quark mass dependence.

Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models

We consider the simplest non-integrable model of multistate Landau-Zener transition. In this model two pairs of levels in two tunnel coupled quantum dots are swept passed each other by the gate voltage. Although this 2 * 2 model is non-integrable, it can be solved analytically in the limit when the inter-level energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 * 1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In 2 * 1 model, the probability for a particle, residing at time t -> -\infty in one dot, to remain in the same dot at t -> \infty falls off exponentially with tunnel coupling. By contrast, in 2 * 2 model, this probability grows exponentially with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as manifestation of the Dicke effect.

Diffusion and Intravoxel Incoherent Motion MR Imaging-based Virtual Elastography: A Hypothesis-generating Study in the Liver.

Purpose To investigate the potential of diffusion magnetic resonance (MR) imaging to provide quantitative estimates of tissue stiffness without using mechanical vibrations in patients with chronic liver diseases and to generate a new elasticity-driven intravoxel incoherent motion (IVIM) contrast. Materials and Methods This retrospective study, conducted from January to April 2016, was approved by an institutional review board that waived the requirement for informed consent. Fifteen subjects were included (13 men and two women; mean age ± standard deviation, 73 years ± 8). MR elastography and diffusion MR imaging were performed at 3 T. A search for an empirical relationship between MR elastographic shear modulus, µMRE, and a shifted apparent diffusion coefficient (sADC) was performed. The sADC was then inverted to estimate patient liver shear modulus directly from diffusion MR imaging signals. Results A significant correlation (r2 = 0.90, P = 1 · 10-7) was observed between µMRE and sADC calculated by using diffusion MR imaging signals acquired with b values of 200 (S200) and 1500 (S1500 ) sec/mm2 (sACD200-1500). On the basis of the relationship between the µMRE and sADC200-1500, a diffusion-based shear modulus, µdiff, could be estimated with the following equation: µdiff = (-9.8 ± 0.8) ln(S200/S1500) + (14.0 ± 0.9). IVIM virtual elastograms also could be generated to reveal new contrast features in lesions, depending on pseudovibration frequency and amplitude. Conclusion Diffusion MR imaging, through a calibration of sADC200-1500 with standard MR elastography, can be converted quantitatively into shear modulus without using mechanical vibrations to provide information on the degree of liver fibrosis; these virtual elastograms require only two b values to be acquired and processed. Propagating shear wave can also be emulated, leading to a new elasticity-driven IVIM contrast with ranges of virtual vibration frequencies and amplitudes not limited by MR elastography or MR imaging hardware capacities. © RSNA, 2017 Online supplemental material is available for this article.

Target and double spin asymmetries of deeply virtual π0 production with a longitudinally polarized proton target and CLAS

The target and double spin asymmetries of the exclusive pseudoscalar channel e→p→→epπ0 were measured for the first time in the deep-inelastic regime using a longitudinally polarized 5.9 GeV electron beam and a longitudinally polarized proton target at Jefferson Lab with the CEBAF Large Acceptance Spectrometer (CLAS). The data were collected over a large kinematic phase space and divided into 110 four-dimensional bins of Q2, xB, −t and ϕ. Large values of asymmetry moments clearly indicate a substantial contribution to the polarized structure functions from transverse virtual photon amplitudes. The interpretation of experimental data in terms of generalized parton distributions (GPDs) provides the first insight on the chiral-odd GPDs H˜T and ET, and complement previous measurements of unpolarized structure functions sensitive to the GPDs HT and E¯T. These data provide a crucial input for parametrizations of essentially unknown chiral-odd GPDs and will strongly influence existing theoretical calculations based on the handbag formalism.

Employing helicity amplitudes for resummation

Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in $4$- and $d$-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for $pp\to H + 0,1,2$ jets, $pp\to W/Z/\gamma + 0,1,2$ jets, and $pp\to 2,3$ jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with $e^+e^-$ and $e^-p$ collisions.

Automated Computation of Scattering Amplitudes from Integrand Reduction to Monte Carlo tools

After a general introduction about the calculation of one-loop scattering amplitudes via integrand-level techniques, which led to the construction of efficient and automated computational tools for NLO predictions, we briefly describe an approach to the reduction of scattering amplitudes based on integrand-level reduction via multivariate polynomial division also applicable beyond one-loop amplitudes. We also review the main features of the GoSam 2.0 automated framework for NLO calculations and show some of its application to Standard Model processes involving the production massive particles, such as the Higgs boson or top-quark pairs, obtained embedding of the virtual amplitudes produced by GoSam within existing Monte Carlo tools.

Resonant magnetotunneling between normal and ferromagnetic electrodes in relation to the three-terminal spin transport

The recently suggested mechanism [Y. Song and H. Dery, Phys. Rev. Lett. 113, 047205 (2014)] of the three-terminal spin transport is based on the resonant tunneling of electrons between ferromagnetic and normal electrodes via an impurity. The sensitivity of current to a weak external magnetic field stems from a spin blockade, which, in turn, is enabled by strong on-site repulsion. We demonstrate that this sensitivity exists even in the absence of repulsion when a single-particle description applies. Within this description, we calculate exactly the resonant-tunneling current between the electrodes. The mechanism of magnetoresistance, completely different from the spin blocking, has its origin in the interference of virtual tunneling amplitudes. Spin imbalance in ferromagnetic electrode is responsible for this interference and the resulting coupling of the Zeeman levels. This coupling also affects the current in the correlated regime.

The role of Glauber exchange in soft collinear effective theory and the Balitsky–Fadin–Kuraev–Lipatov Equation

In soft collinear effective theory (SCET) the interaction between high energy quarks moving in opposite directions involving momentum transfer much smaller than the center-of-mass energy is described by the Glauber interaction operator which has two-dimensional Coulomb-like behavior. Here, we determine this n–n¯ collinear Glauber interaction operator and consider its renormalization properties at one loop. At this order a rapidity divergence appears which gives rise to an infrared divergent (IR) rapidity anomalous dimension commonly called the gluon Regge trajectory. We then go on to consider the forward quark scattering cross section in SCET. The emission of real soft gluons from the Glauber interaction gives rise to the Lipatov vertex. Squaring and adding the real and virtual amplitudes results in a cancelation of IR divergences, however the rapidity divergence remains. We introduce a rapidity counter-term to cancel the rapidity divergence, and derive a rapidity renormalization group equation which is the Balitsky–Fadin–Kuraev–Lipatov Equation. This connects Glauber interactions with the emergence of Regge behavior in SCET.

Virtual amplitudes and threshold behaviour of hadronic top-quark pair-production cross sections

We present the two-loop virtual amplitudes for the production of a top-quark pair in gluon fusion. The evaluation method is based on a numerical solution of differential equations for master integrals in function of the quark velocity and scattering angle starting from a boundary at high-energy. The results are given for the renormalized infrared finite remainders on a large grid and have recently been used in the calculation of the total cross sections at the next-to-next-to-leading order. For convenience, we also give the known results for the quark annihilation case on the same grid. Outside of the kinematical range covered by the grid, we provide threshold and high-energy expansions. From expansions of the two-loop virtual amplitudes, we determine the threshold behavior of the total cross sections at next-to-next-to-leading order for the quark annihilation and gluon fusion channels including previously unknown constant terms. In our analysis of the quark annihilation channel, we uncover the presence of a velocity enhanced logarithm of Coulombic origin, which was missed in a previous study.