We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $q\bar q\to γγγ$. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process $pp\to γγγ$ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.
We calculate the complete set of two-loop leading-colour QCD helicity amplitudes for $γγj$-production at hadron colliders. Our results are presented in a compact, fully-analytical form.
We present the two-loop leading colour QCD helicity amplitudes for the process $pp\to W(\to lν)γ+j$. We implement a complete reduction of the amplitudes, including the leptonic decay of the $W$-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders for phys…
We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom-quark pair at a hadron collider. We take the approximations of leading colour and work in the five flavour scheme, where the bottom quarks are massless while the Yukawa coupling is non-zero. We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the full phase space.
$W$ bosons are produced at LHC from a forward-backward symmetric initial state. Their decay to a charged lepton and a neutrino has a strong spin analysing power. The combination of these effects results in characteristic distributions of the pseudorapidity of the leptons decaying from $W^+$ and $W^-$ of different helicity. This observation may open the possibility to measure precisely the $W^+$ and $W^-$ rapidity distributions for the two transverse polarisation states of $W$ bosons produced at small transverse momentum.
We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with…
We present the full color two-loop six-point all-plus Yang-Mills amplitude in compact analytic form. The computation uses four dimensional unitarity and augmented recursion.
We present the complete two-loop corrections in massless QCD for the production of two photons and a jet, taking into account all color structures. In particular, we analytically compute all two-loop helicity amplitudes for the quark-antiquark, quark-gluon, and antiquark-gluon channel, and check them with an independent calculation of the polarization-summed interference with the tree amplitude. This is the first time that two-loop QCD corrections to a five-point scattering process have been computed beyond the leading-color approximation for all helicity configurations.
We compute the three-loop helicity amplitudes for $q\bar{q} \to gg$ and its crossed partonic channels, in massless QCD. Our analytical results provide a non-trivial check of the color quadrupole contribution to the infrared poles for external states in different color representations. At high energies, the $qg \to qg$ amplitude shows the predicted factorized form from Regge theory and confirms previous results for the gluon Regge trajectory extracted from $qq' \to qq'$ and $gg \to gg$ scattering.
We use the spinor helicity formalism to calculate the cross section for production of three partons of a given polarization in Deep Inelastic Scattering (DIS) off proton and nucleus targets at small Bjorken x. The target proton or nucleus is treated as a classical color field (shock wave) from which the produced partons scatter multiple times. We reported our result for the final expression for the production cross section and studied the azimuthal angular correlations of the produced partons in [1]. Here we provide the full details of the calculation of the production cross section using the …
Apart from its mass and width, the most important property of a new charged gauge boson, $W'$, is the helicity of its couplings to the SM fermions. Such particles are expected to exist in many extensions of the Standard Model. In this paper we explore the capability of the LHC to determine the $W'$ coupling helicity at low integrated luminosities in the $\ell +E_T^{miss}$ discovery channel. We find that measurements of the transverse mass distribution, reconstructed from this final state in the $W-W'$ interference region, provides the best determination of this quantity. To make such measureme…
We report an analytical and numerical investigation into the impact of helicity inversion in LHC processes that do not conserve lepton number $(L)$. As a case study, we focus on the production and decay of Majorana neutrinos $(N)$ through on- and off-shell $W$ bosons in the Phenomenological Type I Seesaw model. Using the Monte Carlo event generator \texttt{MadGraph5\_aMC@NLO} in conjunction with the \texttt{HeavyN} model libraries, we perform exact matrix element (ME) computations without the narrow width approximation. Despite helicity inversion appearing explicitly in MEs, we report the abse…
In this paper, we show how to calculate analytically the one-loop helicity amplitudes for the process $q\bar{q} rightarrow t\bar{t}$ induced by KK gluon, using the spinor-helicity formalism. A minimal set of Feynman rules which are uniquely fixed by gauge invariance and the color representation of the KK gluon are derived and used in the calculation. Our results can be applied to a variety of models containing a massive color octet vector boson.
The novel massive spinor-helicity formalism of Arkani-Hamed, Huang and Huang provides an elegant way to calculate scattering amplitudes in quantum chromodynamics for arbitrary quark spin projections. In this note we compute two families of tree-level QCD amplitudes with one massive quark pair and n-2 gluons. The two cases include all gluons with identical helicity and one opposite-helicity gluon being color-adjacent to one of the quarks. Our results naturally incorporate the previously known amplitudes for both quark spins quantized along one of the gluonic momenta. In the all-multiplicity for…
We explore the on-shell recursion for tree-level scattering amplitudes with massive spinning particles. Based on the factorization structure encoded in the same way by two different recursion relations, we conjecture an all-multiplicity formula for two gauged massive particles of arbitrary spin and any number of identical-helicity gluons. Specializing to quantum chromodynamics (QCD), we solve the on-shell recursion relations in the presence of two pairs of massive quarks and an arbitrary number of identical-helicity gluons. We find closed-form expressions for the two distinct families of color…
We present the gluon-gluon and photon-gluon helicity amplitudes for color singlet and octet charmonium production in polarized and unpolarized hadron-hadron and photon-hadron collisions.
The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity …
We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude, and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms and rational funct…
In this thesis I study applications of effective field theories to understand aspects of QCD jets and their substructure at the Large Hadron Collider. In particular, I introduce an observable, $D_2$, which can be used for distinguishing boosted $W/Z/H$ bosons from the QCD background using information about the radiation pattern within the jet, and perform a precision calculation of this observable. To simplify calculations in the soft collinear effective theory, I also develop a helicity operator basis, which facilitates matching calculations to fixed order computations performed using spinor-…
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in $AA$, $pA$ and $pp$ collisions at the LHC energies basing on the ideas of parton saturation in the Color Glass Condensate.
We study the effect of color octet scalars on the high transverse momenta four-jet cross section at the LHC. We consider both weak singlet and doublet scalars, concentrating on the case of small couplings to quarks. We find that a relatively early discovery at the LHC is possible for a range of scalar masses.
In this work we estimate the heavy quark production in proton-proton and proton-nucleus collisions at LHC energies using the color dipole formalism and the solution of the running coupling Balitsky-Kovchegov equation. Nuclear effects are considered in the computation of the total cross sections and rapidity distributions for scattering on protons and nuclei.
We discuss how to 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 the color-ordered QCD helicity amplitudes. This provides an interface to seamlessly combine fixed-order helicity amplitudes, which are the basic building blocks of state-of-the-art next-to-leading order calculations for multileg processes, with a resummation of higher-order logarithmic corrections using SCET.
Color octet (pseudo)scalars, if they exist, will be copiously produced at the CERN Large Hadron Collider (LHC). However, their detection can become a very challenging task. In particular, if their decay into a pair of top quarks is kinematically forbidden, the main decay channel would be into two jets, with a very large background. In this Brief Report we explore the possibility of using anomaly-induced decays of the color octet pseudoscalars into gauge bosons to find them at the LHC.
We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities an…
We calculate inclusive cross section for $f_2(1270)$ tensor meson production via color singlet gluon-gluon fusion in the $k_t$-factorization approach with unintegrated gluon distribution functions (UGDFs). The process may be potentially interesting in the context of searches for saturation effects. The energy-momentum tensor, equivalent to helicity-2 coupling, and helicity-0 coupling are used for the $g^* g^* \to f_2(1270)$ vertex. Two somewhat different parametrizations of helicity-2 and helicity-0 tensorial structure from the literature are used in our calculations. Some parameters are extra…
We consider a class of supersymmetric models containing baryon number violating processes such as observable neutron - antineutron oscillations that are mediated by color triplet diquark fields. For plausible values of the diquark-quark couplings, the scalar diquark with mass between a few hundred GeV and one TeV or so can be produced in the s-channel at the LHC and detected through its decay into a top quark and a hadronic jet.
We calculate the helicity amplitudes for scattering of a quark from both large and small $x$ gluons of a target proton or nucleus using spinor helicity formalism. We show that scattering from large $x$ gluons of the target results in non-zero spin asymmetry at intermediate $p_t$ as well as rapidity loss of the projectile quark. We comment on how this can also generate angular asymmetries in particle production in high energy collisions.
We investigate threshold resummation effects in the production of a color sextet (antitriplet) scalar at next-to-next-to-leading logarithmic (NNLL) order at the LHC in the frame of soft-collinear effective theory. We show the total cross section and the rapidity distribution with NLO+NNLL accuracy, and we compare them with the NLO results. Besides, we use recent dijet data at the LHC to give the constraints on the couplings between the colored scalars and quarks.
Helicity amplitudes are the fundamental ingredients of many QCD calculations for multi-leg processes. We describe how these can seamlessly be combined with resummation in Soft-Collinear Effective Theory (SCET), by constructing a helicity operator basis for which the Wilson coefficients are directly given in terms of color-ordered helicity amplitudes. This basis is crossing symmetric and has simple transformation properties under discrete symmetries.
The cross section of the $μ^+μ^-$ pair production in $pp$-collisions at the LHC is calculated with acount of the $Z'$ boson induced by the minimal four color quark-lepton symmetry($MQLS$). The $μ^+μ^-$ invariant mass spectrum with account of the $MQLS$ $Z'$ boson is analysed in dependence on the $Z'$ mass. The mass region for the $MQLS$ $Z'$ boson observable at the LHC is found in dependence on the significance and on the integrated luminosity.
The differential cross-sections are calculated for proton-proton and proton-antiproton elastic scattering using the phenomenological model based on the analytic parameterizations for global scattering parameters (total cross-section and $ρ$ - parameter), crossing symmetry and derivative relations. We confront our model predictions with experimental data in wide range of energy and momentum transfer. The suggested method may be useful for PAX Program (GSI) as well as for high-energy experiments at RHIC and LHC.
One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}γ$ productions at the LHC through $\mathcal{O}(ε^2)$
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Dipartimento di Fisica and Arnold-Regge Center, Università di Torino, and INFN, Sezione di Torino（都灵大学物理系及阿诺德-雷杰中心，意大利国家核物理研究所都灵分部）；Dipartimento di Fisica e Astronomia, Università di Bologna e INFN, Sezione di Bologna（博洛尼亚大学物理与天文学系及意大利国家核物理研究所博洛尼部分部）；Department of Physics, Pohang University of Science and Technology（韩国科学技术院物理系）
Elements of the phenomenology of color-octet scalars (sgluons), as predicted in the hybrid N=1/N=2 supersymmetric model, are discussed in the light of forthcoming experiments at the CERN Large Hadron Collider.
Cross sections of the colored scalar particle production in $pp$-collisions are calculated and differential and total cross sections of the corresponding parton subprocesses are obtained. The total cross section of scalar gluon production in $pp$-collisions at the LHC is estimated and the dominant decays of scalar gluons are discussed. The production cross section of scalar gluons $F$ with masses $m_F\lesssim 1300$ GeV is shown to be sufficient for the effective production of these particles at the LHC.
The scalar color octet contribution to the resonance $t\bar{t}$-pair production at the LHC is calculated and analysed with account of the one loop effective two gluon vertex. It is shown that this contribution from the scalar color octet $F_2$ predicted by the minimal model with the four color quark-lepton symmetry is for $\sqrt{s}=13$ TeV of about a few percents for $750 < m_{F_2} < 1800$ GeV and can exceed 10% for $400 < m_{F_2} < 750$ GeV. It is also pointed out that the search for the scalar octet $F_2$ as the resonance in the dijet mass spectra seems to be difficult because of the smallne…
The LHC is the perfect environment for the study of new physics in the top quark sector. We study the possibility of detecting signals of heavy color-octet vector resonances, through the charge asymmetry, in top-antitop+jet events. Besides contributions with the top-antitop pair in a color-singlet state, the asymmetry gets also contributions which are proportional to the color factor f_{abc}^2. This process is particularly interesting for extra-dimensional models, where the inclusive charge asymmetry generated by Kaluza-Klein excitations of the gluon vanishes at the tree level. We find that th…
We study photon-induced coherent production of Upsilon in ultraperipheral heavy ion collisions at LHC and demonstrate that the counting rates will be sufficient to measure nuclear shadowing of generalized gluon distributions. This will establish the transition from the regime of color transparency to the regime of perturbative color opacity in an unambiguous way. We argue that such measurements will provide the possibility to investigate the interaction of ultra-small color dipoles with nuclei in QCD at large energies, which are beyond the reach of the electron-nucleon (nucleus) colliders, and…
We present a study of effects of QCD radiation in the production of heavy colored states, employing inclusive multi-jet samples obtained by matching matrix elements and parton showers. We discuss several examples showing that matched samples are in general not only more accurate than a parton shower alone, but also often indispensable to make reliable predictions of beyond the Standard Model signals.
We propose a simple way to test the Abelian decomposition of QCD, the existence of two types of gluons, experimentally at LHC. The Abelian decomposition decomposes the gluons to the color neutral neurons and colored chromons gauge independently. This refines the Feynman diagram in a way that the color conservation is explicit, and generalizes the quark model to the quark and chromon model. We predict that the neuron jet has the color factor 3/4 and has a sharpest jet radius and smallest particle multiplicity, while the chromon jet with the color factor 9/4 remains the broadest jet. Moreover, t…
In my talk I gave a status update on the extension of the CoLoRFulNNLO subtraction method for computing QCD jet cross sections with hadrons in the initial state. The scheme has been fully worked out previously for electron-positron collisions and recently important steps have been made towards generalizing it to be able to deliver corrections of the same order for LHC processes as well. In particular, the important bottleneck of regularizing multiple real emissions has been addressed. We demonstrate the numerical stability of the CoLoRFulNNLO method by computing the doubly real contribution fo…
We study the factorization and resummation of the transverse momentum spectrum of the color sextet and antitriplet scalars produced at the LHC based on soft-collinear effective theory. Compared to Z boson and Higgs production, a soft function is required to account for the soft gluon emission from the final-state colored scalar. The soft function is calculated at the next-to-leading order, and the resummation is performed at the approximate next-to-next-to-leading logarithmic accuracy. The non-perturbative effects and PDF uncertainties are also discussed.
At a 14 TeV proton-proton collider, the Large Hadron Collider (LHC), we show that top quark pair production is dominated at low invariant mass by the fusion of two like-helicity gluons, producing top quark pairs in the left-left or right-right helicity configurations. Whereas, at higher invariant mass the production is dominated by the fusion of unlike-helicity gluons, producing top quark pairs in the up-down or down-up off-diagonal configurations, identical to top quark pair production via quark-antiquark annihilation. We study in detail the low invariant mass region, and show that the spin c…
One possible extension of the Standard Model scalar sector includes SU(2)_L doublet scalars that are color octets rather than singlets. We focus on models in which the couplings to fermions are consistent with the principle of minimal flavor violation (MFV), in which case these color octet scalars couple most strongly to the third generation of quarks. When the Yukawa coupling of color octet scalars to Standard Model fermions is less than unity, these states can live long enough to bind into color-singlet spin-0 hadrons, which we call octetonia. In this paper, we consider the phenomenology of …
An exact analytical solution to the Balitsky-Kovchegov equation is proposed incorporating Mellin transformation with saddle point approximation. The theoretical significance of this solution is its simplicity in form which requires very less number of parameters. Using this solution along with the idea of color glass condensate, a very good description of RHIC and LHC data on differential yield is obtained for d-Au, p-p and p-Pb collisions. Quantitative prediction for the nuclear modification factors for p-Pb, Pb-Pb and Xe-Xe collisions relevant for very recent LHC run 2 is yielded.
We report on a calculation of the effects of supersymmetry on the cross-section for top-antitop production at LHC. A numerical study is carried out for the ten benchmarks of the Snowmass accord. It is found that the higher order effects involving supersymmetric particles in internal loops can be as high as 6%, both for the cross-section and the (parity even) helicity asymmetry, for one particular benchmark. For other benchmarks smaller but nonetheless observable corrections are found.
We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances, $R_c\simeq 0.3$ fm, allows to extend the BFKL technique from deep inelastic to hadron-hadron scattering. With the account of the absorption corrections our results are in agreement with the LHC data on $σ_{tot}^{pp}$.
We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one loop helicity amplitudes of all $ 2\to 3$ parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all $2\to 4$ parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporat…
The excess in top quark forward-backward asymmetry has been a hot topic in recent years. Although there are many proposals to explain it, most of them can not fit the differential distributions well. The color octet axial-vector like particle, with mass near the top quark pair threshold, is still a good description of the differential distributions. We study how to distinguish the color singlet and octet mediating particles in top quark pair production by adopting the color flow method. For the first time, we show that such a proposal for the froward-backward asymmetry can be cross-checked ind…
The nonleptonic two-body $Λ_b\rightarrow Λψ$ decays with $ψ=J/ψ$ or $ψ(2S)$ are investigated based on the perturbative QCD approach. These are color-suppressed processes in which the nonfactorizable contributions are confirmed to be dominant. Angular momentum conservation allows us to describe the concerned decays by four independent complex helicity amplitudes. It is observed that the negative-helicity states for the $Λ$ baryon are preferred as expected in the left-handed nature of the charged-current interaction. The obtained results for the helicity amplitudes are used to compute the branch…
The modeling of color reconnection has become one of the dominant sources of systematic uncertainty in the top mass determination at hadron colliders. The uncertainty on the top mass due to color reconnection is conventionally estimated by taking the difference in the predictions of a model with and a model without color reconnection. We show that this procedure underestimates the uncertainty when applied to the existing models in {\sc Pythia}~8. We introduce two new classes of color reconnection models, each containing several variants, which encompass a variety of scenarios that could be rea…
A narrow resonance decaying to dijets could be discovered at the 14 TeV run of the LHC. To quickly identify its color structure in a model-independent manner, we introduced a method based on a color discriminant variable, determined from the measurements of the resonance's production cross section, mass and width. This talk introduces a more transparent theoretical formulation of the color discriminant variable that highlights its relationship to the branching ratios of the resonance into incoming and outgoing partons and to the properties of those partons. The formulation makes it easier to p…
Colored dark sectors where the dark matter particle is accompanied by colored partners have recently attracted theoretical and phenomenological interest. We explore the possibility that the dark sector consists of the dark matter particle and a color-octet partner, where the interaction with the Standard Model is governed by an effective operator involving gluons. The resulting interactions resemble the color analogues of electric and magnetic dipole moments. Although many phenomenological features of this kind of model only depend on the group representation of the partner under SU(3)$_c$, we…
We investigate the production of beyond-the-standard-model color-sextet vector bosons at the Large Hadron Collider and their decay into a pair of same-sign top quarks. We demonstrate that the energy of the charged lepton from the top quark semi-leptonic decay serves as a good measure of the top-quark polarization, which, in turn determines the quantum numbers of the boson and distinguishes vector bosons from scalars.
We compute the part of the two-loop virtual amplitude for the process $gg \to V_1 V_2 \to (l_1 \bar l'_{1}) (l_2 \bar l'_2)$, where $V_{1,2}$ are arbitrary electroweak gauge bosons, that receives contributions from loops of massless quarks. Invariant masses of electroweak bosons are allowed to be different from each other. Our result provides an important ingredient for improving the description of gluon fusion contribution to the production of four-lepton final states at the LHC.
Recently we have proved NRQCD color octet factorization of S-wave and P-wave heavy quarkonia production at all orders in coupling constant in QCD in vacuum at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove NRQCD color octet factorization of P-wave heavy quarkonium production in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This proof is necessary to study the quark-gluon plasma at RHIC and LHC.
