The cross section of the single photon in ppBar collision is calculated. There are many subprocesses, for example the LO and NLO collisions, leading to the single photon. The LO collisions, the one of which (Compton scattering) is strongly dependent on the gluon distribution function, are investigated. Both the off-shell (k_t dependent) and on-shell partons are considered in the diffusions, and their differences are discussed. The unintegrated parton distribution functions (UPDFs), used for the off-shell partons, are calculated by the Martin-Ryskin-Watt (MRW) method. In the case of the on-shell partons, the integrated parton distribution functions (PDFs), are obtained by MMHT 2014 LO PDFs which are determined experimentally. To investigate the accuracy of the theoretical results, they are compared with the experimental data that are taken by the DØ and CDF collaborations at Fermilab Tevatron.
The summation of the small x-corrections to hard-scattering QCD amplitudes by collinear factorisation method is reconsidered and the K-factor is derived in leading ln x approximation with a result differing from the corresponding expression by Catani and Hautmann (Nucl. Phys. B 427, 475, 1994). The significance of the difference is demonstrated in the examples of structure function F_L and of exclusive vector meson electroproduction. The formulation covers the channels of non-vanishing conformal spin n paving the way for new applications.
We compute the exclusive electroproduction, $γ^* p \rightarrow V p$, of heavy quarkonia $V$ to NLO in the collinear factorisation scheme, which has been formally proven for this process. The inclusion of an off-shell virtuality $Q^2$ carried by the photon extends the photoproduction phase space of the exclusive heavy quarkonia observable to electroproduction kinematics. This process is relevant for diffractive scattering at HERA and the upcoming EIC, as well as at the proposed LHeC and FCC.
We discuss exclusive $J/ψ$ photoproduction, initially in conventional collinear factorisation at NLO and then subsequently in a refined approach with a programme of low $x$ resummation and implementation of a crucial low $Q_0$ subtraction included. We compare and contrast predictions in both frameworks and remark about the possibility to constrain and ultimately determine the low $x$ and low scale gluon PDF, emphasising the significance of this for future global PDF analyses.
We illustrate how electron Parton Distribution Functions (PDFs) with next-to-leading collinear logarithmic accuracy must be employed in the context of perturbative predictions for high-energy $e^+e^-$-collision processes. In particular, we discuss how the renormalisation group equation evolution of such PDFs is affected by the presence of multiple fermion families and their respective mass thresholds, and by the dependences on the choices of the factorisation and renormalisation schemes. We study the impact of the uncertainties associated with the PDFs on physical cross sections, in order to a…
We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a collinear model which includes higher twist terms. Unlike the simplest collinear model, the BFKL equation leads to effective anomalous dimensions containing higher-twist pieces which grow as a (non-perturbative) power at small x. While these pieces dominate the effective splitting function at very small x they do not lead to a break-down of factorisation in…
We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon. The splitting amplitudes are derived from the analytic Higgs plus four partons amplitudes. We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions. The universality of the collinear factorisation is checked numerically against the full colour six parton squared matrix elements.
After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of factorisation. We show that the matrix elements of fields and Wilson lines that describe soft and collinear radiation in factorised scattering amplitudes can be re-factorised in strongly-ordered limits, providing a systematic method to compute them, to characterise their singularity structure, and to build local subtraction counterterms for strongly-ordered configu…
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 betwee…
Exclusive vector-quarkonium photoproduction at NLO in alpha_s in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation
We present a study within the kT-factorisation scheme on single bottom quark production at the LHC. In particular, we calculate the rapidity and transverse momentum differential distributions for single bottom quark/anti-quark production. In our setup, the unintegrated gluon density is obtained from the NLx BFKL Green function whereas we included mass effects to the Lx heavy quark jet vertex. We compare our results to the corresponding distributions predicted by the usual collinear factorisation scheme. The latter were produced with Pythia 8.1.
Factorisation theorem and pole cancellation in the resolved $Q_1^q$-$Q_{7γ}$ contribution to $\bar{B}\to X_sγ$ at NLO
Institute for Theoretical Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论物理研究所）；Institute for Astroparticle Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院天体粒子物理研究所）；Johannes Gutenberg University（约翰内斯·古腾堡大学）
I review the factorisation properties of tree level amplitudes when three particles $i$, $j$, $k$ are collinear. The triple collinear splitting functions contain both iterated single unresolved contributions, and genuine double unresolved contributions. I make this explicit by rewriting the known triple collinear splitting functions for a quark and two gluons in terms of products of two-particle splitting functions, and a remainder that is explicitly finite when any two of $\{i,j,k\}$ are collinear.
We present an algorithm that evolves hard processes at the amplitude level by dressing them iteratively with (massless) quarks and gluons. The algorithm interleaves collinear emissions with soft emissions and includes Coulomb/Glauber exchanges. It includes all orders in $N_{\mathrm{c}}$, is spin dependent and is able to accommodate kinematic recoils. Although it is specified at leading logarithmic accuracy, the framework should be sufficient to go beyond. Coulomb exchanges make the factorisation of collinear and soft emissions highly non-trivial. In the absence of Coulomb exchanges, we show ho…
Theoretical studies of Higgs production via gluon fusion are frequently carried out in the limit where the top quark mass is much larger than the Higgs mass, an approximation which reduces the top quark loop to an effective vertex. We present a numerical analysis of the error thus introduced by performing a Monte Carlo calculation for gg->h in kT-factorisation, using the parton shower generator CASCADE. We proceed to compare CASCADE to the collinear Monte Carlos PYTHIA, MC@NLO and POWHEG. We study the dependence of parton radiation on the resummation of high-energy corrections taken into accou…
Singular factors originating from the QCD factorisation of scattering amplitudes in soft and collinear limits play a prominent role in both organising and computing high-order perturbative contributions to hard-scattering cross sections. In this talk, we start from the factorisation structure of scattering amplitudes in the collinear limit, and we introduce collinear functions that have a process-independent structure. These collinear functions, which are defined at the fully-differential level, can then be integrated over the appropriate observable-dependent phase space to compute logarithmic…
We study 3-jet event topologies in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13 {\rm\ TeV}$ in a configuration, where one jet is present in the central pseudorapidity region ($|η| < 2.0$) while two other jets are in a more forward (same hemisphere) area ($|η| > 2.0$). We compare various parton level predictions using: collinear factorisation, $\KT{}$-factorisation with fully off-shell matrix elements and the hybrid framework. We study the influence of different parton distribution functions, initial state radiation, final state radiation, and hadronisation. We focus on…
The inclusive large-$p_T$ production of a single pion, jet or direct photon, and Drell-Yan processes, are considered for proton-proton collisions in the kinematical range expected for the fixed-target experiment AFTER, proposed at LHC. For all these processes, predictions are given for the transverse single-spin asymmetry, $A_N$, computed according to a Generalised Parton Model previously discussed in the literature and based on TMD factorisation. Comparisons with the results of a collinear twist-3 approach, recently presented, are made and discussed.
Measurements of jet production in the photoproduction region at HERA are presented, which are sensitive to the underlying event structure. It is argued that in the photoproduction region a significant amount of multi-parton interactions in the collinear factorisation ansatz are needed to describe the measurement. A different approach for higher order parton radiation (CCFM parton showers) can also describe the measurement.
The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N3LO) …
The asymmetry in the angular distribution of Drell--Yan dilepton pairs generated in collisions where just one nucleon is transversely polarised has been examined in the literature with a variety of results, mainly differing by factors of two. We re-evaluate the asymmetry via twist-3 contributions in collinear factorisation. In order to allow complete and in-depth comparison with existing calculations, we supply all calculational details.
The asymptotic collinear factorisation theorem, which holds for diffractive deep-inelastic scattering, has important modifications in the sub-asymptotic HERA regime. We use perturbative QCD to quantify these modifications. The diffractive parton distributions are shown to satisfy an inhomogeneous evolution equation. We emphasise that it is necessary to include both the gluonic and sea-quark t-channel components of the perturbative Pomeron. The corresponding Pomeron-to-parton splitting functions are derived in the Appendix.
We discuss the perturbative QCD description of diffractive deep-inelastic scattering, and extract diffractive parton distributions from recent HERA data. The asymptotic collinear factorisation theorem has important modifications in the sub-asymptotic HERA regime. In addition to the usual resolved Pomeron contribution, the direct interaction of the Pomeron must also be accounted for. The diffractive parton distributions are shown to satisfy an inhomogeneous evolution equation, analogous to the parton distributions of the photon.
The zero-jettiness beam functions describe collinear emissions from initial state legs and appear in the factorisation theorem for cross sections in the limit of small zero-jettiness. They are an important building block for slicing schemes for colour-singlet production at hadron colliders. We report on our ongoing calculation of this quantity at next-to-next-to-next-to-leading order (N$^3$LO) in QCD, highlighting in particular the aspects of partial fraction relations and the calculation of master integrals.
We present a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for the production of a pair of leptons in Drell-Yan process and of Higgs boson in gluon fusion as well as in bottom quark annihilation. We restrict ourselves to contributions from diagonal partonic channels. These logarithms include the distributions $((1-z)^{-1} \ln^i(1-z))_+$ resulting from soft plus virtual (SV) and the logarithms $\ln^i(1-z)$ from next-to-SV (NSV) contributions. We use collinear factorisation and renormalisation group invariance to achieve this. The former allows on…
The theoretical description of photon production at particle colliders combines direct photon radiation and fragmentation processes, which can not be separated from each other for definitions of photon isolation used in experimental measurements. The theoretical description of these processes must account for collinear parton-photon configurations, retaining the dependence on the photon momentum fraction, and includes the parton-to-photon fragmentation functions. We extend the antenna subtraction method to include photon fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD…
We present a new calculation for the production of isolated photon pairs at the LHC with NNLL$'_{\mathcal{T}_0}$+NNLO accuracy. This is the first implementation within the GENEVA Monte Carlo framework of a process with a nontrivial Born-level definition which suffers from QED singularities. Throughout the computation we use a smooth-cone isolation algorithm to remove such divergences. The higher-order resummation of the 0-jettiness resolution variable $\mathcal{T}_0$ is based on a factorisation formula derived within Soft-Collinear Effective Theory which predicts all of the singular, virtual a…
We explore the quark mass effects on inclusive hadron production in proton-nucleus collisions at high energies. We consider two processes. First, we compute the single inclusive cross-section for production of hadrons with open heavy flavour in the proton forward direction at leading order. Next, in the same kinematics, we calculate the heavy-quark contribution to single inclusive production of light or unidentified hadrons at next-to-leading-order. For both studies we exploit the hybrid formalism, that is the collinear factorisation on the proton side while high-density and high-energy effect…
We present approximations to tree level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n+2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n parton amplitudes. When the unresolved particles are not colour connected, the approximations are simple products of the familar eiko…
The O(α) electroweak radiative corrections to the process pp, ppbar\to W \to\ell^\pmν(\ell=e,μ) are calculated. The O(α) corrections can be decomposed into separately gauge invariant contributions to the W boson production and decay processes. Factorizing the collinear singularity associated with initial state photon radiation into the parton distribution functions, we find that initial state corrections have a significantly smaller effect than final state radiative corrections. We study in detail the effect of electroweak radiative corrections on a number of interesting observables: the W tra…
The low $x$ behaviour of the gluon density $xg(x,μ^2)$ at scale $μ^2=2.4$ GeV$^2$ is determined using exclusive $J/ψ$ production data from HERA and LHCb within the framework of collinear factorisation at next-to-leading order (NLO). It is shown that in the interval $3\times 10^{-6} < x <10^{-3}$ the gluon distribution function grows as $xg(x,μ^2)\propto x^{-λ}$ with $λ=0.135\pm 0.006 $. The impact this experimental data will have for the global parton distribution function (PDF) analyses in this low $x$ domain is quantified. No indication in favour of parton density saturation is observed.
In the computation of short-distance cross sections initiated by electrons and photons one can adopt the so-called structure-function approach, in which these particles play formally the same roles as hadrons do in QCD factorisation theorems, and must thus be associated with PDFs (equivalently known as structure functions in this context). At variance with their QCD counterparts, such PDFs are entirely calculable in QED. In this paper we present the results, at the next-to-leading order in the QED coupling constant $α$, for the initial conditions of the unpolarised electron and photon PDFs, wh…
Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but …
We present updated leading-order, next-to-leading order and next-to-next-to-leading order parton distribution functions ("MSTW 2008") determined from global analysis of hard-scattering data within the standard framework of leading-twist fixed-order collinear factorisation in the MSbar scheme. These parton distributions supersede the previously available "MRST" sets and should be used for the first LHC data-taking and for the associated theoretical calculations. New data sets fitted include CCFR/NuTeV dimuon cross sections, which constrain the strange quark and antiquark distributions, and Teva…
Accessing chiral-even quark generalised parton distributions in the exclusive photoproduction of a $ γπ^{\pm} $ pair with large invariant mass in both fixed-target and collider experiments
We extend our studies of a new class of $2 \to 3$ exclusive processes using the collinear factorisation framework by considering the exclusive photoproduction of a $γ\,ρ$ pair, in the kinematics where the pair has a large invariant mass, {and the outgoing $ ρ$-meson has a sufficiently large transverse momentum to not resonate with the nucleon}. We cover the whole kinematical range from medium energies in fixed target experiments to very large energies of colliders, by considering the experimental conditions of JLab~12-GeV, COMPASS, future EIC and LHC (in ultra-peripheral collisions) cases. One…
We derive the light-front wave function (LFWF) representation of the $γ^{\star} γ^{\star} \to η_{c} (1S),η_{c}(2S)$ transition form factor $F(Q^2_1,Q^2_2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of $c\bar{c}$ potentials. We compare our results to the BaBar experimental data for the $η_{c}(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massle…
