Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 -> 2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 -> 2 splitting functions are consistent with the number and momentum sum rules for DPDs.
Off-shell, transverse-momentum dependent splitting functions can be defined from the high-energy limit of partonic decay amplitudes. Based on these splitting functions, we construct Sudakov form factors and formulate a new parton branching algorithm. We present a first Monte Carlo implementation of the algorithm. We use the numerical results to verify explicitly momentum sum rules for TMD parton distributions.
The Parton Branching (PB) approach describes the evolution of transverse momentum dependent (TMD) parton densities. We propose to extend the PB method by including TMD splitting functions, instead of the DGLAP splitting functions which assume strong ordering in transverse momentum. We present the evolution equations and their numerical solution, which is the first Monte Carlo implementation including TMD splitting functions.
At small inter-parton distances, double parton distributions receive their dominant contribution from the splitting of a single parton. We compute this mechanism at next-to-leading order in perturbation theory for all colour configurations of the observed parton pair. Rapidity divergences are handled either by using spacelike Wilson lines or by applying the delta regulator. We investigate the behaviour of the two-loop contributions in different kinematic limits, and we illustrate their impact in different channels.
We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a quark parent in the limit where four partons become collinear to each other. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next-to-next-to-next-to-leading order (${\rm N^3LO}$) in the strong coupling constant. Further, we consider the iterated limit when $m'$ massless partons become collinear to each other within a bigger set of $m$ collinear partons, as well as the limits when one gluon or a $q\bar{q}$ pair or two gluons become soft within a set of $m$ colline…
We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a gluon parent which splits into four collinear partons. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next- to-next-to-next-to-leading order (N$^3$LO) in the strong coupling constant. Combined with our earlier results for a quark parent, this completes the set of tree-level splitting amplitudes required at this order. We also study iterated collinear limits where a subset of the four collinear partons become themselves collinear.
Parton branching methods underlie the Monte Carlo (MC) generators, being therefore of key importance for obtaining high energy physics predictions. We construct a new parton branching algorithm which for the first time incorporates the off-shell, transverse-momentum dependent (TMD) splitting functions, defined from the high-energy limit of partonic decay amplitudes. Based on these TMD splitting functions we construct a new TMD Sudakov form factor. We present the first MC implementation of the algorithm for the evolution of the TMD and integrated parton distribution functions (PDFs). We use thi…
We carry out the first theoretical investigation on yields and the hardest parton splitting of large-radius jets reclustered from small radius ($R=0.2$) anti-$k_t$ jets in Pb+Pb collisions, and confront them with the recent ATLAS measurements.The Linear Boltzmann Transport (LBT) model is employed for jet propagation and jet-induced medium excitation in the hot-dense medium. We demonstrate that, with their complex structures, the medium suppression of the reclustered large radius jets at $R=1$ is larger than that of inclusive $R=0.4$ jets defined conventionally. The large radius jet constituent…
Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.
LHC Sensitivity to Wbb Production via Double Parton Scattering
我们研究了在大型强子对撞机上观察到7 TeV pp -> W bb X -> mu nu bb X的双部分子散射的可能性。我们的分析测试了几个运动学变量在隔离感兴趣的双部分子过程的有效性，从单部分子过程和相关背景的第一个10/fb的积分亮度。这些变量的构造揭示了双部分子散射中两个子过程pp -> mu nu和pp -> bb X的独立性质。我们使用下到领先的顺序微扰预测的双重部分子和单部分子散射组件的W BB和相关的背景。次领先的订单贡献是重要的，我们计算的一些可观的适当的描述。我们发现，只要双部分子散射的有效截面为~ 12 mb，双部分子过程就可以被识别和测量，其显著性为~ 10。
Multi-parton distributions in a proton, the nonperturbative quantities needed to make predictions for multiple scattering rates, are poorly constrained from theory and data and must be modelled. All Monte Carlo event generators that simulate multiple parton interactions (e.g. Pythia) contain such a model of multi-parton PDFs. One important theoretical constraint for the case of double parton distributions is provided by the so-called number and momentum sum rules. In this paper we investigate to what extent the double parton distribution functions used in the Pythia event generator obey these …
Calculation of W b bbar Production via Double Parton Scattering at the LHC
我们研究了在大型强子对撞机上观察到7 TeV下p p -> W b bbar X -> l nu b bbar X的双部分子散射的可能性。我们的分析测试了几个运动学变量在隔离感兴趣的双部分子过程中的功效，从单部分子过程和相关背景的前10个逆FB的积分亮度。这些变量的构造揭示了双部分子散射中两个子过程的独立性质，pp -> l nu X和pp -> b bbar X。我们使用下一个领先的顺序微扰预测的双重部分子和单部分子散射组件的W b bbar和相关的背景。次领先的订单贡献是重要的，我们计算的一些可观的适当的描述。我们发现，只要双部分子散射有效截面sigma_{eff} ~ 12 mb，就可以识别和测量S/sqrt（B）~ 10的双部分子过程.
We present our studies of four-jet double parton scattering production in proton-nucleus collisions within the framework of the PYTHIA8 event generator. We demonstrate that double absorptive processes in pA generated by the Angantyr model in PYTHIA8 give an enhancement of the total double parton scattering cross section similar to the predictions by Strikman and Treleani in 2001. Additionally, we discuss how the growth of activity in a direction of a nucleus affects an A-scaling of a total double parton scattering cross section in proton-nucleus collisions.
Two-parton correlations in the pion, a non perturbative information encoded in double parton distribution functions, are investigated in the Nambu and Jona-Lasinio model. It is found that double parton distribution functions expose novel dynamical information on the structure of the pion, not accessible through one-body parton distributions, as it happens in several estimates for the proton target and in a previous evaluation for the pion, in a light-cone framework. Expressions and predictions are given for double parton distributions corresponding to leading-twist Dirac operators in the quark…
We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.
We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of the evolution scale Q. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small x factorization at large $Q$.
The Large Hadron Collider witnesses the highest ever production cross-section of double parton scattering processes. The production of a Z-boson along with two jets from double parton scattering provides a unique opportunity to explore the kinematics of double parton scattering processes and their dependence on the scale of the second interaction. The experimental measurement of this process is largely contaminated by Z + jets production from single parton scattering. In this paper, fragmentation properties of a jet are explored to check their sensitivity towards double parton scattering. The …
