The production of electroweak $Z$ bosons that decay to neutrinos and recoil against jets with large transverse momentum $p_\perp$ is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benefit from opportunities offered by the future high-luminosity LHC, the theoretical description of the $pp \to Z+j$ process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to $q \bar q \to Z+g$ scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the $Z$ boson mass $m_{Z}$, we present the relevant master integrals as a series expansion in $m_{Z}/p_\perp$.
We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.
Novel Master Formula for Twist-3 Soft-Gluon-Pole Mechanism to Single Transverse-Spin Asymmetry
我们证明了在首阶微扰QCD中，单自旋不对称的扭3软胶子极（SGP）截面取决于运动学和色因子的某个"本原“扭2截面。这揭示了在各种硬过程中SGP截面背后的普遍结构，以及标度不变性在相应的原始截面中的特殊作用，从而导致了无质量粒子产生的SGP截面的显著简化，例如π介子产生p^ \uparrow p \to πX和直接光子产生p^ \uparrow p \to γX的SGP截面。
We study the effect of multiple parton radiation to Higgs boson plus jet production at the LHC, by applying the transverse momentum dependent (TMD) factorization formalism to resum large logarithmic contributions to all orders in the expansion of the strong interaction coupling. We show that the appropriate resummation scale should be the jet transverse momentum, rather than the partonic center of mass energy which has been normally used in the TMD resummation formalism. Furthermore, the transverse momentum distribution of the Higgs boson, particularly near the lower cut-off applied on the jet…
We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W-boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set of master integrals after applying integration-by-parts identities. Since the basis of master integrals is not yet fully known analytically, we identify a set of master integrals with a simple divergence structure using local numerator insertions. This allows for accurate numerical evaluation of the amplitude using sector decomposition methods.
In this paper, the soft gluon resummation effect in the Higgs boson plus two-jet production at the LHC is studied. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of the Higgs boson plus two-jet final state system, are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm. We also compare our result with the prediction of the Monte Carlo event generator Pythia8, and found noticeable difference in the distributions of the total transvers…
We consider the associated production of a vector or Higgs boson with a jet in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet system is much smaller than its invariant mass $Q$, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all orders. We discuss the all-order resummation structure of the logarithmically enhanced contributions up to next-to-leading logarithmic accuracy. Resummation is performed at the differential level with respect to the kinematical variables of the boson-jet system. Soft-parton radiation produces azi…
Recent results on the Higgs plus jet production is reviewed. We have computed the two-loop amplitudes for $ gg \to Hg $, $ q\bar{q} \to Hg $ and $ qg \to Hq $ at the large Higgs transverse momentum. It was long-missing part of NLO corrections to the Higgs plus jet production above the top mass threshold. This results are combined with the real corrections to produce the Higgs boson transverse momentum distribution at NLO.
We study the multiple soft gluon radiation effects in $Z$ boson plus jet production at the LHC. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of the $Z$ boson plus jet final state system, are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm(NLL). We also compare the prediction of our resummation calculation to the CMS data by employing a reweighting procedure to estimate the effect from imposing kinematic cuts on the leptons from…
In this study of the Inert Doublet Model (IDM), we propose that the dijet + missing transverse energy channel at the Large Hadron Collider (LHC) will be an effective way of searching for the scalar particles of the IDM. This channel receives contributions from gauge boson fusion, and $t-$channel production, along with contributions from $H^+$ associated production. We perform the analysis including study of the Standard Model (SM) background with assumed systematic uncertainty, and optimise the selection criteria employing suitable cuts on the kinematic variables to maximise the signal signifi…
Using the standard Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach, with partial inclusion of next-to-leading order effects, we propose the inclusive hadroproduction of a Higgs boson and of a jet, featuring large transverse momenta and well separated in rapidity, as a new channel to probe the BFKL dynamics. Predictions are presented for cross-sections and azimuthal angle correlations in different kinematics configurations for the final-state transverse momenta. We find that the large energy scales provided by the emission of a Higgs boson stabilize the BFKL series.
We investigate the effect of QCD resummation to kinematical correlations in the Higgs boson plus high transverse momentum (Pt) jet events produced at hadron colliders. We show that at the complete one-loop order, the Collins-Soper-Sterman resummation formalism can be applied to derive the Sudakov form factor, which is found to be independent of jet-finding algorithm. We compare the singular behavior of resummation calculation to fixed order prediction in the case that Higgs boson and high Pt jet are produced nearly back-to-back in their transverse momenta, and find a perfect agreement. The phe…
In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234. We compute the integrals by defining differential equations along contours in the kinematic space, and by solving them in terms of one-dimensional generalized power series. This method allows for the efficient evaluation of the integrals in all kinematic regions, with high numerical precision. We show the generality of our approach by considering both the top- and the bottom-quark contributions. This work along …
We discuss the collider signatures of electroweak (1,0)-mode excitations in the framework of two universal extra dimension (2UED) at the LHC and ILC. In general, pair production of electroweak (1,0)-mode particles of 2UED gives rise to multi lepton plus missing transverse momentum signal. Upto 1/R = 400 GeV two lepton plus missing transverse momentum signal and upto 1/R = 600 GeV three lepton plus missing transverse momentum signal stands over the $5σ$ standard deviation of the Standard Model background at the LHC with $100 fb^{-1}$ integrated luminosity. At ILC we study single photon plus mis…
If studies of electroweak gauge boson final states at the Large Hadron Collider, for Standard Model physics and beyond, are sensitive to effects of the initial state's transverse momentum distribution, appropriate generalizations of QCD shower evolution are required. We propose a method to do this based on QCD transverse momentum dependent (TMD) factorization at high energy. The method incorporates experimental information from the high-precision deep inelastic scattering (DIS) measurements, and includes experimental and theoretical uncertainties on TMD parton density functions. We illustrate …
The mono-jet search, looking for events involving missing transverse energy (MET) plus one or two jets, is the most prominent collider dark matter search. We show that multi-jet searches, which look for MET plus two or more jets, are significantly more sensitive than the mono-jet search for pseudoscalar- and scalar-mediated interactions. We demonstrate this in the context of a simplified model with a pseudoscalar interaction that explains the excess in GeV energy gamma rays observed by the Fermi Large Area Telescope. We show that multi-jet searches already constrain a pseudoscalar interpretati…
We investigate the QCD resummation for the Higgs boson plus a high $P_T$ jet production with large rapidity separations in proton-proton collisions at the LHC. The relevant Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Sudakov logs are identified and resummed. In particular, we apply recent developments of the transverse momentum dependent factorization formalism in the impact factors, which provides a systematic framework to incorporate both the BFKL and Sudakov resummations.
We discuss the next-to-next-to-leading order (NNLO) QCD corrections to Z boson production in association with a jet including all partonic channels at all color levels and including the leptonic decay of the Z boson. We focus on the optimization of the numerical evaluation of the double-real contribution and demonstrate that our procedure for spreading the Monte Carlo integration over $\mathcal{O}(1000)$ cores and recombining the results afterwards lead to stable results with sensible error estimates. We apply representative cuts on the jet and charged lepton transverse momenta and pseudorapid…
Fourier transforms of GPDs describe the distribution of partons in the transverse plane. The 2nd moment of GPDs has been identified by X.Ji with the angular momentum (orbital plus spin) carried by the quarks - a fundamental result that is being widely utilized in the spin decomposition of a longitudinally polarized nucleon. However, I will demonstrate that, despite the above results, the Fourier transform of the 2nd moment of GPDs does not describe the distribution of angular momentum in the transverse plane for a longitudinally polarized target.
Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.
We calculate the contributions to the two-loop scattering amplitudes $h \to gg$, $h \to ggg$ and $h \to q \bar q g$ that arise from a modified trilinear Higgs coupling $λ$. Analytic expressions are obtained by performing an asymptotic expansion near the limit of infinitely heavy top quark. The calculated amplitudes are necessary to study the impact of the ${\cal O} (λ)$ corrections to the transverse momentum distributions ($p_{T,h}$) in single-Higgs production at hadron colliders for low and moderate values of $p_{T,h}$.
Usually, the transverse momentum distribution is described by a sum of an exponential decay term plus a decreasing power like contribution representing the soft non-perturbative and hard perturbative QCD collisions, respectively. In this paper, we derive an analytical function that can describe the whole transverse momentum spectrum. This is obtained using a $q$-Gaussian distribution to describe the string tension fluctuations. The parameter $q$ determines the departure of the thermal distribution as well as the minimum length that can be explored at high transverse momentum. We also show that…
In this paper we consider Higgs plus jet production as a process that is sensitive to the linear polarization of gluons inside the unpolarized protons of the LHC. The leading order expressions for the transverse momentum distribution of the Higgs plus jet pair are provided in terms of transverse momentum dependent quark and gluon distributions. This includes both angular independent and azimuthal angular dependent contributions, presented directly in the laboratory frame. Lacking experimental constraints on the linearly polarized gluon distribution, we study its effects on Higgs plus jet produ…
We report on the calculation of the cross section for Higgs boson production in association with three jets via gluon fusion, at next-to-leading-order (NLO) accuracy in QCD, in the infinite top-mass approximation. After including the complete NLO QCD corrections, we observe a strong reduction in the scale dependence of the result, and an increased steepness in the transverse momentum distributions of both the Higgs and the leading jets. The results are obtained with the combined use of GoSam, Sherpa, and the MadDipole/MadEvent framework.
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…
We apply the target rest frame formalism to photon + heavy quark production cross section in hadronic collisions at high energies. We investigate the dependence of the production cross section on the photon and quark rapidities and transverse momenta. It is shown that the photon transverse momentum spectrum is a sensitive probe of color dipole scattering amplitude. The theoretical results are compared to Tevatron measurements of the differential γ+ c + X and γ+ b + X production cross sections at 1.96 TeV. An analysis for proton-proton and proton-lead collisions at the LHC regime is also perfor…
We present a detailed phenomenological study of Z-boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented. We study the impact of different parton distribution functions (PDFs) on predictions for the Z+jet process. Upon inclusion of the NNLO corrections, the residual scale uncertainty is reduced such that both the total rate and the transverse momentum distributions can be used to discriminate between various PDF sets.
The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six.…
We investigate the inclusive hadroproduction of a Higgs boson in association with a jet, featuring large transverse momenta and separated by a large rapidity distance. We propose this reaction, that can be studied at the LHC as well as at new-generation colliding machines, as a novel probe channel for the manifestation of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. We bring evidence that high-energy resummed distributions in rapidity and transverse momentum exhibit a solid stability under higher-order corrections, thus offering us a faultless chance to gauge the feasibility of precision…
We utilize the technology of open quantum systems in conjunction with the recently developed effective field theory for forward scattering to address the question of massless jet propagation through a weakly-coupled quark-gluon plasma in thermal equilibrium. We discuss various possible hierarchies of scales that may appear in this problem, by comparing thermal scales of the plasma with relevant scales in the effective field theory. Starting from the Lindblad equation, we derive and solve a master equation for the transverse momentum distribution of a massless quark jet, at leading orders both …
Analytic Calculation of Prompt Photon plus Associated Heavy Flavor at Next-to-Leading Order in QCD
用解析方法计算了高能强子-强子碰撞中大横动量时伴随产生一个瞬发光子和一个粲夸克的微扰量子色动力学中二阶贡献$O(α^2_s)$.七个部分子过程以$α^2_s$顺序贡献。我们发现重要的更正，最低阶，$O(α_s)$，子过程$c g \rightarrow γc$。我们证明了从$p +\bar{p}\rightarrow γ+ c + X$的数据在何种程度上可以用来测量核子中的粲夸克密度。
We show that the production of a Higgs boson in association with a jet in proton-proton collisions is sensitive to the linear polarization of gluons inside unpolarized protons. We present the analytical expressions, at leading order in perturbative QCD, for various transverse momentum dependent observables, which can be measured at the LHC. Since there are no experimental constraints on the linearly polarized gluon distribution, its effects are studied by adopting two different models. In particular, we find that the $\cos2ϕ$ azimuthal asymmetry is a very promising observable because it could …
In this work, some of the NLO QCD corrections for pp -> VVjj + X are presented. A program in Mathematica based on the structure of FeynCalc which automatically simplifies a set of amplitudes up to the hexagon level of rank 5 has been created for this purpose. We focus on two different topologies. The first involves all the virtual contributions needed for quadruple electroweak vector boson production, i.e. pp -> VVVV + X. In the second, the remaining "bosonic" corrections to electroweak triple vector boson production with an additional jet (pp -> VVV j + X) are computed. We show the factorizat…
The inclusive hadroproduction of a Higgs boson and of a jet, featuring large transverse momenta and well separated in rapidity, is proposed as a novel probe channel for the manifestation of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. Using the standard BFKL approach, with partial inclusion of next-to-leading order effects, predictions are presented for azimuthal Higgs-jet correlations and other observables, to be possibly compared with experimental analyses at the LHC and with theoretical predictions obtained in different schemes.
We study the sensitivity of top pair production with six-fermion decay at the LHC to the presence and nature of an underlying Z' boson, accounting for full tree-level Standard Model ttbar interference, with all intermediate particles allowed off-shell. We concentrate on the lepton-plus-jets final state and simulate experimental conditions, including kinematic requirements and top quark pair reconstruction in the presence of missing transverse energy and combinatorial ambiguity in jet-top assignment. We focus on the differential mass spectra of the cross section and asymmetry observables, espec…
Differential spectra in observables that resolve additional soft or collinear QCD emissions exhibit Sudakov double logarithms in the form of logarithmic plus distributions. Important examples are the total transverse momentum $q_T$ in color-singlet production, N-jettiness (with thrust or beam thrust as special cases), but also jet mass and more complicated jet substructure observables. The all-order logarithmic structure of such distributions is often fully encoded in differential equations, so-called (renormalization group) evolution equations. We introduce a well-defined technique of distrib…
We investigate the inclusive emission in unpolarized proton collisions of a charm-flavored hadron in association with a Higgs boson, featuring large transverse momenta and produced with a large rapidity distance. Taking advantage of a narrow timing coincidence between the ATLAS detector and the future FPF ones, we study the behavior of cross sections and azimuthal correlations for ultraforward rapidities of the detected hadron. We provide evidence that the hybrid high-energy and collinear factorization, encoding the BFKL resummation of large energy logarithms and supplemented by collinear dens…
Institute of Physics, Bhubaneswar（布巴内斯瓦尔物理研究所）；Department of Physics, SGTB Khalsa College（SGTB卡尔萨学院物理系）；Department of Physics and Astrophysics, University of Delhi（德里大学物理与天体物理学系）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
The $J/ψ+Z^0$ associated production at the LHC is an important process in investigating the color-octet mechanism of non-relativistic QCD in describing the processes involving heavy quarkonium. We calculate the next-to-leading order (NLO) QCD corrections to the $J/ψ+Z^0$ associated production at the LHC within the factorization formalism of nonrelativistic QCD, and provide the theoretical predictions for the distribution of the $J/ψ$ transverse momentum. Our results show that the differential cross section at the leading-order is significantly enhanced by the NLO QCD corrections. We conclude t…
