New method for calculating helicity amplitudes of jet-like QED processes for high-energy colliders

Inelastic QED processes, the cross sections of which do not drop with increasing energy, play an important role at high-energy colliders. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles , which yields the dominant contribution to their total cross sections. A new effective method is presented and applied to QED processes with emission of real photons to calculate the helicity amplitudes of these processes. Its basic idea is similar to the well-known equivalent-lepton method. Compact analytical expressions for those amplitudes up to are derived omitting only terms of the order of and higher order. The helicity amplitudes are presented in a compact form in which large compensating terms are already cancelled. Some common properties for all jet-like processes are found and we discuss their origin. Received: 19 December 2001 / Published online: 5 April 2002     

Extended projection method for massive fermions

Tensor reduction is of considerable importance in calculations of multi-loop amplitudes,and the projection method is one of the most popular approaches for tensor reduction.However,the projection method can be problematic when applied to amplitudes with massive fermions,due to the inconsistency between helicity and chirality.We propose an extended projection method for reducing the loop amplitude which contains a fermion chain with two massive spinors.The extension is achieved by decomposing one of the massive spinors into two massless spinors,the"null spinor"and the"reference spinor".The extended projection method can be effectively applied in all processes,including the production of massive fermions.We present the tensor reduction for a virtual Z boson decaying into a top-quark pair as a demonstration of our approach.     

Di-Boson production at hadron colliders with general triple gauge boson couplings. Analytic expressions of helicity amplitudes and cross-sections

We discuss the tests of general Triple Gauge Boson Vertices (TGV) through bosonic pair production at present and future hadron colliders. All bosonic final states are reviewed via the tree level quark-antiquark annihilation sub-processes. The full analytic expressions of the helicity amplitudes and cross-sections are given. These expressions should be useful in any attempt to disentangle the effects of the most general non standard WWV(V = γ,Z) vertices including 14 free parameters. We investigate the sensitivity of the invariant mass and transverse momentum distributions to the full set of anomalous couplings including final state polarization structures. We particularly consider these features at the projected CERN Large Hadron Collider (LHC) energy scale.     

Fast computation of MadGraph amplitudes on graphics processing unit (GPU)

Continuing our previous studies on QED and QCD processes, we use the graphics processing unit (GPU) for fast calculations of helicity amplitudes for general Standard Model (SM) processes. Additional HEGET codes to handle all SM interactions are introduced, as well as the program MG2CUDA that converts arbitrary MadGraph generated HELAS amplitudes (FORTRAN) into HEGET codes in CUDA. We test all the codes by comparing amplitudes and cross sections for multi-jet processes at the LHC associated with production of single and double weak bosons, a top-quark pair, Higgs boson plus a weak boson or a top-quark pair, and multiple Higgs bosons via weak-boson fusion, where all the heavy particles are allowed to decay into light quarks and leptons with full spin correlations. All the helicity amplitudes computed by HEGET are found to agree with those computed by HELAS within the expected numerical accuracy, and the cross sections obtained by gBASES, a GPU version of the Monte Carlo integration program, agree with those obtained by BASES (FORTRAN), as well as those obtained by MadGraph. The performance of GPU was over a factor of 10 faster than CPU for all processes except those with the highest number of jets.     

Forward jet production & quantum corrections to the gluon Regge trajectory from Lipatov’s high energy effective action

We review Lipatov’s high energy effective action and show that it is a useful computational tool to calculate scattering amplitudes in (quasi)-multi-Regge kinematics. We explain in some detail our recent work where a novel regularization and subtraction procedure has been proposed that allows to extend the use of this effective action beyond tree level. Two examples are calculated at next-to-leading order: forward jet vertices and the gluon Regge trajectory.     

General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in $$\mathcal {}$$-cut representation

In this paper, we give the general expressions for a special series of tree amplitudes of the Yang–Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive helicity gluons. With special helicity choices, we use the spinor helicity formalism to express these n-point amplitudes in compact forms, and find a clever way to use the BCFW recursion relations to prove the results. Then these amplitudes are used to form the complete 1-loop all-plus integrand with any number of gluons, expressed in the \(\mathcal {Q}\)-cut representation.     

Diffractive vector mesons beyond the s-channel helicity conservation

We derive a full set, and determine the twist, of helicity amplitudes for diffractive production of light to heavy vector mesons in deep inelastic scattering. For large Q ² all helicity amplitudes but the double-flip are calculable in perturbative QCD and are proportional to the gluon structure function of the proton at a similar hardness scale. We find a substantial breaking of the s-channel helicity conservation, which must persist in real photoproduction also. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 667–673 (10 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

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 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Holonomies of gauge fields in twistor space 5: Amplitudes of gluons and massive scalars

Scattering amplitudes of gluons coupled with a pair of massive scalars, so-called massive scalar amplitudes, provide the simplest yet physically useful examples of massive amplitudes. In this paper we construct an S-matrix functional for the massive scalar amplitudes in a recently developed holonomy formalism in supertwistor space. From the S-matrix functional we derive ultra helicity violating (UHV), as well as next-to-UHV (NUHV), massive scalar amplitudes at tree level in a form that agrees with previously known results. We also obtain recursive expressions for non-UHV tree amplitudes in general. These results will open up a new avenue to the study of phenomenology in the spinor-helicity formalism.     

Vector boson pair production in e−e− collisions with polarized beams

The W-boson pair production in e⁻e⁻ collisions with polarized beams is investigated. The helicity amplitudes are derived for general couplings and the conditions for a good high-energy behaviour of the cross-section are given. The results are applied to the heavy vector boson production in the context of the left-right symmetric model. The Ward identities and the equivalence theorem are also discussed.     

红外光谱的煤精类文物材质判别方法

我国是世界上最早使用煤及煤精的国家之一,但对考古出土煤精文物的研究发现,煤精文物原材料的质地常常偏离宝石学中对有机宝石煤精的定义。在此提出“煤精类文物”的概念,将以往出土文物中如褐煤、烛煤等与煤精文物材质近似但不同的材料归至同一文化概念中。目前对于煤精类文物制品的科学研究仍存在较大空白,其中最为基础的材质种类判别也没有科学的判断方法。以陕西周原贺家墓地、陕西咸阳岩村墓地、新疆吐鲁番胜金店墓地、新疆伊犁吉仁台沟口遗址四个遗址出土的16件煤精制品和原料为研究对象,初步探索漫反射傅里叶变换红外光谱在出土煤精类文物成分分析中的应用。结果表明,不同遗址出土的煤精类文物的红外谱图有较为明显的不同,同一遗址出土的煤精类文物的红外谱图在特征波段具有相似性,不同遗址煤精类文物则差异明显。使用Norris二阶导数法对红外光谱进行处理,提高吸收峰分辨率,为精细研究提供信息,选择特殊红外光谱参数I=A_{820 cm-1}/A_{2 870 cm-1}定量分析不同样品的红外光谱,结合静水称重得到的部分样品的密度信息,对出土的煤精类文物制品材质的煤化程度初步判断。结合红外光谱特征波数的强度进一步通过主成分分析解释煤精类文物的红外光谱信息,来自不同遗址的煤精类文物样品在主成分分析得分图中得到了良好的区分,并且可以与特殊红外光谱参数I判别的初步结论互相对应。验证了以漫反射傅里叶变换红外光谱为主的无损分析方法在煤精类文物材质判别中应用的可行性;若结合不同产地煤精矿样红外光谱,则可以为煤精类文物产地判别提供研究方法。     

Four jet event shapes in electron-positron annihilation

We report next-to-leading order perturbative QCD predictions of 4 jet event shape variables for the process obtained using the general purpose Monte Carlo EERAD2. This program is based on the known `squared' one loop matrix elements for the virtual parton contribution and squared matrix elements for 5 parton production. To combine the two distinct final states numerically we present a hybrid of the commonly used subtraction and slicing schemes based on the colour antenna structure of the final state which can be readily applied to other processes. We have checked that the numerical results obtained with EERAD2 are consistent with next-to-leading order estimates of the distributions of previously determined four jet-like event variables. We also report the next-to-leading order scale independent coefficients for some previously uncalculated observables; the light hemisphere mass, narrow jet broadening and the 4 jet transition variables with respect to the JADE and Geneva jet finding algorithms. For each of these observables, the next-to-leading order corrections calculated at the physical scale significantly increase the rate compared to leading order (the K factor is approximately 1.5–2). With the exception of the 4 jet transition variables, the published DELPHI data lies well above the predictions. The renormalisation scale uncertainty is still large and in most cases the data prefers a scale significantly smaller than the physical scale. This situation is reminiscent of that for three jet shape variables, and should be improved by the inclusion of power corrections and resummation of large infrared logarithms. Received: 17 November 1998 / Revised version: 26 January 1999 / Published online: 7 April 1999     

On the Decay Analysis of Electroproduced Higher-Spin Hadrons

We study exclusive electroproduction of two hadrons where one or both of the hadrons is a higherspin resonance whose decay is analysed. Interesting electroproduction experiments of this type are discussed. A complete formal apparatus is given for the decay analysis of spin-J particles produced in this way with polarized or unpolarized electron beams and targets. The cases J = 1, 3/2, 2 and 5/2 are worked out in detail. A conventional helicity frame analysis in terms of s-channel helicity amplitudes is given. Also we rearrange the formalism for use in the Gottfried-Jackson frame with everything given in terms of t-channel helicity amplitudes. The t-channel formalism makes it possible to completely separate the contributions from longitudinal and transverse virtual photon t-channel helicity states when only the laboratory azimuthal angle between the lepton and hadron planes is variable.     

Gravity, Twistors and the MHV Formalism

We give a self-contained proof of the formula for the MHV amplitudes for gravity conjectured by Berends, Giele & Kuijf and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti-self-dual curvature, we obtain a simple spacetime formula for the scattering of a single, positive helicity linearized graviton into one of negative helicity. Re-expressing our integral in terms of twistor data allows us to consider a spacetime that is asymptotic to a superposition of plane waves. Expanding these out perturbatively yields the gravitational MHV amplitudes of Berends, Giele & Kuijf. We go on to take the twistor generating function off-shell at the perturbative level. Combining this with a twistor action for the anti-self-dual background, the generating function provides the MHV vertices for the MHV diagram approach to perturbative gravity. We finish by extending these results to supergravity, in particular N = 4{\mathcal {N} = 4} and N = 8{\mathcal {N} = 8} .     

The \gamma \gamma \to Z Z process and the search for virtual SUSY effects at a \gamma \gamma Collider

We study the helicity amplitudes of the process in the Standard Model at high energy. These amplitudes receive contributions from the W and charged quark and lepton loops, analogous to those encountered in the cases studied before. But also receives contributions from the Higgs s-channel poles involving the effective Higgs- vertex. At energies , the amplitudes in all three processes are mainly helicity-conserving and almost purely imaginary; which renders them a very useful tool in searching for New Physics. As an example, a SUSY case is studied, and the signatures due to the virtual effects induced by a chargino-, charged slepton- or a lightest stop-loop in , are explored. These signatures, combined with the analogous ones in and , should help identifying the nature of possible New Physics particles. Received: 3 September 1999 / Published online: 3 February 2000     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

QCD Jets at HERA II.O(α s 2 ) four-jet cross-sections

We present exact expressions for theO(α _s ² ) tree graph four-jet cross-sections in neutral current and charged current deep inelasticep scattering initiated by quarks, antiquarks and gluons including lepton polarization effects. Using helicity amplitudes the partonic cross-sections are given in concise form including all colour, flavour and statistical factors. We explicate the electroweak coupling dependence and state how the partonic cross-sections are folded with the respective parton densities to obtain theep jet cross-sections toO(α _s ² ). We present some numerical results for the neutral current one-photon exchange case. We elaborate on the cut dependence of the jet rates and present differential distributions in some basic kinematical variables.     

The \gamma \gamma \to \gamma Z process at high energies and the search for virtual SUSY effects

We study the helicity amplitudes and the observables of the process at high energy. As in the case of the process studied before, the relevant diagrams in the standard model (SM) involve W, charged-quark, and lepton loops, while in SUSY we also have contributions from charginos and charged-sfermion or Higgs-loop diagrams. Above 250 GeV, the dominant SM amplitudes are themselves dominated by the W loop, and as for , they are helicity conserving and almost purely imaginary. We discuss the complementary information provided by for the identification of possible nonstandard effects. This process, together with , should provide very useful information on the nature of possible new physics particles, above the threshold of their direct production. Received: 26 April 1999 / Published online: 8 September 1999     

Probing the CP nature of the Higgs bosons by $t\overline{t}$ productionat photon linear colliders

We study the effects of heavy Higgs bosons on the production process at photon linear colliders. The interference patterns between the resonant Higgs production amplitudes and the continuum QED amplitudes are examined. The patterns tell us not only the CP nature of the Higgs bosons but also the phase of the -Higgs vertex which gives new information about the Higgs couplings to new charged particles. We point out that it is necessary to use circularly polarized photon beams to produce efficiently heavy Higgs bosons whose masses exceed the electron beam energy, and show that the above interference patterns of the production amplitudes can be studied by observing t and decay angular distributions. Analytic expressions for the helicity amplitudes for the sequential process are presented in terms of the generic production amplitudes.Received: 2 June 2003, Published online: 24 October 2003     

Electroweak tri-boson couplings at LEP II and beyond

Possible non-standard model couplings of electroweak vector bosons are studied inW pair production ine ⁺ e ^? collisions. Helicity amplitudes are calculated in a factorized formalism; the choice of helicity basis suggested by this formalism is shown to increase sensitivity of angular correlations to anomalous couplings. In the course of this analysis, the chi-squared test for finite data samples is more carefully formulated. BothCP-conserving andCP-violating couplings are considered.