Adam R. Dalgleish, David C. Dunbar, Warren B. Perkins, Joseph M. W. Strong
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.
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We apply the solution to the recursion relation for the double-off-shell quark current to the problem of computing one loop amplitudes with an arbitrary number of gluons. We are able to compute amplitudes for photon-gluon scattering, electron-positron annihilation to gluons, and gluon-gluon scattering via a quark loop in the case of like-helicity gluons. In addition, we present the result for the one-loop gluon-gluon scattering amplitude when one of the gluons has opposite helicity from the others.
Quasi-Classical Evaluation of Gluon Saturation Induced Helicity Effects
本文通过经典Yang-Mills方程和图解计算推导了胶子饱和诱导的螺旋度效应，揭示其本质为多粒子关联效应，并在极化电子-核碰撞的双喷注产生中评估了该效应对背对背峰的抑制作用，为探测胶子饱和提供了新途径。
We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Glover, Oleari and Tejeda-Yeomans. We also present the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-…
We use twistor inspired rules to compute the one-loop amplitude for a Higgs boson coupling to any number of negative helicity gluons in the large top mass limit.
We present analytic results for the one-loop corrections of the helicity amplitudes of the QCD five-parton subprocesses involving four quarks and one gluon obtained with a standard Feynman diagram calculation using dimensional reduction.
In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use…
The total gluon helicity in a polarized proton, measurable in high-energy scattering, is shown to be the large momentum limit of a gauge-invariant but non-local, frame-dependent gluon spin $\vec{E}\times \vec{A}_\perp$ in QCD. This opens a door for a non-perturbative calculation of this quantity in lattice QCD, and also justifies using free-field expressions in the light-cone gauge as physical observables.
Basing on the Slavnov-Taylor identities, we derive a new prescription to obtain gauge invariant tree-level scattering amplitudes for the process g*g->Ng within high energy factorization. Using the helicity method, we check the formalism up to several final state gluons, and we present analytical formulas for the the helicity amplitudes for N=2. We also compare the method with Lipatov's effective action approach.
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.
We consider hard electroproduction of mesons at twist-3 level and focus our attention on helicity flip amplitudes corresponding to the production of transversely polarized mesons by transverse photons. We demonstrate that helicity-flip amplitude for the transversely polarized particles are closely related to the contributions of the matrix elements of the tensor gluon operator which can serve as pure gluonic probe of the hadrons. Using standard factorisation approach and Wanzura-Wilczek approximation for the twist-3 matrix elements we find that such amplitudes do not have divergencies from the…
We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.
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 use on-shell recursion relations to compute analytically the one-loop corrections to maximally-helicity-violating n-gluon amplitudes in QCD. The cut-containing parts have been computed previously; our work supplies the remaining rational parts for these amplitudes, which contain two gluons of negative helicity and the rest positive, in an arbitrary color ordering. We also present formulae specific to the six-gluon cases, with helicities (- + - + + +) and (- + + - + +), as well as numerical results for six, seven, and eight gluons. Our construction of the n-gluon amplitudes illustrates the r…
We consider a Higgs boson coupled to gluons via the five-dimensional effective operator H tr G_{μν}G^{μν}. We treat H as the real part of a complex field phi that couples to the selfdual gluon field strengths and compute the one-loop corrections to the phi-MHV amplitudes involving phi, two negative helicity gluons and an arbitrary number of positive helicity gluons. Our results generalise earlier work where the two negative helicity gluons were constrained to be colour adjacent. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion…
Weizsäcker-Williams Gluon Helicity Distribution and Inclusive Dijet Production in Longitudinally Polarized Electron-Proton Collisions
本文研究纵向极化电子-质子碰撞中包容性正反夸克双喷注产生的双自旋不对称性，发现背对背极限可探测WW胶子螺旋度TMD，推导其小$x$演化方程并证明与偶极胶子螺旋度分布演化方程相同，为检验小$x$螺旋度演化方程提供途径。
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 contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations.
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering (DIS) experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. We will see that a large gluon polarization emerges, giving a significant contribution to the proton spin.
We compute the top quark contribution to the two-loop amplitude for on-shell $Z$ boson pair production in gluon fusion, $gg \to ZZ$. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision.
Higgs production at RHIC and the positivity of the gluon helicity distribution
本研究指出核子螺旋度结构的次领头阶QCD全局分析得到的负极化胶子分布违反正定性条件，会导致RHIC上希格斯玻色子产生截面为负，证明该负极化胶子分布不符合物理要求。
Little information is known about the polarization of gluons inside a longitudinally polarized proton. I report on the sensitivity of photoproduction experiments to it. Both jet and heavy quark production are considered.
We consider the process containing two quark lines and an arbitrary number of gluons in a spinor helicity framework. A current with two off-shell gluons appears in the amplitude. We first study this modified gluon current using recursion relations. The recursion relation for the modified gluon current is solved for the case of like-helicity gluons. We apply the modified gluon current to compute the amplitude for $q \bar q \rightarrow q \bar q gg \cdots g$ in the like-helicity gluon case.
Two- and Three-gluon Glueballs within the Helicity Formalism
该研究采用组分胶子方法，基于螺旋度形式构建两、三胶子胶球全对称波函数，首次推导两种三粒子态耦合方案的关系，所得能谱与格点QCD模拟整体吻合，且三胶子谱预测了额外低能态。
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…
The Seven-Point Two-Loop Full-Color All-Plus Helicity Yang-Mills Amplitude
该研究通过四维幺正性切割与增广递推方法得到紧凑解析形式的七胶子两圈全色Yang-Mills振幅，给出全色多对数项的n点形式，并借此探究两圈部分振幅间的潜在关系。
We present the one-loop helicity amplitudes with five external gluons. The computation employs string-based methods, new techniques for performing tensor integrals, and improvements in the spinor helicity method.
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.
We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta. The evolution of these distributions with change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon. Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through distinct a…
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 compute the next-to-MHV one-loop n-gluon amplitudes in N=4 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.
We study the polarization of hyperon in different processes in singly polarized $pp$ collisions, in particular its relation to the polarized parton distributions. We show that by measuring hyperon polarization in particularly chosen processes, one can extract useful information on these parton distributions. We show in particular that, by measuring the $Σ^+$ polarization in high $p_T$ direct photon production process, one can extract information on the gluon helicity distribution; and by measuring the transverse polarization of hyeprons with high $p_T$ in singly polarized reactions, one can ob…
We perform a systematic analysis on the off-forward matrix elements of the twist-two quark and gluon helicity-flip operators. By matching the allowed quantum numbers and their crossing channel counterparts (a method developed by Ji & Lebed), we systematically count the number of independent nucleon form factors in off-forward scattering of matrix elements of these quark and gluon spin-flip operators. In particular, we find that the numbers of independent nucleon form factors twist-2, helicity flip quark (gluon) operators are $2n-1$ ($2n-5$) if $n$ is odd, and $2n-2$ ($2n-6$) if $n$ is even, wi…
We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.
Recently a new recursion relation for tree-level gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of zigzag diagrams. We comment on generalizations of this result.
We show that the total gluon helicity $ΔG$ in a polarized nucleon can be calculated on a Euclidean lattice through a universality class of QCD operators that describe the helicity or polarization of the onshell gluon radiation. We in particular find some operators whose matrix elements in a nucleon of momentum $P^z$ are directly related to $ΔG$ with only power-law $(1/P^z)^n (n\ge 2)$ corrections.
We consider the multi-collinear limit of multi-gluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorisation formula to derive timelike splitting functions that are valid for specific numbers of negative helicity gluons and an arbitrary number of positive helicity gluons (or vice versa).
It is shown how tree-level multi-gluon helicity amplitudes with an arbitrary number of off-shell external gluons can be calculated via BCFW recursion. Compact expressions for helicity amplitudes for scattering processes of three and four gluons, with up to three of them off-shell, are presented. Also, maximum-helicity-violating configurations are identified for up to two off-shell gluons, and the expressions for their helicity amplitudes for an arbitrary number of on-shell gluons are derived.
We present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. Our construction of the amplitude does not rely directly on Feynman diagrams, but instead uses its analytic properties in 4 - 2 epsilon dimensions. We evaluate the loop integrals appearing in the amplitude through O(epsilon^0) in terms of polylogarithms.
We present the two-loop helicity amplitudes for the scattering of massless quarks and massless gauge bosons in QCD. We use projector techniques to compute the coefficients of the general tensor describing the two-quark two-boson amplitude in conventional dimensional regularisation and use these coefficients to derive the helicity amplitudes in the 't Hooft-Veltman scheme. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainders for q qbar -> gluon gluon, q qbar -> gluon gamma, q qbar -> gamma gamma and the processes related by c…
We compute the leading probability for a gluon to flip helicity state upon traversing a background plane wave gauge field in pure Yang-Mills theory and QCD, with an arbitrary number of colours and flavours. This is a one-loop calculation in perturbative gauge theory around the gluonic plane wave background, which is treated without approximation (i.e., to all orders in the coupling). We introduce a background-dressed version of the spinor helicity formalism and use it to obtain simple formulae for the flip amplitude with pure external gluon polarizations. We also give in-depth examples for gau…
Recently, X. Chen et al. proposed a new approach to the gauge invariant decomposition of the nucleon spin into helicity and orbital parts. The key ingredient in their construction is the separation of the gauge field into `physical' and `pure gauge' parts. We suggest a simple separation scheme and show that the resulting gluon helicity coincides with the first moment of the conventional polarized gluon distribution measurable in high energy experiments.
In the Catani-Ciafaloni-Hautmann high-energy factorization approach a cross section is expressed as a convolution of unintegrated gluon densities and a gauge-invariant hard process, in which two incoming gluons are off-shell with momenta satisfying certain high-energy kinematics. We present two methods of evaluating the tree-level hard process with multiple final states. The first one assumes that only one of the gluons is off-shell and relies on the Slavnov-Taylor identities. Such asymmetric configuration of incoming gluons is phenomenologically important in small x probing by forward process…
We present a conjecture for the $n$-gluon one-loop amplitudes with maximal helicity violation. The conjecture emerges from the powerful requirement that the amplitudes have the correct behavior in the collinear limits of external momenta. One implication is that the corresponding amplitudes where three or more gluon legs are replaced by photons vanish for $n>4$.
We present a compact analytic expression for the leading colour two-loop five-gluon amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The analytic result is reconstructed from numerical evaluations over finite fields. The numerical method combines integrand reduction, integration-by-parts identities and Laurent expansion into a basis of pentagon functions to compute the coefficients directly from six-dimensional generalised unitarity cuts.
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.
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.
We present an antenna-shower formalism that includes helicity dependence for massless partons. The formalism applies to both traditional (global) showers and to sector-based variants. We combine the shower with VINCIA's multiplicative approach to matrix-element matching, generalized to operate on each helicity configuration separately. The result is a substantial gain in computational speed for high parton multiplicities. We present an implementation of both sector and global showers, with min and max variations, and helicity-dependent tree-level matching applied for vector bosons or Higgs dec…
A scalar cubic action that classically reproduces the self-dual Yang--Mills equations is shown to generate one-loop QCD amplitudes for external gluon all with the same helicity. This result is related to the symmetries of the self-dual Yang--Mills equations.
We present a calculation of the helicity amplitudes for the process $gg\toγγ$ in three-loop massless QCD. We employ a recently proposed method to calculate scattering amplitudes in the 't Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation. Our analytic results for the three-loop helicity amplitudes are remarkably compact, and can be efficiently evaluated numerically. This calculation provides the last missing building block for the computation of NNLO QCD corrections to diphoton production in gluon fusion.
We calculate the differential cross section $dσ/dt$ for the diffractive photoproduction process $γp \to ρp$ and compare to recent data extracted by the CMS collaboration from ultraperipheral proton-lead collisions. Our model is based on two-gluon exchange in the nonperturbative domain. We take into account both helicity conserving and often neglected helicity-flip amplitudes in the $γ\to V$ transition. The letter can contribute at finite $t$. The shape of the differential cross section as well as the role of helicity flip processes is strongly related to the dependence of the unintegrated gluo…
We compute the next-to-leading order (NLO) QCD corrections to the gluon-fusion subprocess of diphoton-plus-jet production at the LHC. We compute fully differential distributions by combining two-loop virtual corrections with one-loop real radiation using antenna subtraction to cancel infrared divergences. We observe significant corrections at NLO which demonstrate the importance of combining these corrections with the quark-induced diphoton-plus-jet channel at next-to-next-to-leading order (NNLO).
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 investigate the effects of an all order QCD resummation of soft gluon emissions for Higgs boson production in association with two hard jets. We consider both the gluon-gluon fusion and weak boson fusion processes and show how to resum a large part of the leading logarithms in the jet veto scale. Our resummation improves on previous analyses which also aim to include the effects of multiple soft gluon radiation. In addition we calculate the interference between weak boson fusion and gluon-gluon fusion and find that it is small.
In the hadronic decays of Z, gluon emission leads to the appearance of the longitudinal component of the fragmentation function, F_L. Measurement of F_L and the transverse component, F_T, could thus provide an insight into the gluon fragmentation function. However, hadronization corrections at low x can be significant. Here we present a method of accounting for such corrections, using the JETSET event generator as illustration.
Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
本文在重顶夸克极限下，利用四维单位性切割方法，构建了自对偶希格斯玻色子与最多四个正螺旋胶子的双环幅度，通过多项式对数部分和有限域积分减少提取出理性的模糊性。
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 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 present analytic results for one-loop Higgs boson + $n$-gluon amplitudes for $n\le 5$ in the full theory including all dependence on the (top) quark mass. In this paper we consider only the case where the gluons all have the same helicity. The amplitudes are expressed in simple formula and display similar structure. Their limiting behaviour in small Higgs momentum and large top mass is studied.
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 consider one-loop amplitudes of a Higgs boson coupled to gluons in the limit of a large top quark mass. We treat the Higgs as the real part of a complex field phi that couples to the self-dual field strengths and compute the one-loop corrections to the phi-NMHV amplitude, which contains one gluon of positive helicity whilst the remaining three have negative helicity. We use four-dimensional unitarity to construct the cut-containing contributions and a hybrid of Feynman diagram and recursive based techniques to determine the rational piece. Knowledge of the phi-NMHV contribution completes th…
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