arXiv subjects

Mao Zeng

Publications and source records attributed to Mao Zeng.

50 records · Page 3Linked to original sources

arXiv2018

Dual Conformal Structure Beyond the Planar Limit

The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.

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arXiv2018

Ultraviolet Properties of N = 8 Supergravity at Five Loops

We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of $N = 8$ supergravity whose leading ultraviolet behavior we analyze using state of the art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is $D_c=24/5$, corresponding to a $D^8 R^4$ counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional $N = 4$ supergravity at three loops and $N = 5$ supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard-symmetry considerations. We express this $D_c=24/5$ divergence in terms of two relatively simple positive-definite integrals reminiscent of vacuum integrals, excluding any additional ultraviolet cancellations at this loop-order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.

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arXiv2017

Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity

We present a calculation of the planar two-loop five-gluon amplitudes. The amplitudes are obtained in a variant of the generalized unitarity approach suitable for numerical computations, which we extend for use with finite field arithmetics. Employing a new method for the generation of unitarity-compatible integration-by-parts identities, all helicity amplitudes are reduced to a linear combination of master integrals for the first time. The approach allows us to compute exact values for the integral coefficients at rational phase-space points. All required master integrals are known analytically, and we obtain arbitrary-precision values for the amplitudes.

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arXiv2017

The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy

We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of N=4 super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes. For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of N=8 supergravity at five loops and beyond. We also present a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.

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arXiv2017

Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector

We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple observation is that dual conformal transformations preserve unitarity cut conditions for any planar integrals, including those without dual conformal symmetry. Such transformations generate differential equations without raised propagator powers, often with the right hand side of the system proportional to the dimensional regularization parameter $ε$. A nontrivial subgroup of dual conformal transformations, which leaves all external momenta invariant, generates integration-by-parts relations without raised propagator powers, reproducing, in a simpler form, previous results from computational algebraic geometry for several examples with up to two loops and five legs. By opening up the two-loop three- and four-point nonplanar diagrams into planar ones, we find a nonplanar analog of dual conformal symmetry. As for the planar case this is used to generate integration-by-parts relations and differential equations. This implies that the symmetry is tied to the analytic properties of the nonplanar sector of the two-loop four-point amplitude of $\mathcal N = 4$ super-Yang-Mills theory.

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arXiv2017

Differential equations on unitarity cut surfaces

We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. We speed up the computation using finite field techniques and rational function reconstruction.

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arXiv2017

Manifesting enhanced cancellations in supergravity: integrands versus integrals

Examples of "enhanced ultraviolet cancellations" with no known standard-symmetry explanation have been found in a variety of supergravity theories. By examining one- and two-loop examples in four- and five-dimensional half-maximal supergravity, we argue that enhanced cancellations in general cannot be exhibited prior to integration. In light of this, we explore reorganizations of integrands into parts that are manifestly finite and parts that have poor power counting but integrate to zero due to integral identities. At two loops we find that in the large loop-momentum limit the required integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry out a nontrivial check at four loops showing that the identities generated in this way are a complete set. We propose that at $L$ loops the combination of Lorentz and SL($L$) symmetry is sufficient for displaying enhanced cancellations when they happen, whenever the theory is known to be ultraviolet finite up to $(L-1)$ loops.

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arXiv2016

Resummation of Jet Veto Logarithms at partial N$^3$LL + NNLO for $W^+W^-$ Production at the LHC

We compute the resummed on-shell $W^+ W^-$ production cross section under a jet-veto at the LHC to partial N$^3$LL order matched to the fixed order NNLO result. Differential NNLO cross sections are obtained from an implementation of $q_T$ subtraction in Sherpa. The two-loop virtual corrections to the $q \bar q \rightarrow W^+ W^-$ amplitude, used in both fixed order and resummation predictions, are extracted from the public code {\tt qqvvamp}. We perform resummation using soft collinear effective theory (SCET), with approximate beam functions where only the logarithmic terms are included at two-loop. In addition to scale uncertainties from the hard matching scale and the factorization scale, rapidity scale variations are obtained within the analytic regulator approach. Our resummation results show a decrease in the jet-veto cross-section compared to NNLO fixed order predictions, with reduced scale uncertainties compared to NNLL+NLO resummed predictions. We include the loop-induced $gg$ contribution with jet veto resummation to NLL+LO. The prediction shows good agreement with recent LHC measurements.

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arXiv2015

Drell-Yan process with jet vetoes: breaking of generalized factorization

Resummation of hadron collision cross sections, when the measurement imposes a hierarchy of scales, relies on factorization. Cancellation of Glauber / Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like processes, the known proofs of cancellation of Glauber gluons are not applicable when jet vetoes are introduced, via jet algorithms or event shape variables such as the beam thrust. A priori, this does not rule out the possibility that an unknown new cancellation mechanism exists, or the possibility that a generalized factorization formalism is correct. To resolve the questions, we construct a direct counter-example in QCD with scalar quarks, contradicting any form of factorization in which the two collinear sectors are decoupled from each other. In the counter-example, decoupling of the two collinear sectors implies zero dependence of the beam thrust distribution on the longitudinal spin of the incoming hadrons, but we find a non-zero spin asymmetry at leading power due to Glauber gluons exchanged between spectators. We discuss implications for resumming large logarithms from jet vetoes.

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arXiv2015

Usefulness of effective field theory for boosted Higgs production

The Higgs + jet channel at the LHC is sensitive to the effects of new physics both in the total rate and in the transverse momentum distribution at high p_T. We examine the production process using an effective field theory (EFT) language and discuss the possibility of determining the nature of the underlying high scale physics from boosted Higgs production. The effects of heavy color triplet scalars and top partner fermions with TeV scale masses are considered as examples and Higgs-gluon couplings of dimension-5 and dimension-7 are included in the EFT. As a by-product of our study, we examine the region of validity of the EFT. Dimension-7 contributions in realistic new physics models give effects in the high p_T tail of the Higgs signal which are so tiny that they are likely to be unobservable.

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arXiv2014

Effective Field Theory for Higgs Plus Jet Production

We use an effective field theory (EFT) which includes all possible gluon-Higgs dimension-5 and dimension-7 operators to study Higgs boson plus jet production in next-to-leading order QCD. The EFT sheds light on the effect of a finite top quark mass as well as any Beyond-the-Standard Model (BSM) modifications of Higgs-gluon effective couplings. In the gluon channel, the accuracy of the heavy-top approximation for differential distributions arises from the non-interference between the helicity amplitudes of the G^3 h and G^2 h operators in the m_h < p_T limit at lowest order. One dimension-7 operator involving quark bilinears, however, contributes significantly at high p_T, and potentially offers a channel for seeing BSM effects. One-loop renormalization of these operators is determined, allowing resummation of large logarithms via renormalization group running. NLO numerical results at the LHC are presented, which include O(1/m_t^2) contributions in the SM limit.

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arXiv2014

Transverse momentum resummation effects in W^+W^- measurements

The W^+W^- cross section has remained one of the most consistently discrepant channels compared to SM predictions at the LHC, measured by both ATLAS and CMS at 7 and 8 TeV. Developing a better modeling of this channel is crucial to understanding properties of the Higgs and potential new physics. In this paper we investigate the effects of NNLL transverse momentum resummation in measuring the W^+W^- cross section. In the formalism we employ, transverse momentum resummation does not change the total inclusive cross section, but gives a more accurate prediction for the p_T distribution of the diboson system. By re-weighting the p_T distribution of events produced by Monte Carlo generators, we find a systematic shift that decreases the experimental discrepancy with the SM prediction by approximately 3-7% depending on the MC generator and parton shower used. The primary effect comes from the jet veto cut used by both experiments. We comment on the connections to jet veto resummation, and other methods the experiments can use to test this effect. We also discuss the correlation of resummation effects in this channel with other diboson channels. Ultimately p_T resummation improves the agreement between the SM and experimental measurements for most generators, but does not account for the measured ~20% difference with the SM and further investigations into this channel are needed.

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arXiv2014

Quantifying Comparisons of Threshold Resummations

We explore similarities and differences between widely-used threshold resummation formalisms, employing electroweak boson production as an instructive example. Resummations based on both full QCD and soft-collinear effective theory (SCET) share common underlying factorizations and resulting evolution equations. The formalisms differ primarily in their choices of boundary conditions for evolution, in moment space for many treatments based on full QCD, and in momentum space for treatments based on soft-collinear effective theory. At the level of factorized hadronic cross sections, these choices lead to quite different expressions. Nevertheless, we can identify a natural expansion for parton luminosity functions, in which SCET and full QCD resummations agree for the first term, and for which subsequent terms provide differences that are small in most cases. We also clarify the roles of the non-leading resummation constants in the two formalisms, and observe a relationship of the QCD resummation function $D(α_s)$ to the web expansion.

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arXiv2013

Threshold Resummed and Approximate NNLO results for W+W- Pair Production at the LHC

The next-to-leading order (NLO) QCD radiative corrections to W+W- production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total W+W- cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross section is the most precise theoretical prediction available. Uncertainties due to scale variation are shown to be small when the threshold logarithms are included. NNLL threshold resummation increases the W+W- invariant mass distribution by ~ 3-4% in the peak region for both \sqrt{S}=8 and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections increase the NLO cross section by 0.5-3% for \sqrt{S}=7, 8, 13, and 14 TeV.

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