Phase Space Cuts Research Articles

Reduction of Feynman integrals in the parametric representation III: integrals with cuts

Phase space cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. By directly parametrizing theta functions and constructing integration-by-parts (IBP) identities in the parametric representation, we provide a systematic method to reduce integrals with cuts. Since the IBP method is available, it becomes possible to evaluate integrals with cuts by constructing and solving differential equations.

New insights on an old problem: resummation of the D-parameter

The D-parameter is one of the oldest and most experimentally well-studied hadronic observables for e+e− collisions. Nevertheless, unlike other classic observables like the C-parameter or thrust, the D-parameter has never been resummed throughout its entire singular phase space. Using insights and techniques motivated by modern multi-differential jet substructure calculations, we are able to predict the D-parameter distribution with no additional phase space cuts. Our approach is to measure both the C- and D-parameters on hadronic final states in e+e− collisions. We can tune the value of the C-parameter with respect to the D-parameter to specify simple, physical configurations of final state particles in which to perform calculations. There are three parametric regions that exist: D ≪C2 ∼1, D ≪C2 ≪1, and D ∼C2 ≪1, and we calculate the D-parameter in each region separately. In the first two of these three regions, we present all-orders factorization theorems and explicitly demonstrate resummation to next-to-leading logarithmic accuracy. The region in which D ∼ C2 ≪ 1 corresponds to the dijet limit and where the D-parameter loses the property of additivity. In this region we introduce a systematically-improvable procedure exploiting properties of conditional probabilities and resum to approximate next-to-leading logarithmic accuracy. The contributions from these regions can be consistently combined, and the value of the C-parameter integrated over to produce the cross section for the D-parameter. With these results, we match to leading fixed order as proof of principle and compare our resummed and matched prediction to data from LEP.

Mass-dependent cuts in longitudinal phase space

Longitudinal phase space analyses as introduced by van Hove provided a simplified method of separating different reaction production mechanisms. Cuts in the longitudinal phase space can help to select specific reaction kinematics but also induce nonflat acceptance effects in angular distributions. We show that in photoproduction reactions dominated by t-channel exchanges, selection of meson or baryon production over a large mass range can be optimized through calculating mass-dependent cut limits compared to cuts on a van Hove plot sector alone. A cut is presented that improves this selection of one type of hadron production by rejecting another. In addition we demonstrate that using cuts in longitudinal phase space preserves sufficient information to reliably extract observables from the angular distribution of the final state particles.

Electroweak corrections to diphoton plus jets

We calculate the next-to-leading order electroweak corrections to the production of a photon pair in association with zero, one and two jets at the LHC. We use GoSam and Sherpa to obtain the results in a fully automated way. For a typical set of fiducial cuts the electroweak corrections lead to a modification of the total cross section of up to 3%, depending on the jet multiplicity. We find substantial contributions in differential distributions, leading to tens of per cent corrections for phase space regions within the reach of the LHC. Furthermore we investigate the importance of photon induced processes as well as subleading contributions. Photon induced processes are found to be negligible, subleading contributions can have a sizeable impact however they can be removed by appropriate phase space cuts.

Next-to-leading-order QCD and electroweak corrections to WWW production at proton-proton colliders

Triple-W-boson production in proton-proton collisions allows for a direct access to the triple and quartic gauge couplings and provides a window to the mechanism of electroweak symmetry breaking. It is an important process to test the Standard Model (SM) and might be background to physics beyond the SM. We present a calculation of the next-to-leading order (NLO) electroweak corrections to the production of WWW final states at proton-proton colliders with on-shell W bosons and combine the electroweak with the NLO QCD corrections. We study the impact of the corrections to the integrated cross sections and to kinematic distributions of the W bosons. The electroweak corrections are generically of the size of 5-10% for integrated cross sections and become more pronounced in specific phase-space regions. The real corrections induced by quark-photon scattering turn out to be as important as electroweak loops and photon bremsstrahlung corrections, but can be reduced by phase-space cuts. Considering that prior determinations of the photon parton distribution function (PDF) involve rather large uncertainties, we compare the results obtained with different photon PDFs and discuss the corresponding uncertainties in the NLO predictions. Moreover, we determine the scale and total PDF uncertainties at the LHC and a possible future 100 TeV pp collider.

Observing the top energy asymmetry at the LHC

The top-antitop energy asymmetry is a promising observable of the charge asymmetry in jet-associated top-quark pair production at the LHC. We present new predictions of the energy asymmetry in proton-proton collisions at 13 TeV, including QCD corrections at the next-to-leading perturbative order. The effect of QCD corrections on the observable is moderate. With suitable phase-space cuts, the asymmetry can be enhanced at the cost of reducing the cross section. For instance, for a cross section of $1\,\text{pb}$ after cuts, we predict an energy asymmetry of $-6.5^{\,+0.1}_{\,-0.2}\%$ at the next-to-leading order in QCD. We also investigate scale uncertainties and parton-shower effects, which partially cancel in the normalized asymmetry. Our results provide a sound basis for a measurement of the energy asymmetry at the LHC during run II.

New physics in the visible final states of B \u2192 D(\u2217)\u03c4\u03bd

We derive compact expressions for the helicity amplitudes of the many-body B → D(∗)(→ DY)τ(→ Xν)ν decays, specifically for X = ℓν or π and Y = π or γ. We include contributions from all ten possible new physics four-Fermi operators with arbitrary couplings. Our results capture interference effects in the full phase space of the visible τ and D∗ decay products which are missed in analyses that treat the τ or D∗ or both as stable. The τ interference effects are sizable, formally of order mτ/mB for the standard model, and may be of order unity in the presence of new physics. Treating interference correctly is essential when considering kinematic distributions of the τ or D∗ decay products, and when including experimentally unavoidable phase space cuts. Our amplitude-level results also allow for efficient exploration of new physics effects in the fully differential phase space, by enabling experiments to perform such studies on fully simulated Monte Carlo datasets via efficient event reweighing. As an example, we explore a class of new physics interactions that can fit the observed R(D(∗)) ratios, and show that analyses including more differential kinematic information can provide greater discriminating power for new physics, than single kinematic variables alone.

Improved effective vector boson approximation revisited

We reexamine the improved effective vector boson approximation which is based on two-vector-boson luminosities $\mathrm{\mathbf{L}}_{\rm pol}$ for the computation of weak gauge-boson hard scattering subprocesses $V_1 V_2\to {\cal W}$ in high-energy hadron-hadron or $e^-e^+$ collisions. We calculate these luminosities for the nine combinations of the transverse and longitudinal polarizations of $V_1$ and $V_2$ in the unitary and axial gauge. For these two gauge choices the quality of this approach is investigated for the reactions $e^-e^+ \to W^- W^+ \nu_e {\bar\nu}_e$ and $e^-e^+ \to t {\bar t} \nu_e {\bar\nu}_e$ using appropriate phase-space cuts.

Power counting to better jet observables

Optimized jet substructure observables for identifying boosted topologies will play an essential role in maximizing the physics reach of the Large Hadron Collider. Ideally, the design of discriminating variables would be informed by analytic calculations in perturbative QCD. Unfortunately, explicit calculations are often not feasible due to the complexity of the observables used for discrimination, and so many validation studies rely heavily, and solely, on Monte Carlo. In this paper we show how methods based on the parametric power counting of the dynamics of QCD, familiar from effective theory analyses, can be used to design, understand, and make robust predictions for the behavior of jet substructure variables. As a concrete example, we apply power counting for discriminating boosted Z bosons from massive QCD jets using observables formed from the n-point energy correlation functions. We show that power counting alone gives a definite prediction for the observable that optimally separates the background-rich from the signal-rich regions of phase space. Power counting can also be used to understand effects of phase space cuts and the effect of contamination from pile-up, which we discuss. As these arguments rely only on the parametric scaling of QCD, the predictions from power counting must be reproduced by any Monte Carlo, which we verify using Pythia8 and Herwig++. We also use the example of quark versus gluon discrimination to demonstrate the limits of the power counting technique.

Rivet user manual

This is the manual and user guide for the Rivet system for the validation and tuning of Monte Carlo event generators. As well as the core Rivet library, this manual describes the usage of the rivet program and the AGILe generator interface library. The depth and level of description is chosen for users of the system, starting with the basics of using validation code written by others, and then covering sufficient details to write new Rivet analyses and calculational components. Program summaryProgram title: RivetCatalogue identifier: AEPS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 571126No. of bytes in distributed program, including test data, etc.: 4717522Distribution format: tar.gzProgramming language: C++, Python.Computer: PC running Linux, Mac.Operating system: Linux, Mac OS.RAM: 20 MBClassification: 11.9, 11.2.External routines:HepMC (https://savannah.cern.ch/projects/hepmc/),GSL (http://www.gnu.org/software/gsl/manual/gsl-ref.html),FastJet (http://fastjet.fr/),Python (http://www.python.org/),Swig (http://www.swig.org/),Boost (http://www.boostsoftware.com/),YAML (http://www.yaml.org/spec/1.2/spec.html)Nature of problem:Experimental measurements from high-energy particle colliders should be defined and stored in a general framework such that it is simple to compare theory predictions to them. Rivet is such a framework, and contains at the same time a large collection of existing measurements.Solution method:Rivet is based on HepMC events, a standardised output format provided by many theory simulation tools. Events are processed by Rivet to generate histograms for the requested list of analyses, incorporating all experimental phase space cuts and histogram definitions.Restrictions:Cannot calculate statistical errors for correlated events as they appear in NLO calculations.Unusual features:It is possible for the user to implement and use their own custom analysis as a module without having to modify the main Rivet code/installation.Running time:Depends on the number and complexity of analyses being applied, but typically a few hundred events per second.

Medium-induced splitting kernels from SCETG

Using the framework of soft-collinear effective theory with Glauber gluons ($\SCETG$), we evaluate medium-induced splitting kernels. Because of the power counting of the effective theory, our results are valid for arbitrary, not necessarily small values of the energy fraction $x$ taken by the emitted parton. In this framework we prove the factorization from the hard process and gauge invariance of the splitting kernels, we also show how nuclear recoil and the phase space cuts can be implemented into the phenomenology.

Fragmentation with a cut on thrust: Predictions forBfactories

When high-energy single-hadron production takes place inside an identified jet, there are important correlations between the fragmentation and phase-space cuts. For example, when one-hadron yields are measured in on-resonance B-factory data, a cut on the thrust event shape T is required to remove the large b-quark contribution. This leads to a dijet final state restriction for the light-quark fragmentation process. Here we complete our analysis of unpolarized fragmentation of (light) quarks and gluons to a light hadron h with energy fraction z in e+ e- -> dijet + h at the center-of-mass energy Q=10.58 GeV. In addition to the next-to-next-to-leading order resummation of logarithms of 1-T, we include the next-to-leading order (NLO) nonsingular O(1-T) contribution to the cross section, the resummation of threshold logarithms of 1-z, and the leading nonperturbative contribution to the soft function. Our results for the correlations between fragmentation and the thrust cut are presented in a way that can be directly tested against B-factory data. These correlations are also observed in Pythia, but are surprisingly smaller at NLO.

Top-quark charge asymmetry with a jet handle

Pairs of top and antitop quarks are produced at the LHC to a large extent in association with a hard jet. We investigate the charge asymmetry in $t\overline{t}+j$ production in quantum chromodynamics (QCD) and with additional massive color-octet vector bosons. The total charge asymmetry at the LHC is suppressed by the large charge-symmetric background from gluon-gluon fusion. We show to what extent the asymmetry can be enhanced by suitable phase space cuts and, in particular, elaborate on the kinematics of the hard jet in the $t\overline{t}+j$ final state. We demonstrate that in QCD, the asymmetry amounts to 1.5% for central jets without an excessive reduction of the cross section. By applying additional kinematical cuts, the asymmetry can be enhanced to 4%, but at the cost of a strong reduction of the cross section. Massive color-octet states can generate sizeable effects in $t\overline{t}+j$ production, both on the charge asymmetry and on the cross section. The charge asymmetry probes both vector and axial-vector couplings to quarks. We show that massive color octets can generate asymmetries up to $\ifmmode\pm\else\textpm\fi{}10%$ for moderate and up to $\ifmmode\pm\else\textpm\fi{}30%$ for strong kinematical cuts to be used in experimental analyses at the LHC. Jet kinematics can be used to obtain further information about the nature of the couplings and thereby to discriminate between different models.

Neutron Decay with PERC: a Progress Report

The PERC collaboration will perform high-precision measurements of angular correlations in neutron beta decay at the beam facility MEPHISTO of the Forschungs-Neutronenquelle Heinz Maier-Leibnitz in Munich, Germany. The new beam station PERC, a clean, bright, and versatile source of neutron decay products, is designed to improve the sensitivity of neutron decay studies by one order of magnitude. The charged decay products are collected by a strong longitudinal magnetic field directly from inside a neutron guide. This combination provides the highest phase space density of decay products. A magnetic mirror serves to perform precise cuts in phase space, reducing related systematic errors. The new instrument PERC is under development by an international collaboration. The physics motivation, sensitivity, and applications of PERC as well as the status of the design and preliminary results on uncertainties in proton spectroscopy are presented in this paper.

Medium-induced parton splitting kernels from Soft Collinear Effective Theory with Glauber gluons

We derive the splitting kernels for partons produced in large Q2 scattering processes that subsequently traverse a region of strongly-interacting matter using a recently-developed effective theory SCETG. We include all corrections beyond the small-x approximation, consistent with the power counting of SCETG. We demonstrate how medium recoil, geometry and expansion scenarios, and phase space cuts can be implemented numerically for phenomenological applications. For the simplified case of infinite transverse momentum kinematics and a uniform medium, we provide closed-form analytic results that can be used to validate the numerical simulations.

Like-sign dimuon charge asymmetry at the Tevatron: Corrections fromBmeson fragmentation

The existing predictions for the like-sign dimuon charge asymmetry at the Tevatron are expressed in terms of parameters related to B mesons' mixing and inclusive production fractions. We show that in the realistic case when phase-space cuts are applied, the asymmetry depends also on the details of the production mechanism for the B mesons. In particular, it is sensitive to the difference in the fragmentation functions of B^0_d and B^0_s mesons. We estimate these fragmentation effects and find that they shift the theory prediction for this observable by approximately 10%. We also point out the approximately 20% sensitivity of the asymmetry depending on which set of values for the B meson production fractions is used: as measured at the Z pole or at the Tevatron. The impact of these effects on the extraction of A^s_{SL} from the D\O measurement is presented.

FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order

We introduce an improved version of the simulation code FEWZ ( Fully Exclusive W and Z Production) for hadron collider production of lepton pairs through the Drell–Yan process at next-to-next-to-leading order (NNLO) in the strong coupling constant. The program is fully differential in the phase space of leptons and additional hadronic radiation. The new version offers users significantly more options for customization. FEWZ now bins multiple, user-selectable histograms during a single run, and produces parton distribution function (PDF) errors automatically. It also features a significantly improved integration routine, and can take advantage of multiple processor cores locally or on the Condor distributed computing system. We illustrate the new features of FEWZ by presenting numerous phenomenological results for LHC physics. We compare NNLO QCD with initial ATLAS and CMS results, and discuss in detail the effects of detector acceptance on the measurement of angular quantities associated with Z-boson production. We address the issue of technical precision in the presence of severe phase-space cuts. Program summary Program title: FEWZ Catalogue identifier: AEJP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJP_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6 280 771 No. of bytes in distributed program, including test data, etc.: 173 027 645 Distribution format: tar.gz Programming language: Fortran 77, C++, Python Computer: Mac, PC Operating system: Mac OSX, Unix/Linux Has the code been vectorized or parallelized?: Yes. User-selectable, 1 to 219 RAM: 200 Mbytes for common parton distribution functions Classification: 11.1 External routines: CUBA numerical integration library, numerous parton distribution sets (see text); these are provided with the code. Nature of problem: Determination of the Drell–Yan Z / photon production cross section and decay into leptons, with kinematic distributions of leptons and jets including full spin correlations, at next-to-next-to-leading order in the strong coupling constant. Solution method: Virtual loop integrals are decomposed into master integrals using automated techniques. Singularities are extracted from real radiation terms via sector decomposition, which separates singularities and maps onto suitable phase space variables. Result is convoluted with parton distribution functions. Each piece is numerically integrated over phase space, which allows arbitrary cuts on the observed particles. Each sample point may be binned during numerical integration, providing histograms, and reweighted by parton distribution function error eigenvectors, which provides PDF errors. Restrictions: Output does not correspond to unweighted events, and cannot be interfaced with a shower Monte Carlo. Additional comments: !!!!! The distribution file for this program is over 170 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: One day for total cross sections with 0.1% integration errors assuming typical cuts, up to 1 week for smooth kinematic distributions with sub-percent integration errors for each bin.

Electroweak Sudakov logarithms and real gauge-boson radiation in the TeV region

Electroweak radiative corrections give rise to large negative, double-logarithmically enhanced corrections in the TeV region. These are partly compensated by real radiation and, moreover, affected by selecting isospin-noninvariant external states. We investigate the impact of real gauge boson radiation more quantitatively by considering different restricted final state configurations. We consider successively a massive abelian gauge theory, a spontaneously broken SU(2) theory and the electroweak Standard Model. We find that details of the choice of the phase space cuts, in particular whether a fraction of collinear and soft radiation is included, have a strong impact on the relative amount of real and virtual corrections.

Radiative corrections in K→π ℓ + ℓ − decays

We calculate radiative corrections to the flavor-changing neutral current process K --> pi l+ l-, both for charged and neutral kaon decays. While the soft-photon approximation is shown to work well for the muon channels, we discuss the necessity of further phase space cuts with electrons in the final state. It is also shown how to transfer our results to other decays such as eta --> gamma l+ l- or omega --> pi0 l+ l-.

Azimuthal angle correlations for Higgs boson plus multi-jet events

At lowest order in perturbation theory, the scattering matrix element for Higgs boson production in association with dijets displays a strong correlation in the azimuthal angle between the dijets, induced by the CP-properties of the Higgs Boson coupling. However, the phase space cuts necessary for a clean extraction of the CP-properties simultaneously induce large corrections from emissions of hard radiation and thus formation of extra jets. The current study concerns the generalization of CP-studies using the azimuthal angle between dijets beyond tree-level and to events with more than just two jets. By analyzing the High Energy Limit of hard scattering matrix elements we arrive at a set of cuts optimized to enhance the correlation, while maintaining a large cross section, and an observable, which is very stable against higher order corrections. We contrast the description of Higgs boson production in association with jets at different levels: for tree-level hjj and hjjj matrix elements, for hjj matrix elements plus parton shower, and in a recent all-order framework, which converges to the full, all-order perturbative result in the limit of large invariant mass between all produced particles.