## Tools & Toys

## AutoDipole - Automated generation of dipole subtraction terms

The package implements the Catani-Seymour subtraction method used to handle

collinear and soft singularities in real corrections.

Written by: K. Hasegawa, S. Moch, P.Uwer

Published in: **Comput.Phys.Commun.181:1802-1817,2010**

e-Print Archive: **arXiv:0911.4371**

The AutoDipole package can be downloaded **here.**

Lectures notes from a presentation at the "Computer Algebra and Particle Physics 2009"

(CAPP 2009) school can be found ** here**.

## CANONICA - Algorithmic transformation of multi-loop master integrals to a canonical basis

The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. CANONICA implements a recently developed algorithm to automatize the transformation to a canonical basis. The transformation is computed by expanding the transformation law in the regulator and solving the resulting equations with a rational ansatz. CANONICA is applicable to differential equations depending on multiple scales.

The algorithm implemented in CANONICA has been described in **arXiv:1611.01087**.

eprint: **arXiv:1705.06252**

The package can be downloaded **here** (md5sum: fb246b68a98ff68cc9607fdfeebbd789)

For the most recent version also check https://github.com/christophmeyer/CANONICA

## HATHOR - HAdronic Top and Heavy quarks crOss section calculatoR

Hathor calculates the total cross section for top-quark pair production in hadronic collisions.

The program takes into account recent theoretical developments such as approximate

next-to-next-to-leading order perturbative QCD corrections and it allows for studies of

the theoretical uncertainty by separate variations of the factorization and renormalization

scales. In addition it offers the possibility to obtain the cross section as a function of the

running top-quark mass. A GUI to simplify the usage is included as well.

Written by: M. Aliev, H. Lacker, U. Langenfeld, S. Moch, P. Uwer and M. Wiedermann

Published in: – HATHOR – HAdronic Top and Heavy quarks crOss section calculatoR

**Comput.Phys.Commun.182:1034-1046,2011**

e-Print archive: **arXiv: 1007.1327**

The latest version of Hathor can be obtained **here**.

## ICE - the Integration-By-Parts Chooser of Equations

In multiloop calculations, when reducing a set of scalar integrals to master integrals, one often faces the problem that the Integration-By-Parts (IBP) and Lorentz Invariance (LI) identities used in the reduction are not linearly independent. Consequently, much time

is spent processing redundant information.

ICE implements a simple Monte Carlo algorithm that identifies a maximal linearly independent set of IBP and/or LI identities. It is meant to be used prior to a reduction with Laporta's Algorithm.

Written by: P. Kant

e-Print Archive: **arXiv:1309.7287**

The package can be downloaded** here**

## Kira - A Feynman Integral Reduction Program

With Kira, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. The algorithmic improvements lead to a significant increase in the performance with respect to previously available programs.

Written by: Philipp Maierhoefer, Johann Usovitsch, Peter Uwer

Published in:

eprint: **arXiv:1705.05610**

The latest Kira version 1.1 has been released on 26.04.2018 and can be obtained **here**

## NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes

We present a computer library for the numerical evaluation of colour-ordered n-gluon

amplitudes at one-loop order in pure Yang-Mills theory. The library uses the recently developed

technique of generalised unitarity. Running in double precision the library yields

reliable results for up to 14 gluons with only a small fraction of events requiring a

re-evaluation using extended floating point arithmetic. We believe that the library presented

here provides an important contribution to future LHC phenomenology. The program may also prove

useful in cross checking results obtained by other methods. In addition the code provides a

sample implementation which may serve as a starting point for further developments

Written by: S. Badger, B. Biedermann and P.Uwer

Published in: NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes

**Comput.Phys.Commun.182:1674-1692,2011**

e-print archive: **arXiv1011.2900**

**NGluon-1.0** can be obtained **here** (md5sum: 38ffeb1edae261ab35ec01a6d668ded8)

On some operating systems the file system cannot distinguish between files called NGluon.cpp and ngluon.cpp. On these systems version 1.0 will not compile. To address this issue we have renamed in version NGluon-1.1 the source file ngluon.cpp into NGluon-demo.cpp. The corresponding executable is now NGluon-demo.

**NGluon-1.1** can be obtained **here** (md5sum: 69f53091d2f64651ed6d32ad0593c6ff).

## NJET -- Numerical evaluation of virtual corrections to multi-jet production in massless QCD.

The NJET package allows the computation of QCD scattering amplitudes including massless quarks at next-to-leading order (NLO) accuracy. As basic building blocs the library calculates primitive amplitudes involving gluons and massless quarks. The multiplicity of the primitive amplitudes is only restricted by numerical accuracy and runtime. Extended precision arithmetics can be used to improve the numerical accuracy. In addition, the package provides explicit results for all color summed squared matrix elements required for four jet and five jet production in hadronic collisions at NLO accuracy. The package has been applied recently to calculate the four jet production at NLO accuracy.

Written by: S.Badger, B.Biedermann, P.Uwer, V.Yundin

Published in: "Numerical evaluation of virtual corrections to multi-jet production in massless QCD", **arXiv:1209.0100**

The calculation of the four jet cross section is described in "NLO QCD corrections to multi-jet production at the LHC with a centre-of-mass energy of sqrt(s)=8 TeV", **arXiv:1209.0098**

**NJET** can be obtained **here**.

More information can also be found at **https://bitbucket.org/njet/njet/**

## XSummer - Transcendental Functions and Symbolic Summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. XSummer implements several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

Written by S. Moch, P. Uwer.

Published in: **Comput.Phys.Commun.174:759-770,2006**

e-Print Archive: **math-ph/0508008**

The package can be downloaded **here**

## EasyNData

EasyNData allows an easy extraction of numerical values from published plots. The EasyNData package can be downloaded **here** as EasyNData.zip The zip-file includes the program code **EasyNData.jar**, two examples as well as a short description of the program. The most recent description of the program be found **here** as pdffile. An older version is available **here**. The program alone can be obtained also as **EasyNData.jar**. To run the program call java -jar EasyNData.jar and follow the instructions outlined in the documentation. Note that the installed Java(TM) version has to be 1.5.0 or later.

No warranty on the correctness of the program is given and use is at own risk.