# NLO Multi-leg

### From Wiki Les Houches 09

**Les Houches topics for WG1 (Standard Model and NLO Multi-leg: Session 1 only)**

## Contents |

## **People in Subgroups working on four main topics**

- Observables
- Higgs phenomenology
- New HO calculations/wish list
- NLO techniques/Standardization/automation
- NLO/PS Matching (Joint with MC group)

## **Contributions expected for writeup**

1) Roberto Pittau <pittau@ugr.es>

Title: "A NLO study of ttH -> ttbb Signal versus ttbb Background"

Description: A few distributions are compared, at the NLO accuracy, between signal and background for the production process of Higgs in association with 2 top quarks. The ttH -> ttbb Signal is computed exactly in the framework of the Helac-1L/CutTools/Helac-Dipole System.

Contributors: G. Bevilacqua, M. Czakon, M.V. Garzelli, C.G. Papadopoulos, R. Pittau, M. Worek

Category: 3) New HO calculations/wish list Length estimate: 4-5 pages

(Note: may be combined with tTH/tTbB contributions listed below.)

2) Simon Badger <badger@ifh.de>

Ruth, Pierpaolo and I would like to contribute a brief section on new advances in analytic calculations for one-loop amplitudes. Clearly it would fit best into the NLO techniques category. I think it would be around 3 pages at most.

The planned outline would be:

"Recent advance in analytic computations of one-loop amplitudes"

- overview of developments since the last Les Houches report:

Spinor integration for closed forms integral coefficients for D-dimnesional cuts with full mass dependence. Forde's direct extraction technique generalisation to masses and extension to D-dimensional cuts. Complex analysis: Cauchy's and Stoke's theorem in triple and double cuts. Single cuts for full gluonic amplitudes.

- Direct computation of tadpole coefficients

A brief overview of the spinor integration approach to tadpole extraction through double cuts.

- Compact analytic expressions for one-loop Higgs plus 2 jets amplitudes

Review the recently completed program for the calculation of all helicity amplitudes for H+2 jet production at Hadron colliders. The final results are extremely compact and are considerably faster to evaluate than the previous semi-numerical code.

Category: 4) NLO techniques/Standardization/Automation Length: 3 pages

3) Achilles Lazopoulos achilleas <lazopoli@phys.ethz.ch>

In response to Joey Huston's email, I would be interested to contribute a very small section on my own fork of D-dimensional unitarity. I've been working on an implementation that can deliver the virtual part of an NLO QCD calculation for a process with an arbitrary number of fermions and gluons (in the direction of 4 jet production) and the code is ready and tested at the moment. Assuming that Giulia will cover the description of the algorithm proposed by Ellis, Giele, Kunszt and Melnikov, I would only need to describe the technical differences between that and what I am doing, in a paragraph or so. Let me know if you think the group would be interested in such a contribution.

Category: 3) NLO techniques/Standardizaton/Automation Length: 3 pages

4) Radja Boughezal <radja.boughezal@physik.uzh.ch>

Title: QCD-electroweak effects and a new prediction for Higgs production in gluon fusion within the SM

We present updated predictions for the inclusive Higgs boson production cross section at the Tevatron and the LHC within the Standard Model, accounting for all the new theoretical calculations and the newest MSTW PDFs. We also discuss the recent derivation of the three-loop ${\cal O}(\alpha\alpha_s)$ contribution to this process.

Category: 3) New HO calculations/wish list Length: 5 pages

5) Isabella Bierenbaum, G. Rodrigo

Title: FIRST STEPS TOWARDS A DUALITY RELATION AT TWO LOOPS

Abstract: We illustrate a duality relation between one--loop integrals and single-cut phase--space integrals. This duality relation is realized by a Lorentz covariant modification of the customary $+i0$ prescription of the Feynman propagators and can be extended to generic one--loop quantities, such as Green's functions, in any relativistic, local and unitary field theories. Additionally, we comment on first steps towards a two--loop duality relation. (submitted, 2p.)

Category: 4) NLO techniques/Standardization/Automation Length: 2 pages

6) Max Huber <maxh@mppmu.mpg.de>

Example implementation of an EW MC/OLP interface between SHERPA and PPLL

Abstract: We describe an interface between the monte carlo program {\sc SHERPA} \cite{Gleisberg:2008ta} (MC) and the one-loop amplitude program {\sc PPLL} \cite{Dittmaier:2009cr} (OLP) for the calculation of electroweak next-to-leading order corrections to the neutral-current Drell--Yan processes.

Page estimate: 4-6 pages ( is this too long/short? )

Contributors: Stefan Dittmaier, Jennifer Archibald, Frank Krauss

Category: 5) NLO/PS Matching Length: 5 pages

7) Title: All-order results for multiparton QCD amplitudes

Contributors: Lorenzo Magnea, Einan Gardi, (Lance Dixon)

As to category, this would best fit with NNLO stuff, which however I don't see in the outline, otherwise it is certainly a `New (very) HO calculation', though I'm not sure whether it is on any experimenter's wish list .. :-)

Category: 3) New HO calculations/wish list Length: 5 pages

8) Title: "Tuned comparison of NLO QCD corrections to $ZZ{+}jet$ production at hadron colliders"

Description: comparison/validation of NLO calculations for a process on the wishlist carried out by two groups

Contributors:Thomas Binoth, Tanju Gleisberg, Stefan Karg, Nikolas Kauer and Stefan Dittmaier, Stefan Kallweit, Peter Uwer

category: 3) New HO calculations/wish list Length: 5 pages

9) Rikkert Frederix <frederix@physik.uzh.ch>

Subject: Les Houches proceedings MadFKS -- BlackHat & Rocket

I would like to contribute (together with Giulia and Daniel) by writing a small section about how we got the interface working between MadFKS and BlackHat and Rocket. Is there already some sort of draft version to put in the proceedings, so that our contribution would be simply some small section in it? Or should I write it from scratch, including introduction to the interface etc? Is there also space to show some results/plots that it's really working, or should this be in a separate section, or even write-up?

Contributors: Rikkert Frederix, Daniel Maitre, Giulia Zanderighi

Category: 5) NLO/PS Matching Length: 7 pages

10) Markus Warsinsky <Markus.Warsinsky@physik.uni-freiburg.de>

Stefan Dittmaier and I would like to contribute with the study I showed at Les Houches about reweighting the Higgs pt in VBF - I redid this with increased statistics.

Title (might change after discussion): Reweighting of distributions in parton-shower Monte Carlos to next-to-leading order calculations in Higgs production in Vector boson fusion.

Outline:

- Introduction
- Setup
- Comparison of Herwig to LO prediction
- Reweighting
- Comparison of reweighted result with NLO prediction
- Conclusions and Outlook

The page count is difficult to assess right now, since it will be quite some figures, but I would expect around 6 to 8 pages.

Contributors: Stefan Dittmaier, Makus Warsinsky

Category: 1) Observables Length: 8 pages

11) Guenther Dissertori <guenther.dissertori@cern.ch>

from "my" side I would like to announce the following contributions:

1) a summary of the recent alpha_s measurements/studies at NNLO in e+e-.

Gudrun Heinrich offered to prepare a draft soon.

2) a summary of the NNLO studies (both for LHC and Tevatron) in H->WW->lnulu,

by Anastasiou, Stoeckli and myself.

Contributors:Babis Anastasiou, Guenther Dissertori, Gudren Heinrich, Fabian Stockli

Category: 1) Observables Length: 15 pages

12) Maria Vittoria Garzelli <garzelli@to.infn.it>

as for the Les Houches proceedings, if possible, I would like to present a contribution on the rational term calculation in 1-loop amplitudes,in the Subsection 4, concerning new NLO techniques and automation.

M.V. Garzelli and I. Malamos "Analytical calculation of the rational part of 1-loop amplitudes: the R2 contribution"

Tentative Abstract: Unitarity inspired techniques allow to reconstruct in a straighforward way the cut-constructible part of 1-loop amplitudes, by means of algebraic reduction methods, implemented in numerical codes. However, a residual part, made by rational terms, cannot be obtained simply by cuts and has to be calculated separately, at least when working in 4 integer dimensions. In the framework of the OPP method, the rational terms have been classified in two groups, according to their origin. The contribution of one of these classes, called R2, can be calculated fully analytically. In this contribution we discuss the effective Feynman rules we have obtained in the Standard Model, needed at this aim.

Contributors: M. Garzelli and I. Malamos

Category: 4) NLO techniques/Standardization/Automation Length: 4 pages

13) Reinhard Schwienhorst <schwier@pa.msu.edu>

Rikker, Fabio, and I wrote a little note comparing their MCFM t-channel 2->3 NLO generator distributions to the CompHEP+Pythia samples used in the D0 single top analysis. We would like to add this text to the writeup. It's only 2.5 pages.

Category: I think 1 or 5 Contributors: Reinhard Schwienhorst, Rikkert Frederix, Fabio Maltoni

Title: Comparison of single top t-channel 2->3 production at NLO with CompHEP-Pythia

Outline: We compare t-channel single top samples between the CompHEP generator interfaced to Pythia and the 2-to-3 NLO calculation in MCFM. We compare the kinematic distributions of the spectator b-quark from gluon splitting. We find good agreement between the 2-to-3 NLO calculation and the Pythia output.

Contributors: Rikkert Frederix, Fabio Maltoni, Reinhardt Schwienhorst

Length: 3 pages Category: 1) Observables

14) Thomas Reiter <thomasr@nikhef.nl>

I would like to propose a contribution in the category "NLO techniques/Standardization/automation" about the efforts of the GOLEM group.

TITLE (preliminary): Recent developments of GOLEM OUTLINE: We report on the the recent progress to important NLO caluclations (qQ>bBbB, pp>ZZj) made using Golem technology. We discuss different possible strategies within the Golem framework (analytic vs. semi-numeric) and the required tools which have been developed by our collaboration, such as the integral library Golem95. CONTRIBUTORS (preliminary): Thomas Binoth, Gavin Cullen, Nicolas Greiner, Alberto Guffanti, Jean-Philippe Guillet, Gudrun Heinrich, Stefan Karg, Nikolas Kauer, Thomas Reiter, J\"urgen Reuter, Mark Rodgers, Ioan Wigmore

Length: 5 pages Category: 4) NLO techniques/Standardization/Automation

(1) Comparisons of W + 3 jet predictions for the LHC (J. Huston, D. Maitre, G. Zanderighi); I'm working with Daniel and Giula to compare LO/NLO predictions at 10 TeV from the Blackhat and Rocket programs. In particular, I'd like to understand the connections between using HT as a global scale and <kT_branch> as a local scale in producing kinematics shapes at LO similar to those at NLO. I will also add to this the study I did of the dependence of K-factors on jet algorithm and parton multiplicity.

(2) Implementations of the Frixione isolation scheme in theory and data: (L. Carminati, S. Gascon-Shotkin, S. Frixione, J-P Guillet, G. Heinrich, J. Huston, K. Mazumdar, et al (probably others, but forgetting them at the moment); we have had a series of discussions about the implementation of the Frixione isolation scheme. This has been carried out both in ATLAS/CMS Monte Carlo as well as in a modification of the 'Phox' family of programs. The contribution will summarize what has been learned and if possible comparison of Monte Carlo and theory predictions.

(3) Heavy flavor benchmarking of PDF codes; (S. Forte, J. Huston, P. Nadolsky, J. Rojo, et al); this will be an attempt to carry out benchmark comparisons of heavy quark schemes in PDF fitting. At the least, we will compare NNPDF to CTEQ, but will try to involve MSTW and perhaps Alekhin.

(4) PDF and alpha_s uncertainties: (S. Forte, J. Huston, J. Rojo et al); both groups have carried out a study of the impact of alpha_s uncertainties on PDF uncertainties for cross sections at the LHC; we find that the alpha_s uncertainties are (1) smaller than the intrinsic PDF uncertainties due to experimental uncertainties in the global fits and (2) uncorrelated with the experimental uncertainties. Thus, the alpha_s uncertainties can be added in quadrature to the normal PDF uncertainties. This is the opposite conclusion arrived at by the MSTW group due to (1) their using a wide range for the uncertainty of alpha_s (including a central value at the edge of the world average uncertainty) and (2) a smaller intrinsic experimental PDF uncertainty than either CTEQ or NNPDF.

(5) studies of tTbB and tTH; this of course overlaps with Roberto's contribution and may involve calculations of tTH(->bB) at NLO from other groups, but we would like to get some experimental inputs/conclusions as well. It hasn't progressed as well as I would like from the experimental side, but I'll try to do some more prodding.

(6) wishlist additions/discussion; I thought we could add this to the introduction

(7)Â Â Standardization of ROOT output format for parton level programs (J. Campbell, J. Huston, P. Nadolsky, F-P. Schilling, J. Weng); Generalization of the FROOT output format currently used in MCFM. There are a few new features, including pointers between events and counter-events in the ntuple file so that statistical error for NLO cross sections can be calculated. Five pages or less is probably sufficient.

- 25 p.

Thomas Binoth <binoth@ph.ed.ac.uk>

MC/NLO interface write-up 25pages (shared with MC) long author list.

## **Les Houches accord on a MC/OLP interface**

**Proposal for a standard interface between LO Monte-Carlo tools and One-Loop-Programs (OLPs)**

A view slides which motivate the discussion on standardization can be found here (June 2009) [[1]]. The starting point for a concrete MC/OLP interface was provided by Tanju Gleisberg and Daniel Maitre in this Draft (June 2009).

After extensive discussions and exchange of ideas we have formulated this (preliminary) proposal [[2]] for a MC/OLP interface in December 2009. Several groups and individuals have provided input for this document and work on implementations now. First working examples are expected to be documented in the Les Houches proceedings. We will try to collect relevant program fragments on the Wiki pages which may serve as guidelines and help for users and providers of MCs and OLPs.

If you want to provide any feedback or input for this initiative feel free to contact me, thomas.binoth@ed.ac.uk, or any author of the document.

## **Original list of identified topics for the NLM working group**

**1. Collecting results of completed higher order calculations**

The primary idea is to collect in a table the cross section predictions for relevant LHC processes where available. Tree-level results should be compared with higher order
predictions (whatever is known) and K-factors defined for specific scale/pdf choices. The table should also contain information on scale and pdf uncertainties. The inclusive case may be compared with standard selection cuts.

Producing such a table would, of course, include a detailed comparison of results originating from different groups.

A collection of plots showing distributions of relevant observables comparing tree and higher order corrections may also be compiled.

A common format for storing parton-level event information in a ROOT-ntuple should be developed; the ntuples would contain the 4-vector information for the final-state particles, the weight for the central pdf as well as the weights for the error pdf's (such as from CTEQ6.6), the LO weight for the event, and possibly the event weights for different choices of renormalization/factorization scale. A scheme for storing such ntuples for higher order processes in accessible locations (CASTOR at CERN, ENSTORE at Fermilab for example) should be developed.

See also item 5.

**2. Higgs cross sections in and beyond the Standard Model**

This issue is too important to be just a sub-part of point 1. Note that in former workshops a separate Higgs working group did exist. Special attention will be given to higher
order corrections of Higgs observables in BSM scenarios (coordinated with the BSM group).

**3. Identifying/analysing observables of interest**

Of special interest are observables which have an improved scale dependence, e.g. ratios of cross sections. Classical examples are W/Z and the dijet ratio. New ideas and proposals
are welcome.

Another issue is to identify jet observables which have no strong dependence on the absolute jet energy, as this will not be measured very precisely during the early running. Recent examples are jet sub-structure, boosted tops, dijet delta-phi de-correlation... This topic has some overlap with the BSM searches and inter-group activity would be welcome.

**4. Identifying important missing processes**

The Les Houches wishlist from 2005/2007 is filling up slowly but progressively. Progress should be reported and a discussion should identify which key processes should be added to
the list. This may also include relevant NNLO corrections. This effort will result in an updated Les Houches list.

**5. Standardization of NLO computations**

A standarization of NLO computations has, of course, may aspects. Different groups would benefit from the possibility to use and exchange different public symbolic/numerical routines to
perform computations. Given the boost such an initiative may induce in the field, such a discussion is highly relevant. An agreement to submit results/tools/code to certain databases for
storing and accessing (e.g. under HEPTOOLS, HEPCode web pages) would already be progress, but is only one aspect of the issue.

For NLO computations, there is a natural split between real and virtual corrections. One could agree on finite output formats for both sectors, such that event re-weighting functions could be defined which could be used in combination with existing event ntuples and/or in combination with (semi-)automated matching of NLO to parton showers (with Tools and Monte Carlo group).

In many cases, it is relatively easy, a priori, to isolate the scale-dependent terms for a higher order cross section. If the scale-dependent terms are isolated in such a fashion, it may be possible to easily calculate/store the scale uncertainties as discussed in item 1.

**6. IR-safe jet algorithms**

Detailed understanding of jet algorithms will play an important role in the LHC era. Much progress has been made in the last several years concerning IR-safe jet algorithms. Studies and
comparisons of different jet algorithms in the NLO context are highly welcome. Of particular interest is how the observables map from the parton level inherent in the pQCD approach to
the particle/detector level.

**7. New techniques for NLO computations and automation**

New techniques (based on unitarity and/or Feynman diagrams) may be compared concerning both efficiency and their potential for automation. Recent developments concerning automated
IR-subtraction indicate that the NLO real emission can be treated in a very general manner, independent from the loop part by using tools such as SHERPA, Whizard, Helac, Madgraph, etc.
Communication with the Monte Carlo group will be very important here.

**8. Combination of NLO with parton showers**

The combination of NLO parton level calculations with parton showers (e.g. MC@NLO, POWHEG, GRACE...) is an important issue for the development of higher order Monte Carlo tools for
the LHC. Again, this will be in collaboration with the Monte Carlo working group.

**Comments on a Les Houches accord on standardisation of NLO computations**

The demand for precise predictions for LHC phenomenology has lead to remarkable progress in the last two years. Monte Carlo programs based on efficient matrix element event generators are on the market which can deal now with multi partonic final states of order 10 particles. Sophisticated methods like multi-channeling, colour and helicity sampling, etc. allow for efficient and numerically stable phase space integration.

The combination with parton showers needs merging procedures which relate soft/collinear and hard phase space regions whit each other, an issue which will be discussed extensively in the Monte Carlo group.

It is very interesting to note that if one wants to promote general purpose Monte Carlo tools to next-to-leading order (NLO) precision, mainly two features have to be added to the developed tree-level technology.

1) Soft/collinear subtraction terms to reshuffle infrared (IR) divergences between tree- and loop-level NLO contributions.

2) A reliable method to evaluate one-loop amplitudes

ad 1) several groups incorporate now dipole subtraction terms a la Catani-Seymour in their ME generators which guarantees highly efficient evaluation phase space integration and an automated frame work.

ad 2) Both the unitarity based and the Feynman diagrammatic approach are capable to evaluate one-loop 2->4 matrix elements. The used algorithms are thus validated and the production of many results along the same line is feasible.

It seems to be exactly the right time to start the discussion on how to combine the tree- and loop-level developments into a more unified and standardised framework before the different NLO groups start their result production phase. It is evident that synergies between the two fields would speed up phenomenological progress substantially. One should just think about how often the wheel has been reinvented in the context of amplitude evaluation and phase space integration!

To promote NLO matrix elements into transportable code which can easily be incorporated into a ME set-up only a very limited number of conventions have to be fixed. In detail the I/O handling of

- 4-vectors
- (Standard) Model parameters
- colour information
- helicity information
- UV treatment
- IR treatment

has to be agreed on.

Note that concerning quantum numbers a loop amplitude corresponds to its LO counterpart. An agreement on certain "industrial standards" must of course not hinder or complicate in any way scientific progress. Using a switch for different information levels would allow for flexibility, e.g. if some groups might just want to provide colour/helicity summed IR/UV subtracted amplitudes this should be of course possible.

We would like to encourage everybody in the NLM and MC working group to discuss these issues at Les Houches with the aim to come to an agreement on how to pass efficiently results in form of transportable computer codes. This would open the door and would be an important step towards a phenomenological description of LHC data at the next-to-leading order level.

The NLM conveners