High multiplicity processes with BlackHat and Sherpa
Jeppe R. Andersen, Stephanie Bartle, Zvi Bern, Fernando Febres Cordero, Stefan Höche, David A. Kosower, Harald Ita, Nicola Adriano Lo Presti, Daniel Maître, Kemal Ozeren
FFR-PHENO-2014-006 IPhT–t14/092 IPPP/14/62LPN14-081 SB/F/440–14 SLAC–PUB–16006 UCLA-14-TEP-105
High multiplicity processes with BlackHat andSherpa
Zvi Bern, Kemal Ozeren
Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547, USAE-mail: [email protected] , [email protected] Stefan Höche
SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USAE-mail: [email protected] , [email protected] Fernando Febres Cordero
Departamento de Física, Universidad Simón Bolívar, Caracas 1080A, VenezuelaE-mail: [email protected]
Harald Ita
Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, D-79104 Freiburg, GermanyE-mail: [email protected]
David Kosower, Nicola Adriano Lo Presti
Institut de Physique Théorique, CEA–Saclay, F–91191 Gif-sur-Yvette cedex, FranceE-mail: [email protected] , [email protected] Stephanie Bartle, Jeppe R. Andersen, Daniel Maître ∗ Institute for Particle Physics Phenomenology, Department of Physics, University of Durham,DH1 3LE, UKE-mail: [email protected] , [email protected] , [email protected] In this contribution, we present an intermediate storage format for next-to-leading order (NLO)events and explain the advantages of presenting a NLO calculation in this format. We also presentsome recent applications, including the calculation of PDF uncertainties and the combination ofdifferent multiplicity samples for the prediction of gap fractions in inclusive dijet events.
Loops and Legs in Quantum Field Theory - LL 2014,27 April - 2 May 2014Weimar, Germany ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ a r X i v : . [ h e p - ph ] J u l igh multiplicity processes with BlackHat and Sherpa Daniel Maître
1. Introduction
In recent years much progress has been achieved in the calculation of QCD predictions tonext-to-leading order (NLO) accuracy (for a summary, see ref. [1]). Even with these advances,high-multiplicity processes, though now feasible, remain computationally expensive. In this con-tribution, we report on a method of using specialized event files, which we call n -tuple files, toreduce the cost of fixed-order NLO calculations. This is important as more and more techniquessuch as NLO parton-shower matching and merging use them as an input. For example, the eventfiles described in this contribution have been used within the LoopSim method [2] to merge NLOcalculations for Z+1 jet and Z+2 jets [3]. In the next section we describe the n -tuple files and alibrary for their use. In the third section we show some applications of the n -tuple files.
2. n-Tuples
Next-to-Leading Order (NLO) calculations are computationally intensive, which means thatunder normal circumstances computing new observables with new cuts is a tedious task. Themost computationally demanding part is the calculation of the matrix elements; other operationssuch as jet clustering, the evaluation of the parton distribution functions and the calculation of theobservables are relatively cheap. We can amortize the cost of the matrix element calculation bystoring the matrix elements and the phase-space information along with a few coefficients of thelogarithms driving the scale dependence in a file. These files can then be re-read to obtain ananalysis with different cuts or observables, or to yield the result one would have obtained witha different PDF or a different choice of renormalization or factorization scale. This is especiallyuseful when computing PDF uncertainties that would otherwise require the same matrix elementto be recomputed a large number of times.The ROOT [4] format has been chosen as a backend to store the matrix elements and asso-ciated information. Table 1 details the hadronic center of mass energy and minimum transversemomentum cuts applied on the jets for each processes available in the n -tuple format. Detailsabout the calculation for the creation of these files can be found in refs. [5, 6, 7, 8, 9, 10, 11].NLO event files such as the one we describe here and in ref. [12] have the added advantage ofmaking it easier to communicate challenging NLO computations with the experimental community.Along with the n -tuple files we provide a C++ library for accessing the information they con-tain. It can either be used out of the box or as a template for a dedicated implementation in adifferent framework. The library also provides a python interface. Figure 1 shows an example ofthe usage of the library to read a n -tuple file (and in this case display the stored momenta insteadof using them to compute an observable or verifying that this particular event passes the analy-sis cuts.) Figure 2 shows an example of the usage of the library to change the factorization andrenormalization scale for a new prediction.In t next section we present some applications of this method that would have been too pro-hibitive in CPU time to perform using straightforward repeated evaluation of the matrix elements.2 igh multiplicity processes with BlackHat and Sherpa Daniel Maître import nTupleReader as NRr=NR.nTupleReader()r.addFile("sample.root")while r.nextEntry():for i in range(r.getParticleNumber()):print "p(%d)=(%f,%f,%f,%f)" % (i,r.getEnergy(i),r.getX(i),r.getY(i),r.getZ(i))
Figure 1:
Example of the usage of the nTupleReader library. The example uses the python interface of thelibrary. import nTupleReader as NRr=NR.nTupleReader()r.addFile("sample.root")r.setPDF("CT10nlo.LHgrid")r.setPDFmember(12)while r.nextEntry():
Figure 2:
Example of the usage of change of scales using the nTupleReader library. The example uses thepython interface of the library. igh multiplicity processes with BlackHat and Sherpa Daniel Maître
Process energy pt cut W + ( → e + ν e ) + , , , W + ( → e + ν e ) + , , W − ( → e − ¯ ν e ) + , , , W − ( → e − ¯ ν e ) + , , Z ( → e + e − ) + , Z ( → e + e − ) + , Z ( → e + e − ) + , , n jets ( n = , , ,
4) 7 TeV 40 GeV n jets ( n = , , ,
4) 8 TeV 40 GeV
Table 1:
Available processes at NLO. The decay of the vector boson into a lepton pair is always included.
3. Applications
Understanding the impact of jet vetoes is very important for current Higgs studies. The behav-ior of observables when a jet veto is applied can be investigated in processes that are under bettertheoretical control than Higgs production. New calculations or techniques can be checked againstdata for simpler processes and that knowledge can be used to improve the our understanding ofHiggs or BSM measurements. One interesting observable for the investigation of jet veto efficien-cies is the gap fraction g , which is defined as the probability of having no jet above a threshold Q between the two tagging jets: g = σ Y / pt ( Q ) σ tot where σ Y / p T ( Q ) is the cross section when vetoing jets with both transverse momentum above thethreshold Q and rapidity between that of the tagging jets. These can be either the two highesttransverse momentum jets ( σ p T ) or the most forward/backward ones ( σ Y ). σ tot is the total crosssection without the jet veto. We use the notation σ g = n , σ g ≥ n to denote the cross section with exactly n jets in the gap , or n jets or more in the gap, respectively.Restricting the precision of the fixed order prediction to NLO, one can give a prediction forthe gap fraction in two different ways. First, one could use only one NLO calculation for each ofthe numerator or denominator: g = σ g = σ tot = − σ g ≥ σ tot = − σ nlo , j ≥ g ≥ σ nlo , j ≥ = − σ nlo , j ≥ − σ nlo , j = g = − σ lo , j = g = σ nlo , j ≥ . (3.1)Alternatively one can try to use more NLO calculations g = σ g = σ tot = σ nlo , j = g = + σ nlo , j = g = + σ nlo , j ≥ g = σ nlo , j = + σ nlo , j = + σ nlo , j ≥ . (3.2)4 igh multiplicity processes with BlackHat and Sherpa Daniel Maître
Figure 3:
Each dot represent a possible contribution.
The two formulae are formally of the same order. Figure 3 illustrates the different contributionsin the plane spanned by the number of jets and the number of jets in the gap. Each term in theformulae above can be identified in this plane.The left pane of figure 4 shows the gap fraction as a function of the rapidity separation ofthe tagging jets. The different sets of curves correspond to different bins in the average transversemomentum of the two tagging jets ¯ p T . Each set of curves is offset with respect to the lower ¯ p T setby 0 .
5. The bins are 240 GeV < ¯ p T <
270 GeV210 GeV < ¯ p T <
240 GeV180 GeV < ¯ p T <
210 GeV150 GeV < ¯ p T <
180 GeV120 GeV < ¯ p T <
150 GeV90 GeV < ¯ p T <
120 GeV70 GeV < ¯ p T <
90 GeV (3.3)The data points are from the ATLAS measurement [13]. We provide theoretical predictions ob-tained using HEJ [14, 15, 16] and NLO predictions obtained by BlackHat+Sherpa [17, 11, 18, 19,20, 21].The right pane of figure 4 shows the ratio to the data for each ¯ p T bin. The green band representsthe HEJ prediction while the blue and red curves correspond to the NLO predictions of formulae(3.1) and (3.2), respectively. The bands represent only the statistical Monte Carlo integration errors. PDF uncertainties are usually computationally intensive, as the same calculation has to be5 igh multiplicity processes with BlackHat and Sherpa
Daniel Maître
Figure 4:
Gap fraction as a function of ∆ y for various slices of ¯ p T . The jets defining ¯ p T and ∆ y are the twojets with the largest p T . preformed with a large number of slightly different PDF fits. Using n -tuple files the expensivepart of the calculation need be performed only once (and in this case it had been done previously,so we get the results at almost no computational cost). Figure 5 shows the ratio of the first jettransverse momentum in W − +4 jets and W + + 4 jets. This ratio is evaluated for different PDFsand the associated uncertainties are shown in the lower pane. We have used the NNPDF21 [22],MSTW2008 [23], CT10 [24] and ABM11 [25] PDF sets. The bands for NNPDF provides the 1- σ error bands, for MSTW2008 we used the 68% confidence level uncertainty estimate, for CT10 thebands represent the 90% confidence level uncertainty estimate. The errors provided with the ABMset represent a 1- σ deviation from the best fit. Figure 6 shows the rapidity of the second jet inevents with a Z boson and 4 jets.
4. Conclusions
In this contribution we have described a format for NLO events and shown some applications.
Acknowledgments
This research was supported by the US Department of Energy under contracts DE–AC02–76SF00515 and DE-FG02-13ER42022. DAK and NALP’s research is supported by the European6 igh multiplicity processes with BlackHat and Sherpa
Daniel Maître
Figure 5: W − +4 jets to W + + 4 jets ratio for the first jet transverse momentum for different PDF sets. Thelower pane shows the ratio to the NNPDF prediction. The different color bands display the uncertainties. Research Council under Advanced Investigator Grant ERC–AdG–228301. DM’s work was sup-ported by the Research Executive Agency (REA) of the European Union under the Grant Agree-ment number PITN–GA–2010–264564 (LHCPhenoNet). SH’s work was partly supported by agrant from the US LHC Theory Initiative through NSF contract PHY–0705682. This research usedresources of Academic Technology Services at UCLA, and of the National Energy Research Sci-entific Computing Center, which is supported by the Office of Science of the U.S. Department ofEnergy under Contract No. DE–AC02–05CH11231.
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