A summary is given of the current status of the next-to-leading order (NLO)
parton-level integrator MCFM. Some details are given about the Higgs + 2-jet
process and the production and decay of $t \bar{t}$, both of which have
recently been added to the code. Using MCFM, comparisons between the Tevatron
running at $\sqrt{s}=2$~TeV and the LHC running at $\sqrt{s}=7$~TeV are made
for standard model process including the production of Higgs bosons. The case
for running the Tevatron until 16fb$^{-1}$ are accumulated by both detectors is
sketched.Comment: Talk presented by R.K Ellis at Loops and Legs in Quantum Field Theory
  2010, Woerlitz, Germany, April 25-30, 2010, (6 pages and 4 figures

Campbell, John M

Ellis, R. K.

English

arXiv

A summary is given of the current status of the next-to-leading order (NLO) parton-level integrator MCFM. Some details are given about the Higgs + 2-jet process and the production and decay of t{bar t}, both of which have recently been added to the code. Using MCFM, comparisons between the Tevatron running at {radical}s = 2 TeV and the LHC running at {radical}s = 7 TeV are made for standard model process including the production of Higgs bosons. The case for running the Tevatron until 16fb{sup -1} are accumulated by both detectors is sketched

Campbell, John M.

Ellis, R.K.

UNT (University of North Texas) Digital Library

arXiv:1007.3492v1  [hep-ph]  20 Jul 2010FERMILAB-CONF-10-244-TMCFM for the Tevatron and the LHCJohn M. Campbella and R. K. EllisaaFermilab, P.O. Box 500, Batavia, IL 60510, USAA summary is given of the current status of the next-to-leading order (NLO) parton-level integrator MCFM.Some details are given about the Higgs + 2-jet process and the production and decay of tt̄, both of which haverecently been added to the code. Using MCFM, comparisons between the Tevatron running at√s = 2 TeV andthe LHC running at√s = 7 TeV are made for standard model process including the production of Higgs bosons.The case for running the Tevatron until 16fb−1 are accumulated by both detectors is sketched.1. MCFMMCFM is a parton-level event integrator whichgives results for a series of processes, especiallythose containing the bosons W,Z and H andheavy quarks, c, b and t. Most processes are in-cluded at next-to-leading order (NLO) and in-clude spin correlations in the decay. Table 1 givesan abbreviated summary of the processes whichare currently treated by the program. Full docu-mentation for the program is available at ref. [1].We will not review these processes in detail butrather concentrate on the new features which arepresent in version 5.8 which was released in April2010.2. Higgs + two jetsA new process which is in MCFM version 5.8is the production of a Higgs boson in associationwith two jets. Sample diagrams contributing toHiggs boson production are shown in Fig. 1. Weshall focus on the process in Fig. 1(c) and otherHiggs + 4 parton processes, which can be con-sidered a background to the vector boson fusionprocess, Fig. 1(d). The calculations underlyingour implementation are performed at NLO usingan effective Lagrangian to express the coupling ofgluons to the Higgs field [22],LintH =C2H trGµν Gµν , (1)where the trace is over the color degrees of free-dom. At NLO the coefficient C is given in theMS scheme by [23,24],C =αS6πv(1 +114παS)+O(α3S) . (2)Table 1Abbreviated summary of MCFM procesesFinal state Notes Ref.W/Z processesW/ZWW/ZZ/WZ [2]Wbb̄ mb = 0 [3]Zbb̄ mb = 0 [4]W/Z + 1 jetW/Z + 2 jets [5]Wc mc 6= 0 [6]Zb nf = 5 [7]Zb+jet nf = 5 [8]H processesH(g.f.)H+1 jet(g.f.)H+2 jets (g.f.) mt → ∞ [9,10,11]WH/ZHH via WBF [12]Hb nf = 5 [13]t processest s and t channel [14]t t channel,nf = 4 [15,16]Wt nf = 5 [6]tt̄ with t decayProcesses not present in released versionWb +jet [17,18]WW +jet [19]J/ψ & Υ [20]γN → J/ψ [21]HHH HW +/Z0W−/Z0(a) (b)(c) (d)Figure 1. Higgs production processes at lowestorder.Here v is the vacuum expectation value of theHiggs field, v = 246 GeV. Phenomenological re-sults on this process at NLO were first publishedin ref. [9] using a semi-numerical method to calcu-late the virtual corrections. Here we shall presentnew phenomenological results for the Higgs + 2jet process, based on analytic calculations of theone-loop Higgs + 4 parton amplitudes which haverecently been completed. The use of analytic re-sults leads to a considerable improvement in thespeed of the code.2.0.1. One-loop H + 4 parton amplitudesThe effective Lagrangian used in the calcula-tion of the Higgs + 4 parton amplitudes was sim-plified by introducing a complex scalar field [25],φ =12(H + iA) , φ† =12(H − iA) , (3)so that the effective Lagrangian, Eq. (1), can bewritten as,LintH,A =C2[H trGµν Gµν + iA trGµν∗Gµν]== C[φ trGSD µν GµνSD+ φ† trGASD µν GµνASD].Table 2Comparison of calculations of refs. [31,10]ADGSW[31] LO NLO NNLOHiggs+0jet X X XHiggs+1jet X XHiggs+2jet XCEW [10] LO NLO NNLOHiggs+0jet X XHiggs+1jet X XHiggs+2jet X XThe gluon field strength has been separated intoa self-dual and an anti-self-dual component,GµνSD=12(Gµν + ∗Gµν), GµνASD=12(Gµν − ∗Gµν)∗Gµν ≡ i2εµνρσGρσ . (4)Calculations performed in terms of the field φ aresimpler than the calculations for the Higgs bo-son and, moreover, the amplitudes for φ† can beobtained from the φ amplitudes by using parity.The full Higgs boson amplitude is written as acombination of φ and φ† components:A(H) = A(φ) +A(φ†) . (5)A nice summary of all the one-loop resultsfor the Higgs + 4 gluon amplitudes is given inref. [26]. Full references for the analytic calcula-tions of the Hq̄qgg amplitudes can be found inref. [28]. Results for the matrix squared for theHqq̄qq̄ process are given in ref. [9] and for theamplitude in ref. [27].2.1. Phenomenological impactIn addition to its importance at the LHC, theHiggs + 2 jet cross section is also important atthe Tevatron. The experiments [30] analyze theevents with different numbers of jets separatelyto make maximal use of the different kinematicstructure. In the spirit of Ref. [31], we can refinethe estimate of the theoretical uncertainty on thenumber of Higgs signal events originating fromQCD parton fusion processesIn Table 2 we contrast the two different ap-proaches to calculating the Higgs + 2 jet crosssections of Ref. [31] and Ref. [10]. Ref. [31] is inTable 3LO and NLO Higgs + two jet cross section at√s = 1.96 TeV, together with theoretical errors.mH [GeV] ΓH [GeV] σLO[fb] σNLO[fb]160 0.0826 0.345+92%−44%0.476+35%−31%essence a NNLO calculation of the total cross sec-tion, which as a byproduct includes the Higgs +2 jet process in leading order. The MCFM imple-mentation [10] only calculates the Higgs + 0 jetcross section at NLO, but also includes the Higgs+ 2 jet cross section at NLO.By using the fractions of the Higgs cross sec-tion in the different multiplicity bins taken fromRef. [32], we can update Eq. (4.3) of Ref. [31] (fora Higgs boson of mass 160 GeV) with,∆N(scale)N=(+13.8%−15.5%)=60% ·(+5%−9%)+ 29% ·(+24%−23%)+ 11% ·(+35%−31%)(6)Only the uncertainty on the Higgs + ≥ 2 jet bin,(which is only 11% of the total) has been modi-fied, using the results from Table 3.The corresponding determination using the un-certainty derived from the LO result for theHiggs + ≥ 2 jet bin is (+20, 0%,−16.9%) [31],so the result in Eq. (6) represents a modest im-provement in the overall theoretical error, but onewhich will have implications for the Higgs searchat the Tevatron.3. Top production and decayAnother new process which is included at NLOis the production of pairs of top quarks includ-ing the decay. The top quarks are kept strictlyon their mass shell, so the processes of produc-tion and decay are separately gauge invariant,but full spin correlations are kept. Althoughthis is not a new result [35,36], it is importan-tant to include it in the MCFM package becausetop pair production is such an important back-ground for many processes at hadron colliders.We can assess the importance of including thesespin correlations by looking at the angular sepa-Figure 2. Effect of spin correlations in top decay.ration of the two charged leptons coming fromtop decay. The expected data sample of topquark pairs at√s = 7 TeV will be too smallto observe these correlations, but they should beobservable at√s = 14 TeV. Fig. 2 shows theazimuthal angle φ in the transverse plane be-tween the two charged leptons in top pair pro-duction events. In addition to standard leptonand jet cuts, pT,l > 20 GeV, pT,bjet > 25 GeV,pT,miss > 40 GeV, ηl, ηbjet < 2.5 we apply the cutpT,l < 50 GeV to constrain the top quarks to beproduced close to threshold [37]. These specificcuts have been suggested by Schulze [38].4. Run III at the TevatronThe basic ratios of cross sections are governedby the parton luminosities. Fig. 3 shows theratios of parton luminosities in pp collisions at√s = 14, 10 and 7 TeV compared to the lumi-nosity in pp̄ collisions at√s = 2 TeV. Consid-ering in detail the case of 7 TeV, in the range√ŝ = 100 − 200 GeV the ud̄ luminosity goes upby a factor of 4 − 5 whereas the gg luminositygrows by at least a factor of 15. This means thatfor qq̄ induced processes the Tevatron has a com-petitive advantage. That is, in a scenario wherethe Tevatron has an accumulated luminosity of10 fb−1 and the LHC has an accumulated lumi-nosity of 1 fb−1 at√s = 7 TeV, the Tevatronstill has a competitive advantage for qq̄ inducedprocesses.We now further discuss the situation if theTevatron were to run for three further years af-ter 2011; after this period the experiments wouldhave accumulated 16 fb−1 per experiment of an-alyzeable luminosity. Fig. 4 shows the numberof events produced for various standard modelprocesses, assuming 16 fb−1 of accumulated lu-minosity for the Tevatron and 1 fb−1 of accum-lated luminosity for the LHC. In this situationthe Tevatron would have a clear advantage for qq̄initiated processes.The situation with regard to the standardmodel Higgs boson is interesting, since at theTevatron the low mass Higgs boson is soughtin association with a vector boson V in the qq̄-initiated mode qq̄ → V H . If we take the preci-sion standard model fits [33] seriously, the stan-dard model 2σ-allowed region for the Higgs bosonmass is 114 < MH < 145 GeV. In this region theprimary decay of the Higgs boson is into bb̄, achannel which is not expected to be observableat the LHC until 30 fb−1 have been accumulatedat√s = 14 TeV [34].If the Tevatron were to accumulate 16 fb−1 ofanalyzeable luminosity, per experiment it couldprovide 3σ evidence for the standard model Higgsboson in the range 100 < mH < 180 GeV [39].This is an important goal, which would providecomplementary information to the information onthe decay H → γγ which will be available from14 TeV running at the LHC.5. ConclusionsThis year has been mainly a consolidation pe-riod for MCFM, but with the introduction of twonew processes at NLO, top pair production withdecay and the Higgs boson + 2 jet production atthe LHC.Using MCFM it has been shown that the Teva-tron can provide important information on qq̄ ini-tiated processes, and that for these processes itwill be superior to the LHC until considerabledata has been accumulated at√s = 14 TeV. 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MCFM for the Tevatron and the LHC

John M. Campbell

R.K. Ellis

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Nuclear Physics B - Proceedings Supplements

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MCFM for the Tevatron and the LHC

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