W + n jet production at NLO Lance Dixon (SLAC) representing the BlackHat Collaboration C. Berger, Z. Bern, L.D., F. Febres Cordero, D. Forde, T. Gleisberg, H. Ita, D. Kosower, D. Maître [hep-ph], [hep-ph], [hep-ph] US ATLAS Hadronic Final State Forum Joint Theory/Experiment Open Session April 9, 2009

L. Dixon W + n jets at NLOAtlas Forum April 9, Because leading order (LO) predictions are only qualitative in normalization, due to poor convergence of expansion in Why NLO? Example: Z production at Tevatron Distribution in rapidity Y LONLONNLO has still ~50% corrections, LO  NLO ADMP (2004) (2007) by NNLO, a precision observable

L. Dixon W + n jets at NLOAtlas Forum April 9, Why W (or Z) + n jets? Early studies using parton shower Monte Carlo PYTHIA overly optimistic ALPGEN based on tree amplitudes, much better than PYTHIA at modeling hard jets But even normalization of ALPGEN quite uncertain Gianotti & Mangano, hep-ph/ Mangano et al. (2002) Supersymmetric cascade: gluinos  squarks  neutralinos (dark matter, escapes detector) Signal: missing energy + jets SM background from Z + jets, when Z  neutrinos still beyond state-of-art

L. Dixon W + n jets at NLOAtlas Forum April 9, Reduction in Uncertainty In going from LO to NLO for “total cross section” for W + n jets at the Tevatron: As we’ll see, “shapes” (distributions within the total event sample) can be affected as well as normalizations

L. Dixon W + n jets at NLOAtlas Forum April 9, W + 2 jets Background for current SM searches at the Tevatron: Single top (with a b tag) WW or WZ with one W/Z  jets (warm-up for WH with H  bb _ CDF, “just missed” D0,  evidence ALPGEN for shape “shape” – slope in dijet invariant mass very important

L. Dixon W + n jets at NLOAtlas Forum April 9, Strong growth in difficulty at one loop (NLO) with number of final-state objects # of jets # 1-loop Feynman diagrams (gluons only)

L. Dixon W + n jets at NLOAtlas Forum April 9, Instead of Feynman diagrams, we use Analyticity “One of the most remarkable discoveries in elementary particle physics has been the existence of the complex plane” -J. Schwinger

L. Dixon W + n jets at NLOAtlas Forum April 9, Analyticity Includes Factorization How amplitudes “fall apart” into simpler ones in special limits

L. Dixon W + n jets at NLOAtlas Forum April 9, Green (Efficient/Fast) Computation Reduce the number of objects – use on-shell amplitudes, not Feynman diagrams Reuse building blocks over & over Recycle lower-point (1-loop) & lower-loop (tree) on-shell amplitudes

L. Dixon W + n jets at NLOAtlas Forum April 9, Ossola, Papadopolous, Pittau, [CutTools] Ossola, Papadopolous, Pittau, Mastrolia, Ossola, Papadopolous, Pittau, Binoth, Ossola, Papadopolous, Pittau, Draggiotis, Garzelli, Papadopoulos, Pittau, van Hameren, Papadopoulos, Pittau, Giele, Kunszt, Melnikov, Giele, Zanderighi, [ROCKET] Ellis, Giele, Kunszt, Melnikov, Ellis, Giele, Kunszt, Melnikov, Zanderighi, Ellis, Melnikov, Zanderighi, Lots of related recent one-loop work by other groups, for example:

L. Dixon W + n jets at NLOAtlas Forum April 9, BlackHat is a “black box” for computing one-loop (virtual) corrections. We also need to add the real radiative corrections Adding real radiation NLO tree + 1 parton 1 loop first, cancel infrared divergences ( ) between virtual & real dim. reg. BlackHat Catani-Seymour dipole subtraction, automated by Gleisberg, Krauss, , incorporated in SHERPA LO convolute with pdfs apply cuts tree Simple Example: Z production

L. Dixon W + n jets at NLOAtlas Forum April 9, Tevatron W + n jets Data NLO (MCFM) n = 1 n = 2 n = 3: only LO was available until this year LO with different matching schemes CDF, [hep-ex]

L. Dixon W + n jets at NLOAtlas Forum April 9, First reproduce W + 2 jets [MCFM] Campbell, Ellis, hep-ph/ Cuts: Central Scale: Range

L. Dixon W + n jets at NLOAtlas Forum April 9, Note on Cone Algorithms CDF data used JETCLU with R = 0.4. JETCLU is IR unsafe, cannot be used at NLO. We used SISCone, an IR safe, seedless and fast cone algorithm, also with R = 0.4. Salam, Soyez, MCFM used midpoint for W2j. For jet E T and  distributions the seeding may not matter much, but if you happen to “look inside the jets” (jet masses, etc.), effects can be ~ 30%. Please adopt an IR safe jet algorithm!

L. Dixon W + n jets at NLOAtlas Forum April 9, A closer look at W + 2 jets “LC NLO” is same as NLO, but it drops subleading-color terms in the finite parts of the one-loop amplitudes. For SU(3)  SU(N c ), these terms are suppressed parametrically by 1/N c 2 or n f /N c,and in fact are only a few percent, for W1j or W2j Yet they are much more expensive to compute. So we will drop them (for now) for W3j.

L. Dixon W + n jets at NLOAtlas Forum April 9, W + 3 jets at Tevatron same cuts, cone algorithms, and scale variation as for W + 2 jets [hep-ph]

L. Dixon W + n jets at NLOAtlas Forum April 9, Distribution in Traditional SUSY search variable

L. Dixon W + n jets at NLOAtlas Forum April 9, On to the LHC SISCone Cuts:

L. Dixon W + n jets at NLOAtlas Forum April 9, LHC total cross section Common scale  for every event Preliminary

L. Dixon W + n jets at NLOAtlas Forum April 9, Tevatron to LHC K factor at  = M W drops from 1 to ½. Much of this can probably be attributed to a shift from quark to gluon initial states as the average x drops: in going from LO to NLO for 0.01 < x < 0.1 g(x) decreases while q(x) increases

L. Dixon W + n jets at NLOAtlas Forum April 9, Pseudorapidity of first jet Preliminary ~ no change in shape from LO to NLO

L. Dixon W + n jets at NLOAtlas Forum April 9, Distance between first and second jet Significant change in shape from LO to NLO. More chance for hardest jets to be closer if extra radiation. Large  separation  more costly in terms of parton luminosity if extra radiation. Preliminary

L. Dixon W + n jets at NLOAtlas Forum April 9, Look for radiation in “gap” Campbell, Huston, Stirling, hep-ph/ Need this fraction to remain small for non-color-singlet exchange at large , in order for central jet veto to be effective in studies of Higgs production via vector boson fusion. LO theory still vs.

L. Dixon W + n jets at NLOAtlas Forum April 9, Distribution in Tail much more suppressed, from LO to NLO, compared with Tevatron Preliminary

L. Dixon W + n jets at NLOAtlas Forum April 9, Conclusions New and efficient computational approaches to one-loop QCD amplitudes exploit analyticity and build loop amplitudes out of on-shell ingredients. They are (finally) producing useful new NLO results for the LHC, in particular for W + 3 jets. Z + 3 jets is also on the way. W/Z + 4 jets is probably also feasible (without waiting another seven years). Shapes as well as normalizations can be affected by NLO corrections, even for complex final states Because the present NLO results are at parton level, and not yet matched to a parton shower (which may take quite a while), some thought should be given to how to make them most useful to you –best distributions to study –best ratios of different processes to take: W  Z, etc. We are looking forward to a fruitful dialog!

L. Dixon W + n jets at NLOAtlas Forum April 9, Extra Slides

L. Dixon W + n jets at NLOAtlas Forum April 9, Tevatron W + n jet cross sections

L. Dixon W + n jets at NLOAtlas Forum April 9, Turning trees into loops BlackHat: C++ program Berger, Bern, LD, Febres Cordero, Forde, H. Ita, D. Kosower, D. Maître, [ph]

L. Dixon W + n jets at NLOAtlas Forum April 9, Inside BlackHat