Challenges and Solutions in High-Multiplicity Jet Production Studies
Theory and methodology challenges in the universality and production of W+multijet events are discussed, emphasizing the importance of accurate predictions and scale independence. The NLO revolution and on-shell methods are explored, along with software tools like BLACKHAT and SHERPA. Managing computations at high multiplicity is complex, but solutions like n-tuples provide a way to efficiently recycle matrix elements and configuration data, facilitating analysis and collaboration.
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Universality in W+Multijet Production David A. Kosower Institut de Physique Th orique, CEA Saclay on behalf of the BLACKHAT Collaboration Z. Bern, L. Dixon, Fernando Febres Cordero, Stefan H che, Harald Ita, DAK, Adriano Lo Presti, Daniel Ma tre, Kemal Ozeren [0907.1984, 1009.2338, 1108.2229, 1304.1253, 1308.3986 & work in progress] Rencontres de Moriond, La Thuile March 27, 2014
Theory for Many Jets Want quantitative predictions Renormalization scale needed to define ??; factorization scale to separate long-distance physics Physical observables should be independent of scales; truncated perturbation theory isn t LO has large dependence NLO reduces this dependence NLO importance grows with increasing number of jets Expect predictions reliable to 10 15% <5% predictions will require NNLO
NLO Revolution: On-Shell Methods Formalism Known integral basis: On-shell Recursion; D-dimensional unitarity via mass Unitarity in D = 4
BLACKHAT + SHERPA BLACKHAT One-loop matrix elements Software library and its eponymous collaboration Automated, numerical implementation of unitarity method COMIX Born + real-emission matrix elements Catani Seymour subtraction terms SHERPA Process Management Phase-space integration No showering
Running at High Multiplicity Managing a high-multiplicity computation is complicated Many different contributions with wide dynamic range Split up into parts of different significance to compute with different statistics Many pieces to baby-sit & combine Computationally intensive Would need to repeat for each scale choice; each PDF within an error set; each new observable Computing matrix elements overwhelmingly dominates computation time at given scale Computing new observables is cheap Varying R, F also cheap once terms within matrix element are known Likewise for choice of parton distributions
n-Tuples Solution: recycle! Compute matrix elements once, save phase-space configurations with weights & coefficients needed to recompute for different R, F, PDFs Save these as ROOT n-tuple files Analyses done with lightweight C++ or ROOT codes Bonus: distribute these to experimenters, who can do their own analyses Only real restriction is to preselected set of jet algorithms Jet, lepton/photon pT, rapidity cuts can be tightened PDFs, scales can be chosen differently Now available publicly for W,Z+ 4 jets, QCD 4 jets, +2 jets (std & VBF)
W+4 Jets Scale variation reduced substantially at NLO; central scale ?T Successive jet distributions fall more steeply Shapes of 4th jet distribution unchanged at NLO but first three are slightly steeper /2
W+5 Jets Scale-uncertainty bands shrink dramatically Last jet shape is stable, harder jets have steeper spectrum at NLO Last three jet shapes look similar, just getting steeper
Jet-Production Ratios Ratios reduce uncertainties both in experiment and theory W+1: missing subprocesses W+2: kinematic restrictions (W cannot be close to leading jet) Looking differentially: relaxation of kinematic restrictions leads to substantial NLO corrections at large pT in W+3/W+2, corrections smaller for higher multiplicity Ratio is not constant as a function of jet or WpT Studies suggest similarities of shapes of ratios
Extrapolations Let s try extrapolating ratios to larger n We know the W+2/W+1 ratio behaves differently from W+n/W+(n 1) ratios, because of kinematic constraints & missing processes (especially at LO) We could extrapolate from W+4/W+3 & W+3/W+2 but with two points and two parameters, how meaningful is that? With the W+5/W+4 ratio, a linear fit (with excellent 2/dof) makes the extrapolation meaningful: W + 6 jets: 0.15 0.01 pb W++ 6 jets: 0.30 0.03 pb Uncertainty estimates from Monte-Carlo simulation of synthetic data
jet Distribution ?T Look at distribution of total transverse energy in jets: good probe into high-pT physics Different peaks Different thresholds Let s try to extrapolate the distribution to W+6 jets
Cant extrapolate point-by-point: different thresholds, different peaks, different phase space Try fitting & extrapolating fit parameters What form should we use? At small HT, integral looks like where ? = [?T/ ? ?Tmin]2 At large HT, phase space becomes constrained, suggesting a factor like 1 ?T/?T ???/??T max ? (previously seen in ?) Try Terrible fit
Extrapolating But for ratios of distributions, this form gives great fits! Extrapolate ?,?: linear extrapolations work well; fit N to total cross section Use numerics or fit form (more convenient) for ???+2/??T
Summary Study of an important Standard-Model process at high jet multiplicity: W+4,5 jets Study of Standard-Model signals in widely-varying kinematic regimes gives confidence in our ability to understand backgrounds quantitatively at high multiplicity Reliability of ratios, signs of universality for 3 jets Extrapolations to W+6 jets
