NLO at the LHCDavid A. Kosower

Institut de Physique Théorique, CEA–Saclayon behalf of the BLACKHAT Collaboration

Z. Bern, L. Dixon, Fernando Febres Cordero, Stefan Höche, Harald Ita, DAK, Daniel Maître, Kemal Ozeren

[]Perimeter CMS Workshop 2012, Waterloo, ON

August 2, 2012

• The NLO revolution• BlackHat snapshot• Matrix Element method at NLO• Parton Shower matching at NLO

Next-to-Leading Order in QCD

• Precision QCD requires at least NLO

• QCD at LO is not quantitative: large dependence on unphysical renormalization and factorization scales

• NLO: reduced dependence, first quantitative prediction

• NLO importance grows with increasing number of jets

• Applications to Multi-Jet Processes: Measurements of Standard-Model distributions & cross sections

Estimating backgrounds in Searches• Expect predictions reliable to 10–15%• <5% predictions will require NNLO

The On-Shell Revolution• Ingredients to NLO calculations

– Tree-level 2 V+n and 2 V+n+1… now with improved efficiency (Britto, Cachazo, Feng, Witten; Dixon, Henn, Plefka, Schuster)

– NLO parton distributions– General framework for numerical programs (Catani & Seymour)– One-loop 2 V+n

The on-shell revolution has broken the bottleneck: n=3,4,5 BLACKHAT Implementation

• Numerical implementation of on-shell methods for one-loop amplitudes

• Automated implementation industrialization• Do algebra numerically, analysis symbolically (“analytically”)• SHERPA for real subtraction, real emission, phase-space integration• Distribute results via ROOT n-tuples

• Lots of revolutionaries roaming the world– BLACKHAT– CutTools+HELAC-NLO: Ossola, Papadopoulos, Pittau, Actis,

Bevilacqua, Czakon, Draggiotis, Garzelli, van Hameren, Mastrolia, Worek & their clients

– Rocket: Ellis, Giele, Kunszt, Lazopoulos, Melnikov, Zanderighi– Samurai: Mastrolia, Ossola, Reiter, & Tramontano– NGluon: Badger, Biedermann, & Uwer– MadLoop: Hirschi, Frederix, Frixione, Garzelli, Maltoni, &

Pittau– Giele, Kunszt, Stavenga, Winter

• Important to have multiple groups working on the same processes

• Ongoing analytic work– Almeida, Britto, Feng & Mirabella

A BLACKHAT Application• CMS asked us to study the uncertainties in the

use of γ+jets data to estimate the (Z )+jets contribution to the missing ET+jets background in the SUSY search

• Data-driven estimate Estimate from W production Estimate from photon production – no , higher

rates

Predicting MET+Jets from γ+Jets

• Define search variables: – |MET| |−∑ET| for all jets with pT > 30 & || < 5– Ht

jets corresponding to jets with pT > 50 & || < 2.5

• Looking in tails of distributions, force vector pT to large values– Hard cuts: control region 13% of signal, search regions 11

and 5.5%  Control Ht

jets > 300, |MET| > 150; signals Htjets > 300, |MET| >

250 & Htjets > 500, |MET| > 150

– Harder cuts: control region 5.8%, search regions 0.06 to 0.7%

  Control Htjets > 350, |MET| > 200; signals Ht

jets > 500, |MET| > 350; & Ht

jets > 800, |MET| > 150; & Htjets > 200, |MET| > 500

• Use Frixione isolation (radius-dependent energy limit) to define photon; difference from standard cone < 1% at large pT

• Scale dependence in raw cross sections shrinks at NLO

• Scale dependence typically used as a proxy for uncertainty

• [Correlated] scale dependence in Z+jets/γ+jets ratio is tiny both at LO & NLO, and vastly underestimates residual uncertainty

• Use comparison to parton shower matched to LO MEs (ME+PS) to estimate residual uncertainty

Some Subtleties• Large logarithms arise in V+3/V+2 ratios• Plausibly cancel in Z+jets/γ+jets ratio• Reliability can be tested in γ+3/ γ+2 data• Details of electroweak-boson matching in the

ME+PS matter: important to ensure that treatment of Z and is same in matched shower

• EW corrections aren’t included, but– Estimates based on Maina, Moretti, Ross & Kuhn,

Kulesza, Pozzorini & Schulze suggest 5–15% corrections for hard to hardest cuts

– Estimate of leading EW real-emission corrections (W emission producing the jet pair) suggests corrections are small (3–4%)

Z/ Ratios in Search Regions

• Last year, assessed estimate & uncertainty using Z+2/+2 ratio

• Here, extend it to Z+3/+3 ratio

• NLO prediction is extremely stable (<3%) under addition of one jet

• LO & ME+PS vary by up to 10%

QCD Uncertainty Estimates

• From Z+3/γ+3 jets at NLO vs ME+PS

• In agreement with earlier analysis suggesting 10%

Z+4 JetsUncertainty bands narrow dramatically at NLO

Last jet distribution shape unchanged at NLO, 1st three become steeper

Z/W ratios are very stable at NLO

Characteristic relative decrease of W− at large pT

W+5 Jets

• Scale dependence narrows substantially at NLO

Jet Ratios

• Relaxation of kinematic restrictions leads to NLO corrections at large pT in V+3/V+2, otherwise stable

• Ratio is not constant as a function of pT — fits to α+β n will have α & β dependent on pTmin

Matrix-Element Method• Want to decide, event by event, which subprocess

is the more likely origin

• Need to determine weights at a given point in the phase space of reconstructed objects (leptons, jets) — that is, fully differentially

• Done at parton level

• Well-established technique at leading order (tree level) e.g. in MADGRAPH (Artoisenet, Lemaitre, Maltoni, Mattelaer [1007.3300])

Matrix-Element Method at NLO

• Current technology computes virtual & real-emission corrections separately over all phase space

• Can put in one or two delta functions — yielding one- or two-dimensional distributions — but more would lead to hopelessly poor statistics

• Need to generate phase space that factorizes the hard-object phase space from the “soft” intra-jet phase space

• One solution: forward-branching phase-space generator Giele, Stavenga, Winter [1106.5045]

• Initial MEM studies Campbell, Giele, Williams [1204.4424]

Approaches to QCD Calculations

• General parton-level fixed-order calculations– Numerical jet programs: general observables– Systematic to higher order/high multiplicity in perturbation

theory – Parton-level, approximate jet algorithm; match detector

events only statistically

• Parton showers– General observables– Leading- or next-to-leading logs only, approximate for higher

order/high multiplicity– Can hadronize & look at detector response event-by-event

Parton Showers and Matching

• Combine approaches, avoiding double-counting• Several approaches/implementations at leading

order: CKKW, L-CKKW (phase-space slicing), MLM in MADGRAPH, ALPGEN, SHERPA

• Widely used• Don’t all agree: having several groups/programs

is particularly important• No uncertainty estimates available

• Overall normalization uncertain• Scale sensitivity is large (to the extent that the

scale can be varied)

Matching at NLO• Efforts date back to pioneering work by Frixione &

Webber (2002)• Two primary approaches until recently: MC@NLO

(Frixione & Webber [ph 0204244]) POWHEG (Frixione, Nason, Oleari [0709.2092])– First emission at NLO, overall rate to NLO– Emission distributions still at LO!

• Reaching maturity: W+3 jets (Siegert, Höche, Krauss, & Schönherr [1206.4873])

• New approach: MEPS@NLO (Gehrmann, Höche, Krauss, Schönherr, & Siegert [1207.5031] ; Höche, Krauss, Schönherr, & Siegert [1207.5030])– Generate matched samples at several multiplicities– Study scale variation

• SHERPA+BLACKHAT MC@NLO for W+3 jets

• MC@NLO– NLO for n-jet observables– LO for (n+1)-jet observables– (N)LL for ≥(n+1)-jet observables

• MENLOPS– NLO for n-jet observables– LO for (n+1)-jet observables– MEPS for ≥(n+1)-jet observables– Here: W+0 @ NLO, W+≤4 @ ME–LO

• MEPS@NLO– NLO for n-jet observables– NLO for (n+1)-jet observables– …– O(αL+1+(N)LL) for ≥L-jet observables– Here: W+ ≤2 @NLO, W+≤4 @ ME–LO

• MEPS@NLO example

Summary• On-shell methods have matured into the method

of choice for NLO QCD calculations for colliders

• Calculations with high multiplicity are mature for experimental comparisons

• Theorists are working hard on extending the matrix-element method to NLO

• And also matching parton showers to NLO calculations