Transcript NLO at the LHC David A. Kosower Institut de Physique Théorique, CEA–Saclay on behalf of the BLACKHAT Collaboration Z.

NLO at the LHC
David A. Kosower
Institut de Physique Théorique, CEA–Saclay
on 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
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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
– Htjets 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 Htjets > 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 Htjets > 500, |MET| > 350; & Htjets >
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
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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 Jets
Uncertainty 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 hardobject 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
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MC@NLO
– NLO for n-jet observables
– LO for (n+1)-jet observables
– (N)LL for ≥(n+1)-jet observables
• MENLOPS
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MEPS@NLO
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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
NLO for n-jet observables
NLO for (n+1)-jet observables
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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 matrixelement method to NLO
• And also matching parton showers to NLO calculations