NNLO vs parton-showers - THEP Mainz

MotivationGluon fusion has been a theoretical laboratory for QCD methods.We needed it all:- QCD calculations at NLO and NNLO- Heavy quark effective theory- Higgs transverse momentum and threshold resummation- Parton-showers- Matched parton-showers and NLO (MC@NLO)With the predictions of all of these methods we can now say that allrelevant Higgs boson cross-sections in the lepton and photonchannels are computed with a precision of better that ~10%.2

Higgs cross-sections with SCET?- An impressive progress using SCET formulations of partonshowers and resummation.- Very important results in jets physics and Drell-Yan.- Gluon fusion to Higgs could become the next theoreticallaboratory for SCET!My job for today: Report on some recent comparisons ofexisting NNLO, parton-shower, and resummationcomputations.3

Inclusive Higgs cross-section• Higgs cross-section in the gluon-fusion channel receives largepertubative corrections:• σ(NLO) ~ 1.7 x σ(LO) (Dawson; Spira, Djouadi, Zerwas)• σ(NNLO) ~ 2.0 x σ(LO) (Harlander, Kilgore; CA, Melnikov;Ravindran, Smith, van Neerven)4

Higgs discovery in the WW channel• many channels are exploitedto discover the Higgs at theLHC• in the mass region ~2 m W theHW channel is mostpromising (BR(HW)~1)• but... in the leptonic W decaymodes there are neutrinos inthe final state• no invariant mass peak can be reconstructed• A peak can be found in a signal-rich phase-space regiondefined in terms of many variables.5

“Scary” cut efficiencies• Cut efficiencies for all process are of the order or less than 2%.• What is the impact of QCD radiation corrections to theseefficiencies?• Theoretical work was/is needed in all three processes.• In a real experiment:• Background events can be measured in signal-free regions andextrapolated into the ‘signal-region’• The signal can only be studied theoretically!8

Differential cross-sections• need fully differential cross-sections in order to impose experimentalcuts• at NLO any cross-section can be computed if the virtual amplitudes areknow• Giele, Glover, Kosower; Frixione, Kunszt, Signer; Catani, Seymour ...• for NNLO collider processes the list is rather short:• Drell-Yan rapidity distribution Anastasiou, Dixon, Melnikov, Petriello (03)• ee jets Anastasiou,Melnikov,Petriello (04); Gehrmann,Gehrmann,Glover (04);Weinzierl (06)• pp+X Anastasiou, Melnikov, Petriello (04)• pp+Xγγ+X Anastasiou, Melnikov, Petriello (04), Catani, Grazzini (07)• pp,Z+X Melnikov, Petriello (06)• pp+XW+Xllνν+X Anastasiou, Dissertori, FS (07), Grazzini (08)• ee jets Gehrmann, Gehrmann, Glover, Heinrich (07)9

Sector decomposition for diff. cross-sections• CA, Melnikov, Petriello; CA, Beerli, Daleo; Lazopoulos, Melnikov, Petriello• NLO and NNLO cross-sections with contributions from loopand real radiation amplitudes are nothing more than multidimensionalintegrals with singularities in d = 4 dimensions• - Write multi-dimensional phase-space or Feynman parameterintegrals- Scan for singularities when d = 4- Divide recursively the integration region until alloverlapping singularities are fully factorized as polesof a single integration variable.- Subtract locally singularities in d = 4 and Taylor expand11

Example(Hepp; Denner, Roth; Binoth, Heinrich)• Factorize:=+=+12

H WW at NNLO(CA, Dissertori, Stoeckli)• used the fully differential NNLO program FEHiP for pp+X• CA, Melnikov, Petriello• added decay matrix-element for the process HWlνlν• large phase-space rejection required reworking the numericalintegration strategy• independent, parallelized VEGAS integration for individual sectors• large improvement of integration adaptation (from no-adaptation toadaptation within a few VEGAS iterations)• easy exploitation of cluster computing• all numbers/plots in our paper required about one week ofrunning time on average 450 CPU’s13

H WW selection cuts• Cross-section after experimental cuts on:• angle between the charged leptons in the transverse plane• missing transverse energy• maximum transverse energy of the harder lepton• invariant mass of the charged lepton-pair• jet-veto• Integrate the differential cross-section on X up to some cut-offvalue X cut which corresponds to a cut14

Jet Veto• jet-veto has no impact at LO (no partons in final state)• jet-veto at NLO corresponds to cut on Higgs transverse momentum• K-factors (σ (N)NLO /σ LO ) depend heavily on cut-value!• inclusive K-factors would fail to describe the picture reliably15

Transverse lepton angle• in contrast to the jet-veto:• the K-factors increase when lowering the cut value on the lepton angle16

Maximum transverse momentum• again inclusive K-factors fail, the cross-section decrease at thenominal cut• Summary:• very complicated picture after restricting the phase-space• inclusive K-factors can NOT be expected to do a good job17

Signal cross-section after cuts• K-factors are at the order of 1• depending on scale choice even < 1• ! inclusive K-factors predict an increase by a factors of 2 !• very small scale variation after cuts are applied• Is this a very precise prediction for the cross-section?18

Are these results reliable?• We could hurry and declare “victory” of the fixed-orderperturbation theory for the signal cross-section:• smaller higher order corrections after cuts• smaller scale variation after cuts• But...• is this accidental?• are effects beyond NNLO important?• The cuts restrict the phase-space significantly, especially thejet-veto (but not exclusively) restricts the Higgs boson phasespaceto the low transverse momentum region...• ... where fixed-order theory might break down!• ... do we need resummation for an accurate prediction?19

Validation• We compare our fixed order prediction to• the LO parton shower event generator HERWIG• incorporates LO hard-scattering amplitudes with partonshower• includes leading logs to all orders and LO color resummation• MC@NLO (Frixione, Webber)• incorporates NLO matrix elements with the parton showerfrom HERWIG• resummed Higgs p Tdistribution (Bozzi, Catani, de Florian, Grazzini)• matches NNLO with NNLL• combines to the ‘highest posssible’ accuracy fixed order andresummation effects20

What can we learn?• It is not obvious from first principles that the efficiencies in theevent generators and the fixed-order prediction agree:• The physics approximations in fixed-order and parton-showersare different; therefore ...• ... a disagreement means that at least one of these approachesdoes not describe the physics process correctly in the signalphase-space (i.e. after the selection cuts)• On the other hand: A good agreement would give confidence inour tools.21

Higgs p T spectrum• we know that if we integrate the fixed-order cross-section overa large enough region the effects of multiple soft and collinearradiation become negligible... But how ‘large’?• we compare the cumulative cross-section in p TH...• ... at NLO:• NLO+NLL and MC@NLOagree very well• need to integrate the fixedorderNLO spectrum up toabout 50 GeV to get a closeresult• NLO prediction will fail whenrestricting to smallerregions!22

• ... and at NNLO:• both spectra agree muchbetter down to much smallerregions• we can ‘trust’ the NNLOspectrum already for a ptmaxvalue of about 20 GeV!• reminder: we veto on jets withp T > 25 GeV23

Rescaled generator spectra• we also compare the inclusively rescaled generator spectra(HERWIG, MC@NLO) to the ‘best’ prediction:• both agree nicely, with HERWIG slightly over- and MC@NLOslightly under-estimating the cross-section24

Cut variables: NNLO vs MC@NLO• jet-v eto: especially in the region where we are cutting verygood agreement• all other variables agree ‘perfectly’25

Signal cross-section26

The di-photon channel(stuied by Dissertori, Holzner, Stoeckli)Cross-sectionsdiffer by globalK-factors!MC@NLO andNNLO have verysimilar efficiencies!27

Is it all done?• a difficult, fully differential NNLO computation is available forthe signal cross-section in the HWl channel• a unique validation opportunity for MC@NLO, LO eventgenerators and NNLO for a process with large perturbativecorrections and a largely reduced, ‘tricky’ final state phasespace• very good agreement between MC@NLO and NNLO, whilefixed-order NLO fails to predict the cross-section reliably.• robust theoretical prediction for the signal cross-section at theLHC (even with respect to had. and UE effects)• Higgs boson = New physics. SM is JUST one scenario amongmany!28

Two-loop gg h amplitude in the MSSM (NEW)CA, Beerli, Daleo-A complicated computationinvolving two-loop diagrams withinfrared, ultraviolet and thresholdsingularities.- A huge challenge to transporta method for IR+UV subtractionson complex domains.- Understanding regularizationin the MSSM is not as easy asin the SM and vice versa- Reducing the Higgs signal (ormaking it disappear) is “verynatural” in the MSSM.Parameters similar to “golden region” of Kitano,Nomura; Perelstein, …29

In BSM we may:NOT HAVE:- Good Light Higgs approximation (e.g. bottom quarks)- or NNLO Light-Higgs effective theory (…too tough to compute the“HQET” Wilson coefficient, eg in the MSSM)- Fixed order NNLO (we just learnt how to do NLO efficiently)We would like to at least have- Threshold and transv. momentum resummation- Matched at NLO parton-showers- Flexibility to scan the parameter space of many extensions of theSMEfforts to improve resummation and parton-showers will be wellappreciated in Higgs physics.30