Work Order: Theoretical CalculationsNeeded for the LHC

Requestor: J. HustonDelivery location: Michigan State UniversityRequested delivery date: before LHC dataTotal (CHF):free

Some references

Also online at ROP

Standard Model benchmarksSee www.pa.msu.edu/~huston/

Les_Houches_2005/Les_Houches_SM.html

http://stacks.iop.org/0034-4885/70/89

Les Houches Physics at TeV colliders 2005, Standard Model and Higgs Working Group:Summary report.C. Buttar et al. hep-ph/0604120

Some background: what to expect at the LHC

…according to a theorist

What to expect at the LHC

According to a currentformer Secretary ofDefense◆ known knowns◆ known unknowns◆ unknown unknowns

…according to a theorist

What to expect at the LHC

According to a formerSecretary of Defense◆ known knowns

▲ SM at the Tevatron▲ (most of) SM at the

LHC

◆ known unknowns▲ some aspects of SM at

the LHC

◆ unknown unknowns▲ ???

…according to a theorist

Discovering the SM at the LHC We’re all looking for BSM physics at

the LHC Before we publish BSM discoveries

from the early running of the LHC, wewant to make sure that wemeasure/understand SM crosssections◆ detector and reconstruction

algorithms operating properly◆ SM physics understood properly◆ SM backgrounds to BSM physics

correctly taken into account ATLAS/CMS will have a program to

measure production of SM processes:inclusive jets, W/Z + jets, heavy flavorduring first inverse femtobarn◆ so experimenters need/have a

program now of Monte Carloproduction and studies to makesure that we understand whatissues are important

◆ and we also need tool andalgorithm and theoreticalprediction developments (suchas at NLO)

Cross sections at the LHC

Experience at the Tevatron isvery useful, but scattering atthe LHC is not necessarilyjust “rescaled” scattering atthe Tevatron

Small typical momentumfractions x in many keysearches◆ dominance of gluon and

sea quark scattering◆ large phase space for

gluon emission and thusfor production of extra jets

◆ intensive QCDbackgrounds

◆ or to summarize,…lots ofStandard Model to wadethrough to find the BSMpony

BFKL?

Known known: Parton distribution functions

Calculation of production crosssections at the LHC relies uponknowledge of pdf’s in the relevantkinematic region

Pdf’s are determined by globalanalyses of data from DIS, DY and jetproduction

Two major groups that provide semi-regular updates to parton distributionswhen new data/theory becomesavailable

◆ MRS->MRST98->MRST99>MRST2001->MRST2002>MRST2003->MRST2004

◆ ->MSTW◆ CTEQ->CTEQ5->CTEQ6

>CTEQ6.1->CTEQ6.5>CTEQ7)

All of the above groups provide waysto estimate the error on the centralpdf◆ methodology enables full

characterization of partonparametrization space inneighborhood of global minimum

▲Hessian method▲Lagrange Multiplier

◆both of above techniques used by CTEQ and MRST▲Hessian method accessible to general user▲NB: the error estimate only covers experimentalsources of errors

▲theory uncertainties▲higher twist/non-perturbative effects

▲choose Q2 and W cuts to avoid▲higher order effects (NNLO)▲heavy quark mass effects (not discussed)

Parton kinematics

To serve as a handy “look-up”table, it’s useful to define aparton-parton luminosity◆ this is from the review paper and

the Les Houches 2005 writeup Equation 3 can be used to

estimate the production rate for ahard scattering at the LHC as theproduct of a differential partonluminosity and a scaled hardscatter matrix element

Cross section estimates

for pT=0.1*sqrt(s-hat)

gq

qQ

gg

PDF luminosities as a function of y

0246

PDF uncertainties at the LHC

gg

gq

qQNote that for much of the SM/discovery range, the pdfluminosity uncertainty is small

Need similar level of precision intheory calculations

It will be a while, i.e. not in thefirst fb-1, before the LHCdata starts to constrain pdf’s

NB: the errors are determinedusing the Hessian method fora Δχ2 of 100 using onlyexperimental uncertainties

Ratios:LHC to Tevatron pdf luminosities Processes that depend on qQ initial

states (e.g. chargino pair production)have small enchancements

Most backgrounds have gg or gqinitial states and thus largeenhancement factors (500 for W + 4jets for example, which is primarilygq) at the LHC

W+4 jets is a background to tTproduction both at the Tevatron andat the LHC

tT production at the Tevatron islargely through a qQ initial states andso qQ->tT has an enhancement factorat the LHC of ~10

Luckily tT has a gg initial state as wellas qQ so total enhancement at theLHC is a factor of 100◆ but increased W + jets

background means that a higherjet cut is necessary at the LHC

◆ known known: jet cuts have to behigher at LHC than at Tevatron

qQgq

gg

The LHC Environment

The LHC will be a very jetty place

Total cross sections for tT andHiggs production saturated by tT(Higgs) + jet production for jet pTvalues of order 10-20 GeV/c

σ W+3 jets > σ W+2 jets

Indication that can expect interestingevents at LHC to be very jetty(especially from gg initial states)

Also can be understood from point-of-view of Sudakov form factors

Sudakov form factors Sudakov form factor gives the

probability for a gluon not tobe emitted; basis of partonshower Monte Carlos

Consider tT production In going from the Tevatron to

the LHC, you are moving fromprimarily qQ initial states to gginitial states

…and to smaller values ofparton x◆ so there’s more phase

space for gluon emission So significantly more extra

jets associated with the tTfinal state

NLO corrections

NLO is the first order forwhich the normalization,and sometimes theshape, is believable

NLO is necessary forprecision comparisons ofdata to theory

Sometimes backgroundsto new physics can beextrapolated from non-signal regions, but this isdifficult to do for lowcross section final statesand/or final states wherea clear separation of asignal and backgroundregion is difficult

NLO corrections

K-factors may differ from one because of new subprocesses/contributions at higher order and/or differences between LO and NLO pdf’s

Sometimes it is useful to define a K-factor (NLO/LO). Note the value of the K-factor depends critically on its definition. K-factors at LHC (mostly) similar to those at Tevatron.

Counterexample:shape dependence of a K-factor

Inclusive jet production probesvery wide x,Q2 range alongwith varying mixture ofgg,gq,and qq subprocesses

Over limited range of pT and y,can approximate effect of NLOcorrections by K-factor but notin general◆ in particular note that for

forward rapidities, K-factor<<1

◆ LO predictions will belarge overestimates

◆ see extra slides fordiscussion as to why

Another example, from the Tevatron

Suppose you measurethe high mtT regionlooking for new physics

Suppose that yourmeasurement agreeswell with Pythia

Have you missedsomething?

Yes, because NLOprediction at high massis about half of LOprediction◆ partially pdf’s◆ partially matrix elements

What about tT at the LHC? The cross section is

dominated by the ggsubprocess so the K-factor isapproximatelyconstant and > 1◆ unlike the Tevatron

Now we come to the “maligned” experimenter’s NLO wishlist

almost 6 yearsto the day andyet not a single calculation finished!Shame

NLO calculation priority list from Les Houches 2005: theory benchmarks

What about time lag in going from availability of matrix elements to having a partonlevel Monte Carlo available? See e.g. H + 2 jets. Other processes are going to be just as complex.

*completed since list+people areworking

*

*

G. Heinrich and J. Huston

+

+

+

tTj An important calculation at

NLO that would have madethe list, except we knew thatDittmaier, Uwer and Weinzierlwere alread working on it◆ see Stefan’s talk on Mon

NLO corrections are smallwith scale choice near mt

Bonus feature: tTj asymmetryat Tevatron small at NLO

bonus becausetT and tTj asymmetries in opposite directions

From LHC theory initiative white paper

Uli Baur Fermilab W&C Aug 18

Higgs productionPerhaps no surprise that many of the calculations on the list relate to Higgs production and backgrounds thereof.

Let’s consider a few of the processes.

WWj In addition to backgrounds to

SUSY processes, WWj is alsoone of primary backgrounds toHiggs(->WW)+jet◆ where we’re interested in

both W’s decaying semi-leptonically

We’ve seen that the Higgs isoften accompanied by a jet, pluswe want to make use of allchannels (H+0 jet, H+1 jet, andH+2 jets) in searching for a Higgssignal

ATLAS plan is to extrapolate frombackground-rich region◆ primarily Δφll>1.2◆ + some other cuts

to signal-rich region◆ primarily Δφll <1.2 (spins anti-

correlated)◆ + some other cuts

By far the largest systematic uncertainty in this analysiscomes from the LO nature of theWWj background and the extrapolation into the signal regionImprovement of this uncertaintyfrom 20% to 5% would significantly improve discovery potential

Higgs + 2 jets production(Campbell, Ellis, Giele, Zanderighi)

VBF production of Higgs is animportant process that will allowmeasurements of Higgs couplings tovector bosons

Larger cross section, though, fromQCD production of Higgs plus two jets

Large scale dependence at LO forH+2jets

Little shape change in going from LOto NLO (K-factor of ~1.25, similar toHiggs+1 jet) but renormalization scaledependence still large

◆ different scales for αs at top/bottomand middle vertices?

A cut of 40 GeV/c has been placedon each of the Jets. For lower pT jets, the renormalization scale dependence is even greater (and σHiggs+3 jets > σHiggs+2jets)

tTbB and tTjj tTH(->bB) is a tough business,

but may be useful fordiscovery of a low mass Higgs

For one W decaying semi-leptonically and the otherhadronically, the final statehas at least 6 jets, a leptonand missing transversemomentum

Large backgrounds from tTbBand tTjj and important tounderstand them well

In order to suppress latter,require 4 b-tagged jets inevent

Even without backgrounds,large combinatorics fromsignal alone

CMS Physics TDR

VVV critical for SUSYtrilepton and other newphysics involving multipleleptons, jets and missing ET infinal state

Calculated by Lazopoulos,Melnikov and Petriello◆ see Kirill’s talk on Monday on

ZZZ Large increase in cross

section, partially due to pdf’sand partially to large virtualcorrections

Scale dependence of LO doesnot give indication of size ofNLO corrections◆ but similar to VV corrections

at NLO Small shape changes at NLO,

so K-factor works

Some issues/questions What if we don’t finish every

process on the Les Houcheslist in time?◆ and/or we think of new

ones Can we make some

generalizations based on◆ type of reaction, initial

state partons, kinematics▲ gg s-channel reactions

have large K-factors?◆ past experience

▲ tTg->tTbB?◆ and data/(LO)theory at

the Tevatron? Can we learn anything more

about NLO multi-jet crosssections from thresholdresummation?

Calculate soft andcollinear approximationsto NLO (GeorgeSterman)?◆ collinear regions in phase

and loop space universal(and fairly simple)

◆ soft gluon regions changewith number of jets, butare also simple

◆ generate a relativelysimple approximation toNLO following from samefactorization formulas usedto prove thresholdresummation

Some issues/questions Once we have the

calculations, how do we(experimentalists) use them?

Best is to have NLO partoniclevel calculation interfaced toparton shower/hadronization◆ but that has been done

only for relatively simpleprocesses and is very(theorist) labor intensive

▲ still waiting forinclusive jets inMC@NLO, forexample

◆ need more automation

Even with partonic levelcalculations, need abilityto write out ROOTntuples of parton levelevents◆ so that can generate once

with loose cuts anddistributions can be re-made without the need forthe lengthy re-running ofthe predictions

◆ what I do for example withMCFM

▲ but 10’s of Gbytes

Something (easy) for the Tevatron:Wcj

A relatively simple process,Wcj production, is still knownonly at LO◆ sensitive to the strange

quark distribution Crucial for understanding W +

jets, where one or more jetshas been tagged asoriginating from heavy flavor

Agreement is withinsystematics but not as goodas we’d like to see in the oneand two jet bins

Note that analytic form for Wcvirtual amplitudes neverpublished◆ if they were made

available John promises toput them in MCFM

Don’t forget NNLO: we need to know

some processes (suchas inclusive jetproduction) at NNLO

Resummation effects:affect important physicssignatures◆ mostly taken into account

if NLO calculations can belinked with partonshowering Monte Carlos

…and BFKL logs: will we finally

see them at the LHC? EW logs: αWlog2(pT

2/mW2) can be

a big number at the LHC

see talkby Scharf

…and jet algorithms

For some events, the jetstructure is very clear andthere’s little ambiguity aboutthe assignment oftowers/particles to the jet

But for other events, there isambiguity and the jetalgorithm must makedecisions that impactprecision measurements

If comparison is to hadron-level Monte Carlo, then hopeis that the Monte Carlo willreproduce all of the physicspresent in the data andinfluence of jet algorithms canbe understood◆ more difficulty when

comparing to parton levelcalculations

CDF Run II events

Jet algorithms at NLO Remember at LO, 1 parton = 1 jet At NLO, there can be two (or more)

partons in a jet and life becomesmore interesting

Let’s set the pT of the second parton= z that of the first parton and let thembe separated by a distance d (=ΔR)

Then in regions I and II (on the left),the two partons will be within Rcone ofthe jet centroid and so will becontained in the same jet◆ ~10% of the jet cross section is in

Region II; this will decrease asthe jet pT increases (and αsdecreases)

◆ at NLO the kT algorithmcorresponds to Region I (forD=R); thus at parton level, thecone algorithm is always largerthan the kT algorithm

z=pT2/pT1

d

Jets and you There is a need/desire to have

available the results of more than onejet algorithm when analyzing an event

A student of mine and I haveassembled some jet algorithmstogether in a routine that runs on 4-vector files

So far, the routine runs JetClu,Midpoint, kT (inclusive and exclusive),Cambridge/Aachen algorithm,SISCone and simple Pythia UA-1 typealgorithm (CellJet)

◆ in a UA-1 type algorithm, the center ofthe jet is taken as the location of thehighest pT tower; a cone is drawnaround the jet and those towers areeliminated from the remaining jetclustering

User specifies the parameters for thejet reconstruction (including whetherto pre-cluster the 4-vectors togetherinto towers), whether to add in extramin bias events (pending), andwhether to make lego plots (with user-specified tower granularity)

Available from www.pa.msu.edu/~huston/lhc_jet/lhc_jet.html

Jet sample with pTmin>2 TeV/c (from website)

…except for exclusive kT (where jets are explicitly broken up) high ET distributions look similar

Jet masses from 2 TeV/c sample

It’s often useful to examine jetmasses, especially if the jetmight be some compositeobject, say a W/Z or even atop quark◆ very popular in recent

literature, LHC Olympics For 2 TeV jets, peak mass

(from dynamical sources) ison order of 125 GeV/c2, butwith long tail◆ Sudakov suppression for low

jet masses◆ fall-off as 1/m2 due to hard

gluon emission◆ algorithm suppression at high

masses▲ jet algorithms tend to split

high mass jets in two

Event from J8 file (5017, 49120)

MidPoint Jets Et eta phi n mass 2622 -0.348 2.92 26 174.5 2509 0.442 6.05 14 59.8 15.5 -0.033 0.40 9 4.7 9.03 -1.55 1.53 13 2.79

A 2.6 TeV/c jet with the massof a top quark

But a real top quark wouldprobably have jet energydistributed differently◆ separate W and b clusters

Need to be able to look insidestructure of jet as well

LHC jet study We’ve started an LHC working group on jets, with the intent to

have ATLAS and CMS (and interested theorists) work on◆ commonality of jet algorithms◆ jet benchmarks

▲ we’re running common events through the ATLAS/CMSmachinery to note any differences

◆ continuing the work begun at the MC4LHC workshop lastsummer

▲ http://mc4lhc06.web.cern.ch/mc4lhc06/▲ to be continued at Les Houches 2007

◆ plus establishing the machinery to allow jet re-clustering to beeasily done at the ntuple level (so no excuse not to comparethe results of several different jet algorithms)

See www.pa.msu.edu/~huston/lhc_jet/lhc_jet.html

Summary

Physics will come flying hot and heavy whenLHC turns on at full energy in 2008

Important to establish both the SM benchmarksand the tools we will need to properlyunderstand this flood of data◆ and in particular, the needed NLO calculations

WG NLO Multi-leg will address the issue ofthe theoretical predictions for multilegprocesses, in particular beyond leadingorder, and the possibility of implementingthese calculations in Monte Carlos. Thisworking group aims at a cross breedingbetween novel approaches (twistors,bootstraps,..) and improvements instandard techniques.

◆ Dave Soper, Borut Kersevan and I are leadinga group dealing with NLO calculations and theiruse

WG SM Handles and Candles  will review andcritically compare existing tools for SMprocesses, covering issues in pdf, jets andHiggs physics.

WG New Physics  is a beyond SM group,subdivided into SUSY and new models ofsymmetry breaking. It will also address theissue of model reconstruction and modelindependent searches based on topologies.

There will also be an intergroup dedicated toTools and Monte Carlos. This intergroup willliaise with all WG with the task ofincorporating some of the issues and newtechniques developed in these groups inview of improving Monte Carlos and settingstandards and accords among the simulationcodes to better meet the experimentalneeds.

http://lappweb.in2p3.fr/conferences/LesHouches/Houches2007/

CTEQ LHC Workshop May 14-15 Kellogg

Biological Station*,Michigan StateUniversity

Program * The LHC environment * Benchmark QCD measurements * W/Z production as luminosity monitor * W/Z/photon+light/heavy-flavor jets * ttbar/single-top production * Simulation tools: from parton-level to

full event * Next generation of parton shower

models * The Tevatron reach to new physics * New physics searches with 1 fb-1

* Theory tools for new physicssearches

http://tigger.uic.edu/~varelas/cteq_lhc_workshop/

*no medical experiments will be performed onparticipants during their stay

Extra slides

Known known: underlying event at the Tevatron

Define regions transverse to the leading jet in theevent

Label the one with the most transverse momentumthe MAX region and that with the least the MINregion

The transverse momentum in the MAX regiongrows as the momentum of the lead jet increases

◆ receives contribution from higher orderperturbative contributions

The transverse momentum in the MIN region staysbasically flat, at a level consistent with minimumbias events

◆ no substantial higher order contributions Monte Carlos can be tuned to provide a

reasonably good universal description of the datafor inclusive jet production and for other types ofevents as well

◆ multiple interactions among low x gluons

Known unknown: underlying event at the LHC

There’s a great deal ofuncertainty regarding the level ofunderlying event at 14 TeV, butit’s clear that the UE is larger atthe LHC than at the Tevatron

Should be able to establishreasonably well with the firstcollisions in 2008

Rick Field is working on somenew tunes◆ fixing problems present in Tune A◆ tunes for Jimmy◆ tunes for CTEQ6.1 (NLO)◆ see TeV4LHC writeup for details

Aside: Why K-factors < 1 for inclusive jet prodution?

Write cross section indicating explicitscale-dependent terms

First term (lowest order) in (3) leadsto monotonically decreasing behavioras scale increases

Second term is negative for µ<pT,positive for µ>pT

Third term is negative for factorizationscale M < pT

Fourth term has same dependence aslowest order term

Thus, lines one and four givecontributions which decreasemonotonically with increasing scalewhile lines two and three start outnegative, reach zero when the scalesare equal to pT, and are positive forlarger scales

At NLO, result is a roughly parabolicbehavior

(1)(2)

(3)(4)

Why K-factors < 1?

First term (lowest order) in (3) leads tomonotonically decreasing behavior as scaleincreases

Second term is negative for µ<pT, positivefor µ>pT

Third term is negative for factorization scaleM < pT

Fourth term has same dependence aslowest order term

Thus, lines one and four give contributionswhich decrease monotonically withincreasing scale while lines two and threestart out negative, reach zero when thescales are equal to pT, and are positive forlarger scales

NLO parabola moves out towards higherscales for forward region

Scale of ET/2 results in a K-factorof ~1 for low ET, <<1 for high ETfor forward rapidities at Tevatron

SM benchmarks for the LHC

pdf luminosities and uncertainties expected cross sections for useful processes

◆ inclusive jet production ▲ simulated jet events at the LHC▲ jet production at the Tevatron

– a link to a CDF thesis on inclusive jet production in Run 2– CDF results from Run II using the kT algorithm

◆ photon/diphoton◆ Drell-Yan cross sections◆ W/Z/Drell Yan rapidity distributions◆ W/Z as luminosity benchmarks◆ W/Z+jets, especially the Zeppenfeld plots◆ top pairs

▲ ongoing work, list of topics (pdf file)

See www.pa.msu.edu/~huston/

Les_Houches_2005/Les_Houches_SM.html(includes CMS as well as ATLAS)

W + jets at the Tevatron

Interesting for tests ofperturbative QCD formalisms◆ matrix element calculations◆ parton showers◆ …or both

Backgrounds to tT production andother potential new physics

Observe up to 7 jets at theTevatron

Results from Tevatron to the right arein a form that can be easilycompared to theoreticalpredictions (at hadron level)◆ see www-cdf.fnal.gov QCD

webpages◆ in process of comparing to

MCFM and CKKW predictions◆ remember for a cone of 0.4,

hadron level ~ parton level

note emissionof each jet suppressed by~factor of αs

agreement withMCFM for lowjet multiplicity

High pT tops At the LHC, there are many

interesting physics signaturesfor BSM that involve highlyboosted top pairs

This will be aninteresting/challengingenvironment for trying tooptimize jet algorithms◆ each top will be a single jet

Even at the Tevatron havetops with up to 300 GeV/c oftransverse momentum