Precision Jet Physics At the LHC

Transcription

1 Precision Jet Physics At the LHC Matthew Schwartz Harvard University

2 JETS AT THE LHC An (almost) universal feature of SUSY is and Source: Atlas TDR

3 SIGNAL VS. BACKGROUND Source: Atlas TDR Can we trust the background?

4 CAN WE TRUST THE BACKGROUNDS? Compare two monte carlos: Alpgen and Herwig Source: M. Mangano Factor of 10 ~ 100 already at 4 jets we need What is the right answer? Much progress over last years (see Johan s talk).

5 WHAT IS THE RIGHT ANSWER? Ask PYTHIA Only includes 2 2 (some 2 3) tree-level matrix elements Only includes LL resummation Ask Madgraph/Alpgen/Sherpa Includes any 2 n matrix element at tree level Ask MC@NLO/Powheg/Rocket/Blackhat 1-loop matrix elements (see Giulia and Lance s talks) Ask the data calibrate detectors How important is resummation???? How do we know? tune Monte Carlos measure PDFs find new physics All at the same time

6 NEED EFFECTIVE FIELD THEORY Separates physics at different energy scales m = mass of jet E = energy of jet Uses the renormalization group to sum large logarithms between scales Eg. exp[ -a log (m/e) ] m << E Soft-Collinear Effective Theory is the effective field theory of jets e + e - jets p + p + jets

7 SOFT-COLLINEAR EFFECTIVE THEORY(SCET) Lagrangian has separate collinear and soft gauge invariance Covariant objects are fermions wrapped in Wilson lines Jets are collections of collinear fermions and gluons c n =

8 THRUST T~ 1 t 1-T ~ 0 t ~ 1/2 Thrust provides some of the best data in the world 1 million clean events from LEP

9 SOFT-COLLINEAR EFFECTIVE THEORY To interpolate between fat jets and thin jets We expand in the transverse size of the jet m~p t At each scale m, the event can be resolved into some number of jets two jets three jets

10 FACTORIZATION FORMULA For the thrust distribution: Fleming, Hoang, Mantry, Stewart (hep-ph/ ) MDS, PRD: (2008) Hard Function: Jet Function: Soft Function:

11 CONVERGENCE Fixed Order Effective Field Theory (matched to Fixed Order) At fixed a s (M Z ) =

12 CONVERGENCE Fixed Order Effective Field Theory (matched to Fixed Order) At fixed a s (M Z ) =

13 CONVERGENCE Fixed Order Effective Field Theory (matched to Fixed Order) At fixed a s (M Z ) =

14 LEP I AND LEP II MDS, T. Becher a s (M Z ) = ±0.002 a s (M Z ) = ±0.005 (fixed order thrust) a s (M Z ) = ±0.002 (World Average) Effective field theory is much more convergent than fixed order QCD improves fit to a s tremendously helps test QCD

15 SCET VS PYTHIA 4 th order Q = 91.2 GeV E CM =90 GeV

16 SCET VS PYTHIA 4 th order Q = 91.2 GeV E CM =90 GeV

17 SCET VS PYTHIA 1 st order 4 th order Q = 91.2 GeV E CM =90 GeV

18 SCET VS PYTHIA 1 st order 4 th order Q = 1 TeV E CM = 1 TeV

19 SCET VS PYTHIA Q = 1 TeV E CM = 1 TeV

20 JETS AT THE LHC Heavy Jet mass at the LHC (according to PYTHIA) Is this correct? What should it really look like??

21 JETS AT HADRON COLLIDERS e + e - jets pp jet+γ Direct photon production γ pp jets γ Threshold direct photon production Initial state: 2 protons Final state: 1 jet + 1 photon+ soft radiation

22 DIRECT PHOTON PRODUCTION Perturbation Theory γ γ Leading Order Compton Channel (important way to measure gluon PDF) Annihilation Channel

23 DIRECT PHOTON PRODUCTION Hard scale Jet scale Soft scale PDF PDF Jet function Soft function

24 FINAL DISTRIBUTION PDF PDF Hard function Jet function NLO (from QCD) SCET: γ H to 3-loops Quark jet to NNLO Gluon jet to NLO γ Jq and γ Jq to 3-loops Soft function both channels to NLO γ S to 3-loops (from RG and Casimir scaling) Direct phot on dist ribut ion w it h NNLL resum m at ion + NLO fixed order

25 RESULTS MDS, T. Becher NNLL + NLO vs CDF dat a Photon p T

26 WHAT ARE THE MATCHING SCALES? Matching scales appear as: = mass of jet Hard scale = p T γ Jet scale = Works for thrust Problematic for direct photon m J is integrated over, including m J =0 would probe Landau pole of QCD power corerctions All matching scales must depend on physical scales of the observable h= h(p T ) J= J(p T ) s= s(p T )

27 JET SCALE IS LOWER Hard scale Jet scale What is going on physically?

28 THRESHOLD ENHANCEMENT (mass everything but the photon) Machine threshold (mass of jet) Partonic threshold Where factorization theorem holds Where partonic logs are large large large large small γ PDFs die fast as x 1 Jet masses are typically much less than the kinematic maximum Use exact PDFs, resum logs of Dynamical Threshold Enhancement resummation unexpectedly useful at hadron collliders!

29 MATCHING SCET valid near threshold (x 1 ~ 1 and x 2 ~ 1) Matching to exact fixed order reduces m f dependence

30 SCALE UNCERTAINTIES

31 RESULTS SCET vs CDF dat a Photon rapidity Photon p T

32 RESULTS Corrected for hadronization with PYTHIA Corrected for photon isolation with JETPHOX

33 PREDICTIONS FOR LHC

34 CONCLUSIONS Understanding jets is critical for the LHC Resummation can be done with SCET Great improvements for LEP event shapes Great improvements for direct photon spectrum Resummation important even at moderate x<1 Next steps W/Z + jets (work in progress) Dijets (work in progress) Exclusive Monte Carlo event generation (on hold)