QCD Phenomenology at High Energy

Transcription

1 QCD Phenomenology at High Energy CERN Academic Training Lectures February 2008 Lecture 5: Matching Fixed Order Matrix Elements with Parton Showers

2 ME-PS Matching Two rather different objectives: Matching parton showers to NLO matrix elements, without double counting POWHEG Matching parton showers to LO n-jet matrix elements, minimizing jet resolution dependence CKKW Dipole MLM Matching Comparisons

3 Recall simple one-dim. example from lecture 2: x = gluon energy or two-parton invariant mass. Divergences regularized by dimensions. Cross section in d dimensions is: Infrared safety: KLN cancellation theorem:

4 Exact identity: J Subtraction Method Two separate finite integrals.

5 σ J = 1 0 Modified Subtraction dx x ( M(x) F J 1 (x) V F J 0 ) + O(1) V F J 0 Now add parton shower: F0,1 J result from showering after 0,1 emissions. But shower adds M MC /x to 1 emission. Must subtract this, and add to 0 emission (so that F0,1 tot = 1 σ tot fixed) 1 σ J dx( = {M(x) MMC (x)} F1 J (x) 0 x {V M MC (x)} F0 J ) + O(1) V F J 0 MC good for soft and/or collinear M MC (0) = M(0) 0 & 1 emission contributions separately finite now! (But some can be negative counter-events )

6 Processes IPROC IV IL 1 IL 2 Spin Process 1350 IL H 1 H 2 (Z/γ )l IL lil + X 1360 IL H 1 H 2 (Z )l IL lil + X 1370 IL H 1 H 2 (γ )l IL lil + X 1460 IL H 1 H 2 (W + )l + IL ν IL + X 1470 IL 1396 H 1 H 2 (W )l IL ν IL + X H 1 H 2 γ ( i f i f i ) + X 1397 H 1 H 2 Z 0 + X 1497 H 1 H 2 W + + X 1498 H 1 H 2 W + X 1600 ID H 1 H 2 H 0 + X 1705 H 1 H 2 b b + X H 1 H 2 t t + X 1706 i j H 1 H 2 (t )bl i + ν i( t ) blj ν j + X 2000 IC 7 H 1 H 2 t/ t + X 2000 IC i H 1 H 2 (t )bl i + ν i/( t ) bli ν i + X 2001 IC 7 H 1 H 2 t + X 2001 IC i H 1 H 2 ( t ) bli ν i + X 2004 IC 7 H 1 H 2 t + X 2004 IC i H 1 H 2 (t )bl i + ν i + X 2600 ID 1 7 H 1 H 2 H 0 W + + X 2600 ID 1 i H 1 H 2 H 0 (W + )l i + ν i + X 2600 ID -1 7 H 1 H 2 H 0 W + X 2600 ID -1 i H 1 H 2 H 0 (W )li ν i + X 2700 ID 0 7 H 1 H 2 H 0 Z + X 2700 ID 0 i H 1 H 2 H 0 (Z )l i li + X H 1 H 2 W + W + X 2850 i j H 1 H 2 (W + )l i + ν i(w )lj ν j + X H 1 H 2 Z 0 Z 0 + X H 1 H 2 W + Z 0 + X H 1 H 2 W Z 0 + X e 1: Processes implemented in MC@NLO 3 3. denotes the Standard Model Higgs b

7 Results WW production at LHC NLO HERWIG Interpolates between MC & NLO in Above both at φ (WW) 0 p (WW) T S Frixione & BW, JHEP 06(2002)029

8 W + W : MC@NLO vs Resummations Plots from M. Grazzini JHEP 0601(2006)095 Highly non-trivial test (of both computations) for shapes and rates! M TWW = (E T ll + /E T ) 2 (p T ll + /p T ) 2 where E T ll = p 2 T ll + m2 ll and /E T /p 2 T + m 2 ll (Rainwater & Zeppenfeld) Cuts involved in definition of M TWW : φ l+ l p (l+,l ) Tmin > 25 GeV, 35 < p (l+,l ) Tmax < 50 GeV, p WW T < π/4, M l + l > 35 GeV, < 30 GeV

9 W + W Spin Correlations Normalized to MCatNLO, no spin corr. MCatNLO, spin corr. included Sherpa Normalized to MCatNLO, no spin corr. MCatNLO, spin corr. included Sherpa "! ll Plots from W. Quayle (preliminary) M ll (GeV)

10 b Production: PS MC vs In parton shower MC s, 3 classes of processes can contribute: FCR GSP FEX! All are needed to get close to data (RD Field, hep-ph/ ): µ µ

11 GSP and FEX contributions in HERWIG PS MC! GSP, FEX and FCR are complementary and all must be generated " GSP cutoff (PTMIN) sensitivity depends on cuts and observable " FEX sensitive to bottom PDF " GSP efficiency very poor, 10 4! All these problems are avoided with 29

12 B Production at Tevatron! B J/ψ results from Tevatron Run II B hadrons Figure 5: CDF J/ψ spectrum from B decays. The theory band represents the FONLL systematic uncertainties, propagated Good from Fig. agreement 2. Two MC@NLO predictions (and are also shown MC (histograms), efficiency) with the same patterns as in Fig. 3. to the hadrons, and vice versa. Effects of this size are consistent with what we showed in Fig. 3. We finally present in Fig. 5 our prediction for the J/ψ spectrum, obtained by convoluting the FONLL result with the J/ψ momentum distribution in inclusive B J/ψ + X decays. 5 The data lie well within the uncertainty band, and are in very good agreement with the central FONLL prediction. We also show the two MC@NLO predictions corre- S Frixione, P Nason & BW, JHEP 0308(2003)007 M Cacciari et al., JHEP 0407(2004)033

13 Di-b Jet Production These observables are very involved (b-jets at hadron level) and cannot be computed with analytical techniques; The underlying event in Pythia is fitted to data; default Herwig model (used in does not fit data well (lack of MPI).

14 b-jets: Improved Underlying Event The JIMMY underlying event model includes multiple parton interactions and interfaces to Herwig interfaces to The importance of the underlying event shows the necessity of embedding precise computations in a Monte Carlo framework.

15 Higgs Production at LHC V Del Duca, S Frixione, C Oleari & BW, in prep. Good agreement with state-of-the-art resummation

16 POWHEG Positive Weight Hardest Emission Generator Method to generate hardest emission first, with NLO accuracy, independent of PSEG Can be interfaced to any PSEG No negative weights Inaccuracies only affect next-to-hardest emission In principle, needs truncated showers P Nason & G Ridolfi, JHEP08(2006)077 S Frixione, P Nason & G Ridolfi, arxiv: S Frixione, P Nason & C Oleari, arxiv:

17 POWHEG How it works (roughly) In words: works like a standard Shower MC for the hardest radiation, with care to maintain higher accuracy. Inclusive cross section Φ n = Born variables Φ r = radiation vars. NLO inclusive cross section. Positive if NL < LO INFINITE INFINITE B (Φ n ) = B(Φ n ) + V (Φn ) + R(Φ n, Φ r ) dφ r FINITE! Sudakov form factor for hardest emission built from exact NLO real emission t = exp θ(t r t) R(Φ n, Φ r ) dφ r B(Φ n ) FINITE because of θ function with t r = k T (Φ n, Φ r ), the transverse momentum for the radiation.

18 POWHEG and comparison: Top pair production Good agreement for all observable considered (differences can be ascribed to different treatment of higher order terms)

19 POWHEG for e + e hadrons O Latunde-Dada, S Gieseke, B Webber, JHEP02 (2007) 051, hep-ph/

20 Truncated Shower In angular-ordered shower, hardest emission is not necessarily the first Need to add softer, wider-angle emissions Checked for up to one such emission in e + e - q z z t (2!x)E k T g! q xe Z/!" (2!x)E q z t (2!x)E (1!z )(2!x)E t q p T t g (1!z) z t (2!x)E

21 Effect of truncated shower Observable Herwig++ ME with truncated shower w/o truncated shower 1 T Thrust Major Thrust Minor Oblateness Sphericity Aplanarity Planarity C Parameter D Parameter M high M low M diff B max B min B sum B diff N ch χ 2 /bin Table 2: χ 2 /bin for all observables we studied. Small but beneficial effect

22 CKKW Matching Use Matrix Elements down to scale Q1 Use Parton Showers below Q1 Correct ME by reweighting Correct PS by vetoing Ensure that Q1 cancels (to NLL) S Catani, F Krauss, R Kuhn & BW, JHEP11 (2001) 063

23 Example: e + e - hadrons 2- & 3-jet rates at scale Q1: Q R 2 (Q, Q 1 ) = [ q (Q, Q 1 )] 2, q Q 1 Q R 3 (Q, Q 1 ) = 2 q (Q, Q 1 ) dq q(q, Q 1 ) Q 1 q (q, Q 1 ) Γ q(q, q) q (q, Q 1 ) g (q, Q 1 ) = 2 [ q (Q, Q 1 )] 2 Q Γ q (Q, q) = 2C F π Q 1 dq Γ q (Q, q) g (q, Q 1 ) α S (q) q ( ln Q q 3 ) 4

24 CKKW reweighting Choose n according to R n (Q, Q 1 ) (LO) use [α S (Q 1 )] n Use exact LO ME to generate n partons Construct equivalent shower history preferably using kt-type algorithm α S (q)/α S (Q 1 ) < 1 Weight vertex at scale q by Weight parton of type i from Qj to Qk by i (Q j, Q 1 )/ i (Q k, Q 1 )

25 CKKW shower veto Shower n partons from creation scales includes coherent soft emission Veto emissions at scales above Q1 cancels leading (LL&NLL) Q1 dependence shower from Q Q q Q 1 shower from q shower from Q, not q

26 Comparisons with Tevatron data dσ/de T [pb/gev] (W eν) + n jets st 1 jet nd 2 jet rd 3 jet th 4 jet CDF Data CDF Run II Preliminary dl = 320 pb e W kin: E T 20[GeV]; η 1.1 W 2 ν M T 20[GeV/c ]; E T 30[GeV] Jets: JetClu R=0.4; η <2.0 hadron level; no UE correction LO Alpgen + PYTHIA CKKW Total σ normalized to Data e -1 σ( 3 jets)/σ( 2jets) (W eυ) + n Jets CDF Run II Preliminary -1 CDF Data dl = 320 pb W kin: e e E T 20 [GeV]; η 1.1 ν W 2 E T 30 [GeV]; M T 20 [GeV/c ] Jets: jet jet JetClu R=0.4; E T 15 [GeV]; η 2.0 Hadron Level; no UE correction 2 jet 2 MCFM Q = <P T > (parton level) 2 2 MCFM Q = M W (parton level) LO MADGRAPH + PYTHIA CKKW Jet Transverse Energy [GeV] Di-jet η(jet 1 - jet 2 ) from JM Campbell, JW Huston & WJ Stirling, Rept.Prog.Phys.70(2007)89 M.E. + PYTHIA CKKW looks good

27 Dipole Matching Implemented in ARIADNE dipole MC Dipole cascade replaces parton shower Construct equivalent dipole history {pti} Rejection replaces Sudakov weights cascade from pti, reject if pt > pti+1 L Lönnblad, JHEP05(2002)046

28 MLM Matching Use cone algorithm for jet definition: R 2 ij = (η i η j ) 2 + (φ i φ j ) 2 E T i > E T min, R ij > R min Generate n-parton configurations with E T i > E T min, R ij > R min (no Sudakov weights) Generate showers (no vetos) Form jets using same jet definition Reject event if njets = npartons

29 Comparisons ALPGEN: MLM matching ARIADNE: Dipole matching HELAC: MLM matching MadEvent: hybrid MLM/CKKW SHERPA: CKKW matching J. Alwall el al., arxiv:

30 W + Multijets (Tevatron) Alpgen Ariadne Helac MadEvent Sherpa "(W +/- +! N jets) / <"> ! 0! 1! 2! 3! 4

31 W + Multijets (Tevatron) d!/de "1 (pb/gev) Alpgen (a) Ariadne Helac MadEvent Sherpa E "1 (GeV) d!/de "2 (pb/gev) (b) E "2 (GeV) d!/de "3 (pb/gev) (c) E "3 (GeV) d!/de "4 (pb/gev) (d) E "4 (GeV)

32 W + Multijets (Tevatron) (1/!)d!/d" (a) Alpgen Ariadne Helac MadEvent Sherpa (1/!)d!/d" (b) " 1 " (1/!)d!/d" (c) (1/!)d!/d" (d) " " 4

33 W + Multijets (LHC) Alpgen Ariadne Helac MadEvent Sherpa "(W + +! N jets) / <"> ! 0! 1! 2! 3! 4

34 d!/de "1 (pb/gev) W + Multijets (LHC) Alpgen (a) Ariadne Helac MadEvent Sherpa E "1 (GeV) d!/de "2 (pb/gev) (b) E "2 (GeV) d!/de "3 (pb/gev) (c) d!/de "4 (pb/gev) (d) E "3 (GeV) E "4 (GeV)

35 W + Multijets (LHC) (1/!)d!/d" (a) Alpgen Ariadne Helac MadEvent Sherpa (1/!)d!/d" (b) " 1 " 2 (1/!)d!/d" (c) (1/!)d!/d" (d) " 3 " 4

36 Summary of Lecture 5 Matching Parton Showers to Matrix Elements comes in different forms: matching to NLO for better precision matching to LO for multijets MC@NLO is main scheme for NLO matching newer POWHEG method looks promising Several options for LO multijets reasonably consistent spread indicates uncertainties (?) Field still very active NLO matching for jets, spin correlations,... building multijet matching into event generators