Precise predictions for di-boson production at the LHC. Fabrizio Caola, CERN

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1 Precise predictions for di-boson production at the LHC Fabrizio Caola, CERN LHC RUN II AND THE PRECISION FRONTIER, KITP, 30 MAR. 06

2 Precision for di-boson: why LHC: sizable cross-section Good control on di-boson processes: Test the SU()xU() SM structure Higgs background, offshell Higgs BSM backgrounds (leptons + Et,miss) [MCFM] LHC Run-: ~0% accuracy no deviation from SM PERCENT-LEVEL EXPERIMENTAL ACCURACY WITHIN REACH

3 Precision predictions for di-boson production at the LHC: outline The quest for precision: NNLO predictions The importance of fiducial measurements: the WW cross section Large effects beyond NNLO: NLO

4 NNLO predictions for di-boson processes

Z Precise predictions: what do we need d = dx dx f (x )f (x )d part (x,x )F J ( + O( QCD /Q)) Require precise input parameters (αs, PDFs) High-Q physics part we have most control on Must describe

5 Z Precise predictions: what do we need d = dx dx f (x )f (x )d part (x,x )F J ( + O( QCD /Q)) Require precise input parameters (αs, PDFs) High-Q physics part we have most control on Must describe realistic conditions (fiducial cuts, arbitrary observables fully differential) Ultimate limitation: NP corrections. For typical EW scale: ~ percent Since αs ~ 0.: percent-level control NNLO PREDICTIONS

-> VV+J In principle, problem-solved. IN PRACTICE: must be very stable and fast.

6 Anatomy of a NNLO computation - I VV UP TO TWO-LOOP FOR QQ -> VV Amplitudes for pp -> VV -> 4l only computed recently [FC, Henn, Melnikov, Smirnov, Smirnov (05); Gehrmann, Manteuffel, Tancredi (05)] RV UP TO ONE-LOOP FOR QQ -> VV+J In principle, problem-solved. IN PRACTICE: must be very stable and fast. For VV processes: OpenLoops proved reliable RR TREE-LEVEL FOR QQ -> VV+JJ So a NNLO computation for VV naturally contains a (N)LO computation for VV+() jet

7 Anatomy of a NNLO computation - II For a long time, the problem of NNLO computations was how to consistently extract IR singularity from double-real emission/real-virtual emission. Knowing all relevant amplitudes not enough (especially problematic for processes with non-trivial color structure) A lot of progress recently. First steps towards an optimal solution Subtraction: antenna, sector-improved FKS, colorful Slicing: qt, N-jettiness In practice, this allowed for computations of -> reactions at the LHC (top-pair, di-jet, single-top, H+J, V+J )

8 σ/ γγ [ / ] NNLO: what does it buy you For Born-like observables (cross-section, m4l, pt,l ) Stabilization of the perturbative expansion / Example: Zγ, ATLAS setup [Grazzini, Kallweit, Rathlev (05)] σlo = % -9.3%, σlo = % -4.3%, σnnlo = % -.4% or KNLO = +7%, KNNLO = +3% σ σ γγ [ ] More reliable scale uncertainty estimates, typically reduced ( discussions about right scale less important) For VV processes: no αs at Bornlevel, lowest order scale uncertainty badly underestimates corrections (also, new channels open up) Example: di-photon, m γγ, CMS setup [Campbell, Ellis, Li, Williams (06)]

(0)] Merged NLO [Höche and Siegert, SHERPA] Isolated diphoton cross-section vs diphoton azimuthal separation

9 NNLO: what does it not buy you For configurations dominated by extra hard radiation, NNLO VV predictions are the same of NLO predictions for VV+J. Example: di-photon opening angle NNLO [Catani et al. (0)] Merged NLO [Höche and Siegert, SHERPA] Isolated diphoton cross-section vs diphoton azimuthal separation ds/ddfgg [pb/rad] 0 0 Data gg+0,j@nlo+,3j@lo MC/Data Df gg [rad] γγ@nnlo gives you γγj@nlo for free, but nothing more

10 NNLO: where do we stand NNLO corrections for almost all di-boson processes. γγ: Catani et al. (0); Campbell, Ellis, Li, Williams (06) VV: Grazzini, Kallweit, Rathlev, Torre, Cascioli, Gehrmann, Maierhöfer, Manteuffel, Pozzorini, Tancredi, Weihs (03-05) Total Cross- Section Fiducial Higgs-region γγ Vγ ZZ WW ~ WZ General picture: good theory/data agreement

11 Sample results: γγ σcms = 7. ± 0. (stat) ±.9 (syst) ± 0.4 (lumi) pb σ +Δσ σ σ σ σmcfm = 7.0 ±. pb [with gg@nlo] Excellent data/nnlo agreement σγγ[ ] gg@nlo sizable effect Nice validation with functional forms used for data-driven fits μ = γγ [ ] ( ) /σ σ/ γγ GeV.6 TeV mγγ

12 Sample results: Vγ [Grazzini, Kallweit, Rathlev, Torre (03); Grazzini, Kallweit, Rathlev (05)] Fiducial region: NNLO vs ATLAS 7 TeV data process p γ T,cut N jet σ LO [pb] σ NLO [pb] σ NNLO [pb] σ ATLAS [pb] σ NLO σ LO σ NNLO σ NLO Kallweit, Moriond 06 Zγ % % 5.3%.3% llγ soft % 9.3% = % % 4.3%.4% hard % 4.5% % 4.0% Zγ % 3.% ννγ % 0.9% = %.3%.3.05 ±0.0 (stat) ±0. (syst) ±0.05 (lumi) ±0.0 (stat) ±0.0 (syst) ±0.04 (lumi) +50% +8% +7% +3% %.8% +79% +7% %.3% % 0.9% Wγ % % 6.8% 4.% lνγ soft % 8.% = % % 5.8%.7% hard % 3.7% % 7.3% ±0.03 (stat) 0.33 ±0.00 (syst) ±0.005 (lumi) ±0.00 (stat) 0.6 ±0.03 (syst) ±0.004 (lumi) ±0.03 (stat) ±0.33 (syst) ±0.4 (lumi) ±0.03 (stat) ±0. (syst) ±0.08 (lumi) +57% +% +% % +36% +9% +60% +7% % 4.7% +4% +6% In general, very good agreement, apart for Z νν (under investigation) NLO scale variation fails to capture NNLO Negligible impact of gg channel

13 Sample results: ZZ [Cascioli et al (04); Grazzini, Kallweit, Rathlev (05)] σ[pb] 5 0 pp ZZ+X NNLO+gg NLO+ggN NLON+gg LONN+gg Largest contribution to NNLO from gg channel (~60%). LO-contribution sis: large interfe σ/σ NLO 8 ATLAS (66 GeV <m ll < 6 GeV) CMS (60 GeV <m ll < 0 GeV) s [TeV] 3 4 Good agreement at 7, 8 and 3 TeV Perfect agreement for eμ channel, consistent within σ for ee, μμ channels ATLAS 8 TeV fiducial channel σ LO [fb] σ NLO [fb] σ NNLO [fb] σ ATLAS [fb] e + e e + e (stat) (syst) () (lumi) +.9% 3.9% 5.047()+.8%.3% 5.79()+3.4%.6% µ + µ µ + µ (stat) (syst) (lumi) e + e µ + µ 6.950() +.9% 3.9% 9.864()+.8%.3%.3()+3.%.5% (stat) (syst) (lumi)

14 WW: total vs fiducial

The WW puzzle Early LHC measurements σatlas,8 = 7.4 +.. (stat) +5.0 4.4 (syst) +.. (lumi) pb σcms,8 = 69.9 ±.8 (stat) ± 5.

15 The WW puzzle Early LHC measurements σatlas,8 = (stat) (syst) +.. (lumi) pb σcms,8 = 69.9 ±.8 (stat) ± 5.6 (syst) ± 3. (lumi) pb Theoretical prediction (MCFM) NNLO corrections: ~ 0 % σnlo = pb SOME TENSION, FOR BOTH ATLAS AND CMS

16 The WW puzzle However, if one looks at the FIDUCIAL REGION e + µ + e µ (stat.)+5.. (syst.) e + e (stat.) (syst.)+..0 µ + µ (stat.) (syst.) TeV pp l + l ν ν pp H l + l ν ν total (lumi.) (lumi.) (lumi.) TENSION SIGNIFICANTLY ALLEVIATED [Monni, Zanderighi (04)] In other words, comparing NLO predictions to what is ACTUALLY MEASURED leads to reasonable data/theory agreement. Note: same data, same theory WHAT IS GOING ON?

17 (ATLAS) analysis for dummies.perform the measurement. By definition, in the fiducial region. Agreement data/theory.use your favorite toy, let s say POWHEG, to extrapolate from the fiducial region to the total cross-section 3.Get the total cross section and compare Disagreement data/theory Step introduced a (a-priori non-needed) theory dependence on the result, and this time got it wrong

18 The problem with extrapolation: jet veto modeling [Monni, Zanderighi (04)] To suppress the large top background, WW analysis require a harsh jet veto, pt,veto = 5 GeV ε(p t,veto ) ε(p t,veto )/ε NLO (p t,veto ) pp W + W - pp, 8 TeV POWHEG + PYTHIA MSTW008 PDFs anti-k t, R=0.4 tune Perugia 350 tune Perugia 340 tune Perugia 346 NLO p t,veto [GeV] Independent on tunes, POWHEG fails to properly model the jet veto efficiency and predicts fiducial cross section which are systematically lower When used for acceptance corrections, it then leads to overestimate the inclusive cross section

19 The problem with extrapolation: jet veto modeling [Monni, Zanderighi (04)] A more refined analysis: POWHEG vs NNLL resummation For pt,veto = 5 GeV, NNLL resummation effects decrease pure NLO by 3-4% POWHEG prediction: -9% Also, other small effects in POWHEG further decrease efficiency NNLO+NNLL partially compensates for NNLO K- factor agreement in the fiducial region should persist / improve at NNLO ε(p t,veto ) ε(p t,veto )/ε NLO (p t,veto ) pp Z pp, 8 TeV m Z /4 < µ R,F, Q < m Z MSTW008 PDFs anti-k t, R=0.4 NNLO+NNLL NLO+NNLL NLO NNLO p t,veto [GeV] THESE EFFECTS COMPLETELY EXPLAIN THE EXCESS IN THE INCLUSIVE MEASUREMENT

20 New analysis: approximate NLO+NNLL σatlas,8 = (stat) (syst) (lumi) pb [Higgs contribution included] σcms,8 = 60. ± 0.9 (stat) ± 3. (exp) ± 3. (th) ±.6 (th) pb [Higgs contribution subtracted] σnnlo = % -.9% % -7.% (Higgs) pb Perfect agreement for CMS Slight ~.5σ tension with ATLAS Calls for COMPARISONS IN THE FIDUCIAL REGION (all ingredients are available, minimize theory error)

Why fiducial region : top contamination At NNLO: huge contamination from (LO) tt production for the inclusive cross-section σ full [pb] 500 NNLO NLON LONN pp W + W +X @ 8 TeV 00 00 50 0 σ 5FNS

21 Why fiducial region : top contamination At NNLO: huge contamination from (LO) tt production for the inclusive cross-section σ full [pb] 500 NNLO NLON LONN pp W + W 8 TeV σ 5FNS full /σ 4FNS Different approaches studies for defining the total cross-section (4FNS, b-veto, resonance expansion) p veto T,bjet [GeV] Should greatly simplify in the FIDUCIAL REGION

22 VV: gluon channel at NLO

23 gg->vv At NNLO, the gg channel enters for the first time sis: large interfe Because of the large gluon flux at the LHC, this contribution is usually big (ZZ/WW: 60%/35% of NNLO corrections) They are separately finite and gauge-invariant usually already included in NLO predictions non trivial interference pattern with Higgs, especially in the high invariant mass region very important for off-shell / interference analysis

24 gg->vv At NNLO, the gg channel enters for the first time sis: large interfe Gluon induced process expect large corrections. Despite being part of the NNLO computation, it is actually LO Corrections to gg->vv are formally part of the N 3 LO corrections to pp->vv, but are expected to give sizable contribution NLO CORRECTIONS FOR GG->VV DESIRABLE

25 Example: γγ [Campbell, Ellis, Li, Williams (06)] σcms = 7. ± 0. (stat) ±.9 (syst) ± 0.4 (lumi) pb σγγ[ ] σ +Δσ σ σ σ σ/ γγ [ / ] σ σ σ/ γγ [ / ] σ +Δσ σ μ = γγ / γγ [ ] / γγ [ ] [ ] σnnlo = 5.8 ± pb Sizable effect δσgg->γγ@nlo =. pb Somewhat improves data/ theory agreement

26 problems Despite being a NLO computation, it involves complicated -loop amplitudes (LO is loop-induced). Similar amplitudes for qq->vv@nnlo Especially for Higgs analysis, important to go at high invariant mass top quark contribution become relevant (same for qq->vv@nnlo) q T Recently computed VERY HARD [important in the off-shell region]

we can identify six different two-loop topologies; t m we can identify six different two-loop topologies; 4 = xz, = x y the differential equations can be m ``rationalized wo-loopthecalculations in

methods ( direct gg->zz@nlo: massless quarks q s method of differential equations ns, differential equations).

27 we can identify six different two-loop topologies; t m we can identify six different two-loop topologies; 4 = xz, = x y the differential equations can be m ``rationalized wo-loopthecalculations in QCD differential equations can be ``rationalized m3 3 with the following (typical) change ofwith variables the following (typical) change of variables p integrals relies on a large number of various methods ( direct gg->zz@nlo: massless quarks q s method of differential equations ns, differential equations). The s ) m = m = ( + x)( + xy), (s m m 4m master integrals for long time, = ( + x)( + xy), m3 starting from papers by Kotikov and m3 990s, however it was never ``the method. t m4 t Z new ideas = xz, = x y fast and dt stable t m4 n m3 m3 G(a, a,..., a, t) = G(an = xz, = x y evelopment in the field is the suggestion by J. Henn to streamline the n n in soft/collinear for FI tn a n m3 al equations in externalqkinematic variables to compute master integralsm3 configurations 0 Real emission -loop amplitude for ZZ* at work (s f~ = A x (x, y, z... )f~ m4 ) 4m3 m4 = m3 x( y) q a) m4 ) b gg=>zz =analytical y) mixedissues: Important finding a suitab G(an, an,..., a, t) =,... a, tn ) +numerical unitarity Figure : Representative Feynman diagrams for thevariables ; 0! gggz(! e bo e+ t choice of ``rational Z df~ = (da) dimensional f,0 A = regularization Ai log i dtn relevant for both the on-shell and the o t is that on the right-hand side, the resonant diagrams (a) are [FC, Henn, Melnikov, Smirnov, Smirnov (04-5); conditions forn solutions G(an, an Double,..., a, t) = G(a,... a, tn )of differe explicitly, and only as a multiplicative pre-factor. It is then possible (Caola, Melnikov, Ronstch t a [FC, Melnikov, Röntsch, Tancredi (05)]and n n Gehrmann, Manteuffel, Tancredi (04-5)] resonant diagrams (b) are only relevant for the oﬀ-shell production Important issues: finding a suitable basis; equations, analytic continuation. 0 ions iteratively since eachz order =order-by-order {x, y, z, + in x,(d-4) y, +inxy, y, + y( + x) z, variables ; computation. See text for details. e above equationchoice containsofno``rational homogeneous terms (boundary so that in Numerical evaluation oflogoncha i xy + z, + x( + y z), + xz, n, the right-hand conditions side is the source for the left-hand side). for solutions of differential NLOmapping Important issues: finding a suitable basis; polylogarithms and their + y z, z + x(z y) + xyz, z y + yz + xyz} We write the interaction vertex of the Z-boson and a fermion pair a equations, analytic continuation. ( + x) large z, X corrections NNPDF3.0, 8 TeV reamlines and simplifies such evaluation computations significantly. Thischoice of ``rationalconventional variables ; boundary polylogarithms. Numerical of Goncharov s (da) advances f, A (=e.g. master Ai log i for Bhabha,V V 5) 0.0 µ f gl,f µ ( + 5 ) + gr,f µ ( impressive integrals Z f, f polylogarithms and their mapping on conditions for solutions of differential yz + xyz} l have interesting consequences for phenomenology. effectconventional on NNLO: +6% polylogarithms. equations, continuation., z,monday, + x,november y, 3, 4 + xy, z y, + y( + x) z, The leftanalytic and right couplings for leptons and quarks are given by an (NNLO scale Numerical evaluation of Goncharov svf ± Af + z, + x( + y z), + xz, gl(r),f =, uncertainty ~ 3%) polylogarithms and their mapping on cos W 0.00 y z, z + x(z y) + xyz, z y + yz + xyz} conventional polylogarithms. 4 where we use i) Vl = / + sin W, Al = / for charged l 5 0 Zt dtn G(an tn a n X 4m3 m4 m3 x( d /dm4l [fb/0 GeV] (s m3 massive loop contribution to σtot ~ % 4/3sin W, Au = / for up-type quarks; and iii) Vd = / + / down-type quarks The 0! gggzz scattering amplitude can be written as a sum of tw m4l [GeV]

28 massless quarks d /dp?, e + e [fb/5 GeV] LO NLO NNPDF3.0, 3 TeV [GeV] p?,e + e d /dp?,l [fb/5 GeV] LO NLO NNPDF3.0, 8 TeV p?,l [GeV] (m4l >mcut) [fb] LO NLO NNPDF3.0, 8 TeV m cut [GeV] realistic final states (leptons) Z off-shell, Z/γ interference ( can study on the Higgs peak) K-factor relatively flat

29 massless quarks [FC, Melnikov, Röntsch, Tancredi (05)] + [fb/5 GeV] d /dp?,l LO NLO NNPDF3.0, 8 TeV p?,l + [GeV] d /d l + l [fb/0.] LO NLO NNPDF3.0, 8 TeV l + l d /dml + l [fb/5 GeV] m l + l LO NLO NNPDF3.0, 8 TeV [GeV] similar corrections to ZZ, K-factor typically stable smaller impact on NNLO (~%) massive loop contribution ~ 0% d /dmt,w W [fb/0 GeV] LO NLO NNPDF3.0, 8 TeV m t,w W [GeV]

gg->ww@nlo: massless quarks [FC, Melnikov, Röntsch, Tancredi (05)] fiducial predictions, ATLAS 8TeV µµ,8 TeV ee,8 TeV eµ,8 TeV gg,lo [fb] 5.94 +.89.35 5.40 +.7.3 9.79 +3.3.4 gg,nlo [fb] 7.0 0.36 0.

30 massless quarks [FC, Melnikov, Röntsch, Tancredi (05)] fiducial predictions, ATLAS 8TeV µµ,8 TeV ee,8 TeV eµ,8 TeV gg,lo [fb] gg,nlo [fb] (rough) combination with NNLO ATLAS result q q+h+gg,nlo µµ,ee,eµ+µe = ( , , ). µµ,ee,eµ+µe = ( , , ) It would be very interesting to properly combine NNLO and gg->vv@nlo in the fiducial region

gg->vv: massive loops [FC, Dowling, Melnikov, Röntsch, Tancredi, in progress] Compute exact two-loop amplitudes mediated by heavy quarks beyond current

31 gg->vv: massive loops [FC, Dowling, Melnikov, Röntsch, Tancredi, in progress] Compute exact two-loop amplitudes mediated by heavy quarks beyond current technology T Intermediate solution: expand in /mt Should give reliable results below the two-top threshold Validation: real emission, can be done exactly

32 gg->vv: massive loops [FC, Dowling, Melnikov, Röntsch, Tancredi, in progress] Validation example: gg->h+j->4l+j vs gg->4l+j signal/background interference Exact result: [Campbell, Ellis, Furlan, Röntsch (04)] dσ/dm 4l [fb/gev] 0-5x0-6 -x x0-5 -x x0-5 -3x x0-5 -4x0-5 massive (mt=73) loops only 30 GeV < p T,j < 80 GeV /mt /mt 4 /mt 6 /mt 8 MCFM Preliminary m 4l [GeV] If enough terms in the expansion are kept: very good agreement Promising results Will allow for accurate description up to m4l ~ 340 GeV

33 Conclusions Precision physics in the di-boson sector will be possible Sophisticated NNLO predictions for almost all processes, almost all in the fiducial region as well Comparison data / theory should be compared in the fiducial region (minimize extrapolation errors, simplify theoretical definitions) Several small effects on top of NNLO can play a relevant role at the few-percent level. One example: gg->vv@nlo. Other example: electroweak corrections (especially at high pt) Looking forward to compare against precise results from Run-!

34 Thank you for your attention!

Vector boson pair production at NNLO

Vector boson pair production at NNLO Massimiliano Grazzini* University of Zurich La Thuile 2015, march 5 2015! *On leave of absence from INFN, Sezione di Firenze Outline Introduction pp Vγ+X at NNLO The