Electroweak LHC NLO QCD

Transcription

1 Electroweak LHC NLO QCD Dept. of physics University of Hawaii A. Lazopoulos Wed 24 oct QCD corrections to tri-boson production Kirill Melnikov (UH), Frank John Petriello (Wisconsin U.), AL / arxiv: [hep-ph] NLO QCD corrections to the production of t anti-t Z in gluon fusion Kirill Melnikov (UH), Frank John Petriello (Wisconsin U.), AL / arxiv: [hep-ph]

2 why NLO? new LHC physics need precise SM tree level theoretical uncertainty dominates NLO necessary wishlists become urgent scale dependence

3 why NLO : example discovery channel? No discovery channel? Is the shape of the background predicted correctly??

4 NLO wishes why are they so hard to get???

5 NLO situation Real emission corrections relatively well understood Virtual problems Too many diagrams Analytical approach = reduction Numerical approach = IR + threshold singularities

6 The method Compute amplitude squared, summed and averaged QGRAF + FORM Cast integral in Feynman parameters form Perform the loop momentum integration analytically MAPLE+FORM UV divergences factorize IR divergences treatment: Sector Decomposition Threshold singularities: Contour Deformation Extract singularities Integrate numerically Feynman parameters C FORTRAN VEGAS VEGAS

7 The method Sector decomposition Contour Deformation Feynman variable xk Im{x} 0 the position of the threshold depends on the PSP and the sector Re{x} 1 This has to happen automagically IR complicated IR simple and extractable

8 ZZZ: first application Not very urgent physically, but a wise choice as a testbed for our method.

9 ZZZ production 6x8 virtual 'diagrams' 1x6 pentagons ~20' per P.S.P. = a couple of days at the farm (University of Wisconsin) mild numerical instabilities easily treated real emission diagrams with two-cutoff phase-space slicing method

10 ZZZ production: results σlo=11.4fb σnlo=15.2fb

11 ZZZ production: results enhanced virtual corrections K factor reweighing accurate to the percent level no significant dependence on kinematics

12 ttz production Tevatron: a top pioneer But top couplings not accessible directly (ttz,ttγ,yukawa) new physics at ttz? Tree level mixing with Z', little Higgs models,... The ttz coupling needs to be measured

13 ttz production LHC will see ttz, tth, ttγ Need for accurate SM prediction tree-level ttz order as2 NLO computation needed to reduce uncertainty

14 ttz production b t jet W Z W t l jet l l b ν [Baur et al.] b jet W t l Z W t b l jet jet jet

15 ttz production b t W Z t W b jet ν jet ν jet jet BG under control thanks to cuts and extrapolations Signal theoretical uncertainty dominates

16 gg2ttz 60% of tree level pp2ttz NLO corrections expected larger technically more involved

17 gg2ttz virtual 162x8 'diagrams' 12x8 pentagons 45' per P.S.P. = a week at the farm stronger numerical instabilities, treated with standard techniques real 50x50=2500 'diagrams' two cutoff slicing method

18 gg2ttz: results NLO corrections effect NLO corrections ~30% if the qq ttz contributes less, overall pp ttz corrections ~20%, so less luminosity needed for the coupling measurement (than 300fb-1).

19 gg2ttz: results residual uncertainty ~5% (μ0/4 to μ0)

20 gg2ttz: results The NLO corrections don't change the shape of the distribution A K-factor of 1.4 describes well the NLO effect

21 Conclusions New method for numerical evaluation of loop diagrams High degree of automation Numerical stability in the cases studied Applied in real processes of physical interest NLO corrections to ttz from gluon fusion completed qq channel to follow More applications of great interest ahead!

22 extra: method checks three different codes in FORTRAN, C 1/ε, 1/ε2 poles cancel exactly at the differential level contour deformation parameter independence

23 Extra:Primary Sector Decomposition x2>x1 x2 x1>x2 x1 The integration volume is divided in N sectors and each sector is mapped back to the unit hypercube The δ-function is eliminated Sector of x2

24 Extra: Secondary Sector Decomposition I(N) I(N,α) I(N,α,j) I(N,α) I(N,α,j) I(N,α) I(N,α,j) quartic term comes from qubic terms without the particular tm in the case that λ=1 I(N,α,j) I(N,α,j,m) I(N,α,j,m) I(N,α,j,m) I(N,α,j,m) I(N,α,j,m,n) I(N,α,j,m,n) I(N,α,j,m,n) I(N,α,j,m,n) There can be at most two itearations before a finite Δ emerges in every sector

25 extra: A general integral

26 extra: Pole extraction and ε-expansion In case any of the exponents is 1+bε, the integral over the corresponding y-variable gives a 1/ε pole that is extracted at this point with the help of The function F(y,ε) can then be safely expanded over ε.