Constraining EFT parameters with simplified template cross sections

Transcription

1 Constraining EFT parameters with simplified template cross sections Chris Hays 1, Veronica Sanz 2, Gabija Žemaitytė 1 1 University of Oxford, 2 University of Sussex LHCHXSWG-INT Higgs Couplings 8 November 2017 Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 1 / 20

2 Overview In LHCHXSWG-INT we outline a procedure for fitting a set of dimension-6 EFT parameters using simplified template cross section (STXS) measurements. Steps: choose a basis implementation identify Higgs-sensitive operators and existing constraints determine operators effect on the STXS regions perform the fit Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 2 / 20

3 EFT at LO dimension-6 EFT at LO, dimension-6 operators: The general form of the Lagrangian including dimension-6 operators L = L SM + c i O i /Λ 2 Assuming flavour universality, the SM EFT has 59 operators. The majority of these operators do not affect Higgs physics at LO. Several operator bases have been defined, we chose to use the HEL implementation of the SILH basis since it was the most complete public implementation at the start of this work. Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 3 / 20

4 Higgs-sensitive operators HEL operator O g = H 2 G A µν GAµν Õ g = H 2 G A Aµν cg µν G O γ = H 2 B µν B µν Õ γ = H 2 B µν Bµν O u = y u H 2 Q L H u R + h.c. Coefficient cg Λ 2 = g2 s m 2 cg W Λ 2 = g2 s m 2 tcg W cγ Λ 2 = g 2 m 2 ca W cγ Λ 2 = g 2 m 2 tca W cu Λ 2 = cu c v 2 d = cd O d = y d H 2 Q L Hd R + h.c. Λ 2 v 2 O l = y l H 2 L c L Hl R + h.c. l Λ 2 = cl ( v 2 O H = 1 µ H 2) 2 c H 2 Λ 2 = ch ( v 2 O 6 = H H) 3 c6 Λ 2 = λ v 2 c6 O HW = i (D µ H) σ a (D ν H)W a c HW µν Λ 2 = g m 2 chw W Õ HW = i (D µ H) σ a (D ν H) W a c HW µν Λ 2 = g m 2 tchw W O HB = i (D µ H) (D ν c H)B HB µν Λ 2 = g m 2 chb W Õ HB = i (D µ H) (D ν c H) B HB µν Λ 2 = g m 2 tchb ( ) W O W = 2 i H σ a D µ H D ν W a c W µν Λ 2 = g m 2 cww ( ) W O B = 2 i H D µ H ν c B B µν Λ 2 = g m 2 cb W At LO, 15 dimension-6 operators reduce to SM Higgs interactions through H vev and are not directly constrained by precision electroweak data. Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 4 / 20

5 Equations derived for STXS bins Cross sections are measured in each STXS truth bin, with correlations. Bins include: σ i B 4l and B i /B 4l ggf VH (H + leptonic V ) = 0-jet = 1-jet (+) 2-jet 2-jet VBF cuts p H T < 200 2j q q VH gg ZH p H T [0, 60] (+) p H T [0, 60] (+) p Hjj T [0, 25] 3j W lν (+) Z ll + ν ν p H T [60, 120] p H T [60, 120] (+) (+) p Hjj T [25, ] p V T [0, 150] p V T [0, 150] p V T [0, 150] p H T [120, 200] BSM p H T [120, 200] BSM p V T [150, 250] p V T [150, 250] p V T [150, ] p H T [200, ] p H T [200, ] (+) = 0-jet 1-jet (+) = 0-jet 1-jet (+) = 0-jet 1-jet p V T [250, ] p V T [250, ] VBF (EW qqh incl. VH qqh) p j1 T [0, 200] p j1 T [200, ] BSM t th b bh th 2-jet VBF cuts 2-jet VH cuts (+) Rest 2j p Hjj T [0, 25] (+) 3j p Hjj T [25, ] (YR4) Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 5 / 20

6 Relating STXS bins to EFT parameters L = L SM + c i O i /Λ 2 To determine the relationship between STXS measurements and EFT parameters, we separate the cross section into SM, SM-BSM interference, and BSM components: σ = σ SM + σ int + σ BSM σ BSM is a subleading term (suppressed by 1/Λ 4 ) but can be included to avoid negative cross sections and improve fit convergence. The dependence of the cross section on the couplings can then be expressed as (we define c i = c i /Λ 2 ): σ = 1 + A i c i + B ij c i c j σ SM i ij Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 6 / 20

7 Extraction of the equation σ = SM + A 1 c 1 + B 11 c A 2 c 2 + B 22 c B 12 c 1 c 2 There are several technical ways to extract equations. It is just linear algebra - we produce MC samples s.t. system of equations is close to diagonal. We use NP^2== syntax in MadGraph: SM, A i and B ij for i = j are obtained directly: NP^2 == 0 : σ 1 = SM NP^2 == 1 : σ A1 = A 1 c 1, σ A2 = A 2 c 2 NP^2 == 2 : σ B11 = B 11 c 2 1, σ B22 = B 22 c 2 2 Extracting B ij for i j: generate a sample with NP^2==2, then σ = B 11 c B 22c B 12c 1 c 2. Technical advantage: precision can be customised for individual prefactors. Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 7 / 20

8 MadGraph validation The equations have been validated to check any assumptions and approximations Madgraph+Pythia samples were generated with a variety of c i values and a statistical precision of <1% The difference between the generated cross section and that calculated with the equations is found to be approximately Gaussian-distributed according to the generator uncertainty A few examples are shown below: STXS region σ MG /σ SM σ eq /σ SM δmg stat gg H ( 2 jets, p H T 200 GeV) gg H ( 2 jets, p H T 200 GeV) q q Hlν (p V T 250 GeV) q q Hlν (p V T 250 GeV) q q Hlν (p V T 250 GeV) gg/q q tth gg/q q tth Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 8 / 20

9 Equations of the interference terms for ggf, qq Hqq and tth production. The equations with all terms will be available on the LHC Working Group 2 twiki. Cross-section region gg H (0-jet) gg H (1-jet, p H T < 60 GeV) 56c gg H (1-jet, 60 p H T < 120 GeV) gg H (1-jet, 120 p H T < 200 GeV) 56c gg H (1-jet, p H T 200 GeV) 56c gg H ( 2-jet, p H T < 60 GeV) 56c gg H ( 2-jet, 60 p H T < 120 GeV) 56c gg H ( 2-jet, 120 p H T < 200 GeV) 56c gg H ( 2-jet, p H T 200 GeV) 56c i A ic i g g + 18c3G + 11c2G g + 52c3G + 34c2G g g + 8c3G + 7c2G g + 23c3G + 18c2G g + 90c3G + 68c2G gg H ( 2-jet VBF-like, p j 3 T < 25 GeV) 56c g gg H ( 2-jet VBF-like, p j 3 T 25 GeV) 56c g + 9c3G + 8c2G qq Hqq (VBF-like, p j 3 T < 25 GeV) 1.0cH 1.0cT + 1.3cWW 0.023cB 4.3cHW 0.29cHB cHQ 5.3cpHQ 0.33cHu cHd qq Hqq (VBF-like, p j 3 T 25 GeV) 1.0cH 1.1cT + 1.2cWW 0.027cB 5.8cHW 0.41cHB cHQ 6.9cpHQ 0.45cHu cHd qq Hqq (p j 200 GeV) 1.0cH 0.95cT + 1.5cWW 0.025cB 3.6cHW T 0.24cHB cHQ 4.5cpHQ 0.25cHu + 0.1cHd qq Hqq (60 m jj < 120 GeV) 0.99cH 1.2cT + 7.8cWW 0.19cB 31cHW 2.4cHB + 0.9cHQ 38cpHQ 2.8cHu + 0.9cHd qq Hqq (rest) 1.0cH 1.0cT + 1.4cWW 0.028cB 6.2cHW 0.42cHB cHQ 6.9cpHQ 0.42cHu cHd gg/q q tth 0.98cH + 2.9cu cG + 310cuG +27c3G 13c2G Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 9 / 20

10 Example fit To demonstrate the procedure we use the equations to perform a fit to the ATLAS STXS measurements in the H γγ and H ZZ* 4l channels (ATLAS-CONF ). The measurement merges STXS regions as follows: Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 10 / 20

11 ATLAS results ATLAS results of merged STXS bins (ATLAS-CONF ) used for the example fit. Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 11 / 20

12 Physics of Wilson coefficients To allow a convergent fit we fit only the leading coefficients affecting the measurements, so we reduce the EFT to an effective Lagrangian containing five parameters We thus neglect the following Higgs-sensitive operators: 4 CP-odd operators that do not have any interference contribution to STXS 2 operators corresponding to lepton and down-type Yukawas not directly constrained by the H ZZ* 4l and H γγ measurements 1 operator corresponding to di-higgs production 1 operator that normalizes the Higgs field and produces a small global change in the rate 1 coefficient combination (cww+cb) constrained by the S parameter This leaves six operator combinations Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 12 / 20

13 Impact of coefficients on STXS The ATLAS merged regions provide little sensitivity to chb We therefore also remove this parameter from the fit, leaving five parameters. Left: STXS stage 1. Right: merged version as in ATLAS-CONF σ / σ SM ca = cww-cb = 0.06 chw = 0.04 chb = 0.15 σ / σ SM 10 ca = cww-cb = 0.06 chw = 0.04 chb = tth qq->hll (pt>250gev) qq->hll (150<pT<250GeV,>0jets) qq->hll (150<pT<250GeV,0jets) qq->hll (pt<150gev) qq->hlν (pt>250gev) qq->hlν (150<pT<250GeV,>0jets) qq->hlν (150<pT<250GeV,0jets) qq->hlν (pt<150gev) qq->hqq(pt>200gev) qq->hqq(rest) qq->hqq(60<mjj<120gev) qq->hqq(vbf like, pt>25gev qq->hqq(vbf like, pt<25gev gg->h(all bins) BR(H-> γ γ )/BR(H->ZZ*->4l) gg->h(all bins) BR(H->γ γ )/BR(H->ZZ*->4l) gg->h-qq->hqq(pt>200gev) gg->h+qq->hqq(pt>200gev) tth gg/qq->hll/hlν qq->hqq(pt<200gev) Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 13 / 20

14 Fit procedure Fit procedure: likelihood minimization with RooFit assume Gaussian uncertainties apply the ATLAS correlation matrix The correlation coefficients with gg H ( 1-jetp H T 200GeV) qq Hqq (pj t 200GeV) bin were not quoted in the ATLAS note due to low experimental sensitivity, so we assumed correlations are 0 with other bins. Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 14 / 20

15 Results Fit to ATLAS STXS measurements (ATLAS-CONF ) -4 cg [ 10 ] LHCHXSWG-INT ca [ 10 cu ] -1 chw [ 10 ] 5-parameter fit. Uncertainties from likelihood scan. For well separated double minima used solution closest to SM. -1 cww - cb [ 10 ] Parameter value Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 15 / 20

16 Likelihood scan ca and cg have well separated double minima - chose solution closest to SM. -2ln(λ) parameter fit -2ln(λ) parameter fit ca cg -2ln(λ) 8 7 LHCHXSWG-INT Fit to measurements of ATLAS-CONF ln(λ) 8 7 LHCHXSWG-INT Fit to measurements of ATLAS-CONF H s -1 = 13 TeV, 36.1 fb γ γ and H ZZ* 4l 6 H s -1 = 13 TeV, 36.1 fb γ γ and H ZZ* 4l ca cg Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 16 / 20

17 Likelihood scan chw and cww do not have a clear second minimum or it is outside fit convergence range. -2ln(λ) 8 7 LHCHXSWG-INT Fit to measurements of ATLAS-CONF ln(λ) 8 7 LHCHXSWG-INT Fit to measurements of ATLAS-CONF s = 13 TeV, 36.1 fb H γ γ and H ZZ* 4l 6-1 s = 13 TeV, 36.1 fb H γ γ and H ZZ* 4l cww - cb chw Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 17 / 20

18 Likelihood scan cu has two minima which are not well separated. -2ln(λ) 8 7 LHCHXSWG-INT Fit to measurements of ATLAS-CONF s = 13 TeV, 36.1 fb H γ γ and H ZZ* 4l cu Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 18 / 20

19 Improvements Possible improvements with the currently available tools and calculations: similar equations can be derived using the recent SMEFT Feynrules implementation that uses the Warsaw basis the theoretical predictions and simulation of kinematic distributions of some Higgs operators could be performed at NLO in QCD using public implementations of the HEL Lagrangian in and POWHEG-BOX NLO Electroweak corrections in decays could be included by interfacing with ehdecay, with the use of Rosetta a combination with electroweak diboson production (and other measurements) could be incorporated within the same framework Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 19 / 20

20 Summary We have described a general procedure for using the STXS framework to constrain EFT parameters, providing a first step towards the use of STXS in the context of the EFT approach. We applied the procedure to ATLAS results and obtained constraints on 5 EFT parameters. The procedure is described in LHCHXSWG-INT Gabija Žemaitytė (University of Oxford) Constraining EFT parameters with simplified template cross sections 20 / 20