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at the LHC Anna Kulesza University of Münster In collaboration with

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1 Associated Top-pair Production with a heavy boson through NNLL+NLO accuracy
at the LHC Anna Kulesza University of Münster In collaboration with L. Motyka, D. Schwartländer, T. Stebel and V. Theeuwes Rencontres de Moriond QCD & High Energy Interactions March 2019

2 Ttbar+Heavy Boson production
A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

3 Associated Higgs Production with Top Quarks
Direct probe of the strength of the top-Yukawa coupling An example of a 2⟶3 process for which full NNLO results are not available yet Crucial for understanding the Higgs sector and in searches for deviations from the SM Far-reaching consequences → stability of our Universe ATLAS, Run1 + Run2: 6.3σ (5.1σ exp.) CMS, Run1 + Run2: 5.2σ (4.9σ exp.) [Buttazzo et al.’13] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

4 TTbar+W,Z ttZ Probes of top-quark couplings
Sensitive to BSM contributions Dominant backgrounds to searches and SM precision measurements (ttH included) Signal strength (CMS): ttW ttZ ATLAS, CMS, A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

5 Theory Status for TTbarH
Fixed order perturbation theory NLO QCD available since (almost) 20 years [Beenakker, Dittmaier, Krämer, Plumper, Spira, Zerwas ’01-’02][Reina, Dawson’01][Reina, Dawson, Wackeroth’02][Dawson,Orr,Reina,Wackeroth’03] [Dawson, Jackson, Orr, Reina, Wackeroth’03] NLO QCD matched with parton showers POWHEG-Box [Garzelli, Kardos,Papadopoulos,Trocsanyi’11] [Hartanto, Jäger,Reina, Wackeroth’15] [Frederix, Frixione, Hirschi, Maltoni, Pittau, Torrielli’11] SHERPA+RECOLA [Biedermann et al.’17] QCD and [Frixione, Hirschi, Pagani,Shao,Zaro’14-’15][Zhang, Ma, Zhang, Chen, Guo’14][Biedermann, Bräuer, Denner, Pellen, Schumann, Thompson’17] NLO QCD [Denner, Feger’15] and EW [Denner,Lang, Pellen, Uccirati’16] with tops off-shell Top decays into b quarks and leptons: pp➝ ttH ➝ W+W-bbH ➝e+νe μ-νμ bb H All resonant, non-resonant, interference and off-shell effects included - A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

6 Theory Status For TTbar+W,Z
Fixed order perturbation theory NLO QCD [Lazopoulos, Melnikov, Petriello’07] [Lazopoulos, McElmurry, Melnikov, Petriello’08] [Kardos, Trocsanyi, Papadopoulos’12 ] with decays at NLO [Campbell, Ellis’12][Roentsch, Schulze’14-’15] NLO interfaced to parton showers in [Alwall, Frederix, Frixione, Hirschi, Maltoni, Mattalaer, Shao Stelzer, Torrieli, Zaro,’14] [Maltoni, Mangano, Tsinikos, Zaro,’14] [Maltoni, Pagani, Tsinikos’15] and POWHEG-Box [Garzelli, Kardos,Papadopoulos,Trocsanyi’12] NLO EW (+QCD) corrections [Frixione, Hirschi, Pagani,Shao,Zaro’14-15][Frederix, Pagani, Zaro’18] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

7 Why Resummation? Extending accuracy of the perturbative prediction beyond fixed-order by adding a systematic treatment of logarithmic contributions due to soft gluon emission is a common standard in precision phenomenology better description of physics: additional corrections to cross sections… especially interesting when NNLO calculations out of reach improvement or, in some cases, restoration of predictive power of perturbation theory reduction of the theory error due to scale variation sums up LL: αsn log n+1 (N) NLL: αsn log n (N) NNLL: αsn log n-1 (N) Factorization at threshold: space of Mellin moments N, taken wrt. M2/S (absolute threshold) or Q2/S (invariant mass threshold) A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

8 Beyond NLO QCD: Resummation
ttH: NLL+NLO resummation in the absolute threshold limit, obtained using direct QCD approach ttH: “Approximated” NNLO based on the SCET approach to resummation in the invariant mass limit ttH: NLL+NLO in the invariant mass limit for production with pseudoscalar Yukawa couplings ttW: NNLL+NLO resummation in the invariant mass limit, SCET [Li, Li, Li’14] ttH, ttW, ttZ: NNLL+NLO resummation in the invariant mass limit, hybrid SCET/direct QCD method [Broggio, Ferroglia, Ossola, Pecjak’16] [Broggio, Ferroglia, Pecjak, Yang’16][Broggio, Ferroglia, Ossola, Pecjak, Samoshima’17] ttH, ttW, ttZ: NNLL+NLO resummation in the invariant mass limit, direct QCD method [AK, Motyka, Stebel, Theeuwes’16], [AK, Motyka, Stebel, Theeuwes’17], [AK, Motyka, Schwartländer, Stebel, Theeuwes’18] 𝑠 → 𝑀 2 =( 𝑚 𝑡 + 𝑚 𝑡 + 𝑚 𝐵 )2 [AK, Motyka, Stebel, Theeuwes’15] 𝑠 → 𝑄 2 = 𝑝 𝑡 + 𝑝 𝑡 + 𝑝 𝐵 2 [Broggio, Ferroglia, Pecjak, Signer, Yang’15] [Broggio, Ferroglia, Fiolhais, Onofre’17] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

9 Resummation for TTbar+B
Threshold limit in the triple invariant mass kinematics: Direct QCD → N space: Factorization ⟷ resummation 𝑠 → 𝑄 2 =( 𝑝 𝑡 + 𝑝 𝑡 + 𝑝 𝐵 ) Hard off-shell Soft wide-angle Collinear Universal, known ✓ Process-dependent Hard and soft functions are now matrices in colour space A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

10 NNLL for Ttbar+B Soft function from the solution of the RG equation =
Soft anomalous dimensions 𝚪 known at two loops for any number of legs [Mert-Aybat, Dixon, Sterman’06] [Becher, Neubert’09] [Mitov, Sterman, Sung’09-’10] [Ferroglia, Neubert, Pecjak, Yang’09] [Beneke, Falgari, Schwinn’09], [Czakon, Mitov, Sterman’09] [Kidonakis’10] ✓ To calculate, eliminate path-ordered exponentials: use basis that diagonalize 𝚪 (𝟏) → enough for NLL accuracy For NNLL, treat matrices U perturbatively [Buras‘80][Buchalla, Buras, Lautenbacher’96] ] [Ahrens, Ferroglia, Neubert, Pecjak, Yang’10] = A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

11 NNLL for Ttbar+B Soft function from the solution of the RGE equation =
Soft anomalous dimensions 𝚪 known at two loops for any number of legs [Mert-Aybat, Dixon, Sterman’06] [Becher, Neubert’09] [Mitov, Sterman, Sung’09-’10] [Ferroglia, Neubert, Pecjak, Yang’09] [Beneke, Falgari, Schwinn’09], [Czakon, Mitov, Sterman’09] [Kidonakis’10] ✓ To calculate, eliminate path-ordered exponentials: use basis that diagonalize 𝚪 (𝟏) → enough for NLL accuracy For NNLL, treat matrices U perturbatively [Buras‘80][Buchalla, Buras, Lautenbacher’96] ] [Ahrens, Ferroglia, Neubert, Pecjak, Yang’10] Hard function H(1) extracted from [Frederix, Frixione, Hirschi, Maltoni, Pittau, Torrielli’11] (ttH, ttW, ttZ) and PowHel (HELAC-NLO [Bevilacqua et al.’11] +POWHEG-Box) package [Garzelli, Kardos, Papadopoulos,Trocksanyi’11] (ttH) = A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

12 Invariant Mass Distribution for TTbarH
[AK, Motyka, Stebel, Theeuwes’17] NNLL+NLO distributions for the two considered scale choices very close, NLO results differ visibly → KNNLL = 𝜎NLO+NNLL / 𝜎NLO factors also different NNLL+NLO error band slightly narrower than NLO (7-point method) A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

13 Invariant Mass Distribution for TTbarH
[AK, Motyka, Stebel, Theeuwes’17] NNLL+NLO distributions for the two considered scale choices very close, NLO results differ visibly → KNNLL = 𝜎NLO+NNLL / 𝜎NLO factors also different NNLL+NLO error band slightly narrower than NLO (7-point method) A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

14 Total Cross Section for TTbarH
[AK, Motyka, Stebel, Theeuwes’17] μ0 KNNLL Q 1.19 Q/2 1.06 M/2 1.01 KNNLL= 𝜎NLO+NNLL / 𝜎NLO A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

15 Total Cross Section for TTbarH
[AK, Motyka, Stebel, Theeuwes’17] Compared to NLO, remarkable stability of NLO+NNLL Stability improves with increasing accuracy of resummation Reduction of the theory scale error “Best” NNLL+NLO prediction in agreement with NLO at μ0 = M/2 A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

16 Total Cross Section for TTbar+W,Z
[AK, Motyka, Schwartläder, Stebel, Theeuwes’18] Significant reduction in the scale dependence of the ttZ total cross section Comparison with SCET results, wherever possible [Li et al.’14], [Broggio et al.’16-’17] ✓ A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

17 Ttbar+W,Z at NLO+NNLL [AK, Motyka, Schwartländer, Stebel, Theeuwes’18] State of the art: QCD NLO+NNLL, combined with (additively) NLO EW [Frixione et al. ’14-15] Central values of the theoretical predictions brought closer to the measured cross section; theory errors reduced (by half for ttZ) A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

18 Summary ttH the LHC is one of the most promising windows onto new physics ttW and ttZ also very important for BSM searches as well as tests of the SM Precise theoretical prediction are essential ➝ a lot of recent progress! Resummed calculations for reach NNLL+NLO accuracy -- first application of resummation to the class of 2->3 processes Remarkable stability of the NNLL+NLO differential and total cross sections w.r.t. scale variation; improving stability with growing accuracy Reduction of the theory error due to scale variation A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

19 BACKUP A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

20 Invariant Mass Kinematics
Problem: hard and soft functions are now (and in general) matrices in colour space Diagonalization procedure leads to, at NLL: [Kidonakis, Oderda, Sterman’98] where λ’s are eigenvalues of the one-loop soft-anomalous dimension matrix A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

21 Invariant Mass Kinematics
Problem: hard and soft functions are now (and in general) matrices in colour space Diagonalization procedure leads to, at NLL: [Kidonakis, Oderda, Sterman’98] where λ’s are eigenvalues of the one-loop soft-anomalous dimension matrix A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

22 Invariant Mass Kinematics Ctnd.
Extending resummation in this kinematics to NNLL requires: Knowledge of the two-loop soft anomalous dimension Amended treatment of the path-ordered exponential to account for it Knowledge of the one-loop hard-matching coefficient A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

23 Invariant Mass Kinematics Ctnd.
Extending resummation in this kinematics to NNLL requires: Knowledge of the two-loop soft anomalous dimension ✔ Soft anomalous dimensions known at two loops for any number of legs [Mert-Aybat, Dixon, Sterman’06] [Becher, Neubert’09] [Mitov, Sterman, Sung’09-’10] [Ferroglia, Neubert, Pecjak, Yang’09] [Beneke, Falgari, Schwinn’09], [Czakon, Mitov, Sterman’09] [Kidonakis’10] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

24 Invariant Mass Kinematics Ctnd.
Extending resummation in this kinematics to NNLL requires: Knowledge of the two-loop soft anomalous dimension Amended treatment of the path-ordered exponential to account for it ✔ Perturbative expansion [Buchalla, Buras, Lautenbacher’96] [Ahrens, Neubert, Pecjak, Yang’10] eigenvalues of Γ(1) A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

25 Invariant Mass Kinematics Ctnd.
Extending resummation in this kinematics to NNLL requires: Knowledge of the two-loop soft anomalous dimension Amended treatment of the path-ordered exponential to account for it Knowledge of the one-loop hard function HIJ needs access to colour structure of virtual corrections ✔ extracted from the results provided by the PowHel (HELAC-NLO [Bevilacqua et al.’11] +POWHEG-Box) package [Garzelli, Kardos, Papadopoulos,Trocksanyi’11] translation between the colour flow and singlet-octet basis implementation checked against colour-averaged virtual corrections obtained from public POWHEG [Hartanto, Jäger,Reina,Wackeroth’15] and implementations [Frederix, Frixione, Hirschi, Maltoni, Pittau, Torrielli’11] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

26 Scale dependence of the total cross section
[AK, Motyka, Stebel, Theeuwes’17] μF = μ0 = Q μR = μ0 = Q Apparent cancellations between μF and μR scale dependence No significant change in dependence on μR while increasing the accuracy: αs running effect μF dependence modified by the hard-matching coefficient 7-point method A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

27 Absolute Threshold Resummation for QQB @NLO+NLL
Colour space basis in which ΓIJ is diagonal in the threshold limit incoming jet factors, known soft-wide angle emission hard function Hab →kl B,I At NLL accuracy Cab →kl B,I = 1 A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

28 One-Loop Soft Anomalous Dimension
singlet-octet colour basis Reduces to the 2->2 case in the limit pB →0, mB→0 Absolute threshold limit: non-diagonal terms vanish Coefficients D(1)ab →kl B,I governing soft emission same as for the QQbar process: soft emission at absolute threshold driven only by the color structure A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

29 The Case of Associated Heavy Boson-Heavy quark Pair Production
Absolute threshold limit but: LO cross section suppressed in the limit β→0 as β4 due to massive 3- particle phase-space Absolute threshold scale M away from the region contributing the most nevertheless: Well defined class of corrections which can be resummed [AK, Motyka, Stebel, Theeuwes’15] - PDF4LHC15_100 pdfs, NLO from [Alwall, Frederix, Frixione, Hirschi, Maltoni, Mattelaer, Shao, Stelzer, Torrielli, Zaro] A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

30 Associated Higgs Production with Top Quarks, Resummation in the absolute threshold limit
[ AK, Motyka, Stebel, Theeuwes’15] Shows also a strong impact of the hard-matching coefficient C on the predictions → contributions away from the absolute threshold matter! Part of these contributions can be accounted for if instead of resummation for total cross section, resummation for invariant mass of the ttbarH system is considered A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

31 Associated Higgs Production with Top Quarks, Resummation in the absolute threshold limit
AK, Motyka, Stebel, Theeuwes’15] Threshold logarithms under scrutiny: NLL accuracy requires knowledge of NLO soft anomalous dimension with 2⟶3 kinematics and NLO cross section at threshold split into colour channels MMHT2014NLO NLO obtained with A. Kulesza, Associated top-pair & heavy boson production through NNLL+NLO accuracy at the LHC Moriond, 24/03/19

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