Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD

Journal of High Energy Physics, Oct 2016

We present the results of the computation of the next-to-leading order QCD corrections to the production cross section of a Higgs boson in association with a top-antitop pair at the LHC, including the three relevant dimension-six operators (O tφ , O φG , O tG ) of the standard model effective field theory. These operators also contribute to the production of Higgs bosons in loop-induced processes at the LHC, such as inclusive Higgs, Hj and HH production, and modify the Higgs decay branching ratios for which we also provide predictions. We perform a detailed study of the cross sections and their uncertainties at the total as well as differential level and of the structure of the effective field theory at NLO including renormalisation group effects. Finally, we show how the combination of information coming from measurements of these production processes will allow to constrain the three operators at the current and future LHC runs. Our results lead to a significant improvement of the accuracy and precision of the deviations expected from higher-dimensional operators in the SM in both the top-quark and the Higgs-boson sectors and provide a necessary ingredient for performing a global EFT fit to the LHC data at NLO accuracy.

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Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD

Received: August Higgs production in association with a top-antitop pair in the Standard Model E ective Field Theory at Fabio Maltoni 0 2 Eleni Vryonidou 0 2 Cen Zhang 0 1 Open Access 0 c The Authors. 0 0 Universite catholique de Louvain 1 Department of Physics, Brookhaven National Laboratory 2 Centre for Cosmology , Particle Physics and Phenomenology (CP3) We present the results of the computation of the next-to-leading order QCD corrections to the production cross section of a Higgs boson in association with a top-antitop pair at the LHC, including the three relevant dimension-six operators (Ot'; O'G; OtG) of the standard model e ective eld theory. These operators also contribute to the production of Higgs bosons in loop-induced processes at the LHC, such as inclusive Higgs, Hj and HH production, and modify the Higgs decay branching ratios for which we also provide predictions. We perform a detailed study of the cross sections and their uncertainties at the total as well as di erential level and of the structure of the e ective eld theory at NLO including renormalisation group e ects. Finally, we show how the combination of information coming from measurements of these production processes will allow to constrain the three operators at the current and future LHC runs. Our results lead to a signi cant improvement of the accuracy and precision of the deviations expected from higher-dimensional operators in the SM in both the top-quark and the Higgs-boson sectors and provide a necessary ingredient for performing a global EFT t to the LHC data at NLO accuracy. pair; in; the; Standard; NLO Computations; Phenomenological Models 1 Introduction E ective operators Calculation setup Theoretical uncertainties Numerical results Total cross sections Distributions RG e ects Constraints on dimension-six operators Summary and conclusions Introduction also become available recently. (c) OtG. available recently [48{51]. size of its coe cient. operators are induced by a top-quark loop. sector [42, 61{65]. information on the operator coe cients. corrections allows us to control these e ects. considered at NLO. E ective operators elds. By employing The Lagrangian of SMEFT can be written as 2 Oi + O( 4) + h:c:; Ot = yt3 O G = yt2 OtG = ytgs(Q GA GA T At) ~GA : vertices, ggtt and gttH, as well as a ve-point ggttH vertex. The second one is a loop2The operator O' also contributes by universally rescaling the Higgs couplings. We operators, this would not be true. for (Ot ; O G; OtG) has a triangle form: dCi( ) ij Cj ( ); = BB 0 7=2 1=2 CC : Using the notations of ref. [91], they can be written as Cu2 = Cq(u8)1133 + Cq(8u)3311; Cd1 = Cq(q3)1331 + Cd2 = Cq(u8)1133 + Cq(8d)3311 : 1 C(8)3311; Consider tt and ttH at 8 TeV (at LO): 8 TeV[pb] = 158 1 + 0:0101 Cu1 + Cu2 + 0:64Cd1 + 0:64Cd2 + 0:65CtG tt 8 TeV[pb] = 0:110 1 + 0:055 Cu1 + Cu2 + 0:61Cd1 + 0:61Cd2 + 2:02CtG ; ttH operator OtG with a four-point contact gttH or a ve-point ggttH vertex, leading to a ratio of the two cross sections: t8tTeV(ps^t>th 1000 GeV) contributes processes is gsf ABC GA G B G C , which would enter by modifying the gluon self-interactions. tt and dijet cross sections. Calculation setup formalism. Ci0 = Zij Cj ; Zij = where EFT is the scale at which we de ne the EFT, and (1 + ) EFT. They run and mix whenever EFT changes. The Zij and ever, in practice, we de ne the Ot and O G operators as Ot = yt3 O G = yt2 v2=2 v2=2 GA GA to rede ne the SM the divergence GA GA + h:c: = O G + mt2GA GA + h:c: : Zgs = Zgs;SM + CtG Zmt = Zyt = Zmt;SM sections we will simply denote O by O. Theoretical uncertainties former class, we can list: Uncertainties due to parton-distribution functions. PDF sets. are expected to be subdominant. These are additional uncertainties, related to the scale EFT, at which the operators Ci( 0) i( 0) + X 1TeV4 Ci( 0)Cj ( 0) ij ( 0) ; Ci( ) i( ) + X 1TeV4 Ci( )Cj ( ) ij ( ) = SM + X 1TeV2 Ci( 0) i( 0; ) + X 1TeV4 Ci( 0)Cj ( 0) ij ( 0; ) : (4.3) where we de ne The ij describes the running of operator coe cients: ij ( 0; ) = ki( ; 0) lj ( ; 0) kl( ) : Ci( ) = ij ( ; 0)Cj ( 0) ; and is given by ij ( ; 0) = exp 0 = 11 2=3nf : varying between ( =1TeV)4 i = SM + X ( =1TeV)2 i (dim6) + X Cdim6Cdim6 i j ( =1TeV)4 ij These two terms are formally O( 4) contributions, but they should be considered sepaexample i(idim6), as an uncertainty estimate. { 10 { Impact of missing higher-dimensional operators. The contribution Numerical results parameters are mt = 172:5 GeV ; mH = 125 GeV ; E1W = 127:9 ; GF = 1:16637 mZ = 91:1876 GeV ; Central scales for Total cross sections = SM + X 1TeV2 Ci i + X 1TeV4 CiCj ij : obtained by independently setting R and F to =2, and 2 , where is the central scale R;F scale { 11 { +0:190+0:043 551:0+71:1+50:8 +0:2415+5:44 +0:0075+0:00301 +0:0643+0:125 19:6+5:47+0:000 +0:439+0:104 +0:0194+0:00732 76:8+9:38+9:11 +0:171+0:332 22:4+6:41+0:000 +0:576+0:118 15:1+4:296+2:06 +0:0225+0:00832 89:5+12:85+10:6 +0:194+0:340 +0:000000+0:00037 +0:000000+0:673 +0:447+0:478 +0:000005+0:0154 +0:000+0:000 +0:000035+0:0053 68:2+7:70+6:29 +0:000029+0:081 = SM LO +0:000+0:000 +0:000004+0:0053 66:7+7:29+6:16 +0:000051+0:102 +0:0000+0:00037 +0:000050+0:676 +0:000062+0:017 23:0+2:50+0:0 = SM LO +0:000+0:000 +0:000065+0:00529 67:3+7:47+6:20 +0:000628+0:092 +0:000003+0:00037 +0:000074+0:673 +0:479+0:473 +0:000046+0:0152 { 13 { = SM NLO = SM NLO H at 8, 13, and 14 TeV at NLO in the in nite top { 14 { +0:152+0:022 +0:246+0:214 +0:051+0:064 +5:091+0:000 +0:393+0:0615 +0:0180+0:0043 +0:625+0:454 +0:134+0:180 +0:451+0:0709 +0:158+0:208 +0:0072+0:00154 +0:000001+0:00037 +0:000+0:000 +0:000027+0:0053 +0:000212+0:132 +0:000276+0:051 +0:000031+0:0154 = SM LO +0:000+0:000 +0:000379+0:00535 +0:000223+0:0857 +0:000008+0:00038 +0:000257+0:0395 +0:000079+0:0157 = SM LO +0:000+0:000 +0:000132+0:0053 +0:001289+0:103 +0:0205+0:00497 +0:000000+0:00037 +0:000567+0:037 +0:000156+0:0156 > 30 GeV cut. Only the R;F and EFT scale uncertainties are shown. { 15 { +0:00313+0:000 +0:000704+0:000086 +0:0676+0:0273 0:0001980:000057 +0:00290+0:00183 +0:000088+0:0000208 +0:00559+0:00133 +0:0186+0:010 +0:277+0:143 +0:000700+0:000546 LO +0:00904+0:000 +0:00209+0:000297 +0:231+0:0948 +0:00804+0:0041 +0:000290+0:000079 +0:0198+0:00505 +0:0506+0:0362 +0:00213+0:00163 +0:914+0:554 LO +0:0105+0:000 +0:00245+0:00031 +0:214+0:118 +0:00929+0:0037 +0:000343+0:000095 +0:0241+0:00605 +0:0520+0:0439 +0:00253+0:00192 +0:000+0:000 +0:00111+0:0113 +0:0244+0:243 +0:00060+0:0028 +0:0289+0:176 +0:00113+0:072 = SM LO +0:000+0:000 +0:00114+0:0116 +0:0271+0:161 +0:000727+0:0031 +0:0650+0:198 +0:000238+0:064 = SM LO +0:000+0:000 +0:00131+0:0117 +0:0271+0:122 +0:00076+0:0031 +0:0753+0:198 +0:0014+0:063 EFT scale uncertainties are shown. HH at 8, 13, and 14 TeV at LO. Only the R;F and { 16 { once taking ratios with respect to SM. On the contrary, the EFT scale uncertainty is R;F scale R;F scale uncertainties as they are at LO. As in the case of ttH we nd that the R;F scale uncertainties get signi cantly We also the well-known large K factors ( 2) for gluon fusion and demonstrate the reduction of the R;F uncertainties. are similar in size to the { 17 { dependence on Distributions CtG = uncertainty are also shown in the lower panels. total cross-section level in table 5. { 18 { SM O LO NLO LO NLO LO NLO SM O LO NLO LO NLO 500 600 700 800 contributions from are shown in of the phase space. RG e ects EFT arises as a These approximation of the complete NLO corrections. Many discussions on these issues are { 19 { LHC13, SM@NLO+dim6@(N)LO SM NLO CtG=-1 NLO CtG=-1 LO e 0.6 l ve o -0.1 e trh 2.5 LHC13, SM@NLO+dim6@(N)LO SM NLO CtG=-1 NLO CtG=-1 LO e 0.6 l u 0.5 va e c 0.1 r e M .t.S 3.5 . w 2.5 o it { 23 { = 1 TeV. Lower panels give the K factors and uncertainties. Relative scale uncertainties bution from . Right: squared contribution . The SM and individual operator contributions are shown. Lower panels give the uncertainties and the ratio over the SM. Relative uncertainties w.r.t. central values Ratio over the SM Relative scale uncertainties Relative scale uncertainties Right: squared contribution panels give the uncertainties and the ratio over the SM. lu 0.5 va l r ve o -0.1 the 1.5 r t a R 0.5 e 0.6 l u 0.5 va n e c 0.1 r e SM 5 the 4 r voe 3 ito 2 a R 1 e 0.6 l u 0.5 va . Right: squared contribution ii. The SM and individual operator contributions are shown. Lower panels give the uncertainties and the ratio over the SM. { 24 { Relative scale uncertainties Relative scale uncertainties OtG NLO 150 200 700 1000 1500 2000 Comparing RG corrections with full NLO. By naive power counting one might Even if we do not resum these log terms, by setting EFT = explicitly in a peri( ; EFT) (i.e. contributions from Ci( ), calculated with EFT) for = 2 TeV. Suppose with three coe cients { 26 { EFT scale as an uncertainty estimator. The RG running can still be used as an gure 12 we can see control by using the full NLO prediction. at scale EFT = mt, and section has a strong EFT, as can be seen from the EFT between mt=2 Constraints on dimension-six operators { 27 { 100 200 500 1000 2000 100 200 500 1000 2000 C G(mt) = 0, and = 1 TeV. Left: pp ! H. Right: pp ! HH. Individual linear contriburtG;tG 1 + P 1Te2V2 Ciri + P be assessed as a function of . channels we use [115{120]; three operators. decay in the following way: = 1 0:0595Ct 1TeV2 At +AW 1TeV2 = 1+0:0335 C t +0:000281 1TeV4 where At and AW are the top- and W boson loop amplitudes entering the Higgs decay into photons. We note that the impact of Ot' is diluted in H as this decay is dominated by the W ] [-0.0072,-0.0063] [-0.021,0.054] [-0.022,0.031] [-0.68,0.62] 2- t is performed to derive the limits. All coe cients in this section are de ned with given in this section correspond to 95% con dence level. will be used to constrain the four-fermion operators. While a global t including both this is beyond the scope of this paper. oating other coe cients) are given in the rst two columns. Interestingly, the CtG limit is already 0:12 < CtG < 0:12 1:0 < CtG < 1:1 ( on CtG is 0:33 < CtG < 0:33 ( marginalised over the four-fermion operators. once this operator is included. { 29 { functions of EFT. = 1 TeV is assumed. the other two operators cannot be neglected. operators to be nonzero. gure 15 left we show at direction in Right: future projection at HL-LHC. gure 15 right. reason, we plot in provide additional information in resolving OtG and O G. { 31 { -0.02 -0.01 -0.02 -0.01 Right: future projection at HL-LHC. LHC current LHC current -0.02 -0.01 -0.02 -0.01 and EFT = 1 TeV (right). result, the dependence of C G on EFT due to mixing from CtG is expected to be canceled by the EFT dependence in the loop. When the scale EFT is changed, the change in total C G plot will gure 17 at two di erent { 32 { Right: future projection at HL-LHC. sensitive to the scale. This is also re ected in gure 14. We conclude that the \individual Finally in help to constrain both operators, while gure 18 right is the situation for future LHC, the two loop-induced contributions. Summary and conclusions two sectors. { 33 { to the full NLO prediction. with this uncertainty. of Energy under Grant Contracts DE-SC0012704. Open Access. 089 [arXiv:1307.3536] [INSPIRE]. (2013) 022 [arXiv:1211.3736] [INSPIRE]. (2014) 3065 [arXiv:1407.5089] [INSPIRE]. [arXiv:1605.04311] [INSPIRE]. couplings to the heavy (2016) 055023 [arXiv:1606.03107] [INSPIRE]. [hep-ph/0107081] [INSPIRE]. [hep-ph/0211352] [INSPIRE]. 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Fabio Maltoni, Eleni Vryonidou, Cen Zhang. Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD, Journal of High Energy Physics, 2016, 123, DOI: 10.1007/JHEP10(2016)123