New ideas in Model Building Antonio Delgado University of Notre Dame SUSY2018 Barcelona, July 23-27, 2018 Internatonal Conference on Supersymmetry and Unification of Fundamental Interactons 2018 Internatonal Advisory Commitee Local Organising Commitee Ignatos Antoniadis, CERN Kaoru Hagiwara, KEK Martne Bosman, IFAE Lluïsa Mir, IFAE Csaba Balazs, Monash University Tao Han, Pitsburgh University Pilar Casado, UAB/IFAE Andrés Pacheco Pagés, IFAE/PIC Wim de Boer, KIT, Karlsruhe Gordon L. Kane, Michigan State University José Ramón Espinosa, ICREA/IFAE Alex Pomarol, UAB/IFAE Marcela Carena, Fermilab and Chicago University Dimitri Kazakov, JINR, Dubna Enrique Fernández, UAB/IFAE Oriol Pujolàs, IFAE Mirjam Cvetc, Pennsylvania State University Jihn E. Kim, Seoul Natonal University Sebastán Grinstein, ICREA/IFAE Mariano Quirós, IFAE, co-Chair Athanasios Dedes, Ioannina University Pyungwon Ko, KIAS, Seoul Aurelio Juste, ICREA/IFAE Javier Rico, IFAE Keith Dienes, Arizona State University Paul G. Langacker, IAS, Princeton Ilya Korolkov, IFAE Imma Riu, IFAE Herbi Dreiner, University of Bonn Joseph D. Lykken, Fermilab Mario Martnez, ICREA/IFAE, co-Chair Sebastán Grinschpun, IFAE John Ellis, King’s College UK & CERN Rabindra N. Mohapatra, University of Maryland Ramon Miquel, ICREA/IFAE Jonathan L. Feng, UC Irvine Pran Nath, Northeastern University Gian F. Giudice, CERN Apostolos Pilafsis, Manchester University Rohini M Godbole, CHEP, IISc, Bangalore Fernando Quevedo, ICTP Manoranjan Guchait, TIFR, Mumbai Graham G. Ross, University of Oxford John Gunion, UC Davis Sandip Trivedi, TIFR, Mumbai Pre-SUSY School July 17-20, 2018 susy2018.ifae.es Universitat Autònoma de Barcelona Organised by Supported by GOBIERNO MINISTERIO DE ESPAÑA DE ECONOMÍA, INDUSTRIA Y COMPETITIVIDAD Institut de Física d’Altes Energies Epicycles over epicycles Epicycles over epicycles Turtles over turtles • More seriously I am going to give my personal view on the status of Model Building. • More seriously I am going to give my personal view on the status of Model Building. • Disclaimer: I have not been very careful about citations so I apologize to everybody in advance. • More seriously I am going to give my personal view on the status of Model Building. • Disclaimer: I have not been very careful about citations so I apologize to everybody in advance. • In my opinion model building has focused lately on finding ways of reconciling the fact that the LHC has not found any new physics with the general expectation that new physics would have something to do with the TeV scale: • More seriously I am going to give my personal view on the status of Model Building. • Disclaimer: I have not been very careful about citations so I apologize to everybody in advance. • In my opinion model building has focused lately on finding ways of reconciling the fact that the LHC has not found any new physics with the general expectation that new physics would have something to do with the TeV scale: • Naturalness • More seriously I am going to give my personal view on the status of Model Building. • Disclaimer: I have not been very careful about citations so I apologize to everybody in advance. • In my opinion model building has focused lately on finding ways of reconciling the fact that the LHC has not found any new physics with the general expectation that new physics would have something to do with the TeV scale: • Naturalness • DM • More seriously I am going to give my personal view on the status of Model Building. • Disclaimer: I have not been very careful about citations so I apologize to everybody in advance. • In my opinion model building has focused lately on finding ways of reconciling the fact that the LHC has not found any new physics with the general expectation that new physics would have something to do with the TeV scale: • Naturalness • DM • Flavour? I. INTRODUCTION The LHC experimental discovery of the Higgs boson, along with the measurement of Higgs properties that are in rough agreement with the Standard Model (SM) predictions, suggests that the SM is a valid e↵ective theory at the weak scale. The lack of new particles up to the TeV scale makes possible the parametrization of possible high scale physics e↵ects in terms of higher dimension operators containing only SM fields [1]. In this paper we study new physics contributions to Higgs decays in the context of the dimension-6 Standard Model E↵ective Field Theory (SMEFT). When compared with precise theoretical calculations, • Since the discovery of the Higgs in 2012 there has been measurements of Higgs propertieslots of attention serve and to work constrain on the SMEFT the coefficients of the higher dimension • It allows to include Dim 5,6,7,8,…. operators to the operators and restrict possiblerenormalizable beyond lagrangian the SM of the (BSM) SM without physics any prejudice at energies ⇤ >> v. on the possible new physics that causes those deviations We study Higgs decaysfrom to Zthe bosonSM prediction. pairs and to Zγ in the context of the SMEFT, where new physics is described by a tower of operators, k n i k 1 = SM + ⌃k=5⌃i=1 Ck 4 Oi . (1) L L ⇤ − The dimension-k operators are constructed from SM fields and the BSM physics e↵ects k reside in the coefficient functions, Ci . For large ⇤, it is sufficient to retain only the lowest dimensional operators. We assume lepton number conservation, so the lowest dimension relevant operators are dimension-6. Ignoring flavor, there are 59 dimension-6 operators that are SU(3) SU(2) U(1) invariant combinations of the SM fields [1, 2]. The operators ⇥ ⇥ have been classified in several di↵erent bases, which are related by the equations of motion [1–4]. In this paper we will use the Warsaw basis of Ref. [2]. A detailed understanding of Higgs properties requires the inclusion of the dimension- 6 tree level SMEFT e↵ects, along with radiative corrections in the e↵ective field theory. Measurements at the Higgs mass scale, MH , that are sensitive to a set of SMEFT coefficients, (M ), at leading order will develop logarithmic sensitivity to other coefficients when the Ci H renormalization group evolved to the scale ⇤,duetotherenormalizationgroupmixingof the coefficients [5–9]. There are also finite contributions that may be of the same numerical size as the logarithmic terms. We compute the one-loop electroweak SMEFT contributions to the decays H ZZ and ! H Zγ. These corrections include the one-loop SM electroweak corrections, along with ! the one-loop corrections due to the SMEFT operators of Eq. (1). Our results are interesting 2 10 000 000 000 7 557 369 962 2 795 173 575 1 000 000 000 175 373 592 100 000 000 75 577 476 10 000 000 4 614 554 5 474 170 2 092 441 3 472 266 1 000 000 261 485 257 378 100 000 90 456 44 807 15 456 10 000 11 962 3045 1000 1542 993 No. of independent ops 560 100 84 30 10 12 2 1 5 6 7 8 9 10 11 12 13 14 15 Mass dimension Figure 1.GrowthofthenumberofindependentoperatorsintheSMEFTuptomassdimensionNumber of operators in the SMEFT as a function of the dimension 15. Points joined by the lower solid(Henning, line are Lu, for Melia, one fermion Murayama) generation; those joined by the upper solid line are for three generations. DashedAlso: linesLehman, are to Martin guide the eye to the growth of the even and odd mass dimension operators in both cases. (which exhibit some rather large prime numbers!). The number of independent operators evaluated for Nf =1and Nf =3up to dimension 15 are plotted in Fig. 1. We see the growth is exponential, which is to be expected on general grounds [43]. 5Discussion The method we have outlined in this paper can be extended trivially to determining the content and number of higher dimension operators for any four-dimensional relativistic gauge theory with scalar and fermionic matter. The master equation is eq. (3.14), which needs to be modified from the SM to the theory of interest. The pieces of eq. (3.14) which are SM specific are the gauge groups (and as such the Haar measures that need to be integrated over to produce gauge singlets), and the field content (which enters the plethystic exponential). In the present work we studied the expansion of eq. (2.7) in powers of mass dimension, ✏. However, in our previous work in (0+1) dimensions [11] we were able to obtain all-order formulae for Hilbert series, revealing a fascinating analytic structure which could not be seen in any finite order expansion. Can we hope to attack eq. (2.7) directly? Could this reveal some previously hidden all-order structure of the SM EFT? While lofty, questions along these lines merit detailed investigation of the structure underlying operator bases, which we take up in [1]. –16– • Dim 5 is just the Weinberg operator. • All odd dimensions violate L or B • Dim 6 was first studied by Buchmüller and Wyler in 1986 and then completed by Grzadkowski et al. in 2010. X3 ϕ6 and ϕ4D2 ψ2ϕ3 ABC Aν Bρ Cµ † 3 † ¯ QG f Gµ Gν Gρ Qϕ (ϕ ϕ) Qeϕ (ϕ ϕ)(lperϕ) ABC Aν Bρ Cµ † † † QG! f Gµ Gν Gρ Qϕ! (ϕ ϕ)!(ϕ ϕ) Quϕ (ϕ ϕ)(¯qpurϕ) IJK Iν Jρ Kµ † µ ⋆ † † QW ε W!µ Wν Wρ QϕD ϕ D ϕ ϕ Dµϕ Qdϕ (ϕ ϕ)(¯qpdrϕ!) IJK Iν Jρ Kµ " # " # QW" ε Wµ Wν Wρ X2$ϕ2 ψ2Xϕ ψ2ϕ2D ↔ † A Aµν ¯ µν I I (1) † ¯ µ QϕG ϕ ϕ GµνG QeW (lpσ er)τ ϕWµν Qϕl (ϕ iDµ ϕ)(lpγ lr) ↔ † A Aµν ¯ µν (3) † I ¯ I µ QϕG! ϕ ϕ GµνG QeB (lpσ er)ϕBµν Qϕl (ϕ iDµ ϕ)(lpτ γ lr) ↔ † I Iµν µν A A † µ QϕW ϕ ϕ W!µνW QuG (¯qpσ T ur)ϕ Gµν Qϕe (ϕ iDµ ϕ)(¯epγ er) ↔ † I Iµν µν I I (1) † µ QϕW" ϕ ϕ WµνW QuW (¯qpσ ur)τ ϕ!Wµν Qϕq (ϕ iDµ ϕ)(¯qpγ qr) ↔ † µν µν (3) † I I µ QϕB ϕ ϕ$BµνB QuB (¯qpσ ur)ϕ!Bµν Qϕq (ϕ iDµ ϕ)(¯qpτ γ qr) ↔ † µν µν A A † µ QϕB! ϕ ϕ BµνB QdG (¯qpσ T dr!)ϕ Gµν Qϕu (ϕ iDµ ϕ)(¯upγ ur) ↔ † I I µν µν I I † ¯ µ QϕWB ϕ τ ϕ!Wµν B QdW (¯qpσ dr)τ ϕ Wµν Qϕd (ϕ iDµ ϕ)(dpγ dr) † I I µν µν † µ QϕWB" ϕ τ ϕ Wµν B QdB (¯qpσ dr)ϕ Bµν Qϕud i(ϕ Dµϕ)(¯upγ dr) $ Table 2: Dimension-six operators other than the four-fermion! ones.