# Global Searches for New Physics with Top Quarks

SSNSN-323-63February 10, 2021

Global Searches for New Physics with Top Quarks

Susanne Westhoff

Institute for Theoretical PhysicsHeidelberg University, D-69120 Heidelberg, GERMANY

This is a brief summary of the latest searches for virtual eﬀects of newphysics in the top sector. In the framework of the Standard Model Ef-fective Field Theory (SMEFT), I show how to resolve the structure ofeﬀective couplings by combining observables at the LHC and at ﬂavorexperiments in a global ﬁt. With this approach we start exploring thefeatures of a UV theory at energies beyond current colliders.PRESENTED AT th International Workshop on Top Quark PhysicsDurham, UK (videoconference), 14–18 September, 2020 a r X i v : . [ h e p - ph ] F e b Introduction

In our search for new physics, the top quark is interesting in two respects. At theLHC, direct top production allows us to probe virtual eﬀects of heavy new particlesat high energies and in various precision observables. At ﬂavor experiments, the topquark induces meson decays and mixing, which are rare in the Standard Model (SM)and therefore very sensitive to new physics. In combination, both areas allow us toresolve fundamental interactions at energies above the reach of the LHC.Assuming that new interactions, if present, preserve the SM gauge symmetries, wecan consider the Standard Model as an eﬀective ﬁeld theory, SMEFT, that describesthe low-energy appearance of a fundamental theory at high energies. This frameworkallows us to classify eﬀects of new physics at scales Λ > C i called Wilson coeﬃcients. Based on the eﬀectiveLagrangian L SMEFT = L SM + C Λ O + (cid:88) i C i Λ O i + . . . , (1)we calculate LHC observables as polynomials of SMEFT coeﬃcients σ = σ SM + (cid:88) i C i Λ σ i + (cid:88) i,j C i C j Λ σ ij , (2)which can be compared with data. In a concrete model, UV physics imprints itselfonto certain Wilson coeﬃcients, which leave a pattern of eﬀects in observables atlower energies. Most models generate eﬀects of several Wilson coeﬃcients in severalobservables. To resolve the SMEFT parameter space and pin down the features ofthe UV theory, a global analysis is required.In the top sector, several global SMEFT analyses of LHC data have demonstratedsensitivity to new physics above, but not far above the TeV scale [1, 2, 3, 4]. Themain asset of the top sector, however, is not the reach in energy, but the large numberof precise observables, which allow us to resolve much of the set of relevant Wilsoncoeﬃcients. In Sec. 2, we will combine precise observables in top-antitop productionresolve the chiral structure of eﬀective four-quark couplings.Combining LHC observables with ﬂavor observables greatly improves the sensitiv-ity to new physics and probes blind directions in global ﬁts of LHC data [5, 6, 7, 8].Below the scale of electroweak symmetry breaking, interactions of light fermions, thephoton and the gluon are well described by the Weak Eﬀective Theory (WET) L WET = L QED + L QCD + (cid:88) a C a O a + . . . . (3)The set of Wilson coeﬃcients {C a } in WET is diﬀerent from and smaller than the set { C i } in SMEFT, mainly because the top quark and the weak bosons are no longer1ynamical constituents of the theory. Both sets are connected through the renor-malization group. The respective eﬀects in high-energy and low-energy observables,however, depend on the assumed ﬂavor structure of the SMEFT coeﬃcients. In Sec. 3,we will show how to resolve the ﬂavor structure of a UV theory in a combined analysisof top and bottom observables. To illustrate how to probe the features of new physics interactions in top observables,we focus on two SMEFT operators O tq = ( t R γ µ T A t R )( q L γ µ T A q L ) , O , Qq = ( Q L γ µ T A Q L )( q L γ µ T A q L ) , (4)where q = ( u L , d L ) and Q = ( t L , b L ) stand for weak doublets of left-handed quarksfrom the ﬁrst two and from the third generation, respectively. These two operatorsonly diﬀer by the chirality of the heavy quarks, i.e., t R versus t L for the tops. Distin-guishing between the eﬀects of O tq and O , Qq in observables means probing the chiralstructure of a UV theory that induces them. This example is part of a comprehen-sive analysis performed in Ref. [3], to which we refer you, dear interested reader, fordetails.Top-antitop production is a good test ground for chiral top-quark couplings.Charge-symmetric observables like the total cross section probe mostly vector-like L + R couplings, while charge asymmetries probe axial-vector couplings L − R . Interms of Wilson coeﬃcients, they read σ tt = σ SM + σ V V ( C , Qq + C tq ) + O ( C ) (5) A C = (cid:16) σ A SM + σ AA ( C , Qq − C tq ) (cid:17) /σ tt + O ( C ) . Quadratic contributions of O ( C ) have been neglected here, but are numerically rel-evant when comparing the predictions with data. In Fig. 1, left, we show the resultsof ﬁts to LHC top data with charge-symmetric observables (red contours), chargeasymmetries (black contours), and the combination of both sets (blue areas). Thehyperbola-shaped bounds obtained from the asymmetries leave a blind direction along C , Qq + C tq , which is broken when adding charge-symmetric observables. This simpleexample demonstrates how to resolve blind directions in a ﬁt by adding observablesthat probe complementary directions in the SMEFT parameter space. The resolutioncan be improved by adding observables like the energy asymmetry in top-antitop-jetproduction [9] or observables of the top polarization like spin correlations, which aresensitive to other combinations of the two couplings.When combining diﬀerent observables in global ﬁts, it is crucial to include correla-tions in both predictions and measurements. We illustrate the impact of correlations2 orrelatedUncorrelated Figure 1: Left: bounds on the chiral four-quark couplings C , Qq and C tq obtained froma combined ﬁt to charge-symmetric tt observables (red), charge asymmetries (black),and both sets of observables combined (blue) [3]. Right: impact of correlations in acombined ﬁt of tt observables [10]; shown are the bounds obtained by assuming thatsystematic uncertainties in bins of diﬀerential distributions are uncorrelated (black)and 100% correlated (red). Solid and dashed lines mark the Gaussian equivalent of∆ χ = 1 , σ tt , σ dσdm tt , σ dσd ∆ y tt , A C . (6)In the ﬁrst ﬁt, we assume that the systematic uncertainties in bins of diﬀerentialdistributions are fully correlated; in the second ﬁt, we assume no correlations. Theresults in Fig. 1, right, show that the correlations relax the bounds on the Wilsoncoeﬃcients, providing us with a more realistic interpretation of the data than withoutcorrelations. More details can be found in Refs. [3, 11]. New physics eﬀects in top observables at the LHC are linked to eﬀects in ﬂavorobservables through the renormalization group. Each WET coeﬃcient C a at thebottom mass scale m b can be expressed as a linear combination of SMEFT coeﬃcients { C i } at the top mass scale m t , C a ( m b ) = F ( C i ( m t )) . (7)3y including ﬂavor observables in global ﬁts, we probe new directions in the SMEFTspace and improve the sensitivity to new physics.The relative impact of top and bottom observables in a combined analysis stronglydepends on the ﬂavor structure of the Wilson coeﬃcients. This is due to the fact thattop observables probe mostly ﬂavor-diagonal couplings, while bottom observablesare also very sensitive to ﬂavor-changing couplings. We can exploit the top-bottomconnection to probe the ﬂavor structure of a UV theory.Here we show how to resolve the ﬂavor structure of the Wilson coeﬃcients in theframework of minimal ﬂavor violation. Details are given in Ref. [8]. We focus on twooperators O (1) φq = ( H † ←→ iD µ H )( Q k γ µ Q l ) , O (3) φq = ( H † ←→ iD µ τ a H )( Q k γ µ τ a Q l ) , (8)where the two currents in O (1) φq transform as singlets under weak interactions, while O (3) φq has a triplet structure encoded in the SU (2) generators τ a . Furthermore, Q k and Q l stand for the left-handed quark doublets of generation k, l = { , , } . Assumingthat the only sources of ﬂavor symmetry breaking in the UV theory are – as in theStandard Model – the Yukawa couplings, we can expand the Wilson coeﬃcients as( C ) kl = (cid:16) a + b Y U Y † U + c Y D Y † D + . . . (cid:17) kl = a δ kl + by t δ k δ l + O ( y b ) . (9)The parameter a corresponds to ﬂavor-universal couplings, and b induces ﬂavor-breaking couplings. In Fig. 2, left, we illustrate how the ﬂavor parameters contributeto the rare meson decay B → X s γ (orange) and to hadronic ttZ production (blue). ∗ By combining top and bottom observables, we can probe the ﬂavor structure of UVinteractions by distinguishing between ﬂavor-universal and ﬂavor-breaking couplings.In Fig. 2, right, we show the bounds resulting from a combined ﬁt of top observ-ables, as well as the meson decays B → X s γ and B s → µ + µ − . While the top ﬁt alone(blue) leaves space for ﬂavor breaking along b , the combined ﬁt (orange) resolves thisdirection and suggests that ﬂavor-breaking contributions, if present, should be small.Interestingly, this insight relies on one-loop eﬀects of O (3) φq to B → X s γ , which arevery sensitive to ﬂavor breaking. Notice also that electroweak contributions to ttZ production with a virtual Z boson are important to correctly describe this process inSMEFT. These two examples illustrate how to resolve the structure of Wilson coeﬃcients inthe SMEFT framework by combining top and bottom observables. The ﬁt results ∗ The combinations a ( − ) = a (1) − a (3) etc. parametrize the coupling to up-type quarks, and A = a + b y t is the relevant combination for third-generation quarks. a (3) q /⇤ [TeV ] b ( ) q / ⇤ [ T e V ] Figure 2: Left: SMEFT contributions of O (1) φq and O (3) φq to B → X s γ (top) and to pp → ttZ (bottom) in minimal ﬂavor violation. Right: bounds obtained from acombined ﬁt of the ﬂavor parameters { a (3) φq , b (3) φq , a ( − ) φq , b ( − ) φq } to top observables (blue),top & B ( B s → µ + µ − ) (green) and top & B ( B s → µ + µ − ) & B ( B → X s γ ) (orange).The ﬂavor parameters a, b are deﬁned at the top mass scale m t . Details in Ref. [8].are presented at the top mass scale, but can be translated to any scale Λ > m t byevolving the Wilson coeﬃcients via the renormalization group, where they can bematched with any concrete UV theory that does not involve new light particles.Much more can be learned about UV physics by strategically building on this proofof principle. Good places to look for indirect signs of new physics are observables thatare precise and/or suppressed in the Standard Model. At the LHC, associated tZ , tW , th production are very sensitive processes [12], as well as tails of kinematic distri-butions that probe new physics at the highest available energies [13, 14]. Combinedﬁts to LHC data in the top, Higgs, and electroweak sectors [15], as well as combina-tions of Higgs and electroweak observables with ﬂavor observables [6] are promisingsteps towards a truly global SMEFT analysis that will allow us to resolve more andmore of what might be hiding in the UV. ACKNOWLEDGEMENTS

I thank the organizers of Top 2020 for inviting me and for bringing the lastest newsfrom the top to our living rooms. This work has been supported by the DFG (GermanResearch Foundation) under grant no. 396021762–TRR 257.5 eferences [1] A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Rus-sell and C. D. White, JHEP , 015 (2016) doi:10.1007/JHEP04(2016)015[arXiv:1512.03360 [hep-ph]].[2] N. P. Hartland, F. Maltoni, E. R. Nocera, J. Rojo, E. Slade, E. Vry-onidou and C. Zhang, JHEP , 100 (2019) doi:10.1007/JHEP04(2019)100[arXiv:1901.05965 [hep-ph]].[3] I. Brivio, S. Bruggisser, F. Maltoni, R. Moutaﬁs, T. Plehn, E. Vryonidou,S. Westhoﬀ and C. Zhang, JHEP , 131 (2020) doi:10.1007/JHEP02(2020)131[arXiv:1910.03606 [hep-ph]].[4] G. Durieux, A. Irles, V. Miralles, A. Pe˜nuelas, R. P¨oschl, M. Perell´oand M. Vos, [erratum: JHEP , 195 (2021)] doi:10.1007/JHEP12(2019)098[arXiv:1907.10619 [hep-ph]].[5] S. Bißmann, J. Erdmann, C. Grunwald, G. Hiller and K. Kr¨oninger, Eur. Phys.J. C , no.2, 136 (2020) doi:10.1140/epjc/s10052-020-7680-9 [arXiv:1909.13632[hep-ph]].[6] R. Aoude, T. Hurth, S. Renner and W. Shepherd, JHEP , 113 (2020)doi:10.1007/JHEP12(2020)113 [arXiv:2003.05432 [hep-ph]].[7] S. Bißmann, C. Grunwald, G. Hiller and K. Kr¨oninger, [arXiv:2012.10456 [hep-ph]].[8] S. Bruggisser, R. Sch¨afer, D. van Dyk and S. Westhoﬀ, [arXiv:2101.07273 [hep-ph]].[9] A. Basan, P. Berta, L. Masetti, E. Vryonidou and S. Westhoﬀ, JHEP , 184(2020) doi:10.1007/JHEP03(2020)184 [arXiv:2001.07225 [hep-ph]].[10] Courtesy of Sebastian Bruggisser.[11] S. Bißmann, J. Erdmann, C. Grunwald, G. Hiller and K. Kr¨oninger, Phys. Rev. D , 115019 (2020) doi:10.1103/PhysRevD.102.115019 [arXiv:1912.06090 [hep-ph]].[12] C. Degrande, F. Maltoni, K. Mimasu, E. Vryonidou and C. Zhang, JHEP ,005 (2018) doi:10.1007/JHEP10(2018)005 [arXiv:1804.07773 [hep-ph]].[13] C. Englert, L. Moore, K. Nordstr¨om and M. Russell, Phys. Lett. B , 9-15(2016) doi:10.1016/j.physletb.2016.10.021 [arXiv:1607.04304 [hep-ph]].614] F. Maltoni, L. Mantani and K. Mimasu, JHEP10