Ter a - Z o o m i ng i n on light (composite) ALPS Giacomo Cacciapaglia IP2I Lyon, France Based on: 2104.11064, GC, A. Deandrea, A.Iyer, K. Sridhar Motivation The TeraZ option will produce 10^12 Z’s: does it make sense to search for new light states in Z decays? In composite Higgs models, light (pseudo)scalars are allowed and likely to exist! Composite ALP Lagrangian is “calculable”: predictive power! Access to high composite scales. Ideal physics case for FCC-ee @ 90 GeV! [Synergy with EWPTs] Composite Higgs models 101 Symmetry broken by a condensate (of TC-fermions) Misalignment, Higgs and longitudinal Z/W emergefor a Goldstone-Higgsas mesons (pions) Scales: v f ⇠ f : Higgs decay constant v : EW scale v f m 4⇡f ⌧ ⇢ ⇠ EWPTs + Higgs coupl. limit: v f 4v 1 TeV sin ✓ = Vacuum & f ⇠ misalignment Composite Higgs models 101 How can light states emerge? To p lo o p s Gauge loops TC-fermion masses W, Z top X 2 2 2 2 φ y f g f m f ⇠ t ⇠ ⇠ 2 2 2 = y2v2 2 2 2 2 2 h yt f s✓ t g f s✓ = g v X (h massless for ⇠ vanishing v) ⇠ m f a X X ⇠ This can be small! Composite Higgs models 101 T.Ryttov, F.Sannino 0809.0713 Galloway, Evans, Luty, Tacchi 1001.1361 The EW symmetry is embedded in the global flavour symmetry SU(4) ! The global symmetry is broken: SU(4)/Sp(4) Witten, Kosower 5 Goldstones (pions) arise: 5 (2, 2) (1, 1) Sp(4) ! ⊕ Higgs additional singlet be above 1MeV. In Section 4 the preferred region of parameter space in which an ALP can explain the anomalous magnetic moment of the muon is derived. Section 5 is devoted to a detailed discussion of the exotic Higgs decays h Za and h aa. We discuss which regions 1 ! ! of parameter space can be probed with 300 fb− of integrated luminosity in Run-2 of the LHC, and which regions can already be excluded using existing searches. In Section 6 we extend this discussion to the exotic decay Z γa, and we study Z-pole constraints from electroweak precision tests. We conclude in Section! 7. Technical details of our calculations are relegated to four appendices. 2E↵ective Lagrangian for ALPs We assume the existence of a new spin-0 resonance a, which is a gauge-singlet under the SM gauge group. Its mass ma is assumed to be smaller than the electroweak scale. A natural way to get such a light particle is by imposing a shift symmetry, a a + c, where c is a constant. We will furthermore assume that the UV theory is CP invariant,! and that CP is broken only by the SM Yukawa interactions. The particle a is supposed to be odd under CP. Then the most general e↵ective Lagrangian including operators of dimension up to 5 (written in the unbroken phase ofTypical the electroweak symmetry)ALP Lagrangian: reads [51] 2 µ D 5 1 µ ma,0 2 @ a = (@ a)(@ a) a + ¯ C γ Le↵ 2 µ − 2 ⇤ F F µ F F X (1) 2 a A µ⌫,A 2 a A µ⌫,A 2 a µ⌫ + g C G G˜ + g C W W˜ + g0 C B B˜ , s GG ⇤ µ⌫ WW ⇤ µ⌫ BB ⇤ µ⌫ where we have allowed for an explicit shift-symmetry breaking mass term ma,0 (see below). A A Gµ⌫, Wµ⌫ Theand B couplingsµ⌫ are the field C’s strength are tensorstypically of SU (3)chosenc, SU(2) Ltoand beU (1)O(1)Y ,andgs, g and g0 denote the corresponding coupling constants. The dual field strength tensors are defined as B˜µ⌫ = 1 ✏µ⌫↵βB etc. (with ✏0123 =1).Theadvantageoffactoringoutthegaugecouplings 2 Composite↵ models demonstrate how a in the terms in the second line is that in this way the corresponding Wilson coefficients are scale invariantdeparture at one-loop from order (see the e.g. [52]conventional for a recent discussion “generic” of the evolution equations beyondvalues leading order).can Thelead sum to in theinteresting first line extends phenomenology over the chiral fermion multiplets F of the SM. The quantities CF are hermitian matrices in generation space. For the couplings of a to the U(1)Y and SU(2)L gauge fields, the additional terms arising from a constant shift a a + c of the ALP field can be removed by field redefinitions. The coupling to QCD gauge ! fieldsThis is not invariant analysis under a continuousis also shift applicable transformation because to ofALPs instanton e↵ects, which however preserve a discrete version of the shift symmetry. Above we have indicated the suppression ofthat the dimension-5 exhibit operators similar with a new-physics properties! scale ⇤, which is the characteristic scale of global symmetry breaking, assumed to be above the weak scale. In the literature on axion phenomenology one often eliminates ⇤ in favor of the “axion decay constant” fa, defined 2 such that ⇤/ CGG =32⇡ fa. Note that at dimension-5 order there are no ALP couplings to the Higgs doublet| |φ. The only candidate for such an interaction is µ µ (@ a) g (@ a) 2 OZh = φ† iDµ φ +h.c. Zµ (v + h) , (2) ⇤ !2cw ⇤ 4 be above 1MeV. In Section 4 the preferred region of parameter space in which an ALP can explain the anomalous magnetic moment of the muon is derived. Section 5 is devoted to a detailed discussion of the exotic Higgs decays h Za and h aa. We discuss which regions 1 ! ! of parameter space can be probed with 300 fb− of integrated luminosity in Run-2 of the LHC, and which regions can already be excluded using existing searches. In Section 6 we extend this discussion to the exotic decay Z γa, and we study Z-pole constraints from electroweak precision tests. We conclude in Section! 7. Technical details of our calculations are relegated to four appendices. 2E↵ective Lagrangian for ALPs We assume the existence of a new spin-0 resonance a, which is a gauge-singlet under the SM gauge group. Its mass ma is assumed to be smaller than the electroweak scale. A natural way to get such a light particle is by imposing a shift symmetry, a a + c, where c is a constant. We will furthermore assume that the UV theory is CP invariant,! and that CP is broken only by the SM Yukawa interactions. The particle a is supposed to be odd under CP. Then the most general e↵ective Lagrangian including operators of dimension up to 5 (written in the unbroken phase ofTypical the electroweak symmetry)ALP Lagrangian: reads [51] 2 µ D 5 1 µ ma,0 2 @ a = (@ a)(@ a) a + ¯ C γ Le↵ 2 µ − 2 ⇤ F F µ F F X (1) 2 a A µ⌫,A 2 a A µ⌫,A 2 a µ⌫ + g C G G˜ + g C W W˜ + g0 C B B˜ , s GG ⇤ µ⌫ WW ⇤ µ⌫ BB ⇤ µ⌫ where we have allowed for an explicit shift-symmetry breaking mass term ma,0 (see below). A A Gµ⌫, Wµ⌫ and Bµ⌫ are theComposite field strength tensors Higgs of scenario:SU(3)c, SU(2)L and U(1)Y ,andgs, g and g0 denote the corresponding coupling constants. The dual field strength tensors are defined as µ⌫ 1 µ⌫↵β 0123 B˜ = ✏ B↵ etc. (with ✏ =1).Theadvantageoffactoringoutthegaugecouplings CWW2 CBB NTC C in the terms in the second line is that in this way the correspondingGG Wilson=0 coefficients are scale invariant⇤ ⇠ at one-loop⇤ ⇠ order64 (seep2 e.g.⇡ [52]2f for a recent discussion⇤ of the evolution equations beyond leading order). The sum in the first line extends over the chiral fermion multiplets F of the SM. The quantities CF are hermitian matrices in(Poor generation bounds space. at the For LHC) the couplings of a to the(CUγγ(1)Y=andCWWSU(2)+L CgaugeBB) fields, the additional terms arising from a constant shift a a + c of the ALP field can be removed by field redefinitions. The coupling to QCD gauge ! fields is not invariant under a continuous shift transformation because of instantonf e↵ects, which however preserve a discrete version of the shift symmetry. Above we have indicated the suppressionCF of theis dimension-5loop-induced: operators with a new-physics scale ⇤a, which is the characteristic scale of global symmetry breaking, assumed to be above the weak scale. In thef literature on axion phenomenologyM.Bauer one et often al, 1708.00443 eliminates ⇤ in favor of the “axion decay constant” fa, defined 2 such that ⇤/ CGG =32⇡ fa. Note that at dimension-5 order there are no ALP couplings to the Higgs doublet| |φ. The only candidate for such an interaction is µ µ (@ a) g (@ a) 2 OZh = φ† iDµ φ +h.c. Zµ (v + h) , (2) ⇤ !2cw ⇤ 4 be above 1MeV. In Section 4 the preferred region of parameter space in which an ALP can explain the anomalous magnetic moment of the muon is derived. Section 5 is devoted to a detailed discussion of the exotic Higgs decays h Za and h aa. We discuss which regions 1 ! ! of parameter space can be probed with 300 fb− of integrated luminosity in Run-2 of the LHC, and which regions can already be excluded using existing searches. In Section 6 we extend this discussion to the exotic decay Z γa, and we study Z-pole constraints from electroweak precision tests. We conclude in Section! 7. Technical details of our calculations are relegated to four appendices. 2E↵ective Lagrangian for ALPs We assume the existence of a new spin-0 resonance a, which is a gauge-singlet under the SM gauge group.