Tera-Zooming in on Light (Composite) Axion-Like Particles

Tera-Zooming in on light (composite) axion-like particles

G. Cacciapaglia1,2,∗ A. Deandrea1,2,† A.M. Iyer1,2,5,‡ and K. Sridhar3,4§ 1University of Lyon, Universit´eClaude Bernard Lyon 1, F-69001 Lyon, France 2Institut de Physique des 2 Inﬁnis de Lyon (IP2I), UMR5822, CNRS/IN2P3, F-69622 Villeurbanne Cedex, France 3 Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai-400005, India 4Krea University, Sri City, Andhra Pradesh-517646, India 5 Department of Physics, Indian Institute of Technology Delhi, New Delhi-110016, India

The Tera-Z phase of future e+e− colliders, FCC-ee and CepC, is a goldmine for exploring Z portal physics. We focus on axion-like particles (ALPs) that can be produced via Z decays with a monochromatic photon. As a template model, we consider composite Higgs models with a light pseudo-scalar that couples through the Wess-Zumino-Witten term to the electroweak gauge bosons. For both photophilic and photophobic cases, we show that the Tera-Z can probe composite scales up to 100s of TeV, well beyond the capability of the LHC and current precision physics. Our results also apply to generic ALPs and, in particular, severely constrain models that explain the muon g −2 anomaly.

New physics extensions of the Standard Model (SM) ded in several UV frameworks, two scenarios of inter- often contain additional scalar bosons. Their presence est are ALPs [17, 18] and models of composite Higgs can be linked to symmetries, as is the case for axions [1, 2] [5, 31, 39, 45]. In either case, the pseudo-scalar a emerges and for the second Higgs doublet in supersymmetry [3], as a pseudo Nambu-Goldstone Boson (pNGB) of a spon- or to the composite nature of the SM extension [4–6]. taneously broken global symmetry and, therefore, can be Extended scalar sectors are also popular as they offer in- much lighter that the scale Λ. Due to the absence of cou- teresting model building avenues: multiple doublets [7, 8] plings to gluons and fermions, direct and indirect bounds enrich the Higgs sector of the SM, while triplets emerge are relatively weak, especially in the mass range between in neutrino type-II see-saw models [9] and the custodial 1 GeV and the Z mass (e.g., see [20, 28, 46]). Couplings Georgi-Machacek model [10, 11]. Singlets can provide to fermions are, in fact, generated at loop level [28], and Dark Matter candidates [12, 13] or help achieving an elec- their effect is fully taken into account in this work. troweak first order phase transition [14, 15], as required In this letter we point out that future electron-positron by baryogenesis and leptogenesis [16]. Pseudo-scalars are colliders running at the Z pole, like FCC-ee [47] and of special interest, as they exhibit different properties CepC [48], are discovery machines for these light a’s from those of the Higgs boson. While these states map thanks to the leading-order coupling Zaγ contained in to several Beyond the Standard Model (BSM) scenar- Eq. (1). With a projected number of Z bosons produced ios, they can be broadly classified on the basis of the in the few times 1012 ballpark, the so-called Tera-Z run nature of their interactions. In this letter, we focus on has the capability of probing the composite nature of the Axion-Like Particles (ALPs) [17, 18], which, being gauge Higgs boson up to very large scales. In this work, we will singlets, couple to the SM gauge bosons and fermions via focus on two distinct scenarios: dimension-5 operators. They have had implications for a) Photophobic, corresponding to C = −C and have been studied in several areas of particle physics: B W in Eq. (1). In this case, the coupling to pho- flavour [19–27], colliders [28–34], as a dark matter can- tons (C = C + C ) vanishes. Composite didate [18, 25, 35–40]. For a comprehensive insight into γγ W B models based on SU(4)/Sp(4) [4, 39, 45] and these models, see for example [34, 41, 42]. arXiv:2104.11064v1 [hep-ph] 22 Apr 2021 SU(4)2/SU(4) [49] fall under this category. Cur- In particular, motivated by composite Higgs models, rent bounds have been collected in [46]. we will study a special case where only Wess-Zumino- Witten (WZW) couplings [43, 44] to the electroweak b) Photophilic, corresponding to CB = CW . In this gauge bosons are present at the leading order: case, the dominant coupling for masses below the Z is to two photons. Composite models based on 2 CW µν 02 CB µν LWZW = a g Wµν W˜ + g Bµν B˜ , (1) SU(5)/SO(5) [5, 50, 51] fall in this category. The Λ Λ current bounds mainly relying on the photon coupling are summarised in [20]. We should also note where W, B are the electroweak bosons of the SU(2) × L that loop induced couplings to the Higgs in compos- U(1) gauge group respectively and a is the pseudo- Y ite models are suppressed once compared to generic scalar field. Here, Λ is the mass scale in the effective ALP scenarios [30]. theory where the couplings are generated, while the co- efficients CW,B are determined by the ultraviolet (UV) A remarkable class of composite ALPs, which falls in completion. While these couplings could be embed- the Photophilic class, is composed of U(1) pNGBs in 2 models with top partial compositeness [29, 31, 40]: while iii) For L > 100 cm, we consider the signature of a they feature leading order couplings to gluons, the LHC to be missing energy, as it will decay outside the bounds remain relatively weak [29]. As already men- tracker and leave no identifiable trace in the detec- tioned, the results we present in this work are not spe- tor. cial to composite models and can be applied straightfor- wardly to a generic ALP scenario. We use the composite The regions in the 2-dimensional parameter space corre- Higgs framework as a template to visualize the results. sponding to the above three classes are highlighted by the As such, the coupling CW can be expressed as shaded regions in Fig. 3 for both Photophobic and Pho- tophilic ALPs. Thanks to the prompt decay into photons, C d W = √ ψ , (2) the Photophilic ALP has reduced regions with long-lived Λ 64 2π2f or missing energy phenomenology. For the Photophobic case, the prompt decays only occur above the b¯b thresh- where f is the decay constant of the composite Higgs (it is old. implicitly assumed that f is larger than the Higgs vacuum The Tera-Z phase of the FCC-ee and CepC collid- expectation value v) and d counts the internal degrees of ψ ers presents a unique opportunity for studying Z por- freedom of the fermions confined in the composite Higgs. tal physics. With the projected integrated Luminosity, In the numerical study, we will fix d = 4 following the ψ ∼ 6 × 1012 Z bosons will be produced, thus promis- most minimal cases [52]. The results will also be shown ing a remarkable reach for very rare Z decays. In the in terms of the so-called fine-tuning parameter v/f. models under consideration, we obtain branching ratios Z → aγ between 10−8 and 10−12, for values of f between 1 and 100 TeV . Thus, the Tera-Z run has the potential to probe compositeness scales f well beyond what current electroweak precision and the LHC can do, as they probe f up to a 2–3 TeV [41]. Using a UFO model file from FEYNRULES [53], we generated the matrix element of interest for the signal, M(e+e− → Z → aγ), using MADGRAPH [54]. We pass the events through PYTHIA for the showering and hadronization. The IDEA detector card of DELPHES [55] is used for the fast detector simula- tion. FIG. 1. Branching ratios (B.R.) for the pseudo-scalar a in the Prompt decays. In the Photophobic models, prompt Photophobic case, as a function of its mass. decays take place for masses above the b¯b threshold, where the dominant final state comprises bottom quarks. We use the results from [28], including loop-induced Thus we consider the main signal to be Z → γa → γb¯b, couplings to fermions and photons, to calculate the par- leading to one isolated monochromatic photon and a pair tial decay widths of the pseudo-scalar a. As all the cou- of b-jets. The jets are reconstructed using the AK4 [56] plings are proportional to the same coefficient CW /Λ, algorithm, requiring each jet to have a minimum trans- the branching ratios only depend on the a mass, as illus- min verse momentum pT = 4 GeV. Furthermore, we de- trated in Fig.1 for the Photophobic case. The dominant mand that at least one of the jets is tagged as a b- decay is always into the heaviest accessible quark, while jet. Given the absence of data for a pT specific b- sub-leading decays into photons grow towards the Z mass tagging efficiency for the IDEA detector, we assume a threshold. In the Photophilic Case, the dominant decay pT -independent tag rate of 80%, with a mis-tag rate of is always into two photons, independent of the mass. The 1%. The dominant background is due to the decay of only physical quantities that depend on the WZW cou- Z → b¯bγ where the photon is radiated off one of the b pling are the branching ratio of Z → aγ and the lifetime quarks (while Z → jjγ is suppressed by the jet mis-tag of a. The former fixes the number of signal events ex- rate). The energy of the monochromatic photon depends pected at the Tera-Z run, while the latter will determine on the mass of the associated pseudo-scalar a, and can the search strategies to be adopted. As the design for be used as the main discriminant against the background. the detector is not finalized, we will use the typical size In the top plot of Fig. 2 we illustrate the distribution of of a central tracker to define the following three classes, the photon energy E for three different masses of the based on the a lifetime L: pseudo-scalar a: 15, 50 and 80 GeV. The corresponding i) For L < 2 cm, we consider the decays prompt. background distribution is shown by the black dashed line. We see that, as the mass of the pseudo-scalar in- ii) For 2 < L < 100 cm, we consider a being long-lived creases, the energy of the photon moves closer to that as the decay off the beam pipe can be tracked and of the background distribution. Hence, the differentia- identified. tion of the signal will become increasingly ineffective. To 3 quantify the discrimination power, and define our search photons in decreasing order of pT as γ1, γ2, γ3. We ob- strategy, we bin the events by 2 GeV. We then use the fol- serve that for a masses larger than 50 GeV, in most of lowing expression to evaluate the signal sensitivity [57]: the events it’s the two leading photons that reconstruct the resonance, while for masses below 50 GeV it’s the v two sub-leading photons. Hence, we define a discrimi- u N uX si nant variable as Z = t 2(si + bi) log 1 + − 2si , (3) bi 2 i=1 (pγ1 + pγ2 ) for ma < 50 GeV mγγ = 2 (4) (pγ2 + pγ3 ) for ma > 50 GeV where the sum runs over all the bins and si/bi are signal/background events in the ith bin. The right plot of depending on the a mass we are probing. This variable Fig. 3 shows the reach in the (ma, f) plane for the Pho- is illustrated in the bottom plot of Fig. 2 for three repre- tophobic composite models: in the blue-shaded region, sentative masses, showing that our strategy does indeed the red and black contours show the Z = 2σ sensitiv- well reconstruct the resonance. For the background, we ity for integrated Luminosities of 3 ab−1 and 150 ab−1, first consider the irreducible process e+e− → γγγ. As respectively. The contours clearly highlight the loss of for the signal, we define the background distribution in sensitivity for masses close to the Z mass, which is also mγγ by grouping either the leading (BGγ1γ2 ) or sub- due to a reduction in the B.R. of the Z boson. With this leading (BGγ2γ3 ) photons, as shown by the solid and channel we, therefore, expect to be sensitive to Higgs dashed black lines. The former is used for the computa- composite scales f up to 5 TeV, well above the current tion of the signal sensitivity for masses ma ≤ 50 GeV, reach. while the latter is used for the heavier masses. The blue arrow represents the transition point. An interest-

ing feature in the BGγ1γ2 distribution is its sharp fall above 80 GeV. This can be attributed to the fact that the third photon carries a small but non-negligible energy. With a precise knowledge of the centre-of-mass energy and the fact that the three photons must nec- essarily reconstruct to mass around the Z pole, the invariant mass of the two leading photons must exhibit falling distributions as one approaches the Z pole. We also considered the background from e+e− → e+e−γ, where both electrons are mis-identified as photons. The distribution of this background off the Z pole is similar to that of the 3-photon one, and it can be kept below 2.5% of the irreducible background as long as the mis-id rate is kept below 0.0005. To understand how reason- able this value is, we can compare with the study of a light-mass resonance decaying into photons in CMS [58], where the double-fake rate at the Z-pole was estimated to be ∼ 0.0015. A more detailed knowledge of the detector and a data-driven analysis is required for a better un- derstanding of this background. Similarly, the region for FIG. 2. Illustration of the signal and background distribu- m > 80 GeV will be populated dominantly by mis-id tion for a given analysis. Top: energy of the leading isolated γγ backgrounds, thus we remove this region from our anal- photon for the signal and the background. Bottom: construc- tion of the invariant mass using di-photon events for different ysis. To quantify the sensitivity of this search, we use masses and the background. For ma ≤ 50 GeV, we use the the same binned likelihood function in Eq. 1 for mγγ . As two sub-leading photons (γ(1)γ(2)) while for other masses we before, the red and black contours correspond to Z = 2σ use the two leading photons (γ(0)γ(1)). The corresponding for 3 and 150 ab−1. In the composite Higgs scale, this background is illustrated by solid-black (Bγ1γ2 ) and dashed channel allows to probe f up to 20 TeV in the prompt black (Bγ2γ3 ) line respectively. decay region (blue shade). We checked that other bounds on the photon coupling [28] only apply for f < 1 TeV due In the Photophilic models, the prompt region extends to the loop suppression in Eq. (2). to masses as low as 1 GeV, and the dominant decay pro- Long-lived ALP signature. Pseudo-scalars with a rel- duces two photons. The signal final state is Z → γa → atively long lifetime, such that a displaced vertex can γγγ, thus containing three isolated photons. The pho- be reconstructed, possibly give the most optimist pic- tons are reconstructed with a minimum transverse mo- ture due to the absence, in practice, of irreducible back- γ mentum of pT > 2 GeV. Furthermore, we will order the grounds. Yet, it is difficult to give reliable estimates with- 4

Photophobic Photophilic

3 ab-1 3 ab-1 0.1 150 ab-1 -3 150 ab-1 10 ) 1 v -

0.01 TeV f ( -1 -4 3 ab 10 W 3 ab-1 Λ C

0.001 150 ab-1 150 ab-1 10-5 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80

ma (GeV) ma (GeV)

FIG. 3. Butterfly plot showing the parameter space for the photophilic (right wing) and photophobic (left wing) models. The shaded regions correspond to prompt decays (blue), long-lived (orange) and missing energy signature (green). The 2σ reach of the Tera-Z run is indicated for integrated Luminosities of 3 (black) and 150 ab−1 (red). The conversion between the ALP coupling CW /Λ and the compositeness scale f is given in Eq. (2) with dψ = 4. out a precise definition of the detector. Here, therefore, in detail in Ref. [59]. Here, decays of the Z into a we will provide an estimate of the number of events ex- dark photonγ ¯ are considered, with a projected bound pected in each case assuming a negligible background. of B(Z → γγ¯) = 2.3 × 10−11 for the Tera-Z. Our case In the Photophobic case, the dominant decays involve is slightly different, as the dark photon is replaced by a hadrons, as shown in Fig. 1. The contours in the orange pseudo-scalar, however we do not expect large differences region in the left plot of Fig. 3 represent the benchmark in the reach. Thus, we simply reinterpreted the bound in of 2 events with displaced hadrons +γ for an integrated our parameter space, as shown by the horizontal red line luminosity of 3 and 150 ab−1. This shows that the Tera- in the green shaded regions of Fig. 3. The limit is the Z run has the potential of being sensitive to f scales same for both models, as it is independent on the decay up to 600 TeV. For the Photophilic case, the long-lived products of the a. It illustrates the sensitivity for scales signal can only occur for masses below 20 GeV due to as heavy as ∼ 90 TeV. the leading coupling to photons. The signal thus consists of a monochromatic photon with energy between In conclusion, we have considered the Tera-Z run at 35 and 45 GeV depending on the a mass, and two pho- future e+e− colliders as a discovery machine for ALPs tons originating from a displaced vertex. In this case produced in the Z decays. We consider composite Higgs too, we conservatively provide contours that give a size- models as a template, where the light ALP is a pseudo- able number of events (20) for integrated luminosities of Nambu-Goldstone boson that couples to the electroweak 3 and 150 ab−1, as shown in the right plot of Fig. 3. The gauge bosons via the topological WZW term. We con- potential reach in f is similar to the Photophobic case. sider both photophilic and photophobic scenarios, including loop-induced couplings to fermions and photons. Our Missing energy signature. For large life-times, which analysis shows that the Tera-Z can probe the Higgs com- allow for decays outside of the tracker, the a can be con- posite scale up to 5 or 20 TeV for prompt decays, and sidered as missing energy as it will not be reconstructed hundreds of TeV for long-lived or missing energy signa- in the detector. The signature, therefore, consists of tures. Thus, the Tera-Z can zoom in the composite na- a single monochromatic photon and has been studied ture of the Higgs to much better precision than the LHC. 5

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