On the behaviour of composite resonances breaking lepton flavour ...

On the behaviour of composite resonances breaking lepton flavour universality Mikael Chala and Michael Spannowsky

arXiv:1803.02364v1 [hep-ph] 6 Mar 2018

Institute of Particle Physics Phenomenology, Physics Department, Durham University, Durham DH1 3LE, UK Within the context of composite Higgs models, recent hints on lepton-flavour non-universality in B decays can be explained by a vector resonance V with sizeable couplings to the Standard Model leptons (`). We argue that, in such a case, spin-1/2 leptonic resonances (L) are most probably light enough to open the decay mode V → L`. This implies, in combination with the fact that couplings between composite resonances are much larger than those between composite and elementary fields, that this new decay is dominating over other decay modes. Its discovery, however, requires a dedicated search strategy. Employing jet substructure techniques, we analyse the final state with largest branching ratio, namely µ+ µ− Z/h, Z/h → jets. We show that (i) parameter space regions that were believed excluded by di-muon searches are still allowed, (ii) these regions can already be tested with the dedicated search we propose and (iii) V masses as large as ∼ 3.5 TeV can be probed at the LHC during the high-luminosity phase.

I.

INTRODUCTION

Experimental data collected during the last few years by LHCb [1–6], Belle [7] and the LHC [8, 9] suggest departures from Lepton Flavor Universality (LFU) in B meson decays with respect to Standard Model (SM) predictions. In particular, the measured values of the very clean observables RK (∗) ≡

B(B +(0) → K +(∗) µ+ µ− ) B(B +(0) → K +(∗) e+ e− )

(1)

depart from the SM prediction [10, 11] by more than 2 σ, while a naive combination results in a discrepancy of about 4 σ [12]. These observations hint to a possible breaking of LFU. Among other possibilities, it has been proposed that the origin of LFU violation relies on a composite spin1 resonance V with sizeable couplings to the SM leptons [12–19]. This kind of particle arises naturally in composite Higgs models (CHMs) [20, 21], which are further motivated by the gauge-hierarchy problem. For concreteness, we will focus on the muon case, but most of the discussion and results can be extended straightforwardly to electrons [12, 15]. As we will argue, this solution implies that vectorlike partners (L) of the SM leptons (`), can very well be lighter than V . In that case, the channel V → L` opens and it can actually dominate the V decay width. It is certainly surprising that no single study has taken this effect into account. This has two major implications. (i) Contrary to the standard case studied so far, this setup survives all constraints from LHC data, including the strongest ones from di-muon searches. (ii) In already collected events containing two muons and a fat jet resulting from a Z or Higgs boson, new dedicated searches can reveal a clear p peak in the invariant mass distribution of mµ1 j1 = (pµ1 + pj1 )2 , with µ1 and j1 being the highest-pT muon and jet, respectively.

The structure of the paper is therefore as follows. In section II we discuss why current LFU data together with partial compositeness in CHMs and naturalness arguments suggest that new leptonic resonances might be lighter than V . In section III we study current constraints on the model, and the need for very dedicated searches. Finally, in section IV we work out a new analysis relying on jet-substructure techniques, that can reveal the presence of the new resonances. We conclude in section V.

II.

MODEL

The phenomenological Lagrangian describing the interactions between the spin-1 singlet V and the SM leptons is given by ∆L =

1 2 m Vµ V µ + Jµ V µ + · · · 2 V

(2)

where mV is the mass of V and the ellipsis encode the kinetic term as well as other interactions not relevant for the subsequent discussion. We further define i γ qj , Jµ = gV `` λ`ij `iL γµ `jL + gV qq λqij qL µ L

(3)

with ` and q SM leptons and quarks, respectively. Let us consider for simplicity λ`ij ∼ δi2 δj2 and λqij ∼ δi3 δj3 , so that mainly the second-generation leptons and the third-generation quarks couple to the vector resonance. Likewise, the LFU violating term can be estimated to be λq23 ∼ VcbCKM , with V CKM the Cabbibo-KobayashiMaskawa matrix. Reproducing the LFU anomalies requires [22] gV qq ∼ 0.05

m2V TeV2

(4)

2 for gV `` ∼ 1. Much larger values of this latter parameter are disfavoured by limits on neutrino trident production [23]. On the other hand, smaller values are disfavoured by measurements of ∆Ms for values of mV in the natural region of CHMs, namely mV ∼ few TeV. We thus stick to this value henceforth, which is allowed even by the latest measurement of ∆Ms [22]. The key point is that, if V is a resonance in a CHM, its couplings to the SM fermions originate from partial compositeness [24]. The more fundamental Lagrangian reads 1 MV2 (gc V µ − ge B µ )2 2 gc2 / − gc V/ − ML )L + Q(iD / − gc V/ − MQ )Q + L(iD   + ∆L `L L + ∆Q qQ + h.c. + · · · (5)

∆L =

where V/ = γµ V µ , ge (gc ) is a weak (strong) coupling, / is the SM covariant derivative, ML,Q , ∆L,Q are diD mensionful constants, Q = (T B)t and L = (E N )t are composite SU (2)L fermion doublets and V and B are composite and elementary vectors, respectively. The physical vectors are admixtures of the latter with mixing angle θ. Likewise for the fermions. With a slight abuse of notation, we denote the physical fields with the same letters. After rotating the heavy and the light degrees of freedom, the following relations hold: ge , g 0 = ge cos θ = gc sin θ , mV = MV cos θ , gc ∆L,Q ML,Q , tan φ`,q = , (6) = cos φ`,q ML,Q

tan θ = mL,Q

with mL,Q the physical masses before Electroweak Symmetry Breaking (EWSB) of the vector-like fermions and g 0 the U (1)Y gauge coupling. In the expected limit gc  ge , we find gV `` ∼ g 0 sin2 φ` cot θ,

gV L` ∼ g 0

sin φ` cos φ` , sin θ cos θ

(7)

where gV L` parametrises the strength of the V L` interaction; see a pictorial representation in Fig. 1. Similar expressions hold in the quark sector. In this limit, cot θ is large, the mixing between V and the SM gauge bosons is small and V production in the s-channel at proton colliders is dominated by bottom quarks. Following Eq. 4, we obtain sin2 φ` ∼

1 , g 0 cot θ

sin2 φq ∼

0.05 m2V . g 0 cot θ TeV2

(8)

This implies that the degree of compositeness of the second-generation leptons is large, even larger than that of the left-handed quarks. In particular, sin φ` ∼ 0.35 and sin φq ∼ 0.15 for mV ∼ 2 TeV and cot θ ∼ 20. On another front, the Higgs in CHMs is an approximate

FIG. 1. Different ways in which the composite vector V interacts with the SM fermions. The left diagram is suppressed by the smallness of ge /gc . The right one is suppressed by one more power of sin φ` with respect to the center one.

Goldstone boson. Its mass is generated radiatively and grows with ∆L,Q , because these are the main sources of explicit breaking of the shift symmetry. Thus, in order not to advocate a large cancellation between different breaking sources to keep the Higgs light, ∆L must be small. Given the large value of sin φ` , this implies a small mL ; see Eq. 6. The preferred values of mQ , namely . 1 TeV [25–31], are in tension with current LHC data, at least in the minimal CHM [32]. Even masses as large as mQ ∼ 1.5 TeV have been already ruled out in some scenarios. However, there is no experimental reason for mL not to be in the TeV region favoured by naturalness arguments. In fact, due to the small EW pair-production cross section for heavy vector-like leptons, they can be as light as few hundreds GeVs [33]. Very dedicated searches will be needed to unravel larger masses even in the LHC High-Luminosity (HL) phase [34]. If this is the case, the large value of gV L` could make V decay with a sizeable branching ratio into fermionic resonances, as we will show in the next section. Altogether, we can conclude that in the composite colorless singlet model, suitable to explain the anomalies in B decays, it is very likely that the the spin-1 resonance decays mainly into heavy muons. III.

COMPOSITE VECTOR PHENOMENOLOGY

The leading-order decay widths for V in the limit mV  m` , mq are 1 2 g mV , (9) 24π V `` 1 2 = g mV , 8π V qq    1 2 m2 m2L m4L = gV L` mV 1 − 2L 1 − − . 24π mV 2m2V 2m4V

ΓV →`` = ΓV →qq ΓV →L`

We willl restrict ourselves to the regime mV < 2mL . Otherwise, the decay into two heavy fermions opens and V becomes typically too broad to be treated as a resonance [35]. We will consider a Benchmark Point (BP) defined by mV = 2 TeV, mL = 1.2 TeV and cot θ = 20. Departures from this assumption will be also discussed. We note that, while gV qq depends on mV and is weak, gV `` and gV L` are approximately fixed and given by ∼ 1

3

B(E ± → Zµ± ) ' B(E ± → hµ± ) ' 0.5, ± ∓

B(N → W µ ) ' 1 .

(10) (11)

Hereafter, we assume this to be the case. + − The production cross section √ for pp → V → µ µ in the BP at the LHC with s = 13 TeV is depicted by the thin black solid line in Fig. 2. The thin black dashed line represents the would-be cross section in the absence of light L. The region above the thick red dashed curve is excluded according to the recent ATLAS analysis of Ref. [39]. Clearly, in the region where the heavylight topology is kinematically forbidden, di-muon constraints are extremely important, the limit on mV being

1

2

This reference showed also that this choice modifies the Zνν coupling, making the Z invisible decay width fit better the observed deficit by LEP. It should be noted that, even if the composite fermions transform in the fundamental representation of SO(5), 5 = (2, 2) + (1, 1), the singlet is expected to be the heavier resonance (because the bi-doublet is the one that needs to couple sizeably to the SM) and therefore it does not modify sensibly the phenomenology of V . This results extends to other representations.

10−3

σ(pp → V 0 → f f¯) [pb]

µ+ µ−

di-muon limit

10−4

10−51.0

E ± µ∓

and ∼ 2.5, respectively. √They are all below the perturbative unitarity limit ∼ 4π. Likewise, ΓV /mV is never above 30 %. A perturbative approach to the collider phenomenology of V is therefore justified. We do not aim to focus on any particular UV realization of the simplified Lagrangian in Eq. 5. Our aim is rather highlighting the implications of light lepton partners for the phenomenology of V . However, it must be noticed that composite muons give generally large corrections to the ZµL µL coupling. These can be avoided in left-right symmetric implementations of lepton compositeness [36]. This requires however the introduction of more degrees of freedom. For example, secondgeneration leptons in the minimal CHM [37] might mix with composite resonances transforming in the representation 10 of SO(5); see Ref. [13]1 . The latter reduces to (2, 2) + (3, 1) + (1, 3) under the custodial symmetry group SO(4). Interestingly, the extra degrees of freedom, namely (1, 3) and (3, 1), do not affect the spin-1 vector decays for several reasons. (i) In the regime we are interested in, pair-production of heavy leptons mediated by V is kinematically suppressed. (ii) The custodial triplets do not mix with the SM fermions before EWSB. (Note also that the product of (2, 2) times any of the custodial triplets can not be a singlet, and hence the corresponding current does not couple to V .) Therefore, the extra new fermions can only be produced in association with SM fermions with a strength further suppressed by a factor of Y v/M , being Y the typical coupling between composite fermions2 . Provided this is not extremely large, the extra states can be ignored [38]. In this regime the following relations hold with good accuracy:

1.5

2.0

2.5

mV [TeV]

3.0

3.5

FIG. 2. Production cross section for E ± µ∓ (thick solid blue) and µ+ µ− (thin solid black) in the BP. The thin dashed black line represents the cross section for µ+ µ− for mL > mV /2. In dashed red, we see the current limits on this cross section from ATLAS [39].

close to 1.8 TeV. However, in the presence of light lepton partners, and given that the coupling between composite particles is larger than that between composite and elementary fields, the cross section pp → V → E ± µ∓ dominates (thick blue solid line). The limit on mV imposed by di-muon searches gets then reduced by more than 500 GeV. Additionally, dijet searches as well as tt searches are less constraining. Other LHC searches are sensitive to the heavy-light channel. In particular, we considered searches for electroweakinos in multilepton events with large missing energy, such as that in Ref. [40]. The 13 fb−1 version of this analysis was first presented in Ref. [41]. The latter is fully included in CheckMATE v2 [42]. Therefore, the reach of the former can be estimated by scaling p the signal over the 95% CL limit by the luminosity ratio 36/15. We obtain that values of mV above 1 TeV are not constrained. Other studies, such as searches for evidence of the typeIII seesaw mechanism [43], focus on final states with more than two leptons, which are almost absent in our scenario. On balance, we find imperative to develop a dedicated search to unravel the origin of LFU in CHMs. IV.

NEW SEARCHES

Among the different heavy-light topologies, we focus on the channel pp → V → E ± µ∓ , E ± → Z/h µ± , with Z/h decaying hadronically3 . Signal events are generated using MadGraph v5 [44] and Pythia v6 [45], after including the relevant interactions in an UFO model [46] using Feynrules v2 [47]. For

3

The leptonic Z channel, although extremely clean, produces less than 10 events before cuts for mV > 2 TeV even with a luminosity L = 3000 fb−1 .

4

1/σ dσ/dmj1 [GeV−1 ]

0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

0

20

40

60 80 100 mj1 [GeV]

120

140

FIG. 3. Normalized distribution of mj1 before mass drop and filtering for the BP (dashed red) and the background (solid blue).

0.40 0.35 dσ/dmj1 [GeV−1 ]

the subsequent analysis, we have used home-made routines based on Fasjet v3 [48] and ROOT v6 [49]. Muons are defined by pT > 20 GeV and |η| < 2.7. Jets are clustered according to the Cambridge-Aachen algorithm [50, 51] with R = 1.2. Muons with pT > 50 GeV are removed from hadrons in the clustering process. The dominant background is given by µ+ µ− + jets. We matched Monte Carlo background events with 1 and 2 jets using the MLM merging scheme [52] with a matching scale Q = 30 GeV. At the generator level, we also impose a cut on the pT of the muons, pµT > 100 √ GeV. The matched cross section we obtain at LO at s = 13 TeV is ∼ 1.2 pb; we generated 10 million events. As basic cuts we require, first, the presence of exactly two opposite charged muons and at least one jet. The leading pT jet, j1 , is required to have a significant mass drop [53], characterized by µ = 0.67, ycut = 0.3. This jet is further filtered [53, 54] using a finer angular scale given by Rfilt = min{0.3, 0.5×R12 }, with R12 the angular separation of the two sub-jets obtained in the mass-drop procedure. The invariant mass of this jet before and after mass drop and filtering is shown in Figs. 3 and 4, respectively. It is remarkable how this method impacts on the background by systematically moving mj1 to smaller values. Likewise, the h and Z boson mass peaks in the signal become significantly narrower. We also impose both muons to have a pT > 200 GeV. This stringent cut is motivated by the fact that muons originate from the decay of very heavy particles, while the background is mostly populated by soft leptons. More sophisticated jet substructure methods can improve on our result further [55, 56]. Finally, we enforce the leading jet to have an invariant mass 80 GeV ≤ mj1 ≤ 130 GeV. A summary of the basic selection cuts is given in Tab. I. Their efficiency in the BP as well as in the background are also displayed. Interestingly, while a large fraction of the signal is kept,

0.30 0.25 0.20 0.15 0.10 0.05 0.00

0

20

40

60 80 100 mj1 [GeV]

120

140

FIG. 4. Normalized distribution of mj1 after mass drop and filtering in the BP (dashed red) and the background (solid blue).

the background is reduced by more than two orders of magnitude.

(BP ) 2 muons 90 > 1 jet, j1 tagged and filtered 70 µ pT1,2 > 200 GeV 93 80 GeV < mj1 < 130 GeV 58 Total 34

(b) 99 45 16 7.0 0.49

TABLE I. Basic cuts and efficiencies (in percent) for the BP and the main background

After these basic cuts, mV can be reconstructed just as the invariant mass mrec V = m(µ1 + µ2 + j1 ). The normalized distribution in the BP and in the background after the basic cuts is depicted in Fig. 6. Clearly, a cut on mrec V & 1 TeV separates further the signal from the SM. For large mL , the muon coming from E is typically that with largest pT , i.e. µ1 . mL can then be obtained just as the invariant mass mrec L = m(µ1 + j1 ). The corresponding distribution in the signal as well as in the background after the basic cuts and after enforcing mrec V > 1 TeV is depicted in Fig. 7. Note that, in this case, we normalize to the expected number of events at L = 1 fb−1 . Remarkably, the signal is already comparable to the background in number of events, while concentrating at much larger values of mrec L . Given our ignorance on mV and mL , we set further cuts depending on these parameters. In particular, we rec require mrec V > 0.75 × mV , |mL − mL | < 100 GeV. Denoting by S and B the number of signal and background events, respectively, after all cuts, we estimate the signif-

1.5

2.0 2.5 mV [TeV]

3.0

3.5

1.5

2.0 2.5 mV [TeV]

3.0

3.5

0 )∼ L` → (V

mL [TeV] BR(V → LL) > 0

1.8 1.6 1.4 1.2 1.0 0.8 0.6 1.0

BR

0 )∼ L` → (V

mL [TeV] BR(V → LL) > 0

1.8 1.6 1.4 1.2 1.0 0.8 0.6 1.0

BR

0 )∼ L` → (V

1.8 1.6 1.4 1.2 1.0 0.8 0.6 1.0

BR

mL [TeV]

5

BR(V → LL) > 0

1.5

2.0 2.5 mV [TeV]

3.0

3.5

FIG. 5. Left) Parameter space region in the plane mV –mL that can be excluded at the 95 % CL using di-muon searches (solid red) and using our dedicated analysis (solid green) for L = 70 fb−1 . Center) Same as before but for L = 300 fb−1 . Right) Same as before but for L = 3000 fb−1 ; the region enclosed by the dashed green line assumes half of the expected cross section into the target final state (due e.g. to the presence of additional decay modes).

icance as

0.08 (12)

In Fig. 5 we show, in green, the regions that can be excluded at the 95% CL (S = 2) as a function of mL and mV for different values of the collected luminosity. These are to be compared with the reach of di-muon searches, depicted in red. In the grey regions, the composite spin-1 resonance does not decay sizeably into L`. The reason is, that in the upper triangle L is heavier than (or very close in mass to) V . In the lower triangle, V decays mostly into pairs of heavy leptons. Remarkably though, regions not yet tested by the LHC can start to be probed. Moreover, contrary to di-muon searches, our new analysis will also shed light on the high mass region.

−1 dσ/dmrec L [GeV ]

0.07 S S=√ . S+B

0.06 0.05 0.04 ×5

0.03

×5

0.02 0.01 0.00

0

500

−1 1/σ dσ/dmrec V [GeV ]

0.10 0.08 0.06 0.04 0.02 0.00

0

500

1000 1500 2000 mrec V [GeV]

2500

3000

FIG. 6. Normalized distribution of mrec in the BP (dashed V red) and the background (solid blue).

1500

2000

−1 in the FIG. 7. Event distribution of mrec L for L = 1 fb BP (dashed red) and in the background (solid blue). The BP with mL = 1.6 TeV is also shown in red. Both signals are multiplied by a factor of ×5 to increase the readability.

V.

0.12

1000 mrec L [GeV]

CONCLUSIONS

If the origin of the apparent breaking of Lepton Flavour Universality (LFU) in B meson decays is due to a composite spin-1 resonance V , this has to couple to rather composite light leptons. Focusing on the case of composite muons, we have argued that V decays mostly into a muon and a composite fermionic resonance. Therefore, V should not be searched in di-muon final states, as it has been done so far, but rather into final states consisting of two muons and a boosted gauge or Higgs boson which express mainly as fat jets. Unravelling the physics responsible for breaking LFU in such a final state requires dedicated and tailored analyses to its kinematic features. We have worked out one such analysis based on jet substructure techniques. Three main conclusions can be pointed out. (i) Parameter space regions that were thought excluded by searches for di-muon resonances,

6 are still allowed. They are not even ruled out by other beyond the Standard Model analyses, including multilepton searches for electroweakinos or heavy leptons. (ii) Some of the allowed regions can already be probed at the 95% CL with our dedicated analysis. (iii) With more luminosity, e.g. 300 (3000) fb−1 , heavier resonances can be tested, e.g mV ∼ 2 (3) TeV. Had we assumed λ`33 ∼ λ`22 in Eq. 3 4 , the cross section for our target final state would be reduced by an O(1) factor. The analogous topology with taus instead of muons would be also important. Not taking the latter into account, we estimate the reduced reach to this setup in the right panel of Fig. 5; see dashed green line. On

balance, we strongly encourage a re-analysis of current data.

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4

In principle λ`11 could also be large [12, 15], but the naive expectation in composite Higgs models is that composite particles couple stronger to heavier states.

ACKNOWLEDGMENTS

We acknowledge Shankha Banerjee for help with the analysis, and Adri´an Carmona and Luca Di Luzio for the useful discussions and detailed comments on the manuscript. MC is supported by the Royal Society under the Newton International Fellowship programme. MC acknowledges the hospitality of the Weizmann Institute during the completion of this work.

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