Revealing timid pseudo-scalars with taus at the LHC.

A light pseudo-scalar that is copiously produced at the LHC may still be allowed by present searches. While masses above 65 GeV are effectively covered by di-photon searches, the lower mass window can be tested by a new search for boosted di-tau resonances. We test this strategy on a set of composite Higgs models with top partial compositeness, where most models can be probed with an integrated luminosity below 300 fb - 1 .

Introduction

The search for new resonances is one of the main physics goals at the LHC, with the discovery of a Higgs boson being an illustrious example [1, 2]. The efforts continue, mainly focusing on high mass objects typically heavier than the Higgs itself. There are in fact few searches exploring invariant masses of two Standard Model (SM) particles below, say, 100 GeV: one notable case is the search for a di-photon resonance [3, 4], mostly motivated by models that feature an extended Higgs sector, like two Higgs doublet models [5] and the next-to-minimal supersymmetric SM [6].

In this article, we focus on the LHC phenomenology of a light new scalar with a mass between 10 and 100 GeV. Generically, light new scalars are strongly constrained from electroweak precision measurements (indirectly) and from direct searches at LEP and Tevatron. At the LHC, besides the above-mentioned di-photon channel, light (pseudo)-scalars are usually searched for in the decays of the 125 GeV Higgs boson. Below roughly 10 GeV, strong bounds arise from searches related to mesons, or in experiments looking for light axion-like particles (ALPs) [7-10]. Thus, the common lore is that a new scalar, in order to escape detection, needs to be either very heavy or weakly coupled to the SM.

Note, however, that it is enough to have small couplings to electrons and to the electroweak gauge bosons in order to escape direct LEP searches and electroweak precision bounds, as well as small couplings to the Higgs to avoid the Higgs portal constraints. Couplings to gluons (and heavy quarks) are less constrained, and may lead to sizable production rates at the LHC. Candidates of this kind arise naturally in composite Higgs models that enjoy a fermion-gauge underlying description [11-15] providing a partial UV completion. Recent lattice results [16] have started to address the mass spectrum in a specific model [17].

In this article, we will consider this class of models to explore the 10–100 GeV mass window and show that it is, in fact, poorly tested. A timid composite pseudo-scalar (TCP) arises as the pseudo-Nambu-Goldstone boson associated with an anomaly-free U(1) global symmetry in all models of partial compositeness that enjoy a UV completion, as defined in Ref. [12]. All the possible models can be classified, and give precise predictions for the properties of the TCP candidate [15], thus mapping out a complete landscape of possibilities. We show that, while some models are already partly tested by the low mass di-photon searches, others are unconstrained. We point out that searches for boosted di-tau resonances (which could reach a lower invariant mass than the current value of 90 GeV [18, 19]) give very promising signals and could be a powerful complementary probe to the di-photon channel, or even be the only way to access this class of TCPs.

Description of the models

The effective Lagrangian we consider is the SM Lagrangian augmented by the following terms, up to dimension five operators (counting powers of ):A pseudo-scalar a described by this general Lagrangian arises, for example, in UV completions of composite Higgs models, which were classified and studied in Refs [12, 15]. In this section, we briefly summarize the main results relevant for our phenomenological study. Further background information on the models is provided in Appendix A.

Within this class of models, the coupling to the SM fermions in Eq. (1) is only the first term of the expansion of the spurion coupling (generating the fermions masses), which breaks explicitly the U(1) shift symmetry. A derivative coupling of the TCP to fermions of the form is absent in these models since the SM fermions are neutral under the TCP U(1) charge. Although such a coupling can be obtained by using the fermion equations of motion on the leading term given in Eq. (1), the two couplings are of genuinely different origin [20], as manifested in the higher-order expansion of the spurion coupling. Starting from the complete spurion term, couplings of the Higgs to two TCPs, as well as to one TCP and Z boson, arise at loop level and are given by (see Appendix A.1 for the derivation) where we list only the effect of the log-divergence (), is the axial coupling of the Z to tops, and are the corrections from compositeness to the couplings of the Higgs to vectors and tops, respectively. As , our result agrees with the fact that the only non-zero contribution to the hZa coupling arises from a dimension 7 operator [21].

The couplings to gauge bosons in Eq. (1) arise as anomalous couplings if the TCP is a (SM singlet) bound state of underlying SM charged fermions. In this case, the anomaly coefficients are fully determined by the charges of the hyper-fermions. We refer to [15] for an extensive description of a classification of UV completions giving rise to this TCP, which yields twelve models. For the purpose of this article, the TCP dynamics in the twelve models is fully specified1 by the numerical couplings in Table 1. Note that, due to the small TCP mass, top loops also give additional sizable contributions to the couplings to gauge bosons (not included in the table, but included in our analysis).

Table 1

Couplings in the twelve models [15] used as benchmarks. For the top, several possibilities arise depending on the choice of top partner representation: here, as an illustration, we take the same coupling as for lighter fermions, whose mass arise from bilinear four-fermion interactions. is an estimate of the ratio between the TCP decay constant and the composite Higgs decay constant

	M1	M2	M3	M4	M5	M6	M7	M8	M9	M10	M11	M12
K_g	- 7.2	- 8.7	- 6.3	- 11.	- 4.9	- 4.9	- 8.7	- 1.6	- 10.	- 9.4	- 3.3	- 4.1
K_W	7.6	12.	8.7	12.	3.6	4.4	13.	1.9	5.6	5.6	3.3	4.6
K_B	2.8	5.9	- 8.2	- 17.	0.40	1.1	7.3	- 2.3	- 22.	- 19.	-5.5	-6.3
C_f	2.2	2.6	2.2	1.5	1.5	1.5	2.6	1.9	0.70	0.70	1.7	1.8
f_af_ψ	2.1	2.4	2.8	2.0	1.4	1.4	2.4	2.8	1.2	1.5	3.1	2.6

Our goal is to confront the TCP with the existing searches and to propose a new, more sensitive search for such object. We treat the mass and the decay constant of the TCP as free parameters. In composite Higgs UV completions, is related to the composite Higgs decay constant , entering in the usual alignment parameter , by a relative coefficient that was estimated in [15] and is summarized in Table 1. Since bounds on composite Higgs models require , is expected to be naturally of the order of  TeV.

Bounds from existing searches

Since the TCP is a gauge singlet, its couplings to Z and W are induced by the anomaly and by top loops, thus they are always much smaller than those of a SM Higgs boson. Hence, bounds from all LEP searches for a light Higgs, which are based on Z associated production, are evaded. At hadron colliders the TCP is copiously produced via gluon fusion. However, only very few Tevatron or LHC two-body resonant searches reach down to resonance masses below GeV. Relevant bounds arise from Run–I ATLAS [3] and Run–II CMS [4] di-photon searches, which reach down to masses of 65 and 70 GeV, respectively, as well as ATLAS and CMS low-mass di-muon searches [22, 23], reaching up to 14 GeV. The bounds on from these searches are shown in Fig. 1,2 for our models. The bounds are obtained by calculating the leading order TCP production cross section following from the Lagrangian (1) with PDF set NNPDF23_nnlo_as _0119_qed [25] and a conservative k-factor of 3.3 applied [26], and using branching ratios into and (computed at NLO following Ref. [9]) for the models listed in Table 1. Figures on the production cross sections and branching ratios in the twelve sample models are provided in Appendix A.2. Resonant di-tau searches reach values of the mass as low as 90 GeV [18, 19], however the current bounds are never competitive with the di-photon ones in that range, mainly due to the presence of the Z-peak background. As noted in Ref. [10], a CMS search looking for boosted in di-jet [27] may give additional bounds above 50 GeV.

Fig. 1

Constraints on as a function of for the benchmark models M1 - M12, defined in Table 1. The bounds arise from di-muon searches [22, 23] in the low mass range, di-photon searches [3, 4] in the higher one, and from the BSM decay width of the Higgs [24] below 65 GeV. We have also indicated the current bounds obtained by adapting the results in [10] in the region between 20 and 65 GeV for the two models (M9 and M10) where they are the strongest

For other processes, a recent comprehensive review of the existing bounds on ALPs [9] can be directly used to confront TCPs. Firstly, the one-loop suppression () of couplings to vector bosons in the TCP Lagrangian (1) renders bounds from vector-boson-fusion or photon-fusion production very weak. This includes processes and production by photon fusion in Pb–Pb ultra-peripheral collisions [28]. The up-to-date most constraining searches in the mass window between 14 and 65 GeV rely on the indirect production via Higgs portal, . As compared to the generic ALP model discussed in Ref. [9], the bounds from direct searches are weakened due to the smallness of the branching fraction following from Eq. (2), and due to the smallness of the and branching fractions. Nevertheless, indirect constraints arise from the bounds on the BSM decay width of the Higgs, which is currently below [24]: as shown in Fig. 1, the lower bound on always falls short of 1 TeV for the models under consideration.3 For there is also a bound from (following from Eq.(3)), however it turns out even weaker than the Higgs portal one. Associated tta production may yield a bound on TCPs: using the results of the feasibility study [30] at 14 TeV with 3 ab, which focuses on in the mass range between 20 and 100 GeV, significant bounds on can be found only for a few models in the low mass end. Associated bba production yields weaker bounds [31]. Lastly, we should mention that the contribution of the TCP to the anomalous magnetic moment of the muon [32, 33] is also small. For and it varies from for M9 to for M7, the current discrepancy being .

As shown, the TCP represents an example of a light pseudo-scalar which would evade all existing bounds, while being copiously produced at the LHC in gluon fusion. Searches in final states from which current bounds arise can be extended in mass range. The low-mass di-muon search [23] (performed at  TeV) terminated at  GeV, but the first severe physical barrier at higher mass is the di-muon background from Drell-Yan Z production. However, a dedicated low-mass di-muon trigger and a very high invariant mass resolution would be required.4

A recent study on inclusive di-photon cross section measurements [10] has shown how to extend the low-mass reach of di-photon searches for a generic ALP. Applying their projected reach to our models we find a nice complementarity between the di-photon channel and our proposal to use the di-tau channel to be discussed below.5

Boosted di-tau searches as a chance to explore the TCP

As TCP decays to muons and photons have small rates, it is of interest to also look at other final states. The dominant TCP decay channels are gg and , but both have very large irreducible QCD background.6 The next-most frequent final state is : sizable rates of a few % are possible and the models with the lowest rates are the ones with better di-photon reach (see Fig. 1). Compared to the di-muon channel, the branching ratios are larger by a factor of .

One of the main challenges for low-mass di-tau resonant searches is the trigger. The topology that we find most promising is that of a boosted TCP recoiling against an initial state radiation (ISR) jet, and then decaying into . The boost needs to be sufficient to allow the event to pass the high-level trigger requirement in at least one category (jet, tau or lepton ) and yet leave enough observable signal. Boosted di-tau pairs have already been considered by CMS [37] in searches for heavy resonances which decay to hh, hZ, or hW. In our case, the mass of the TCP is not known, thus it may not be necessary to require a full reconstruction of the taus with subsequent increase of the systematic uncertainty associated to the procedure. Furthermore, we are interested in light TCPs with a large boost, and thus smaller separation angles between the di-tau decay products can be expected. All decay modes of the di-tau system – fully hadronic, semi-leptonic, and leptonic – are potentially interesting. However, for the reasons mentioned above, we focus on the opposite flavor leptonic channel, in which one decays to an electron and the other to a muon. One crucial issue, to be discussed more extensively in Appendix B, is related to the minimum angular separation between the leptons, since the boosted tau pairs have a small separation angle. We generate the signal sample for  GeV with up to two jets at the partonic level using MadGraph [38]. We shower and hadronize with Pythia [39] and run the fast detector simulation of Delphes [40] using the standard CMS card after removing the isolation requirement between electrons and muons. Table 2 shows the value of the signal cross section times the efficiency expected for each of the benchmark models with  TeV after imposing the following requirements:7  GeV,  GeV, , ,  GeV, ,  GeV. The upper cut on the separation is essential in reducing the background from W’s [41], while we do not impose any minimum value yet. (This last issue is discussed below and in Appendix B.)

Table 2

The values of in fb for  TeV for each of the models defined in Table 1. The main backgrounds are di-top and single-top (59.2 fb), (24.7 fb), and di-bosons (11.0 fb)

m_a	10	20	30	40	50	60	70	80	90	100
M1	30.	14.	9.3	6.6	5.3	3.7	3.0	2.3	1.7	1.4
M2	44.	20.	13.	9.5	7.7	5.4	4.4	3.2	2.4	2.0
M3	26.	12.	8.4	6.1	5.0	3.6	2.9	2.2	1.6	1.4
M4	28.	11.	6.1	3.8	2.9	1.9	1.5	1.1	0.80	0.67
M5	14.	6.3	4.2	3.0	2.4	1.7	1.4	1.0	0.74	0.63
M6	14.	6.3	4.2	3.0	2.4	1.7	1.4	1.0	0.74	0.63
M7	44.	20.	13.	9.5	7.7	5.4	4.4	3.2	2.4	2.0
M8	4.0	2.1	1.8	1.6	1.6	1.3	1.2	0.96	0.76	0.69
M9	8.3	3.1	1.6	0.95	0.70	0.47	0.36	0.26	0.19	0.16
M10	8.1	3.0	1.6	0.95	0.70	0.46	0.36	0.26	0.19	0.16
M11	9.4	4.7	3.5	2.8	2.4	1.8	1.5	1.2	0.87	0.74
M12	13.	6.4	4.7	3.6	3.1	2.3	1.9	1.4	1.1	0.92

The leading irreducible SM backgrounds are single top, and VV, the last one being mainly . Our simulation of these backgrounds yields , 25 and 11 fb, respectively, after imposing the same cuts as above. As discussed in Appendix B, we expect the reducible backgrounds of single vector boson+fakes and QCD to be sub-leading (of the order of a few fb) in the channel. Note that we do not require full reconstruction of the tau momentum.

To be able to estimate the reach of Run II + III at the LHC, it is essential to know the systematic uncertainties because we are in a situation where the signal over background ratio is small, , as can be seen from Table 2. Since a search of this type has not been done by the experimental collaborations, we cannot reliably quantify the systematic uncertainties yet. Data driven techniques can certainly be used to reduce the systematic uncertainties on the different backgrounds. For the lepton identification, the systematic uncertainties typically amount to 1% [41], while we do not require tau identification, which would increase the systematics to 10–20%. To assess the feasibility of the analysis, we will include the systematic uncertainty in the significance according the approximate formulawhere S and B are the number of signal and background events at a given integrated luminosity and the relative systematic error on the background. Eq. (4) works quite well in the regime of interest for this work when compared to the more general treatment in [42]. A projection of the bound on for the various models after 300 integrated luminosity is shown in Fig. 2, including an estimated systematic uncertainty of 1%. We can see that for all models with exception of M9 and M10, the boosted di-tau search we propose can probe the mass range of 10–70 GeV with integrated luminosity below 300 fb.

Fig. 2

Values of for models M1 - M12 for which in the proposed di-tau search after an integrated Luminosity of 300 . We assume a systematic error on the background . Shown in grey are the current bounds as of Fig. 1

n Fig. 3 we show the relative change in the projected bound on if a minimum cut of 0.1 or 0.2 is imposed as well as its dependence on a change in systematic uncertainty from 1 to 0, 0.5, and 2%. These changes apply to all models in a universal way. We can see a loss of sensitivity for masses below GeV when raising , while above this mass range the search is barely affected. Thus, being able to remove or reduce the minimum separation angle is important for the lowest mass region, as long as it does not imply an increase in the systematic errors.

Fig. 3

Relative change in the projected bounds on with 300 of data. We plot the relative change against the baseline presented in Fig. 2 for different values of systematic uncertainties and (green, blue, black, and red) and choosing three different separation cuts (solid) 0.1 (dashed) and 0.2 (dotted) respectively

The plot also clearly shows the importance of controlling the systematic uncertainties to a level close to 1%. The latter values are what CMS and ATLAS typically require for opposite sign leptons [41] in current searches.

It is possible to improve sensitivity by imposing variable cuts on the invariant mass and particularly on the angular separation of the lepton pair depending on the mass range of interest. For guidance we show in Fig. 4 the kinematic distribution of for the most relevant backgrounds and the signal with and 80 GeV before imposing the  GeV and cuts.

Fig. 4

Angular separation () between the two leptons for two signal (SG) masses (20 and 80 GeV) compared to the most relevant backgrounds (BG). Small separation angles can be a good discriminant particularly for low masses

As mentioned above, fully or semi-hadronic decays of the di-tau system may also be testable by designing appropriate di-tau jet algorithms. For the semi-hadronic case, a sophisticated isolation procedure has been used by CMS for boosted Higgs tagging in the di-tau channel. However, large systematic uncertainties, or the order of 20–30% [37], are introduced due to the modified isolation and tau-identification procedures. Furthermore, the signal we are interested in features smaller separation between the two taus, thus a better performance may be achieved by a dedicated identification procedure. For instance, the technique of “mini-isolation” proposed in Ref. [43] may be adapted to this case, although this is beyond the scope of this paper. For the fully hadronic case, preliminary studies in Refs. [44, 45] show that a good discrimination between di-tau jets and single tau or QCD jets can be achieved using sub-jet variables. However, a correct estimate of the background (especially from QCD) can only be done with data driven techniques, thus we do not attempt to quantify the sensitivity of these channels.

Conclusions

The search for new resonances at the LHC continues, and many searches for high-mass resonances are being performed. Nevertheless, complementary searches for lower-mass resonances which have evaded current constraints must not be forgotten. We observe that light pseudo-scalars in the mass regime between 14 and 65 GeV can be copiously produced at the LHC while avoiding current experimental constraints.

We propose to search for boosted di-tau resonances, produced via gluon fusion, that can effectively cover this open window. We test this strategy on a set of twelve benchmark models of composite Higgs with top partial compositeness, which have a simple gauge-fermion underlying description. Low mass di-photon searches effectively cover masses above 65 GeV. Extending the di-photon search to lower masses is challenging due to triggers (but potential solutions have been presented  [10]), while resuming low-mass di-muon resonant searches and extending them to higher masses is possible but challenging due to increased muon trigger thresholds. The boosted di-tau search we propose allows to access the open window below 65 GeV, and, for some models, it can be competitive with the di-photon channel at higher masses.

Table 3

The first column shows the EW and color cosets, respectively. The column indicates the ratio of charges of the fermions under the non anomalous U(1) combination. HC is the confining hyper-color gauge group. and denote the fundamental and anti-symmetric representation of HC

Coset	HC	ψ	χ	-q_χ/q_ψ	Y_χ	Model
SU(5)SO(5)×SU(6)SO(6)	SO(7)	5×F	6×Spin	5 / 6	1/3	M1
SU(5)SO(5)×SU(6)SO(6)	SO(9)	5×F	6×Spin	5 / 12	1/3	M2
SU(5)SO(5)×SU(6)SO(6)	SO(7)	5×Spin	6×F	5 / 6	2/3	M3
SU(5)SO(5)×SU(6)SO(6)	SO(9)	5×Spin	6×F	5 / 3	2/3	M4
SU(5)SO(5)×SU(6)Sp(6)	Sp(4)	5×A_2	6×F	5 / 3	1/3	M5
SU(5)SO(5)×SU(3)^2SU(3)	SU(4)	5×A_2	3×(F,F¯)	5 / 3	1/3	M6
SU(5)SO(5)×SU(3)^2SU(3)	SO(10)	5×F	3×(Spin,Spin¯)	5 / 12	1/3	M7
SU(4)Sp(4)×SU(6)SO(6)	Sp(4)	4×F	6×A_2	1 / 3	2/3	M8
SU(4)Sp(4)×SU(6)SO(6)	SO(11)	4×Spin	6×F	8 / 3	2/3	M9
SU(4)^2SU(4)×SU(6)SO(6)	SO(10)	4×(Spin,Spin¯)	6×F	8 / 3	2/3	M10
SU(4)^2SU(4)×SU(6)SO(6)	SU(4)	4×(F,F¯)	6×A_2	2 / 3	2/3	M11
SU(4)^2SU(4)×SU(3)^2SU(3)	SU(5)	4×(F,F¯)	3×(A_2,A_2¯)	4 / 9	2/3	M12

Table 4

Values of for the various possible top partner assignment. For the last two columns, the values correspond to for models (), and for models (). In the paper we used the assignment (2, 0) which is also common to all other fermions

(n_ψ,n_χ)	(±2,0)	(0,±2)	(4, 2) or (2, 4)	(-4,2) or (2,-4)
M1	±2.2	∓1.8	- 1.4	5.8
M2	±2.6	∓1.1	0.44	4.8
M3	±2.2	∓1.8	2.5	- 6.2
M4	±1.5	∓2.4	0.49	- 5.3
M5	±1.5	∓2.4	- 3.4	6.3
M6	±1.5	∓2.4	- 3.4	6.3
M7	±2.6	∓1.1	0.44	4.8
M8	±1.9	∓0.63	3.2	- 4.4
M9	±0.70	∓1.9	- 0.47	- 3.3
M10	±0.70	∓1.9	- 0.47	- 3.3
M11	±1.7	∓1.1	2.2	- 4.4
M12	±1.8	∓0.81	2.8	- 4.5

Table 5

Values of for the models M1 - M12 and  GeV. For the values given, we chose the discrete charges of the top partners to be the same as those of the other fermions

m_a [GeV]	10	20	30	40	50	60	70	80	90	100
M1	6.7	3.4	2.5	1.9	1.5	1.2	0.95	0.79	0.66	0.57
M2	9.7	4.8	3.6	2.7	2.1	1.7	1.4	1.1	0.96	0.82
M3	5.7	2.9	2.2	1.8	1.4	1.1	0.91	0.76	0.65	0.56
M4	6.2	2.6	1.6	1.1	0.79	0.60	0.47	0.39	0.32	0.27
M5	3.0	1.5	1.1	0.84	0.66	0.52	0.42	0.35	0.30	0.25
M6	3.0	1.5	1.1	0.84	0.66	0.52	0.42	0.35	0.30	0.25
M7	9.7	4.8	3.6	2.7	2.1	1.7	1.4	1.1	0.96	0.82
M8	0.88	0.50	0.48	0.46	0.43	0.40	0.36	0.33	0.30	0.28
M9	1.9	0.74	0.42	0.27	0.19	0.14	0.11	0.091	0.076	0.064
M10	1.8	0.73	0.41	0.27	0.19	0.14	0.11	0.091	0.076	0.064
M11	2.1	1.1	0.94	0.79	0.66	0.55	0.47	0.40	0.35	0.30
M12	2.9	1.5	1.3	1.0	0.85	0.70	0.59	0.50	0.43	0.37

Table 6

The values of in fb for  TeV for each of the models defined in Table 1 if a seperation cut is imposed. The main backgrounds are di-top and single-top (59.2 fb), (24.0 fb), and di-bosons (10.9 fb)

m_a	10	20	30	40	50	60	70	80	90	100
M1	9.9	12.	9.0	6.5	5.3	3.7	3.0	2.3	1.7	1.4
M2	14.	17.	13.	9.3	7.7	5.4	4.4	3.2	2.4	2.0
M3	8.5	10.	8.2	6.0	5.0	3.6	2.9	2.2	1.6	1.4
M4	9.1	9.2	5.9	3.8	2.9	1.9	1.5	1.1	0.80	0.67
M5	4.5	5.2	4.0	2.9	2.4	1.7	1.4	1.0	0.74	0.63
M6	4.5	5.2	4.0	2.9	2.4	1.7	1.4	1.0	0.74	0.63
M7	14.	17.	13.	9.3	7.7	5.4	4.4	3.2	2.4	2.0
M8	1.3	1.7	1.8	1.6	1.6	1.3	1.2	0.96	0.76	0.69
M9	2.7	2.6	1.5	0.93	0.70	0.46	0.36	0.26	0.19	0.16
M10	2.7	2.5	1.5	0.93	0.70	0.46	0.36	0.26	0.19	0.16
M11	3.1	3.9	3.4	2.7	2.4	1.8	1.5	1.2	0.87	0.74
M12	4.3	5.3	4.6	3.5	3.1	2.3	1.9	1.4	1.1	0.92

Table 7

The values of in fb for  TeV for each of the models defined in Table 1 if a seperation cut is imposed. The main backgrounds are di-top and single-top (55.9 fb), (22.6 fb), and di-bosons (10.5 fb)

m_a	10	20	30	40	50	60	70	80	90	100
M1	0.86	4.7	6.8	5.6	4.9	3.5	2.9	2.2	1.7	1.4
M2	1.2	6.8	9.8	8.1	7.1	5.0	4.2	3.2	2.4	2.0
M3	0.74	4.1	6.1	5.2	4.7	3.3	2.8	2.1	1.6	1.4
M4	0.79	3.7	4.4	3.3	2.7	1.8	1.5	1.1	0.80	0.66
M5	0.39	2.1	3.0	2.5	2.2	1.6	1.3	0.99	0.74	0.62
M6	0.39	2.1	3.0	2.5	2.2	1.6	1.3	0.99	0.74	0.62
M7	1.2	6.8	9.8	8.1	7.1	5.0	4.2	3.2	2.4	2.0
M8	0.11	0.71	1.3	1.4	1.4	1.2	1.1	0.94	0.76	0.68
M9	0.24	1.0	1.1	0.81	0.65	0.44	0.35	0.26	0.19	0.16
M10	0.23	1.0	1.1	0.81	0.65	0.43	0.35	0.26	0.19	0.16
M11	0.27	1.6	2.6	2.4	2.2	1.7	1.5	1.1	0.86	0.74
M12	0.37	2.2	3.5	3.1	2.9	2.1	1.8	1.4	1.1	0.92