Single Top as Window on Heavy Quarks and Other New Physics

Abstract

This paper discusses what the study of the electroweak production of single top quarks can tell us about additional quark generations, and how to distinguish the new quarks hypothesis from other kinds of new physics. We also suggest some new studies that become possible for the first time thanks to the large statistics of single top quarks produced at the LHC.

1. Introduction

The top quark is the heaviest elementary particle discovered so far, and in many ways it is a very uncommon quark. The fact that its electroweak decay is faster than the hadronization timescale implies that the top quark exists only as a free quark, so that the effects from new physics could show up very clearly by comparing measurements with the precise Standard Model (SM) predictions. While the pair-production process (𝑡𝑡) has already entered several years ago the domain of “precision physics,” the study of single top production, started with the discovery at Tevatron in 2009 [1, 2], has been limited so far. The complexity of its final state demands a good control of the experimental apparatus, and other SM processes (including 𝑡𝑡) provide an overwhelming background.

The “rediscovery” of single top quark production at the Large Hadron Collider (LHC) with the early 7 TeV data has been a major milestone for the ATLAS [3] and CMS [4] experiments, which are now working towards the ultimate precision and the full coverage of all production channels at 7 TeV and 8 TeV. Collisions at the Tevatron and at the LHC give access to different mixtures of electroweak single top processes: 𝑡-channel and 𝑠-channel production (Figures 1(a) and 1(b)) contribute less evenly at 7 TeV (65 pb and 4.6 pb, resp.) than at 1.96 TeV (2 pb and 1 pb), and 𝑊-associated production (𝑡𝑊, Figure 1(c)) which is virtually inaccessible at the Tevatron becomes the second-largest contributor at the LHC (15 pb). A feature of SM single top production at LHC, absent at Tevatron, is the asymmetry between top and antitop production in 𝑡-channel (43 versus 23 pb at 7 TeV) and 𝑠-channel (3.1 versus 1.4 pb at 7 TeV). The first evidence of 𝑡𝑊 production has been reported by the ATLAS collaboration [5], followed by CMS [6], using 7 TeV data. Both measurements are systematics-limited, and reaching the 5𝜎 level will require clever analysis improvements and more precise constraints of the leading systematics (related to 𝑡𝑡 modeling and, in the CMS case, to 𝑏-tagging efficiency).

(a)

(b)

(c)

Figure 1 

Representative diagrams for single top production in the Standard Model: 𝑡-channel (a), 𝑠-channel (b), and 𝑊-associated production or 𝑡𝑊 (c).

ATLAS and CMS recorded more than 5 fb⁻¹ of pp collisions delivered by the LHC at 7 TeV during 2011, and the same amount has been reached within a few months of running at 8 TeV in 2012. Significant improvements of the 𝑡-channel cross-section measurement at 7 TeV [7, 8] and the first measurement of the 𝑡-channel cross-section at 8 TeV [9, 10] have been performed by both collaborations. The first 𝑡𝑊 cross s-ction measurement at 8 TeV is expected very soon. The signal-to-background ratio improves from 7 to 8 TeV for the 𝑡𝑊 production, whose cross-section is expected to increase by 40%, and for 𝑡-channel which increases by 35%, against a 20% increase for inclusive 𝑊 production and 25% for the 𝑊𝑄(𝑄) process (with 𝑄=𝑏,𝑐). The 𝑠-channel cross-section, instead, increases by only 20%. A possibility not yet exploited by the LHC analyses is to take advantage of the different dependencies of these processes on energy, for example, by simultaneous fits to 7 and 8 TeV data with 𝜎_𝑏𝑘𝑔(8TeV)/𝜎_𝑏𝑘𝑔(7TeV) ratios constrained to SM expectations.

Table 1 shows the state of the art for theory predictions and experimental measurements of the cross-section of the three production mechanisms. Figure 2 shows the dependence of the cross-section for 𝑡-channel production on centre-of-mass energy. This is the only single top process whose cross-section has been measured at three centre-of-mass energies so far.

Table 1 

Cross-sections as predicted by the SM with 3 generations and as measured for single top production. Standard model predictions are at next-to-leading order with next-to-next-to-leading logarithm resummation [15] for a top mass of 173 GeV and MSTW2008 NNLO parton distribution functions. The first theory uncertainty is from scale variation (𝑚_𝑡/2<𝜇<2𝑚_𝑡), and the second is from the parton distribution function at 90% confidence level. When two experimental uncertainties are quoted, the first is statistical and the second is systematic, and when a third uncertainty is quoted it corresponds to the luminosity uncertainty.

Figure 2 

Single top cross-section in the 𝑡-channel versus centre-of-mass energy, comparing the existing measurements at Tevatron and LHC with the QCD expectations computed at NLO with MCFM in the 5-flavour scheme [24] and at NLO + NNLL [25]. The error band (width of the curve) includes the uncertainty on the top mass, the PDF uncertainty estimated according to the HEPDATA recommendations [26], and the factorization and renormalization scales changed coherently by a factor two up and down.

The rest of this paper elaborates on what the study of the properties of singly produced top quarks can tell us about physics beyond the SM, with particular attention to what it can tell us about new heavy quarks. Section 2 discusses the most straightforward connection between single top studies and new sequential quark generations, which is the extraction of |𝑉_𝑡𝑏| from the single top cross-section under some assumptions, which are critically discussed. Section 3 is devoted to single top polarization, a crucial feature of 𝑡-channel production in the SM which would hold true also with the inclusion of sequential quark generations in the model and can be a powerful discriminator with respect to other forms of new physics. Section 4 elaborates more generally on which kind of new physics can be suspected to be at play in case of different patterns of deviations from the SM expectations in the phase space sampled by single top analyses, with a bottom-up approach. Finally, Section 5 mentions some single top signatures which are absent in the SM.

2. Single Top and |𝑉_𝑡𝑏|

Typically, a single top cross-section measurement paper ends with the inference of the |𝑉_𝑡𝑏| interval corresponding to the measured cross-section, under the simplifying assumption that, whatever the values, the relationships |𝑉_𝑡𝑏|≫|𝑉_𝑡𝑑| and |𝑉_𝑡𝑏|≫|𝑉_𝑡𝑠| hold true. Also implicit is the assumption of purely left-handed 𝑡𝑏𝑊 coupling (i.e., left-handed and right-handed helicity fractions 𝑓_𝐿=1,𝑓_𝑅=0). Table 2 shows the |𝑉_𝑡𝑏| intervals extracted by the Tevatron and LHC experiments under these assumptions, with and without the unitarity constraint 0≤|𝑉_𝑡𝑏|≤1. The most precise determination from single top [8] reached a comparable precision with the best one derived from the branching ratio 𝑅_𝑏≡Γ(𝑡→𝑊𝑏)/Γ(𝑡→𝑊𝑞), where 𝑞=𝑑,𝑠,𝑏 [11], which is interpreted as 𝑅_𝑏=|𝑉_𝑡𝑏|²/(|𝑉_𝑡𝑑|²+|𝑉_𝑡𝑠|²+|𝑉_𝑡𝑏|²) under the same assumptions (and, therefore, can be used to infer |𝑉_𝑡𝑏| directly only if the additional assumption |𝑉_𝑡𝑑|²+|𝑉_𝑡𝑠|²+|𝑉_𝑡𝑏|²=1 is imposed).

Table 2 

Measurements of |𝑉_𝑡𝑏| at Tevatron and LHC, under the assumptions 𝑓_𝐿=1,|𝑉_𝑡𝑏|≫|𝑉_𝑡𝑑|, and |𝑉_𝑡𝑏|≫|𝑉_𝑡𝑠|, with and without the unitarity constraint 0≤|𝑉_𝑡𝑏|≤1.

Some papers [12–14] examined how single top cross-sections are modified under the hypothesis of additional quarks mixing with the known up-type quarks, and therefore of a violation of unitarity for the 3×3 components of the extended CKM matrix. While the sum |𝑉_𝑡𝑑|²+|𝑉_𝑡𝑠|²+|𝑉_𝑡𝑏|²+|𝑉_𝑡𝑏′|² and, a fortiori, the sum |𝑉_𝑡𝑑|²+|𝑉_𝑡𝑠|²+|𝑉_𝑡𝑏|² is bound to be ≤1 also in the extended matrix, the limits on |𝑉_𝑡𝑑| and |𝑉_𝑡𝑠| derived from precision physics under the SM assumption do not hold. Therefore, contrary to common intuition, additional quark generations could result in an enhancement, and not only necessarily a deficit, of the single top cross-section in 𝑡-channel and 𝑡𝑊 productions, due to the large parton densities of 𝑑 and 𝑠 quarks in the proton (much larger than the 𝑏 density), causing an amplification of the effect of any 𝑉_𝑡𝑑 or 𝑉_𝑡𝑠 value larger than the SM expectation, which can overcome the deficit due to a smaller 𝑉_𝑡𝑏.

References [13, 14] performed the exercise of deriving less model-dependent limits on all the three |𝑉_𝑡𝑞| matrix elements by reexamining the measurements of single top cross-sections and 𝑅_𝑏 published at the time. This typically imposes several approximations and shortcuts, not having access to the raw data. A particularly tricky case for the reinterpretation are single top analyses based on multivariate techniques, because several of the input variables are related to the kinematics of a reconstructed top quark, and the choice itself of the jet that is assumed to come from the decay of the top quark is made under the assumption that it is a 𝑏 jet, and therefore |𝑉_𝑡𝑏|≈1. It is, therefore, important that the experimental collaborations carry out such an exercise themselves, with minimal model dependence at every stage of the analysis, possibly training the multivariate discriminators for different |𝑉_𝑡𝑏| scenarios.

3. What Can Be Learned from Angular Observables

A crucial property of the top quark is its lifetime which is shorter than the QCD decoherence timescale (𝜏≈4×10⁻²⁵ s the former, two orders of magnitude more the latter), causing its decay products to retain memory of its helicity. This provides additional powerful tools in the search for new physics in single top studies: single top production in 𝑡- and 𝑠-channel yields 100% polarized top quarks if only electroweak interactions are involved (which stays true if the only extension to the SM is a sequential new family of quarks), while different new physics models yield different polarizations. Relevant to this paper is the fact that, in case of hints of new physics in the single top sector, observing or not a SM-like (i.e., close to 100%) polarization of the top quark would discriminate between a trivial extension of the SM with additional quarks and other models.

The general form of the angular distribution (𝜃_𝑋) of decay product 𝑋 (=𝑊,ℓ,𝜈,𝑏) in the top quark rest frame is 𝑑Γ𝑑cos𝜃_𝑋=Γ21+𝑃_𝑡𝛼_𝑋cos𝜃_𝑋, (1) where 𝑃_𝑡 is the single top polarization (due to the production vertex) along a given direction chosen to quantise the top spin, and 𝛼_𝑋 is a spin-analysing power specific of the decay particle (maximum for the charged lepton [20, 21], which is also preferred in this kind of studies because of the identification cleanness of electrons and muons). Both parameters can be affected by top quark anomalous couplings [20].

Single top polarization in the 𝑡-channel process is already manifest in the slope of the cos𝜃^∗_ℓ distribution (see Figure 3 for a selection of enriched in 𝑡-channel events, from [8]), where 𝜃^∗_ℓ is defined as the angle between the charged lepton and the light jet (𝑗^′) in the reconstructed top quark rest frame. The rationale for this definition is that the (light) quark recoiling against the single top quark tends to have a direction parallel to the spin direction of the top quark at the production vertex [21]. The SM expectation 𝑃_𝑡×𝛼_ℓ≈1 has even been built-in in the foundations of one of the earliest cross-section measurements at the LHC [22] which made use of the cos𝜃^∗_ℓ distribution to fit the SM signal (this is named the “2D analysis” in [22], being based on a likelihood fit to the bidimensional distribution in the (cos𝜃^∗_ℓ,𝜂_𝑗′) plane. In the same paper, this is combined with the result of a fit to a boosted decision trees where cos𝜃^∗_ℓ is one among many inputs) and it is part of the implicit assumptions of all the multivariate analyses at Tevatron and LHC. It is crucial to perform unbiased precision measurements of both the cross-section and 𝑃_𝑡 to decouple the issue of measuring the SM-like component from the search for new physics. This is straightforward as a further step of a cut-based analysis or of the simple strategy of the “𝜂_𝑗′ analysis” [8, 10] ([8] makes use of three complementary analysis strategies, two of which are multivariate analyses), thanks to the small and calculable correlation between 𝜂_𝑗′ and cos𝜃^∗_ℓ, while more care has to be taken in multivariate analyses, where several input observables are correlated with the polarization. A promising way out in this case is the use of orthogonalization techniques, like “deboosting” [23], to ensure that the MVA discriminator used for event selection is uncorrelated with cos𝜃^∗_ℓ.

Figure 3 

Distribution of cos𝜃∗ℓ in the |𝜂𝑗′|>2.8 region, from [8].

Other angular variables can be defined in single top events for the purpose of measuring top quark polarization in a model-independent way (see, e.g., [27]). Several angular observables can be useful, alone or combined, thanks to their sensitivities to the helicity states of the 𝑊 from top decay, to constrain the parameters of the most general Lagrangian term that one can write for the 𝑡𝑏𝑊 coupling up to six-dimensional gauge invariant operators [28] (under the approximation 𝑉_𝑡𝑏=1): ℒ_𝑡𝑏𝑊𝑔=−√2𝑏𝛾^𝜇𝑓_𝐿𝑃_𝐿+𝑓_𝑅𝑃_𝑅+𝑖𝜎^𝜇𝜈𝑞_𝜈𝑀_𝑊𝑔_𝐿𝑃_𝐿+𝑔_𝑅𝑃_𝑅×𝑡𝑊⁻_𝜇+h.c., (2) where the SM predicts 𝑓_𝐿=1,𝑓_𝑅=𝑔_𝐿=𝑔_𝑅=0. The D0 collaboration has set constrains on these parameters by means of a neural network analysis combining several angular and kinematical inputs, with different networks trained for nonzero values of each of the anomalous parameters 𝑓_𝑅,𝑔_𝐿, and 𝑔_𝑅 [29]. Due to the higher centre-of-mass energy, given that the new physics effects would enter in the production vertex, LHC experiments are expected to be more sensitive to deviations to the SM. The simultaneous measurement of the cross-section and of the parameters of the generalized 𝑡𝑏𝑊 coupling would help to get rid of the simplifying assumption about |𝑉_𝑡𝑏| implicit in (2).

4. Deficits and Excesses: A Bottom-Up Approach

Different beyond-SM models predict different effects in the different production channels [12]. Here, we outline a few examples, reasoning in a bottom-up approach, that is, starting from the possible observations of deficits or excesses to infer which model (including the SM itself) could provide the most natural explanation.(i)A deficit in all three channels would naturally lead to suspect |𝑉_𝑡𝑏|<1 (hence the existence of new quarks); this can be verified by precisely measuring 𝑅_𝑏≡𝐵𝑅(𝑡→𝑊𝑏)/𝐵𝑅(𝑡→𝑊𝑞) in 𝑡𝑡 events; (ii)an excess in the 𝑠-channel, not confirmed in the other two, would induce to suspect a charged resonance (e.g., a right-handed 𝑊^′, whose coupling to light fermions would be suppressed by helicity conservation and would, therefore, be visible in the 𝑡𝑏 final state and not in electronic or muonic decays), which would be confirmed by a peak or a peak-dip structure in the 𝑀_𝑡𝑏 spectrum; (iii)an excess in the 𝑡-channel, not confirmed in the other two, could be due to new interactions causing flavour-changing neutral currents (FCNCs): even with tiny 𝑢𝑡𝛾 and 𝑢𝑡𝑍 couplings, the very large up-quark density at high 𝑥 in the proton would allow a visible signal to show up; important checks would be the differential measurements of 𝑑𝜎^𝑡-channel_𝑡/𝑡/𝑑𝑦 and of the single top polarization; (iv)an excess in the 𝑡-channel and in the 𝑡𝑊 channel, with no deviation from the SM in the polarization of the top quark, and a deficit in the 𝑠-channel could be due to large |𝑉_𝑡𝑑| or |𝑉_𝑡𝑠| (nonunitarity of the CKM matrix, hence possible existence of new quarks), to be checked by measuring 𝑑𝜎^𝑡-channel_𝑡/𝑡/𝑑𝑦 and 𝑅_𝑏.

Some of these new physics effects in 𝑡-channel and 𝑡𝑊 production might be mimicked by discrepancies in the gluon or 𝑏-quark PDFs at large 𝑥 and it is, therefore, necessary to be able to rule out this possibility by additional dedicated inputs. Precision measurements of all three production modes will have a deep impact on PDF constraints, with the three channels being complementary to each other and also to 𝑡𝑡 production. For example, 𝑡-channel and 𝑡𝑊 cross-sections are sensitive to the 𝑏-quark PDF and anticorrelated with the 𝑊/𝑍 cross-section, while the 𝑠-channel (essentially a Drell-Yan process) is insensitive to the 𝑏-quark PDF and can therefore act as a control process, and it is correlated with the 𝑊/𝑍 cross-section, like the 𝑡𝑡 cross-section [30]. Moreover, the integrated or differential charge asymmetry in 𝑡-channel production will provide a very powerful input for constraining PDFs, similar to the 𝑊 production case, in a region of 𝑥 very relevant for several other searches. The first measurement of the integrated charge asymmetry (𝑅_𝑡≡𝜎(𝑡)/𝜎(𝑡)) from the ATLAS collaboration [31] at 7 TeV has already disfavoured some PDF sets, as illustrated in Figure 4. Differential distributions of 𝑅_𝑡 as a function of rapidity and transverse momentum of the top quark will provide significant additional discriminating power. Another useful input for constraining PDFs is the measurement of the ratio of single top cross-sections between 7 and 8 TeV, as done by the CMS collaboration in the 𝑡-channel case by taking the ratio of results of the 𝜂_𝑗′ analysis at the two energies [10].

Figure 4 

Measured 𝑅𝑡 value in ATLAS, compared to the values calculated for different NLO PDF sets. The error on the calculated values contains the uncertainty on the renormalisation and factorisation scales. The combined statistical and systematic uncertainty of the measurement is shown in green, while the statistical uncertainty is represented by the yellow error band. Taken from [31].

5. Exotic Single Top Signatures

While the “𝑡-channel like” signature, as mentioned in Section 4, is sensitive to FCNC couplings of the kinds 𝑢𝑡𝛾 and 𝑢𝑡𝑍, which can also be constrained by looking for the 𝑡→𝑍𝑞 and 𝑡→𝛾𝑞 decays in pair-produced top quark events (searches for the 𝑡→𝑍𝑞 decay have been already performed by both LHC collaborations at 7 TeV [32, 33]), the exotic signature of a “very single top” (i.e., a 2→1 partonic reaction producing a top quark, see Figure 5) is by far the most powerful handle to constrain the FCNC couplings of the kind 𝑢𝑡𝑔, given the overwhelming SM background in the 𝑡𝑡 decays. The CDF and ATLAS collaborations performed a search in the very-single-top final state [34, 35], with the tightest bounds to date coming from ATLAS at 7 TeV: 𝐾_𝑡𝑔𝑢Λ<0.0069TeV⁻¹,𝐾_𝑡𝑔𝑐Λ<0.016TeV⁻¹. (3)(4) The D0 collaboration chose a different strategy, based on the SM-like signature of a single top quark in association with a light quark [36] (same signature as 𝑡-channel production in the SM). With a similar integrated luminosity as CDF (2.3 fb⁻¹ versus 2.2 fb⁻¹ for CDF), they obtained more stringent limits, demonstrating that the “top + jet” signature (mostly initiated by quark-quark collisions) is more sensitive than the “very-single-top” signature in the Tevatron conditions. Nevertheless, at the LHC energies the gluon flux is much more intense than at Tevatron in comparison to the quark flux; therefore, the balance is likely in favour of the “very single top” (A proper comparison, beyond the scope of this paper, would demand to take into account any effect susceptible to increase the jet multiplicity of the event, like initial state radiation and pileup).

Figure 5 

Leading order diagram for a “very single top” produced by an anomalous (FCNC) coupling of the kind 𝑢𝑡𝑔.

New physics can produce a single top quark in association with invisible particles, hence large missing transverse energy (this signature is known in the literature as “monotops”) [37], or a single top in association with a 𝑍 boson, which in turn can give the monotop signature (when the 𝑍 boson decays into a neutrino pair) or a spectacular final state of three leptons, a b jet and large transverse missing energy. No experimental collaboration published a search for these final states yet. It can be remarked, in the context of this volume dedicated to new heavy quarks, that both signatures can be originated by the production of heavy vector-like partners of the top quark, which would have the FCNC decay 𝑡^′→𝑡𝑍 [38]. Given the very tight limits on a sequential fourth generation with SM-like couplings, the exploration of these alternative new quark scenarios becomes even more interesting, and single production is kinematically favoured over pair production, despite the larger QCD coupling, when the quark is very heavy.

6. Conclusions

The single top final states are an important place to look for indirect evidences of new heavy quarks, and the measurements of the properties of single top quarks are crucial to gain sensitivity to non-SM interactions and to get some insight into the kind of new physics at hand in case of deviations from the SM hypothesis.

Acknowledgments

The author wishes to thank Paris Sphicas and George Hou for their suggestions, and the Estonian Academy of Science for supporting this work with the Mobilitas Top Researcher Grant MTT59.