Searching for Leptoquarks at IceCube and the LHC
In the light of recent experimental results from IceCube, LHC searches for scalar leptoquark, and the flavor anomalies and , we analyze two scalar leptoquark models with hypercharge and . We consider the 53 HESE events from IceCube and perform a statistical analysis, taking into account both the Standard Model and leptoquark contribution together. The lighter leptoquark states that are in agreement with IceCube are strongly constrained from LHC di-lepton+dijet search. Heavier leptoquarks in the TeV mass range are in agreement both with IceCube and LHC. We furthermore show that leptoquark that explains the -physics anomalies and does not have any coupling with third generation of quarks and leptons, can be strongly constrained.
The recent discovery of the Higgs boson Aad:2012tfa (); Chatrchyan:2012xdj () completes the Standard Model (SM) of particle physics as an effective, well-tested, theory up to the energy range around the electroweak scale. However, it fails to explain apparent observations in nature, e.g. the observed neutrino mass, matter-antimatter asymmetry or dark matter, and it cannot provide a fundamental reason for the quantisation of the particles’ charges or a possible unification of the standard model gauge groups. Thus, the primary task of experiments that can access the high-energy regime is to search for new particles and interactions which are necessary ingredients to the extensions of the SM.
Leptoquarks (LQ), particles that simultaneously carry lepton number (L) and baryon number (B), are predicted by a large variety of new physics scenarios, in particular by grand unified theories (GUTs) Georgi:1974sy (); Fritzsch:1974nn (), the Pati-Salam model Pati:1974yy () and extended technicolor models Farhi:1980xs (); Gabriel:1993ai (). Assuming that leptoquark interactions with SM particles are invariant and have dimensionless couplings, there are only twelve different types of leptoquarks, according to the possible assignments of their respective quantum numbers Dorsner:2016wpm (). Half of the leptoquark types are of scalar nature and the other half of vector nature. Yet, in each case the coupling structure to different SM generations can be highly complex, unless constrained by the UV theory from which the leptoquark descends.
Historically, experimental searches for leptquarks have been a high priority and have been performed at a wide range of collider experiments, e.g. at HERA Aid:1995wd (); Abramowicz:2012tg (), the Tevatron GrossoPilcher:1998qt (), LEP Abreu:1993bc () or the LHC Aad:2015caa (); Aaboud:2016qeg (); Khachatryan:2016jqo (); Sirunyan:2017yrk (). The ATLAS and CMS collaborations searched for leptoquarks coupled predominantly to the first two generation SM fermions, focusing on final states with two electrons or muons and two jets Aad:2015caa (); Aaboud:2016qeg (); CMS:2014qpa (); CMS:2016qhm (); CMS:2016imw (). Absence of deviations from SM backgrounds limits the leptoquark mass to GeV at 90 C.L. Aaboud:2016qeg (). Additionally, searches by CMS have further constrained third-generation leptoquarks to GeV Sirunyan:2017yrk (); Khachatryan:2016jqo (). Previous bounds on their masses were GeV from HERA Abramowicz:2012tg () and GeV from the Tevatron GrossoPilcher:1998qt ().
Interestingly, recent flavor anomalies, indicating the violation of lepton-flavor universality in rare -transitions measured by ATLAS ATLAS-CONF-2017-023 (), CMS CMS-PAS-BPH-15-008 () and LHCb Aaij:2014pli (); Aaij:2014ora (); Aaij:2015esa (); Aaij:2015yra (); Aaij:2017vbb (), have reignited the interest in leptoquark phenomenology Sakaki:2013bfa (); Hiller:2014yaa (); Gripaios:2014tna (); Varzielas:2015iva (); Becirevic:2015asa (); Fajfer:2015ycq (); Becirevic:2016yqi (); Aaij:2015oid (); Wehle:2016yoi (); Becirevic:2016oho (); Das:2016vkr (); Crivellin:2017zlb (); Becirevic:2017jtw (); Hiller:2017bzc (); Cai:2017wry (); Aloni:2017ixa (); DiLuzio:2017vat ().
Other than the collider constraints, leptoquark can also be searched in the high energy neutrino-neucleon interactions, namely at the IceCube Neutrino Observatory in Antarctica Aartsen:2013jdh (); Aartsen:2014gkd (); Aartsen:2015zva (). The four year high-energy starting events (HESE) sample Aartsen:2014gkd (); Aartsen:2015zva (), reported by IceCube collaboration span an energy range from 22 TeV to 2 PeV. The three events above a PeV in energy have raised a considerable amount of interests in recent years Barger:2013pla (); Bhattacharya:2014yha (); Dutta:2015dka (); Dey:2015eaa (); Dev:2016uxj (); Dev:2016qbd (); Dey:2016sht (); Mileo:2016zeo (); Bhattacharya:2016tma (); Dev:2016qeb (); Kistler:2016ask (); Chauhan:2017ndd (); Bhattacharya:2017jaw (); Borah:2017xgm (); Palladino:2017qda (). A primary goal of this work is to constrain leptoquark mass and coupling using all the HESE sample. We also critically re-examine the idea that scalar leptoquarks can provide a natural explanation to the three events seen above a PeV at the IceCube. Indeed, the centre of mass energy scale of a PeV neutrino colliding with a nucleon at rest is just the right scale to excite a TeV leptoquark resonance Anchordoqui:2006wc (). Many studies have made the claim that such a process can improve the fit to the observed event rate Barger:2013pla (); Dutta:2015dka (); Dey:2015eaa (); Dev:2016uxj (); Dey:2016sht (); Mileo:2016zeo (). These are often framed in terms of an excess that requires a non-standard explanation; however, it should be stressed that the observed event rate falls within the expected Waxman-Bahcall flux 1999PhRvD..59b3002W (), consistent with a common origin with cosmic rays (see also Waxman:2015ues () for a review).
In this work, analysing the leptoquark contribution to the IceCube events, we pinpoint few major improvements as compared to the existing analysis. These include 1) the inclusion of the whole energy range 10 TeV – 10 PeV, including the energy bins in which no events have been observed; and 2) a simultaneous fit of new physics and SM contribution to the 53 observed events in 4 years of data. While point 1) generally reduces the goodness of fit of any new component on top of the SM event rate, point 2) represents a very crucial improvement: we will find that by allowing the spectral index and normalizations of the incoming astrophysical flux and atmospheric backgrounds to vary freely, it is not possible to single out a LQ signal while remaining consistent with model still allowed by LHC data. Any small improvement in the goodness of fit furthermore remains much lower than the 1 level.
This paper is structured as follows: we begin by describing the details of the two benchmark models that we consider in Sec. 2. We then examine the effect of these models on the observed neutrino event rate at IceCube in Sec. 3. We present the exclusions from LHC and the discussion on flavor anomalies in Sec. 4 and Sec. 5, respectively. Appendices A and B provide the detailed cross sections used for our IceCube analysis. We conclude in Sec. 6.
In this section we briefly review the models of interest: A) leptoquark having the representations , and B) leptoquarks having the representation under the SM gauge group . can be represented as , where and are the components of doublets; the superscripts represent their corresponding electromagnetic charges. The other leptoquark has the form . Below, we discuss the Lagrangian for the two leptoquarks mentioned above:
The leptoquark : The Yukawa interaction of with SM fermions can be given as,
where is the doublet lepton, are the charged leptons, and represent the generation indices of the leptons. In addition to the Yukawa Lagrangian, the field has the kinetic and mass terms
respectively, where denotes the covariant derivative, and is the mass of the leptoquark. Note that the leptoquark interacts only with down type of quarks ().
The leptoquark : The leptoquark has similar and charges, and non-trivial hypercharge . The Lagrangian of this leptoquark field has the following form:
The kinetic and mass terms are
where is the covariant derivative
The leptoquarks and have interactions with the SM fermions. As we will discuss in the next sections, the leptoquark components and can have observable consequences at IceCube.
3 IceCube events
In this section we discuss the interaction of neutrinos (and antineutrinos) with detector protons and neutrons, mediated by the heavy leptoquarks, with the goal of improving the spectral fit to the observed high-energy PeV IceCube events. The leptoquark mediates the neutral current interactions and . We show the Feynman diagram for these two processes in Fig. 1. The leptoquark has both the neutral current as well as charged current interactions, , , . Note that, the leptoquark does not interact with the light neutrinos, and hence does not contribute to the IceCube neutrino-nucleon interaction. For Model A, the relevant processes are
mediated by s-channel LQ, and similarly ,
mediated by the t-channel LQ, and similarly .
In addition to the above, the SM contribution has both the mediated charged current (CC), and mediated neutral current (NC) contributions that give rise to , , , and interactions. The expressions for neutrino-nucleon cross sections are given for both NC and CC processes in Appendices A and B.
The leptoquark can only produce shower events, while the leptoquark can produce both shower and muon track events if is nonzero for or . For this analysis, we only allow the final-state charged lepton (i.e. no final-state muons or taus), so that both CC and NC interactions lead only to showers.
3.1 Energy deposition rates at IceCube
We calculate the number of events at IceCube following the formalism laid out in Palomares-Ruiz:2015mka (). The relevant observable at IceCube is the event rate per deposited EM-equivalent energy. We distinguish between the incoming neutrino energy , the “true” EM-equivalent energy deposited in the ice, and the deposited energy in the detector, . The latter two are related by a gaussian smearing function , with a width . The neutral current event rate for an incoming neutrino of flavour is:
In the above, is the astrophysical neutrino flux; the flavour dependence of the cross section arises from the leptoquark couplings . is the exposure time (1347 days for the four-year HESE sample), and is Avogadro’s number, representing the number of target nucleons per gram of ice111Remembering that ice is not isoscalar; rather: must be used when computing cross sections.. At energies above 10 TeV, the neutrino mean free path becomes smaller than the diameter of the Earth, which is included in the attenuation factor . To properly take this into account, one should compute the directionally-dependent attenuation rate by solving the transport equation. We will use angle-averaged attenuation rates computed by Palomares-Ruiz:2015mka (); Ref. Mileo:2016zeo () have shown that the impact of LQs on attenuation is quite small. is the effective detector mass as a function of the true electromagnetic equivalent energy, and can be seen as the fiducial IceCube volume times an energy-dependent detector efficiency. A parametrization of this function can be found in Ref. Palomares-Ruiz:2015mka (). Though IceCube provides effective masses as a function of the incoming neutrino energies, these depend implicitly on the cross sections: since we are searching for effects of new physics, the method of Eq. 5 must be used. Finally, the true energy , where the hadronic energy . For we use the parametrization from Ref Gabriel:1993ai ():
with , GeV and Kowalski ().
For Model B, CC events can also occur. If the final state is an electron, then the deposition rate is the same as Eq. (5), but with the cross section replaced with the relevant CC cross section (detailed in Appendix B.2), and with to take into account the electron’s energy deposition.
Finally, we include other Standard Model processes: tau neutrino CC interactions, which can produce both showers and muon tracks, as well as muon neutrino CC interactions, which produce tracks. We furthermore include electron antineutrino interactions with ice electrons, which become dominant around the Glashow resonance at PeV. Though we are interested in new physics contributions to the total cascade rate, we include the Standard Model track events as a way of constraining the total astrophysical flux. The details of these rates are in Appendix B of Palomares-Ruiz:2015mka (). We employ the CT14QED Schmidt:2015zda () PDF sets, accessed via LHAPDF6 Buckley:2014ana ().
The dominant production mechanism for astrophysical neutrinos is expected to be charged pion decay, from high energy and collisions. These produce neutrinos in a ratio = . After oscillation over large, uncorrelated distances, this should average to a composition very close to which we take to be the flavour composition of our astrophysical neutrino flux. Known oscillation physics prevents large deviations from this flavour ratio, and, in fact, as long as production remains pion-dominated, it remains difficult to stray far from the composition in new physics scenarios Arguelles:2015dca ().
In addition to astrophysical neutrinos, a non-negligible fraction of the HESE sample is composed of atmospheric neutrinos, as well as veto-passing muons from atmospheric showers. We take the shape of the atmospheric shower spectrum from Vincent:2016nut ()222We note that the LQ interactions should also affect the atmospheric neutrino detection rate; however, this is a subdominant effect for the LQ masses under consideration here, given the lower energy range of the atmospheric contribution ( TeV). We therefore take the post-interaction atmospheric background from Vincent:2016nut (), thereby avoiding some of the systematics (e.g. self-veto rates) involved in modelling the atmospheric neutrino flux.. The atmospheric muon flux uses the parametrization of Eq. (1) from the same reference.
Finally, it has been shown Palomares-Ruiz:2015mka (); Aartsen:2015ivb (); Vincent:2016nut () that a non-zero misidentification rate of tracks as showers (e.g. from large muon inelasticity, events near the detector edge, etc.) affects reported event topologies. This was notably the reason behind the lower-than-expected track-to-shower ratio in the HESE data sets since the first two years’ data Mena:2014sja (); Palomares-Ruiz:2014zra (); Vincent:2015woa (). We include this by making the replacements to expected track (tr) and shower (sh) event rates :
with the mis-ID probability is set to . This is lower than the published value of 0.3 Aartsen:2015ivb (), which also included lower-energy (MESE) events for which track reconstruction is inherently more difficult. We note that a proper quantification of has never been performed, and we will return to the effects of varying this quantity in Sec. 3.3.
3.2 Comparison with IceCube data
Out of the 53 events333Though 54 were reported, one was a coincident muon track whose energy could not be reconstructed. in the four-year HESE sample, 14 are muon tracks and 39 are cascades. Among these roughly 14 are expected to be from atmospheric muons, and 7 from atmospheric neutrino events Aartsen:2014gkd (); Aartsen:2015zva (). We are interested in the effect of a new scalar leptoquark on the goodness of fit of the model (SM+LQ) to the four-year publicly available data. We make two crucial changes with respect to previous studies:
We simultaneously fit the background (Standard Model) contribution, by allowing the following four parameters to vary: the astrophysical spectral index , the astrophysical flux normalization , the atmospheric neutrino rate , and the veto-passing atmospheric muon rate .
We include all energy bins from 10 TeV to 10 PeV, including bins in which zero events were observed. We separate this range into 15 logarithmically spaced bins for showers, and the same number for muon tracks. This distinction is important, as the different contributions to the event rates have very different topological signatures.
These are crucial: previous studies Barger:2013pla (); Dutta:2015dka (); Dey:2015eaa (); Dey:2016sht (); Mileo:2016zeo () have examined the impact of an extra leptoquark-induced interaction (or a similar R-parity violating SUSY model Dev:2016uxj ()) on the best-fit fluxes reported by the IceCube collaboration. However, this is not self-consistent, as the fluxes were derived using the same data set. Indeed, there is a large degeneracy between the flux normalization, spectral component, and new physics contribution; these must all be taken into account simultaneously, along with the atmospheric flux normalizations. The inclusion of zero-event bins is also critical, as we will find that any improvement to the fit to the three observed PeV events is accompanied by a worse fit to those empty bins, especially at and above the 6.3 PeV Glashow resonance.
We also do not employ the narrow width approximation (NWA), as was done in previous studies, and instead use the full expressions (20, 23), which include terms that mix SM and LQ contributions. We do note that for couplings , the NWA does provide fairly accurate corrections to the neutrino-nucleus cross sections.
We take the event rate in each bin to follow Poisson statistics. For each point in parameter space, we first maximise the fit with respect to the four nuisance parameters (), before evaluating the goodness of fit, parametrized via the p-value. This is done via a Monte Carlo event simulation of the Poisson process.
Even with known model parameters, the systematic uncertainties in energy deposition make the enhanced cross sections shown in Fig. 3 difficult to distinguish from the standard case. An unknown inelasticity for each event means that only a fraction of the neutrino energy might end up deposited in the ice, which smears the detected spectrum – in addition to the error on reconstructed event energy .
We perform the fitting procedure detailed above, including event energy and topology information from the 53 IceCube HESE events. In the case where no new physics interactions are present (SM only), we find a best fit spectrum
with and GeV cm s sr. Backgrounds are best fit by 10.7 atmospheric neutrinos, and 4.9 veto-passing atmospheric muons.
We then perform a scan over LQ masses between 400 and 1500 GeV, and couplings between zero and 10. From these likelihood evaluations, we note the following results:
The addition of a leptoquark-mediated interaction can generally be compensated by a change in the spectral index and overall normalization of the atmospheric flux, with no significant improvement in the -value with respect to the standard model. For Model A, we find no parameter combination with that produces a significant change in the fit to the IceCube data. In contrast, Model B produces changes that are large enough to produce a mild exclusion line. It is not possible to obtain an event distribution that reproduces the PeV events without also increasing the expected event rate in the bins where no events were observed. This is mainly because the large required couplings also yield a decay width that is too large, both suppressing and widening the signal. These exclusions are shown in the first panel of Fig. 4. It can be seen that they do not reach the 2 () threshold.
The best fit astrophysical spectral index varies around the Standard Model value, between and 3, while atmospheric flux is decreased by a factor between 6 and 8, at the point of largest LQ contribution (). An additional atmospheric neutrino component is usually required to compensate for the low-energy showers removed by this rescaling. The number of atmospheric muons is unsurprisingly stable, since these overwhelmingly produce track-like events. These degeneracies are shown in the right-hand panels of Fig. 4.
The addition of a scalar LQ coupling in both models can lead to a slight improvement in the fit to the data, though this is not statistically distinguishable from the zero-coupling (Standard Model) line. In either model, we see improvement in the -value by 0.05, which is not distinguishable from the SM value (). The exact mass of the best fit point is also difficult to pinpoint, given the flatness of the likelihood at couplings below a few. For Model B, the best fit point is at GeV, . The resulting spectrum (dashed blue) is shown in the right-hand panel of Fig. 5; this is clearly indistinguishable from the SM-only case (solid blue). We have separated out showers (blue, with black data points) from tracks (red).
Model A gives rise to a qualitatively very different solution, though it remains statistically indistinguishable from the SM case: by suppressing the astrophysical flux to 1/3 of its SM value (i.e. GeV cm s sr) , a very strongly-coupled leptoquark ( GeV, ) can yield an event distribution for cascade events that is compatible with observations, while suppressing the expected rate around the Glashow peak. This improvement in the fit is somewhat compensated by a worse fit to the observed track-like events. This leads to an overall small () improvement in goodness of fit. We must furthermore discount this solution, since it is incompatible with the collider constraints we will find in the next section.
One may ask whether the addition of a shower-producing LQ coupling can mitigate the need for a large track misidentification rate . We find that this is not the case: taking lower values of leads to an overall worse fit, which the LQ contribution is unable to compensate in either model.
Finally, if the spectral index is fixed to , near the 4-year best fit reported by IceCube, such a best fit point is not recovered in either model; rather, the largest -value is found with , and the overall goodness of fit is reduced in the entire parameter space. In contrast, adopting a two-component power law leads to an improvement in the overall fit, but the best LQ contribution remains at zero.
We end this section by noting that we have not used angular information, nor have we allowed the flavor composition of the astrophysical flux to vary. Ref. Dev:2016uxj () have shown that this can help, notably by removing the component leading to the Glashow peak. We anticipate that angular information would lead to a slight improvement in the significance of our results, whereas allowing the flavor composition to vary would weaken it, and require extra motivation to explain the lack of a flux.
4 Constraints from LHC
The leptoquarks corresponding to both models can be produced at the LHC and can be detected via its distinct signatures Kohda:2012sr (); Queiroz:2014pra (); Allanach:2015ria (); Mandal:2015vfa (); Mandal:2015lca (); Dorsner:2016wpm (); Dumont:2016xpj (); Das:2017kkm (). Dedicated searches for the first two generations of leptoquarks that couple with electrons or muons have been performed at the LHC Aaboud:2016qeg (). CMS has constrained the leptoquark mass GeV assuming a branching ratio of leptoquark decaying into a charged lepton and jet. Recently, searches for scalar leptoquark coupled to and -jets have resulted in the constraint GeV (again assuming a 100 branching ratio). Additionally, in the models considered, the leptoquark can also decay into a neutrino and a quark, giving rise to multijet final states associated with large missing energy. Therefore a number of SUSY searches for multijet and MET events can be used to further constrain the model’s parameters.
4.1 Di-lepton + Dijet
In Model A, the leptoquark can be pair-produced and decays to a charged lepton and quark. A similar signal can be mimicked by and in Model B. We consider the pair production of leptoquarks and the following signal topologies
In the above, and we consider the light quarks i.e., and , which lead to the most conservative limits on the couplings. Below, we derive the limits on the relevant couplings using the combined 8 TeV and 13 TeV limit on the branching ratios of a leptoquark decaying into a charged lepton and a quark Aaboud:2016qeg (). The branching ratio of for Model A is
where is the total decay width of and has the form
With the experimental limit on the branching ratio of LQ denoted as , and using the observed limit from Aaboud:2016qeg (), an upper limit on can be derived as
These are the same couplings that also contribute to the IceCube events.
For Model B, the leptoquark can decay to both and final states, hence it can potentially be constrained both from IceCube and from the LHC. The constraints on the coupling that connects with electron and light quark result in
where we have considered interacts only with and quark; and with light neutrinos (all flavors) and quarks. Similar expressions can also be derived for muons.
We show the limits on the couplings in Fig. 6, for both models. The lines correspond to the limits on the branching ratios of the leptoquarks decaying into an electron and jet pair Aaboud:2016qeg (). Comparable limits can be derived for the muon final state.
For Model A we assume , while we vary the leptoquark mass and the coupling . The gray region is excluded from the letptoquark search in the channel444In Fig. 6 and Fig. 8, we represent the leptoquark mass as , i.e., for Model A, and Model B, this represents and , respectively.. In this scenario, IceCube cannot put stringent constraint on the relevant coupling and the mass of . The most stringent bound appears from the search presented in Aaboud:2016qeg ().
For Model B we consider the following illustrative benchmarks (a) both couplings and are equal, i.e. we set and and, (b) , , while all other couplings are zero. We vary the leptoquark mass and the relevant coupling . The disallowed regions correspond to the area covered by the brown solid (for (a)) and purple dotted lines (for (b)) in Fig. 6 555For other choices of coupling the bound on will be rescaled as , hence, naively follow a simple re-scaling..
As discussed in Sec. 3, the best-fit data point for Model B is GeV with . Assuming all other couplings to be zero leads to . However, this parameter point is already ruled out by existing searches at the LHC Aaboud:2016qeg (). Even for other leptoquark masses, and with , the branching ratio of leptoquark decaying to electron and jet remains similar. Following Aaboud:2016qeg (), this imposes a limit GeV. Leptoquark with relatively higher mass TeV is still unconstrained from the present LHC searches, while being in agreement with 4-yr HESE data from IceCube.
Additionally, Model B can also receive further constraint from the leptoquark . The bound on the mass of is even more stringent TeV Aaboud:2016qeg () (as Br ) for and all other couplings to be zero. The severe bound can however be relaxed if additional interactions with the third-generation quarks i.e., or are present. For a substantial branching ratio , the limit on the branching ratios of will be relaxed, resulting in a weaker constraint on the coupling. We show this in Fig. 7 for the scenario 0. The LQ state however does not couple to light neutrinos and hence is not relevant for the IceCube analysis.
4.2 Dijet + MET
The leptoquarks of Model A and Model B can further be constrained from multijet searches. We adopt the 13 TeV ATLAS search Aaboud:2016zdn () and derive the constraints on the mass and coupling using CheckMATE Drees:2013wra (). The leptoquarks and mediate the processes
For Model A, we consider that the couplings and are fixed to the benchmark values 0.1. For lower mass and large couplings, strong bounds exist on the leptoquark mass. In Fig. 8, we show the contour plots for the statistical parameter , defined as
where and represent the signal events and its uncertainity, and the numerator denotes the C.L limit on the number of signal events from CheckMATE and the denominator determines the experimental limit. The excluded regions correspond to . A number of cuts have been used to derive the limits, such as, the jet transverse momentum , the missing transvese energy , and the . See Aaboud:2016zdn () for further detail.
For lower masses such as GeV, the coupling is ruled out, as shown in Fig. 8. With increasing leptoquark mass, such as, TeV or larger, the limit on is strongly relaxed. A Comparison betwen di-lepton+dijet (Fig. 6) and jet+MET (Fig. 8) for Model A shows that gives a stronger bound on the leptoquark coupling . For Model B, we do not explicity show the constraints on the parameter space. For the best fit points and GeV as discussed in Sec. 3.3, the branching ratio is predicted to be , which leads to coupling being largely unconstrained.
5 Flavor anomalies
Recent LHCb observations on rare -meson decays show deviations from the SM in the observables and Aaij:2014ora (); Aaij:2017vbb (). There are quite a few studies Hiller:2014yaa (); Gripaios:2014tna (); Varzielas:2015iva (); Becirevic:2015asa (); Fajfer:2015ycq (); Becirevic:2016yqi (); Aaij:2015oid (); Wehle:2016yoi (); Becirevic:2016oho (); Das:2016vkr (); Crivellin:2017zlb (); Becirevic:2017jtw (); Hiller:2017bzc (); Cai:2017wry (); Aloni:2017ixa (); DiLuzio:2017vat () which explain these deviations using the leptoquarks of Model B. We therefore deem it relevant to add a short discussion on the implications of these flavour anomalies on the leptoquark models that we are considering.
Leptoquarks with hypercharge from Model B, have been proposed to explain the flavor anomalies in the decays Becirevic:2017jtw (), where the transition occurs through one-loop processes, mediated by the leptoquark . This can successfully explain both the and anomalies. In order to explain the experimental results, fairly large couplings , are required, close to the edge of the perturbative regime. Below, we examine in detail the collider constraints on such large coupling. The partial decay width of the leptoquark decaying in the and states have the following form:
We consider the following two scenarios:
Only and are non-zero and fairly large . This is required to satisfy the flavor anomalies and is in agreement with Becirevic:2017jtw (). As an illustrative example, we consider two masses and GeV.
Additionally, the couplings including top-quark and is non-zero and large, i.e., , while .
|650 (*)||0||0.87 (>Br1)||0||0.13|
|1000 (*)||1.2||0||0.89 (>Br2)||0||0.10|
These above benchmark values of the couplings ensure the agreement in the measurement of and Becirevic:2017jtw (). However, these can be further constrained from other LHC searches, in particular di-lepton+dijet. In the absence of coupling , the lower leptoquark mass 650 GeV with large and gives a sizeable branching ratio , larger than the experimental limit . For heavier or lower masses with additional decay mode open, the branching ratio into is yet unconstrained. Hence, a heavier leptoquark or lighter leptoquark with additional coupling with third generation quark and lepton can successfully explain both the anomalies, while remaining consistent with di-lepton+dijet search. The leptoquark does not couple with light neutrinos. Hence, a direct comparison with the IceCube constraint can not be performed.
In this work, we have analyzed the constraints on scalar leptoquarks with hypercharge and that arise from neutrino as well as collider experiments. Strongly interacting scalar leptoquarks can contribute to the high-energy IceCube events, which we have explored in detail.
Previous studies have shown that such a new scalar can successfully improve fits to the high energy PeV events. However, we show that this generically tends to worsen the fit to bins where zero events were observed, once the entire range 10 TeV to 10 PeV is taken into account. Furthermore, we have shown that self-consistently allowing the astrophysical and atmospheric flux to vary strongly reduces the power to distinguish a leptoquark signal. Once the full range is taken into account, the high-energy events seen at IceCube do not carry sufficient statistical power to exclusively confirm or exclude the presence of the scalar leptoquark.
We further consider a number of LHC searches, such as collider constraint for first-generation leptoquark in the final state, the dijet+met constraint, as well as the recently reported flavor anomalies and by LHCb. We show that both light and heavier leptoquarks in the 400-1200 GeV mass range can be in agreement with the IceCube events. However, lighter leptoquark states, e.g. with masses around 500 GeV, are further constrained from search. Heavier leptoquark in the TeV mass range, can be in agreement with both IceCube and LHC. We further examine the models in the context of the anomalies and find that the low mass leptoquark can consistently explain the flavor anomalies and can be in agreement with di-lepton+dijet bound, if the branching ratio of the leptoquark decaying to a charm and muon is less that 10.
Here we present all the relevant expressions for the neutrino-nucleon cross section for both Model A and Model B.
Appendix A Neutrino-nucleon interactions for Model A
For Model A, the relevant interactions for IceCube are the neutrino-nucleon neutral current interactions mediated by the leptoquark. Note that, in this model, the leptoquark does not generate any charged current type interactions that can contribute in IceCube. Below, we write all the possible interaction terms, taking into account the SM contribution.
Considering the NC-type processes ( and ), the differential cross section for neutrino-nucleon666Note that here corresponds to either the proton or the neutron; we have not followed the common approach of averaging over nucleons (which yields terms proportional to ), since ice is not isoscalar. (-) interaction will be given by,
where the sum is over the quark flavors, and the PDFs are: (we ignore top contributions) and . The and coefficients contain the information about the interactions (both SM and LQ) between neutrino flavor and quark flavor . For mediated processes only down-type quarks take part. Dropping the neutrino () index when the LQ interaction is not present, and recalling , these coefficients are:
and , and likewise for the coefficients. Note that only the components interfere with the SM exchange. We have used the kinematical quantities:
Here with being the energy loss of the incoming neutrino. The - differential cross section can be written following Eq. 20 by interchanging .
Appendix B Neutrino-nucleon interactions for Model B
The leptoquark from Model B can contribute in NC type as well as CC type processes, as shown in Fig. 2. The relevant neutrino-nucleon cross sections are discussed below.
b.1 NC type processes
Considering the NC-type processes ( and ), the differential cross section for antineutrino-nucleon (-) interaction in this case is the same as for Model A (20). For the NC type processes only up type quarks take part. This time, the explicit forms of and are given by,
Once more, the second and third generation couplings are the same as and , except that we set the LQ couplings to zero. The NC type - differential cross section can be written following with the interchanges .
b.2 CC type processes
Since the LQ can also lead to charged leptons in the final state of neutrino-quark interactions it will lead to CC type processes (e.g., and ) also, see Fig. 2. The differential cross section for the neutrino nucleon cross section in this case is given by,
The ’s and ’s are:
The antineutrino-nucleon differential cross section can again be obtained from Eq. 23 by interchanging the quark and antiquark PDFs.
UKD acknowledges the support from Department of Science and Technology, Government of India under the fellowship reference number PDF/2016/001087 (SERB National Post-Doctoral Fellowship). MM acknowledges the support from DST INSPIRE Faculty Research grant (IFA14-PH-99) of India and Royal Society International Exchange Programme. MM thanks IPPP, Durham University, UK for their hospitality. DK thanks National Research Foundation, South Africa for support in forms of CSUR and Incentive funding. ACV is supported by an Imperial College Junior Research Fellowship.
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