## Archive for November, 2014

### Quark contact interactions at the LHC

So far, no convincing sign of new physics has been uncovered by the CMS and ATLAS collaborations. Nonetheless, the scientists continue to look using a wide variety of approaches. For example, a monumental work on the coupling of the Higgs boson to vector particles has been posted by the CMS Collaboration (arXiv:1411.3441). The authors conducted a thorough and very sophisticated statistical analysis of the kinematic distributions of all relevant decay modes, with the conclusion that the data for the Higgs boson are fully consistent with the standard model expectation. The analysis and article are too long for a blog post, however, so please see the paper if you want to learn the details.

The ATLAS Collaboration posted a paper on generic searches for new physics signals based on events with three leptons (e, μ and τ). This paper (arXiv:1411.2921) is longish one describing a broad-based search with several categories of events defined by lepton flavor and charge and other event properties. In all categories the observation confirms the predictions based on standard model processes: the smallest p-value is 0.05.

A completely different search for new physics based on a decades-old concept was posted by CMS (arXiv:1411.2646). We all know that the Fermi theory of weak interactions starts with a so-called *contact interaction* characterized by an interaction vertex with four legs. The Fermi constant serves to parametrize the interaction, and the participation of a vector boson is immaterial when the energy of the interaction is low compared to the boson mass. This framework is the starting point for other effective theories, and has been employed at hadron colliders when searching for deviations in quark-quark interactions, as might be observable if quarks were composite.

The experimental difficulty in studying high-energy quark-quark scattering is that the energies of the outgoing quarks are not so well measured as one might like. (First, the hadronic jets that materialize in the detector do not precisely reflect the quark energies, and second, jet energies cannot be measured better than a few percent.) It pays, therefore, to avoid using energy as an observable and to get the most out of angular variables, which are well measured. Following analyses done at the Tevatron, the authors use a variable χ = exp(|y_{1}-y_{2}|), which is a simple function of the quark scattering angle in the center-of-mass frame. The distribution of events in χ can be unambiguously predicted in the standard model and in any other hypothetical model, and confronted with the data. So we have a nice case for a goodness-of-fit test and pairwise hypothesis testing.

The traditional parametrization of the interaction Lagrangian is:

where the η parameters have values -1, 0, +1 and specify the chirality of the interaction; the key parameter is the mass scale Λ. An important detail is that this interaction Lagrangian can interfere with the standard model piece, and the interference can be either destructive or constructive, depending on the values of the η parameters.

The analysis proceeds exactly as one would expect: events must have at least two jets, and when there are more than two, the two highest-pT jets are used and the others ignored. Distributions of χ are formed for several ranges of di-jet invariant mass, M_{JJ}, which extends as high as 5.2 TeV. The measured χ distributions are unfolded, i.e., the effects of detector resolution are removed from the distribution on a statistical basis. The main sources of systematic uncertainty come from the jet energy scale and resolution and are based on an extensive parametrization of jet uncertainties.

Since one is looking for deviations with respect to the standard model prediction, it is very important to have an accurate prediction. Higher-order terms must be taken into account; these are available at next-to-leading order (NLO). In fact, even electroweak corrections are important and amount to several percent as a strong function of χ — see the plot on the right. The scale uncertainties are a few percent (again showing the a very precise SM prediction is non-trivial event for pp→2J) and fortunately the PDF uncertainties are small, at the percent level. Theoretical uncertainties dominate for M_{JJ} near 2 TeV, while statistical uncertainties dominate for M_{JJ} above 4 TeV.

The money plot is this one:

Optically speaking, the plot is not exciting: the χ distributions are basically flat and deviations due to a mass scale Λ = 10 TeV would be mild. Such deviations are not observed. Notice, though, that the electroweak corrections do improve the agreement with the data in the lowest χ bins. Loosely speaking, this improvement corresponds to about one standard deviation and therefore would be significant if CMS actually had evidence for new physics in these distributions. As far as limits are concerned, the electroweak corrections are “worth” 0.5 TeV.

The statistical (in)significance of any deviation is quantified by a ratio of log-likelihoods: q = -2ln(L_{SM+NP}/L_{SM}) where SM stands for standard model and NP for new physics (i.e., one of distinct possibilities given in the interaction Lagrangian above). Limits are derived on the mass scale Λ depending on assumed values for the η parameters; they are very nicely summarized in this graph:

The limits for contact interactions are roughly at the 10 TeV scale — well beyond the center-of-mass energy of 8 TeV. I like this way of presenting the limits: you see the expected value (black dashed line) and an envelope of expected statistical fluctuations from this expectation, with the observed value clearly marked as a red line. All limits are slightly more stringent than the expected ones (these are not independent of course).

The authors also considered models of extra spatial dimensions and place limits on the scale of the extra dimensions at the 7 TeV level.

So, absolutely no sign of new physics here. The LHC will turn on in 2015 at a significantly higher center-of-mass energy (13 TeV), and given the ability of this analysis to probe mass scales well above the proton-proton collision energy, a study of the χ distribution will be interesting.

### Looking for milli-charged particles at the LHC

Andrew Haas, Chris Hill, Eder Izaguirre and Itay Yavin posted an interesting and imaginative proposal last week to search for milli-charged particles at ATLAS and CMS (arXiv:1410.6816) and I think it is worth taking a look.

Milli-charged particles can arise in some models with extra gauge bosons. The word “milli-charged” refers to the fact that the electric charge is much less than the charge of the electron. Such small charges do not arise due to some fundamental representation in the gauge theory. Rather, they arise through a (kinetic) mixing of the new gauge boson with the hyper charge field B_{μ}. If e’ is the charge associated with the new gauge boson and κ controls the degree of mixing, then the electric charge of the new particle ψ is ε = κe’ cosθ_{W}/e. The weak charge is smaller by a factor of tanθ_{W}. So the motivation for the search is good and the phenomenology is clear enough, and general.

A pair of hypothetical milli-charged particles would be produced through the Drell-Yan process. There are contributions from both virtual photon and Z exchange; nonetheless, the cross section is small because the charge is small. If the milli-charged particles are light enough, they can also be produced in decays of J/ψ and Υ mesons. The authors provide a plot:

Detecting a milli-charged particle is not easy because the ionization they produce as they pass through matter is much smaller than that of an electron, muon or other standard charged particle. (Recall that the ionization rate is proportional to the square of the charge of the particle.) Consequently, the trail of ions is much sparser and the amount of charge in a ionization cluster is smaller, resulting in a substantially or even dramatically reduced signal from a detector element (such as a silicon strip, proportional wire chamber or scintillator). So they cannot be reliably reconstructed as tracks in an LHC or other general-purpose detector. In fact, some searches have been done treating milli-charged particles as effectively invisible – i.e., as producing a missing energy signature. Such approaches are not effective, however, due to the large background from Z→νν.

A special detector is required and this is the crux of the Haas, Hill, Izaguirre and Yavin proposal.

This special detector must have an unusually low threshold for ionization signals. In fact, normal particles will produce relatively large signals that help reject them. Clearly, the sensitivity to very small milli-charges, ε, is determined by how low the noise level in the detector is. The main problem is that normal particles will swamp and bury any signal from milli-charged particles that may be present. One needs to somehow shield the detector from normal particles so that one can look for small-amplitude signals from milli-charged particles.

Fortunately, the main challenge of detecting milli-charged particles turns out to be a virtue: normal particles will eventually be absorbed by bulk matter – this is the principle behind the calorimeter, after all. Milli-charged particles, however, lose their energy through ionization at a much slower rate and will pass through the calorimeters with little attenuation. This is the principle of the beam-dump experiment: look for particle that are *not* absorbed the way the known particles are. (Implicitly we assume that the milli-charged particles have no strong interactions.)

The authors propose to install a carefully-crafted scintillator detector behind a thick wall in the CMS and/or ATLAS caverns. Typically, electronic readout devices for the normal detector are housed in a shielded room not far from the detector. This new scintillator detector would be installed inside this so-called counting room.

The scintillator detector is not ordinary. It must be sensitive to rather small ionization signals which means the amplification must be large and the noise rate low. In order to fight spurious signals, the detector is divided into three parts along the flight path of the milli-charged particle and a coincidence of the three is required. In order to fight backgrounds from ordinary particles produced in the pp collisions, the detector is segmented, with each segment subtending only a very small solid angle: essentially each segment (which consists of three longitudinal pieces) forms a telescope that points narrowly at the interaction point, i.e., the origin of the milli-charged particles. Even with many such segments (“bars”), the total solid angle is miniscule so only a very small fraction of the signal would be detected – we say that the acceptance is very small. Sensitivity to the production of milli-charged particles is possible because the luminosity of the LHC will be high. Basically, the product of the cross section, the acceptance and the luminosity is a few even though the acceptance is so small. The authors estimated the reach of their experiment and produced this figure:

It is worth pointing out that this detector runs parasitically – it will not be providing triggers to the ATLAS or CMS detectors. Its time resolution should be good, about 10 ns, so it might be possible to correlate a signal from a milli-charged particle with a particular bunch crossing, but this is not really needed.

The upcoming run will be an exciting time to try this search. Evidence for milli-charged particles would be a huge discovery, of course. I do not know the status of this proposal vis-a-vis CERN and the LHC experiments. But if a signal were observed, it would clearly be easy to enhance it by building more detector. My opinion is that this is a good idea, and I hope others will agree.