Transverse masses and kinematic constraints: from the boundary to the crease

We re-examine the kinematic variable m_T2 and its relatives in the light of recent work by Cheng and Han. Their proof that m_T2 admits an equivalent, but implicit, definition as the `boundary of the region of parent and daughter masses that is kinematically consistent with the event hypothesis' is far-reaching in its consequences. We generalize their result both to simpler cases (m_T, the transverse mass) and to more complex cases (m_TGen). We further note that it is possible to re-cast many existing and unpleasant proofs (e.g. those relating to the existence or properties of "kink" and "crease" structures in m_T2) into almost trivial forms by using the alternative definition. Not only does this allow us to gain better understanding of those existing results, but it also allows us to write down new (and more or less explicit) definitions of (a) the variable that naturally generalizes m_T2 to the case in which the parent or daughter particles are not identical, and (b) the inverses of m_T and m_T2 -- which may be useful if daughter masses are known and bounds on parent masses are required. We note the implications that these results may have for future matrix-element likelihood techniques

Weighing wimps with kinks at colliders: invisible particle mass measurements from endpoints

We consider the application of endpoint techniques to the problem of mass determination for new particles produced at a hadron collider, where these particles decay to an invisible particle of unknown mass and one or more visible particles of known mass. We also consider decays of these types for pair-produced particles and in each case consider situations both with and without initial state radiation. We prove that, in most (but not all) cases, the endpoint of an appropriate transverse mass observable, considered as a function of the unknown mass of the invisible particle, has a kink at the true value of the invisible particle mass. The co-ordinates of the kink yield the masses of the decaying particle and the invisible particle. We discuss the prospects for implementing this method at the LHC

The Case for Future Hadron Colliders From B→K(∗)μ+μ−B \to K^{(*)} \mu^+ \mu^- Decays

Recent measurements in $B \to K^{(*)} \mu^+ \mu^-$ decays are somewhat discrepant with Standard Model predictions. They may be harbingers of new physics at an energy scale potentially accessible to direct discovery. We estimate the sensitivity of future hadron colliders to the possible new particles that may be responsible for the anomalies: leptoquarks or $Z^\prime$s. We consider luminosity upgrades for a 14 TeV LHC, a 33 TeV LHC, and a 100 TeV $pp$ collider such as the FCC-hh. Coverage of $Z^\prime$ models is excellent: for narrow particles, with perturbative couplings that may explain the $b$-decay results for $Z^\prime$ masses up to 20 TeV, a 33 TeV 1 ab$^{-1}$ LHC is expected to cover most of the parameter space up to 8 TeV in mass, whereas the 100 TeV FCC-hh with 10 ab$^{-1}$ will cover all of it. A smaller portion of the leptoquark parameter space is covered by future colliders: for example, in a $\mu^+\mu^-jj$ di-leptoquark search, a 100 TeV 10 ab$^{-1}$ collider has a projected sensitivity up to leptoquark masses of 12 TeV (extendable to 21 TeV with a strong coupling for single leptoquark production), whereas leptoquark masses up to 41 TeV may in principle explain the anomalies.Comment: 24 pages, 10 figures. v2: Improved discussion and references added, version submitted to JHE

Gluon Correlators in the Kogan-Kovner Model

The Lorentz-invariant gluon correlation functions, corresponding to scalar and pseudo-scalar glueballs, are calculated for Kogan's and Kovner's variational ansatz for the pure SU(N) Yang-Mills wavefunctional. One expects that only one dynamical mass scale should be present in QCD; the ansatz generates the expected scale for both glueballs, as well as an additional scale for the scalar glueball. The additional mass scale must therefore vanish, or be close to the expected one. This is shown to constrain the nature of the phase transition in the Kogan-Kovner ansatz.Comment: 9 pages, no figure

Polynomials, Riemann surfaces, and reconstructing missing-energy events

We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.Comment: 28 pages, 6 figures; version accepted for publication, with discussion of Higgs to tau tau deca

Anatomy of the ATLAS diboson anomaly

We perform a general analysis of new physics interpretations of the recent ATLAS diboson excesses over Standard Model expectations in LHC Run I collisions. Firstly, we estimate a likelihood function for the true signal in the $WW$, $WZ$, and $ZZ$ channels, finding that the maximum has zero events in the $WZ$ channel, though the likelihood is sufficiently flat to allow other scenarios. Secondly, we survey the possible effective field theories containing the Standard Model plus a new resonance that could explain the data, finding just two possibilities, viz., a vector that is either a left- or right-handed $SU(2)$ triplet. Finally, we compare these models with other experimental data and determine the parameter regions in which they provide a consistent explanation.This work has been partially supported by STFC grant ST/L000385/1. We thank M. Redi, J. Tattersall, J. Thaler, A. Wulzer and members of the Cambridge SUSY Working Group for discussions. BG acknowledges MIAPP and King's College, Cambridge. DS acknowledges the support of Emmanuel College, Cambridge.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.92.05500