Matthew D. Schwartz

Effective field theory for massive gravitons and gravity in theory space

Abstract We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan–Coleman–Wess–Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M Pl and a mass m g , we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m g . Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz–Pauli form of the Lagrangian, the presence or absence of the van Dam–Veltman–Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz–Pauli term are easily determined. The cutoff scales as Λ ∼( m g 4 M Pl ) 1/5 for the Fierz–Pauli theory, but can be raised to Λ ∼( m g 2 M Pl ) 1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.

Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks

In this paper, we review recent theoretical progress and the latest experimental results in jet substructure from the Tevatron and the LHC. We review the status of and outlook for calculation and simulation tools for studying jet substructure. Following up on the report of the Boost 2010 workshop, we present a new set of benchmark comparisons of substructure techniques, focusing on the set of variables and grooming methods that are collectively known as ‘top taggers’. To facilitate further exploration, we have attempted to collect, harmonize and publish software implementations of these techniques.

Boosted objects and jet substructure at the LHC: Report of BOOST2012, held at IFIC Valencia, 23rd-27th of July 2012

This report of the BOOST2012 workshop presents the results of four working groups that studied key aspects of jet substructure. We discuss the potential of first-principle QCD calculations to yield a precise description of the substructure of jets and study the accuracy of state-of-the-art Monte Carlo tools. Limitations of the experiments’ ability to resolve substructure are evaluated, with a focus on the impact of additional (pile-up) proton proton collisions on jet substructure performance in future LHC operating scenarios. A final section summarizes the lessons learnt from jet substructure analyses in searches for new physics in the production of boosted top quarks.

Unification and hierarchy from 5D anti-de Sitter space.

In AdS5, the coupling for bulk gauge bosons runs logarithmically, not as a power law. For this reason, one can preserve perturbative unification of couplings. Depending on the cutoff, this can occur at a high scale. We discuss subtleties in the calculation and present a regularization scheme motivated by the holographic correspondence. We find that generically, as in the standard model, the couplings almost unify. For specific choices of the cutoff and number of scalar multiplets, there is good agreement between the measured couplings and the assumption of high scale unification.

Quark and Gluon Tagging at the LHC

Being able to distinguish light-quark jets from gluon jets on an event-by-event basis could significantly enhance the reach for many new physics searches at the Large Hadron Collider. Through an exhaustive search of existing and novel jet substructure observables, we find that a multivariate approach can filter out over 95% of the gluon jets while keeping more than half of the light-quark jets. Moreover, a combination of two simple variables, the charge track multiplicity and the p(T)-weighted linear radial moment (girth), can achieve similar results. Our study is only Monte Carlo based, so other observables constructed using different jet sizes and parameters are used to highlight areas that deserve further theoretical and experimental scrutiny. Additional information, including distributions of around 10,000 variables, can be found at http://jets.physics.harvard.edu/qvg/.

Resummation and NLO Matching of Event Shapes with Effective Field Theory

The resummed differential thrust rate in e{sup +}e{sup -} annihilation is calculated using soft-collinear effective theory (SCET). The resulting distribution in the two-jet region (T{approx}1) is found to agree with the corresponding expression derived by the standard approach. A matching procedure to account for finite corrections at T<1 is then described. There are two important advantages of the SCET approach. First, SCET manifests a dynamical seesaw scale q=p{sup 2}/Q in addition to the center-of-mass energy Q and the jet mass scale p{approx}Q{radical}((1-T)). Thus, the resummation of logs of p/q can be cleanly distinguished from the resummation of logs of Q/p. Second, finite parts of loop amplitudes appear in specific places in the perturbative distribution: in the matching to the hard function, at the scale Q, in matching to the jet function, at the scale p, and in matching to the soft function, at the scale q. This allows for a consistent merger of fixed order corrections and resummation. In particular, the total NLO e{sup +}e{sup -} cross section is reproduced from these finite parts without having to perform additional infrared regulation.

Resummation of heavy jet mass and comparison to LEP data

The heavy jet mass distribution in e+e− collisions is computed to next-to-nextto-next-to leading logarithmic (N3LL) and next-to-next-to leading fixed order accuracy (NNLO). The singular terms predicted from the resummed distribution are confirmed by the fixed order distributions allowing a precise extraction of the unknown soft function coefficients. A number of quantitative and qualitative comparisons of heavy jet mass and the related thrust distribution are made. From fitting to ALEPH data, a value of αs is extracted, αs(mZ) = 0.1220 ± 0.0031, which is larger than, but not in conflict with, the corresponding value for thrust. A weighted average of the two produces αs(mZ) = 0.1193 ± 0.0027, consistent with the world average. A study of the non-perturbative corrections shows that the flat direction observed for thrust between αs and a simple non-perturbative shape parameter is not lifted in combining with heavy jet mass. The Monte Carlo treatment of hadronization gives qualitatively different results for thrust and heavy jet mass, and we conclude that it cannot be trusted to add power corrections to the event shape distributions at this accuracy. Whether a more sophisticated effective field theory approach to power corrections can reconcile the thrust and heavy jet mass distributions remains an open question.

Direct photon production with effective field theory

The production of hard photons in hadronic collisions is studied using Soft-Collinear Effective Theory (SCET). This is the first application of SCET to a physical, observable cross section involving energetic partons in more than two directions. A factorization formula is derived which involves a non-trivial interplay of the angular dependence in the hard and soft functions, both quark and gluon jet functions, and multiple partonic channels. The relevant hard, jet and soft functions are computed to one loop and their anomalous dimensions are determined to three loops. The final resummed inclusive direct photon distribution is valid to next-to-next-to-leading logarithmic order (NNLL), one order beyond previous work. The result is improved by including non-logarithmic terms and photon isolation cuts through matching, and compared to Tevatron data and to fixed order results at the Tevatron and the LHC. The resummed cross section has a significantly smaller theoretical uncertainty than the next-to-leading fixed-order result, particularly at high transverse momentum.

Constructing gravitational dimensions

It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. In fact, any model with only nearest neighbor interactions is doomed. If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass

The Two-loop Hemisphere Soft Function

{m}_{g},