Rare b and c Decays and the CKM Matrix

I report on developments in the experimental and phenomenological understanding of the rare decays of mesons containing b and c quarks, especially as they pertain to the understanding of the CKM matrix and the testing of the standard model. Some related measurements are also discussed.Comment: Talk given at "Physics in Collision," Cracow, June 10, 1995. 16 pages of self extracting, compressed, encoded postscrip

Unsafe but Calculable: Ratios of Angularities in Perturbative QCD

Infrared- and collinear-safe (IRC-safe) observables have finite cross sections to each fixed-order in perturbative QCD. Generically, ratios of IRC-safe observables are themselves not IRC safe and do not have a valid fixed-order expansion. Nevertheless, in this paper we present an explicit method to calculate the cross section for a ratio observable in perturbative QCD with the help of resummation. We take the IRC-safe jet angularities as an example and consider the ratio formed from two angularities with different angular exponents. While the ratio observable is not IRC safe, it is "Sudakov safe", meaning that the perturbative Sudakov factor exponentially suppresses the singular region of phase space. At leading logarithmic (LL) order, the distribution is finite but has a peculiar expansion in the square root of the strong coupling constant, a consequence of IRC unsafety. The accuracy of the LL distribution can be further improved with higher-order resummation and fixed-order matching. Non-perturbative effects can sometimes give rise to order one changes in the distribution, but at sufficiently high energies Q, Sudakov safety leads to non-perturbative corrections that scale like a (fractional) power of 1/Q, as is familiar for IRC-safe observables. We demonstrate that Monte Carlo parton showers give reliable predictions for the ratio observable, and we discuss the prospects for computing other ratio observables using our method.Comment: 41 pages, 14 figures, 1 table, small changes in v.

Aspects of Jets at 100 TeV

We present three case studies at a 100 TeV proton collider for how jet analyses can be improved using new jet (sub)structure techniques. First, we use the winner-take-all recombination scheme to define a recoil-free jet axis that is robust against pileup. Second, we show that soft drop declustering is an effective jet grooming procedure that respects the approximate scale invariance of QCD. Finally, we highlight a potential standard candle for jet calibration using the soft-dropped energy loss. This latter observable is remarkably insensitive to the scale and flavor of the jet, a feature that arises because it is infrared/collinear unsafe, but Sudakov safe.Comment: 9 pages, double column, 7 figures, based on a talk by A.L. at the "Workshop on Physics at a 100 TeV Collider" at SLAC from April 23-25, 2014; v.2: PRD versio

Gaining (Mutual) Information about Quark/Gluon Discrimination

Discriminating quark jets from gluon jets is an important but challenging problem in jet substructure. In this paper, we use the concept of mutual information to illuminate the physics of quark/gluon tagging. Ideal quark/gluon separation requires only one bit of truth information, so even if two discriminant variables are largely uncorrelated, they can still share the same "truth overlap". Mutual information can be used to diagnose such situations, and thus determine which discriminant variables are redundant and which can be combined to improve performance. Using both parton showers and analytic resummation, we study a two-parameter family of generalized angularities, which includes familiar infrared and collinear (IRC) safe observables like thrust and broadening, as well as IRC unsafe variants like $p_T^D$ and hadron multiplicity. At leading-logarithmic (LL) order, the bulk of these variables exhibit Casimir scaling, such that their truth overlap is a universal function of the color factor ratio $C_A/C_F$. Only at next-to-leading-logarithmic (NLL) order can one see a difference in quark/gluon performance. For the IRC safe angularities, we show that the quark/gluon performance can be improved by combining angularities with complementary angular exponents. Interestingly, LL order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations between observables, but there are significant differences in the predicted quark/gluon discrimination power. For the IRC unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative "weighted-energy function", providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination.Comment: 30+26 pages, 21 figures; v2: fixed binning artifact for some figures in appendix D; v3: JHEP version, clarified quark/gluon definition, added appendix A.2 proving better observables have higher truth overla

Sudakov Safety in Perturbative QCD

Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling $\alpha_s$. Observables that are calculable in this way are known as "safe". Recently, a class of unsafe observables was discovered that do not have a valid $\alpha_s$ expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each $\alpha_s$ order are regulated by an all-orders Sudakov form factor. In this letter, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of $\alpha_s$.Comment: 4+5 pages, 4 figures, 1 table. Version accepted for publication in PR

GenEvA (I): A new framework for event generation

We show how many contemporary issues in event generation can be recast in terms of partonic calculations with a matching scale. This framework is called GenEvA, and a key ingredient is a new notion of phase space which avoids the problem of phase space double-counting by construction and includes a built-in definition of a matching scale. This matching scale can be used to smoothly merge any partonic calculation with a parton shower. The best partonic calculation for a given region of phase space can be determined through physics considerations alone, independent of the algorithmic details of the merging. As an explicit example, we construct a positive-weight partonic calculation for e+e- -> n jets at next-to-leading order (NLO) with leading-logarithmic (LL) resummation. We improve on the NLO/LL result by adding additional higher-multiplicity tree-level (LO) calculations to obtain a merged NLO/LO/LL result. These results are implemented using a new phase space generator introduced in a companion paper [arXiv:0801.4028].Comment: 60 pages, 22 figures, v2: corrected typos, added reference

Energy Correlation Functions for Jet Substructure

We show how generalized energy correlation functions can be used as a powerful probe of jet substructure. These correlation functions are based on the energies and pair-wise angles of particles within a jet, with (N+1)-point correlators sensitive to N-prong substructure. Unlike many previous jet substructure methods, these correlation functions do not require the explicit identification of subjet regions. In addition, the correlation functions are better probes of certain soft and collinear features that are masked by other methods. We present three Monte Carlo case studies to illustrate the utility of these observables: 2-point correlators for quark/gluon discrimination, 3-point correlators for boosted W/Z/Higgs boson identification, and 4-point correlators for boosted top quark identification. For quark/gluon discrimination, the 2-point correlator is particularly powerful, as can be understood via a next-to-leading logarithmic calculation. For boosted 2-prong resonances the benefit depends on the mass of the resonance.Comment: 45 pages, 28 figures, update to JHEP version, some minor typos fixed, added discussion at end of section

GenEvA (II): A phase space generator from a reweighted parton shower

We introduce a new efficient algorithm for phase space generation. A parton shower is used to distribute events across all of multiplicity, flavor, and phase space, and these events can then be reweighted to any desired analytic distribution. To verify this method, we reproduce the e+e- -> n jets tree-level result of traditional matrix element tools. We also show how to improve tree-level matrix elements automatically with leading-logarithmic resummation. This algorithm is particularly useful in the context of a new framework for event generation called GenEvA. In a companion paper [arXiv:0801.4026], we show how the GenEvA framework can address contemporary issues in event generation.Comment: 54 pages, 20 figures, v2: corrected typos, added reference

Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969

Algebraic methods for analysis and design of control system

Casimir Meets Poisson: Improved Quark/Gluon Discrimination with Counting Observables

Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a "soft drop multiplicity" which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.Comment: 38+10 pages, 21 figures; v2: discussions added to match JHEP versio