Delays in Open String Field Theory

We study the dynamics of light-like tachyon condensation in a linear dilaton background using level-truncated open string field theory. The equations of motion are found to be delay differential equations. This observation allows us to employ well-established mathematical methods that we briefly review. At level zero, the equation of motion is of the so-called retarded type and a solution can be found very efficiently, even in the far light-cone future. At levels higher than zero however, the equations are not of the retarded type. We show that this implies the existence of exponentially growing modes in the non-perturbative vacuum, possibly rendering light-like rolling unstable. However, a brute force calculation using exponential series suggests that for the particular initial condition of the tachyon sitting in the false vacuum in the infinite light-cone past, the rolling is unaffected by the unstable modes and still converges to the non-perturbative vacuum, in agreement with the solution of Hellerman and Schnabl. Finally, we show that the growing modes introduce non-locality mixing present with future, and we are led to conjecture that in the infinite level limit, the non-locality in a light-like linear dilaton background is a discrete version of the smearing non-locality found in covariant open string field theory in flat space.Comment: 48 pages, 14 figures. v2: References added; Section 4 augmented by a discussion of the diffusion equation; discussion of growing modes in Section 4 slightly expande

Is the bump significant? An axion-search example

Many experiments in physics involve searching for a localized excess over background expectations in an observed spectrum. If the background is known and there is Gaussian noise, the amount of excess of successive observations can be quantified by the runs statistic taking care of the look-elsewhere effect. The distribution of the runs statistic under the background model is known analytically but the computation becomes too expensive for more than about a hundred observations. This work demonstrates a principled high-precision extrapolation from a few dozen up to millions of data points. It is most precise in the interesting regime when an excess is present. The method is verified for benchmark cases and successfully applied to real data from an axion search. The code that implements our method is available at https://github.com/fredRos/runs .Comment: 18 pages, 8 figures. v2 fixes arxiv's parsing of the URL in the abstrac

Extracting Angular Observables without a Likelihood and Applications to Rare Decays

Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events. Instead, we apply the method of moments that relies both on the orthogonality of angular functions and the estimation of integrals by Monte Carlo techniques. The big advantage of this method is that the joint distribution of all observables can be easily extracted, even for very few events. The method of moments is shown to be robust against mismodeling of the angular distribution. Our main result is an explicit algorithm that accounts for systematic uncertainties from detector-resolution and acceptance effects. Finally, we present the necessary process-dependent formulae needed for direct application of the method to several rare decays of interest.Comment: 13 pages, 4 figure

Erratum to: Comprehensive Bayesian analysis of rare (semi)leptonic and radiative B decays

The available data on |∆B| = |∆S| = 1 decays are in good agreement with the Standard Model when permitting subleading power corrections of about 15% at large hadronic recoil. Constraining new-physics effects in C7, C9, C10, the data still demand the same size of power corrections as in the Standard Model. In the presence of chirality-flipped operators, all but one of the power corrections reduce substantially. The Bayes factors are in favor of the Standard Model. Using new lattice inputs for B → K* form factors and under our minimal prior assumption for the power corrections, the favor shifts toward models with chirality-flipped operators. We use the data to further constrain the hadronic form factors in B → K and B → K* transitions

A Test Statistic for Weighted Runs

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the ordering of observations and provides additional sensitivity to local deviations from expectations. The exact distribution of the statistic in the non-parametric case is derived and an algorithm to compute $p$-values is presented. The computational complexity of the algorithm is derived employing a novel identity for integer partitions.Comment: 20 pages, 4 figures. Match published paper as close as possibl

Bayesian Fit of Exclusive b→sℓˉℓb \to s \bar\ell\ell Decays: The Standard Model Operator Basis

We perform a model-independent fit of the short-distance couplings $C_{7,9,10}$ within the Standard Model set of $b\to s\gamma$ and $b\to s\bar\ell\ell$ operators. Our analysis of $B \to K^* \gamma$, $B \to K^{(*)} \bar\ell\ell$ and $B_s \to \bar\mu\mu$ decays is the first to harness the full power of the Bayesian approach: all major sources of theory uncertainty explicitly enter as nuisance parameters. Exploiting the latest measurements, the fit reveals a flipped-sign solution in addition to a Standard-Model-like solution for the couplings $C_i$. Each solution contains about half of the posterior probability, and both have nearly equal goodness of fit. The Standard Model prediction is close to the best-fit point. No New Physics contributions are necessary to describe the current data. Benefitting from the improved posterior knowledge of the nuisance parameters, we predict ranges for currently unmeasured, optimized observables in the angular distributions of $B\to K^*(\to K\pi)\,\bar\ell\ell$.Comment: 42 pages, 8 figures; v2: Using new lattice input for f_Bs, considering Bs-mixing effects in BR[B_s->ll]. Main results and conclusion unchanged, matches journal versio

Computing in High Energy and Nuclear Physics (CHEP) 2012

The Bayesian Analysis Toolkit (BAT) is a C++ library designed to analyze data through the application of Bayes' theorem. For parameter inference, it is necessary to draw samples from the posterior distribution within the given statistical model. At its core, BAT uses an adaptive Markov Chain Monte Carlo (MCMC) algorithm. As an example of a challenging task, we consider the analysis of rare B-decays in a global fit involving about 20 observables measured at the B-factories and by the CDF and LHCb collaborations. A single evaluation of the likelihood requires approximately 1 s. In addition to the 3 -- 12 parameters of interest, there are on the order of 25 nuisance parameters describing uncertainties from standard model parameters as well as from unknown higher order theory corrections and non-perturbative QCD effects. The resulting posterior distribution is multi-modal and shows significant correlation between parameters as well as pronounced degeneracies, hence the standard MCMC methods fail to produce accurate results. Parallelization is the only solution to obtain a sufficient number of samples in reasonable time. We present an enhancement of existing MCMC algorithms, including the ability for massive parallelization on a computing cluster and, more importantly, a general scheme to induce rapid convergence even in the face complicated posterior distributions