119159946
Inflating with Large Effective Fields
We re-examine large scalar fields within effective field theory, in particular focussing on the issues raised by their use in inflationary models (as suggested by BICEP2 to obtain primordial tensor modes). We argue that when the large-field and low-energy regimes coincide the scalar dynamics is most effectively described in terms of an asymptotic large-field expansion whose form can be dictated by approximate symmetries, which also help control the size of quantum corrections. We discuss several possible symmetries that can achieve this, including pseudo-Goldstone inflatons characterized by a coset G/H (based on abelian and non-abelian, compact and non-compact symmetries), as well as symmetries that are intrinsically higher dimensional. Besides the usual trigonometric potentials of Natural Inflation we also find in this way simple large-field power laws (like V ∝ φ{sup 2}) and exponential potentials, V(φ) = ∑{sub k}V{sub x}e{sup −kφ/M}. Both of these can describe the data well and give slow-roll inflation for large fields without the need for a precise balancing of terms in the potential. The exponential potentials achieve large r through the limit |η| || e and so predict r ≅ (8/3)(1-n{sub s}); consequently n{sub s} ≅ 0.96 gives r ≅ 0.11 but not much larger (and so could be ruled out as measurements on r and n{sub s} improve).more » We examine the naturalness issues for these models and give simple examples where symmetries protect these forms, using both pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries following familiar techniques from chiral perturbation theory) and extra-dimensional models.« less
118724352
Gravitational forces on a codimension-2 brane
A bstractWe compute the gravitational response of six dimensional gauged, chiral supergravity to localized stress energy on one of two space-filling branes, including the effects of compactifying the extra dimensions and brane back-reaction. We find a broad class of exact solutions, including various black-brane solutions. Several approximate solutions are also described, such as the near-horizon geometry of a small black hole which is argued to be approximately described by a 6D Schwarzschild (or Kerr) black hole, with event horizon appropriately modified to encode the brane back-reaction. The general linearized far-field solutions are found in the 4D regime very far from the source, and all integration constants are related to physical quantities describing the branes and the localized energy source. The localized source determines two of these, corresponding to the source mass and the size of the strength of a coupling to a 4D scalar mode whose mass is parametrically smaller than the KK scale. At large distances the solutions agree with those of 4D general relativity, but for an intermediate range of distances (larger than the KK scale) the solutions better fit a Brans-Dicke theory. For a realistic choice of parameters the KK scale could lie at a micron, while the crossover to Brans-Dicke behaviour could occur at around 10 microns. While allowed by present data this points to potentially measurable changes to Newton’s Law arising at distances larger than the KK scale.
53692432
Distributed SUSY breaking: dark energy, Newton’s law and the LHC
A bstractWe identify the underlying symmetry mechanism that suppresses the low-energy effective 4D cosmological constant within some 6D supergravity models, generically leading to results suppressed by powers of the KK scale, mK K2, relative to the much larger size, m4, associated with mass-m particles localized in these models on codimension-2 branes. These models are examples for which the local conditions for unbroken supersymmetry can be satisfied locally everywhere within the extra dimensions, but are obstructed only by global conditions like flux quantization or by the mutual inconsistency of the boundary conditions required at the various branes. Consequently quantities (like vacuum energies) forbidden by supersymmetry cannot become nonzero until wavelengths of order the KK scale are integrated out, since only such long wavelength modes can see the entire space and so ‘know’ that supersymmetry has broken. We verify these arguments by extending earlier rugby-ball calculations of one-loop vacuum energies within these models to more general pairs of branes within two warped extra dimensions. For the Standard Model confined to one of two otherwise identical branes, the predicted effective 4D vacuum energy density is of order ρvac ⋍ C(mMg/4πMp)4 = C(5.6 × 10−5 eV)4, where Mg ≳ 10 TeV (corresponding to extra-dimensional size r ≲ 1 μm) and Mp = 2.44 × 1018 GeV are the 6D and 4D rationalized Planck scales, and m is the heaviest brane-localized particle. (For numerical purposes we take m to be the top-quark mass and take Mg as small as possible, consistent with energy-loss bounds from supernovae.) C is a constant depending on the details of the bulk spectrum, which could easily be of order 500 for each of hundreds of fields in the bulk. The value C ∼ 6 × 106 would give the observed Dark Energy density.
3581209
EFT beyond the horizon: stochastic inflation and how primordial quantum fluctuations go classical
A bstractWe identify the effective field theory describing the physics of super-Hubble scales and show it to be a special case of a class of effective field theories appropriate to open systems. Open systems are those that allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as would be appropriate for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate ‘low-energy’ limit is instead a Lindblad equation describing the time-evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in de Sitter (and near-de Sitter) spacetimes and derive two of its implications. We show that the evolution of the diagonal density-matrix elements quickly approach the Fokker-Planck equation of Starobinsky’s stochastic inflationary picture. This allows us both to identify the leading corrections and provide an alternative first-principles derivation of this picture’s stochastic noise and drift. (As applications we show that the noise for massless fields is independent of the details of the window function used, and also compute how the noise changes for systems with a sub-luminal speed of sound, cs< 1.) We then argue that the presence of interactions drive the off-diagonal density-matrix elements to zero in the field
118339212
Technically natural vacuum energy at the tip of a supersymmetric teardrop
A minimal supersymmetric brane-world model is presented which has: i) zero classical four-dimensional vacuum curvature, despite the large naive vacuum energy due to contributions from Standard Model particles; ii) one-(bulk)-loop quantum corrections to the vacuum energy with a size set by the radius of the extra-dimensional spheroid. These corrections are technically natural because a BPS-like relation between the brane tension and R-charge---which would have preserved (half of) the bulk supersymmetry---is violated by the requirement that the stabilizing R-symmetry gauge flux be quantized. The extra-dimensional geometry is similar to previous rugby-ball geometries, but is simpler in that there is only one brane and so fewer free parameters. Although the sign of the renormalized vacuum energy ends up being the unphysical one for this model (in the limit considered here, where the massive bulk loop is the leading contribution), it serves as an illustrative example of the relevant physics.
53667729
Accidental SUSY: enhanced bulk supersymmetry from brane back-reaction
A bstractWe compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane- localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.
10836022
Numerical object oriented quantum field theory calculations
The qft++ package is a library of C++ classes that facilitate numerical (not algebraic) quantum field theory calculations. Mathematical objects such as matrices, tensors, Dirac spinors, polarization and orbital angular momentum tensors, etc. are represented as C++ objects in qft++. The package permits construction of code which closely resembles quantum field theory expressions, allowing for quick and reliable calculations.
209834699
Analysis of the resonant components in B¯º → J/ ψπ+π-
Interpretation of CP violation measurements using charmonium decays, in both the B¯o and B¯os systems, can be subject to changes due to "penguin" type diagrams. These effects can be investigated using measurements of the Cabibbo-suppressed B¯o → J/ ψπ+π- decays. The final state composition of this channel is investigated using a 1.0 fb(-1) sample of data produced in 7 TeV pp collisions at the LHC and collected by the LHCb experiment. A modified Dalitz-plot analysis is performed using both the invariant mass spectra and the decay angular distributions. An improved measurement of the B¯o → J/ ψπ+π- branching fraction of (3.97 ± 0.09 ± 0.11 ± 0.16) x 10(-5) is reported where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty of the branching fraction of the decay B¯ → J/ ψ K¯ used as a normalization channel. Significant production of fₒ(500) and ρ(770) resonances is found in the substructure of the J/ ψπ+π- final state, and this indicates that they are viable final states for CP violation studies. In contrast evidence for the fₒ(980) resonance is not found. This allows us to establish the first upper limit on the branching fraction product Β(B¯o → J/ ψfₒ (980)) x Β(fₒ(980) → π+π- < 1.1 x 10(-6), leading to an upper limit on the absolute value of the mixing angle of the fₒ(980) with the fₒ(500) of less than 31°, both at 90% confidence level.
117676442
An Ad-Hoc Method for Obtaining chi**2 Values from Unbinned Maximum Likelihood Fits
A common goal in an experimental physics analysis is to extract information from a reaction with multi-dimensional kinematics. The preferred method for such a task is typically the unbinned maximum likelihood method. In fits using this method, the likelihood is a goodness-of-fit quantity in that it effectively discriminates between available hypotheses; however, it does not provide any information as to how well the best hypothesis describes the data. 
In this paper, we present an {\em ad-hoc} procedure for obtaining chi**2/n.d.f. values from unbinned maximum likelihood fits. This method does not require binning the data, making it very applicable to multi-dimensional problems.
17491315
Multivariate side-band subtraction using probabilistic event weights
A common situation in experimental physics is to have a signal which can not be separated from a non-interfering background through the use of any selection criteria. In this paper, we describe a procedure for determining, on an event-by-event basis, a quality factor (Q-factor) that a given signal candidate originated from the signal sample. This procedure generalizes the ``side-band'' subtraction method to higher dimensions without requiring the data to be divided into bins. The Q-factors can then be used as event weights in subsequent analysis procedures, allowing one to more directly access the true spectrum of the signal.
118294173
A measurement of the inclusive branching ratio for $b o sgamma$ with the ALEPH detector at LEP