Jet shapes have been measured in inclusive jet production in proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ using $3{\mathrm{pb}}^{-1}$ of data recorded by the ATLAS experiment at the LHC. Jets are reconstructed using the anti-$k_t$ algorithm with transverse momentum $30\mathrm{GeV}<p_T<600\mathrm{GeV}$ and rapidity in the region $|y|<2.8$. The data are corrected for detector effects and compared to several leading-order QCD matrix elements plus parton shower Monte Carlo predictions, including different sets of parameters tuned to model fragmentation processes and underlying event contributions in the final state. The measured jets become narrower with increasing jet transverse momentum and the jet shapes present a moderate jet rapidity dependence. Within QCD, the data test a variety of perturbative and nonperturbative effects. In particular, the data show sensitivity to the details of the parton shower, fragmentation, and underlying event models in the Monte Carlo generators. For an appropriate choice of the parameters used in these models, the data are well described.

We present measurements of the branching fractions, longitudinal polarization, and direct $CP$-violation asymmetries for the decays $B^{+}\to {\rho }^0{K}^{*+}$ and $B^{+}\to f_0(980)K^{*+}$ with a sample of $(467\pm 5)\times {10}^{6}B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at the SLAC National Accelerator Laboratory. We observe $B^{+}\to {\rho }^0{K}^{*+}$ with a significance of $5.3\sigma$ and measure the branching fraction $\mathcal{B}(B^{+}\to {\rho }^0{K}^{*+})=(4.6\pm 1.0\pm 0.4)\times {10}^{-6}$, the longitudinal polarization $f_L=0.78\pm 0.12\pm 0.03$, and the $CP$-violation asymmetry ${\mathcal{A}}_{CP}=0.31\pm 0.13\pm 0.03$. We observe $B^{+}\to f_0(980)K^{*+}$ and measure the branching fraction $\mathcal{B}(B^{+}\to f_0(980)K^{*+})\times \mathcal{B}(f_0(980)\to {\pi }^{+}{\pi }^{-})=(4.2\pm 0.6\pm 0.3)\times {10}^{-6}$ and the $CP$-violation asymmetry ${\mathcal{A}}_{CP}=-0.15\pm 0.12\pm 0.03$. The first uncertainty quoted is statistical and the second is systematic.

It is known that the ${\gamma }_5$ scheme of Breitenlohner and Maison in dimensional regularization requires finite counterterm renormalization to restore gauge symmetry and implementing this finite renormalization in practical calculation is a daunting task even at 1-loop order. In this paper, we show that there is a simple and straightforward method to obtain these finite counterterms by using the rightmost ${\gamma }_5$ scheme in which we move all the ${\gamma }_5$ matrices to the rightmost position before analytically continuing the dimension. For any 1-loop Feynman diagram, the difference between the amplitude regularized in the rightmost ${\gamma }_5$ scheme and the amplitude regularized in the Breitenlohner and Maison scheme can be easily calculated. The differences for all 1-loop diagrams in the chiral Abelian-Higgs gauge theory and in the chiral non-Abelian gauge theory are shown to be the same as the amplitudes due to the finite counterterms that are required to restore gauge symmetry.

We discuss a deformation of superspace based on a Hermitian twist. The twist implies a $\star$-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.

We generalize here our earlier results on particle acceleration by naked singularities. We showed recently [M. Patil and P. S. Joshi, Phys. Rev. D 82, 104049 (2010).] that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as the final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.

In the standard cosmological model, the dimming of distant Type Ia supernovae is explained by invoking the existence of repulsive “dark energy” which is causing the Hubble expansion to accelerate. However, this may be an artifact of interpreting the data in an (oversimplified) homogeneous model universe. In the simplest inhomogeneous model which fits the SNe Ia Hubble diagram without dark energy, we are located close to the center of a void modeled by a Lemaítre-Tolman-Bondi metric. It has been claimed that such models cannot fit the cosmic microwave background (CMB) and other cosmological data. This is, however, based on the assumption of a scale-free spectrum for the primordial density perturbation. An alternative physically motivated form for the spectrum enables a good fit to both SNe Ia (Constitution/Union2) and CMB (WMAP 7-yr) data, and to the locally measured Hubble parameter. Constraints from baryon acoustic oscillations and primordial nucleosynthesis are also satisfied.

We consider the Einstein equations within the Dirac-Born-Infield (DBI) scenario for a spatially flat Friedmann-Robertson-Walker (FRW) spacetime without a cosmological constant. We derive the inflationary scenario by applying the symmetry transformations which preserve the form of the Friedmann and conservation equations. These form invariance transformations generate a symmetry group parametrized by the Lorentz factor $\gamma$. We explicitly obtain an inflationary scenario by the cooperative effect of adding energy density into the Friedmann equation. For the case of a constant Lorentz factor, and under the slow roll assumption, we find the transformation rules for the scalar and tensor power spectra of perturbations as well as their ratio under the action of the form invariance symmetry group. Within this case and due to its relevance for the inflationary paradigm, we find the general solution of the dynamical equations for a DBI field driven by an exponential potential and show a broad set of inflationary solutions. The general solution can be split into three subsets and all these behave asymptotically as a power-law solution at early and at late times.

The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest $[\mathbf{70},1^{-}]$ multiplet are calculated in the $1/N_c$ expansion to order $1/N_c$ with a new method which allows one to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.

We consider renormalizable standard model extensions that violate Lorentz symmetry at high energies, but preserve $CPT$, and do not contain elementary scalar fields. A Nambu–Jona-Lasinio mechanism gives masses to fermions and gauge bosons and generates composite Higgs fields at low energies. We study the effective potential at the leading order of the large-$N_c$ expansion, prove that there exists a broken phase, and study the phase space. In general, the minimum may break invariance under boosts, rotations, and $CPT$, but we give evidence that there exists a Lorentz invariant phase. We study the spectrum of composite bosons and the low-energy theory in the Lorentz phase. Our approach predicts relations among the parameters of the low-energy theory. We find that such relations are compatible with the experimental data within theoretical errors. We also study the mixing among generations, the emergence of the CKM matrix, and neutrino oscillations.

A canonical signature of the minimal supersymmetric standard model (MSSM) is the presence of a neutral Higgs boson with mass bounded from above by about 135 GeV and standard model (SM)-like couplings to the electroweak gauge bosons. In this paper we investigate the reach of the Tevatron collider for the MSSM Higgs sector parameter space associated with a variety of high-scale minimal models of supersymmetry (SUSY) breaking, including the constrained MSSM, minimal gauge-mediated SUSY breaking, and minimal anomaly-mediated SUSY breaking. We find that the Tevatron can provide strong constraints on these models via Higgs boson searches. Considering a simple projection for the efficiency improvements in the Tevatron analyses, we find that with an integrated luminosity of $16{\mathrm{fb}}^{-1}$ per detector and an efficiency improvement of 20% compared to the present situation, these models could be probed essentially over their entire ranges of validity. With 40% analysis improvements and $16{\mathrm{fb}}^{-1}$, our projection shows that evidence at the $3\sigma$ level for the light Higgs boson could be expected in extended regions of parameter space.

We present a benchmark in the parameter space of the next-to-minimal supersymmetric standard model (NMSSM) that provides for a dramatic multilepton signal and no jets containing 5 or more leptons resulting from the cascade decays of the third lightest neutralino, ${\chi }_3^0$, and the lightest chargino, ${\chi }_1^{\pm }$, via light charged sleptons. This is a very clean signal with almost no standard model (SM) background. In some cases, a total signal of $\ge 3\mathrm{\text{leptons}}+0\mathrm{\text{jets}}$ can be detected at the $5\sigma$ level at the LHC running at $\sqrt{s}=7\mathrm{TeV}$ with approximately $3{\mathrm{fb}}^{-1}$ of data and with less than $1{\mathrm{fb}}^{-1}$ when running at $\sqrt{s}=14\mathrm{TeV}$. In addition, kinematic edges in the invariant mass distributions of 2, 3, and 4 leptons are easily detectable with large integrated luminosities ($\sim 600{\mathrm{fb}}^{-1}$) which can lead to simple measurements of the mass differences of heavy particles in the decay chains, including all combinations of the three lightest neutralinos.

We have analytically solved the LO perturbative QCD singlet DGLAP equations [V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)][G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977)][Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)] using Laplace transform techniques. Newly developed, highly accurate, numerical inverse Laplace transform algorithms [M. M. Block, Eur. Phys. J. C 65, 1 (2010)][M. M. Block, Eur. Phys. J. C 68, 683 (2010)] allow us to write fully decoupled solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ as $F_s(x,Q^2)={\mathcal{F}}_s(F_{s0}(x_0),G_0(x_0))$ and $G(x,Q^2)=\mathcal{G}(F_{s0}(x_0),G_0(x_0))$, where the $x_0$ are the Bjorken $x$ values at $Q_0^2$. Here ${\mathcal{F}}_s$ and $\mathcal{G}$ are known functions—found using LO DGLAP splitting functions—of the initial boundary conditions $F_{s0}(x)\equiv F_s(x,Q_0^2)$ and $G_0(x)\equiv G(x,Q_0^2)$, i.e., the chosen starting functions at the virtuality $Q_0^2$. For both $G(x)$ and $F_s(x)$, we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy—a computational fractional precision of $O({10}^{-9})$. Armed with this powerful new tool in the perturbative QCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet $F_s$ distributions [A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009)], starting from their initial values at $Q_0^2=1{\mathrm{GeV}}^2$ and $1.69{\mathrm{GeV}}^2$, respectively, using their choice of ${\alpha }_s(Q^2)$. This allows an important independent check on the accuracies of their evolution codes and, therefore, the computational accuracies of their published parton distributions. Our method completely decouples the two LO distributions, at the same time guaranteeing that both $G$ and $F_s$ satisfy the singlet coupled DGLAP equations. It also allows one to easily obtain the effects of the starting functions on the evolved gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$, being equally accurate in devolution ($Q^2<Q_0^2$) as in evolution ($Q^2>Q_0^2$). Further, it can also be used for nonsinglet distributions, thus giving LO analytic solutions for individual quark and gluon distributions at a given $x$ and $Q^2$, rather than the numerical solutions of the coupled integral-differential equations on a large, but fixed, two-dimensional grid that are currently available.

In this work we construct the $\pi \pi$ scattering amplitude $T_0^0$ with regular analytical properties in the $s$ complex plane, which describes simultaneously the data on the $\pi \pi$ scattering, $\varphi \to {\pi }^0{\pi }^0\gamma$ decay, and $\pi \pi \to K\overline{K}$ reaction. The chiral shielding of the $\sigma (600)$ meson and its mixing with the $f_0(980)$ meson are also taken into account. The data agrees with the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons. The amplitude in the range $-5m_{\pi }^2<s<0.64{\mathrm{GeV}}^2$ also agrees with results, obtained on the base of the chiral expansion, dispersion relations, and the Roy equations.

We present an analysis on the exclusive rare radiative decay modes ${\Sigma }_b\to \Sigma \gamma$ and ${\Xi }_b\to \Xi \gamma$. The transition form factors which parametrize these processes are calculated using QCD light-cone sum rules. The decay widths we predict are $\Gamma ({\Sigma }_b\to \Sigma \gamma )=(7.21\pm 0.04)\times {10}^{-18}\mathrm{GeV}$ and $\Gamma ({\Xi }_b\to \Xi \gamma )=(1.34\pm 0.07)\times {10}^{-16}\mathrm{GeV}$. The branching ratio of ${\Xi }_b\to \Xi \gamma$ is predicted to be $\mathrm{Br}({\Xi }_b\to \Xi \gamma )=(3.03\pm 0.10)\times {10}^{-4}$.

The forward-backward asymmetry $A_{\mathrm{FB}}$ in top quark pair production, measured at the Tevatron, is probably related to the contribution of new particles. The Tevatron result is more than a $2\sigma$ deviation from the standard model prediction and motivates the application of alternative models introducing new states. However, as the standard model predictions for the total cross section ${\sigma }_{tt}$ and invariant mass distribution $M_{tt}$ for this process are in good agreement with experiments, any alternative model must reproduce these predictions. These models can be placed into two categories: One introduces the $s$-channel exchange of new vector bosons with chiral couplings to the light quarks and to the top quark, and another relies on the $t$-channel exchange of particles with large flavor-violating couplings in the quark sector. In this work, we employ a model which introduces both $s$- and $t$-channel nonstandard contributions for the top quark pair production in proton-antiproton collisions. We use the minimal version of the $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$ model (3-3-1 model) that predicts the existence of a new neutral gauge boson, called $Z^{\prime }$. This gauge boson has both flavor-changing couplings to up and top quarks and chiral coupling to the light quarks and to the top quark. This very peculiar model coupling can correct the $A_{\mathrm{FB}}$ for top quark pair production for two ranges of $Z^{\prime }$ mass while leading to a cross section and invariant mass distribution quite similar to the standard model ones. This result reinforces the role of the 3-3-1 model for any new physics effect.

We explore the sensitivity of flavor-changing $b\to s$ transitions to a (sub-) GeV hidden sector with generic couplings to the standard model through the Higgs, vector, and axion portals. The underlying two-body decays of $B$ mesons, $B\to X_s\mathcal{S}$, and $B^0\to \mathcal{S}\mathcal{S}$, where $\mathcal{S}$ denotes a generic new GeV-scale particle, may significantly enhance the yield of monochromatic lepton pairs in the final state via prompt $\mathcal{S}\to l\overline{l}$ decays. Existing measurements of the charged lepton spectrum in neutral-current semileptonic $B$ decays provide bounds on the parameters of the light sector that are significantly more stringent than the requirements of naturalness. New search modes, such as $B\to X_s+n(l\overline{l})$ and $B^0\to n(l\overline{l})$ with $n\ge 2$, can provide additional sensitivity to scenarios in which both the Higgs and vector portals are active, and are accessible to (super-) $B$ factories and hadron colliders.

This paper reports the Feynman-parametric representation of the vacuum-polarization function consisting of 105 Feynman diagrams of the eighth order, and its contribution to the gauge-invariant set called Set I(i) of the tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set is carried out using FORTRAN codes generated by an automatic code generation system gencodevpN developed specifically for this purpose. The contribution of diagrams containing an electron loop to the electron $g-2$ is $0.01747(11)(\alpha /\pi {)}^5$. The contribution of diagrams containing a muon loop is $0.00000167(3)(\alpha /\pi {)}^5$. The contribution of a tau-lepton loop is negligible at present. The sum of all these terms is $0.01747(11)(\alpha /\pi {)}^5$. The contribution of diagrams containing an electron loop to the muon $g-2$ is $0.0871(59)(\alpha /\pi {)}^5$. This is to be compared with the unpublished asymptotic analytic result $(0.25237+O(m_e/m_{\mu }))(\alpha /\pi {)}^5$. The contribution of a tau-lepton loop to $a_{\mu }$ is $0.000237(1)(\alpha /\pi {)}^5$. The total contribution to $a_{\mu }$, the sum of these terms and the mass-independent term, is $0.1048(59)(\alpha /\pi {)}^5$.

This paper reports the tenth-order contributions to the $g-2$ of the electron $a_e$ and those of the muon $a_{\mu }$ from the gauge-invariant Set II(c), which consists of 36 Feynman diagrams, and Set II(d), which consists of 180 Feynman diagrams. Both sets are obtained by insertion of sixth-order vacuum-polarization diagrams in the fourth-order anomalous magnetic moment. The mass-independent contributions from Set II(c) and Set II(d) are $-0.116489(32)(\alpha /\pi {)}^5$ and $-0.24300(29)(\alpha /\pi {)}^5$, respectively. The leading contributions to $a_{\mu }$, which involve electron loops only, are $-3.88827(90)(\alpha /\pi {)}^5$ and $0.4972(65)(\alpha /\pi {)}^5$ for Set II(c) and Set II(d), respectively. The total contributions of the electron, muon, and tau-lepton loops to $a_e$ are $-0.116874(32)(\alpha /\pi {)}^5$ for the Set II(c), and $-0.24310(29)(\alpha /\pi {)}^5$ for the Set II(d), respectively. The contributions of the electron, muon, and tau-lepton loop to $a_{\mu }$ are $-5.5594(11)(\alpha /\pi {)}^5$ for the Set II(c) and $0.2465(65)(\alpha /\pi {)}^5$ for the Set II(d), respectively.

We submit recent claims of hints of primordial tensor perturbations and a scale-dependent spectral index in the WMAP data to a closer scrutiny. Our approach differs in that we use different best-fit values at which to fix the parameters not to be varied, and in that we use CosmoMC, thus incorporating the WMAP likelihood code and $EE$ and $BB$ mode data. We introduce a new parameter to test the claims of a scale-dependent spectral index. While we do find some hints of a scale-dependent spectral index over the multipole range $\ell =2–220$, the change in maximum likelihood is too small to justify introducing a new parameter. We conclude that there is no significant detection of primordial tensor perturbations, and that the assumption of a scale-independent spectral index in this multipole range has little effect on the amount of primordial gravitational waves found.

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that, although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are isomorphic at the level of Hopf-algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. The deformed Leibniz rule, the Hopf structure, and the star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations, are discussed. The same generalized Hopf-algebraic structures are considered as well in the case of an arbitrary allowable kind of realization, and results are given perturbatively up to second order in deformation parameters.