Precision Probes of QCD at High Energies

New physics, that is too heavy to be produced directly, can leave measurable imprints on the tails of kinematic distributions at the LHC. We use energetic QCD processes to perform novel measurements of the Standard Model (SM) Effective Field Theory. We show that the dijet invariant mass spectrum, and the inclusive jet transverse momentum spectrum, are sensitive to a dimension 6 operator that modifies the gluon propagator at high energies. The dominant effect is constructive or destructive interference with SM jet production. We compare differential next-to-leading order predictions from POWHEG to public 7 TeV jet data, including scale, PDF, and experimental uncertainties and their respective correlations. We constrain a New Physics (NP) scale of 3.5 TeV with current data. We project the reach of future 13 and 100 TeV measurements, which we estimate to be sensitive to NP scales of 8 and 60 TeV, respectively. As an application, we apply our bounds to constrain heavy vector octet colorons that couple to the QCD current. We project that effective operators will surpass bump hunts, in terms of coloron mass reach, even for sequential couplings.Comment: 40 pages, 13 figures, 8 tables. Minor changes. Accepted on JHE

Mixtures and products in two graphical models

We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the interior of the probability simplex, and are equal up to closure. We give a semi-algebraic description of the model in terms of six binomial inequalities and obtain closed form expressions for the maximum likelihood estimates. We briefly discuss extensions to larger models.Comment: 18 pages, 7 figure

Metric on the space of quantum states from relative entropy. Tomographic reconstruction

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor corrections. References adde

Quantum suprematism picture of Malevich's squares triada for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics

Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for Franck--Condon factors. Density matrices of qudit states are expressed in terms of probabilities of artificial qubits as well as the quantum suprematism approach to geometry of these states using the triadas of Malevich squares is developed. Examples of qubits, qutrits and ququarts are considered.Comment: the material of the talk given at Symmetries in Science Symposium, Bregenz, 201

Supersymmetry discovery potential of the LHC at s=\sqrt{s}=10 and 14 TeV without and with missing ETE_T

We examine the supersymmetry (SUSY) reach of the CERN LHC operating at $\sqrt{s}=10$ and 14 TeV within the framework of the minimal supergravity model. We improve upon previous reach projections by incorporating updated background calculations including a variety of $2\to n$ Standard Model (SM) processes. We show that SUSY discovery is possible even before the detectors are understood well enough to utilize either $E_T^{\rm miss}$ or electrons in the signal. We evaluate the early SUSY reach of the LHC at $\sqrt{s}=10$ TeV by examining multi-muon plus $\ge4$ jets and also dijet events with {\it no} missing $E_T$ cuts and show that the greatest reach in terms of $m_{1/2}$ occurs in the dijet channel. The reach in multi-muons is slightly smaller in $m_{1/2}$, but extends to higher values of $m_0$. We find that an observable multi-muon signal will first appear in the opposite-sign dimuon channel, but as the integrated luminosity increases the relatively background-free but rate-limited same-sign dimuon, and ultimately the trimuon channel yield the highest reach. We show characteristic distributions in these channels that serve to distinguish the signal from the SM background, and also help to corroborate its SUSY origin. We then evaluate the LHC reach in various no-lepton and multi-lepton plus jets channels {\it including} missing $E_T$ cuts for $\sqrt{s}=10$ and 14 TeV, and plot the reach for integrated luminosities ranging up to 3000 fb$^{-1}$ at the SLHC. For $\sqrt{s}=10$ TeV, the LHC reach extends to $m_{gluino}=1.9, 2.3, 2.8$ and 2.9 TeV for $m_{squark}\sim m_{gluino}$ and integrated luminosities of 10, 100, 1000 and 3000 fb$^{-1}$, respectively. For $\sqrt{s}=14$ TeV, the LHC reach for the same integrated luminosities is to m_{gluino}=2.4,\3.1, 3.7 and 4.0 TeV.Comment: 34 pages, 25 figures. Revised projections for the SUSY reach for ab^-1 integrated luminosities, with minor corrections of references and text. 2 figures added. To appear in JHE