Optimal Charge and Color Breaking conditions in the MSSM

In the MSSM, we make a careful tree-level study of Charge and Color Breaking conditions in the plane $(H_2, \tilde{u}_L, \tilde{u}_R)$, focusing on the top quark scalar case. A simple and fast procedure to compute the VEVs of the dangerous vacuum is presented and used to derive a model-independent optimal CCB bound on $A_t$. This bound takes into account all possible deviations of the CCB vacuum from the D-flat directions. For large $\tan \beta$, it provides a CCB maximal mixing for the stop scalar fields $\tilde{t}_1,\tilde{t}_2$, which automatically rules out the Higgs maximal mixing $|A_t|=\sqrt{6} m_{\tilde{t}}$. As a result, strong limits on the stop mass spectrum and a reduction, in some cases substantial, of the one-loop upper bound on the CP-even lightest Higgs boson mass, $m_h$, are obtained. To incorporate one-loop leading corrections, this tree-level CCB condition should be evaluated at an appropriate renormalization scale which proves to be the SUSY scale.Comment: 41 pages, 7 eps figures, minor corrections, references added, to appear in Nucl. Phys.

Flavour-Dependent Type II Leptogenesis

We reanalyse leptogenesis via the out-of-equilibrium decay of the lightest right-handed neutrino in type II seesaw scenarios, taking into account flavour-dependent effects. In the type II seesaw mechanism, in addition to the type I seesaw contribution, an additional direct mass term for the light neutrinos is present. We consider type II seesaw scenarios where this additional contribution arises from the vacuum expectation value of a Higgs triplet, and furthermore an effective model-independent approach. We investigate bounds on the flavour-specific decay asymmetries, on the mass of the lightest right-handed neutrino and on the reheat temperature of the early universe, and compare them to the corresponding bounds in the type I seesaw framework. We show that while flavour-dependent thermal type II leptogenesis becomes more efficient for larger mass scale of the light neutrinos, and the bounds become relaxed, the type I seesaw scenario for leptogenesis becomes more constrained. We also argue that in general, flavour-dependent effects cannot be ignored when dealing with leptogenesis in type II seesaw models.Comment: 19 pages, 8 figures; v3: minor additions, typos corrected, results and conclusions unchange

Carving Out the Space of 4D CFTs

We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N=1 superconformal theories, we place strong bounds on dim(Phi*Phi), where Phi is a chiral operator. These bounds asymptote to the line dim(Phi*Phi) <= 2 dim(Phi) near dim(Phi) ~ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Phi x Phi OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N=1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.Comment: 60 pages, 22 figure

Dependent randomized rounding for clustering and partition systems with knapsack constraints

Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with "knapsack" and "partition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds are very useful in inferring properties of large networks using few samples

A Geometric Approach to CP Violation: Applications to the MCPMFV SUSY Model

We analyze the constraints imposed by experimental upper limits on electric dipole moments (EDMs) within the Maximally CP- and Minimally Flavour-Violating (MCPMFV) version of the MSSM. Since the MCPMFV scenario has 6 non-standard CP-violating phases, in addition to the CP-odd QCD vacuum phase \theta_QCD, cancellations may occur among the CP-violating contributions to the three measured EDMs, those of the Thallium, neutron and Mercury, leaving open the possibility of relatively large values of the other CP-violating observables. We develop a novel geometric method that uses the small-phase approximation as a starting point, takes the existing EDM constraints into account, and enables us to find maximal values of other CP-violating observables, such as the EDMs of the Deuteron and muon, the CP-violating asymmetry in b --> s \gamma decay, and the B_s mixing phase. We apply this geometric method to provide upper limits on these observables within specific benchmark supersymmetric scenarios, including extensions that allow for a non-zero \theta_QCD.Comment: 34 pages, 16 eps figures, to appear in JHE

Fast Parallel Randomized QR with Column Pivoting Algorithms for Reliable Low-rank Matrix Approximations

Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven themselves empirically to be highly competitive with high-performance implementations of QR in processing time, on uniprocessor and shared memory machines, and as reliable as QRCP in pivot quality. We show that RQRCP algorithms can be as reliable as QRCP with failure probabilities exponentially decaying in oversampling size. We also analyze efficiency differences among different RQRCP algorithms. More importantly, we develop distributed memory implementations of RQRCP that are significantly better than QRCP implementations in ScaLAPACK. As a further development, we introduce the concept of and develop algorithms for computing spectrum-revealing QR factorizations for low-rank matrix approximations, and demonstrate their effectiveness against leading low-rank approximation methods in both theoretical and numerical reliability and efficiency.Comment: 11 pages, 14 figures, accepted by 2017 IEEE 24th International Conference on High Performance Computing (HiPC), awarded the best paper priz