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1. On the sensitivity reach of $$\textrm{LQ}$$ production with preferential couplings to third generation fermions at the LHC

   https://doi.org/10.1140/epjc/s10052-023-12177-4  

   Flórez, A. ; Jones-Pérez, J. ; Gurrola, A. ; Rodriguez, C. ; Peñuela-Parra, J. ( November 2023 , The European Physical Journal C)

   Leptoquarks ($$\textrm{LQ}$$$\text{LQ}$s) are hypothetical particles that appear in various extensions of the Standard Model (SM), that can explain observed differences between SM theory predictions and experimental results. The production of these particles has been widely studied at various experiments, most recently at the Large Hadron Collider (LHC), and stringent bounds have been placed on their masses and couplings, assuming the simplest beyond-SM (BSM) hypotheses. However, the limits are significantly weaker for$$\textrm{LQ}$$$\text{LQ}$models with family non-universal couplings containing enhanced couplings to third-generation fermions. We present a new study on the production of a$$\textrm{LQ}$$$\text{LQ}$at the LHC, with preferential couplings to third-generation fermions, considering proton-proton collisions at$$\sqrt{s} = 13 \, \textrm{TeV}$$$\sqrt{s}=13\text{TeV}$and$$\sqrt{s} = 13.6 \, \textrm{TeV}$$$\sqrt{s}=13.6\text{TeV}$. Such a hypothesis is well motivated theoretically and it can explain the recent anomalies in the precision measurements of$$\textrm{B}$$$\text{B}$-meson decay rates, specifically the$$R_{D^{(*)}}$$$R_{D^{(\ast )}}$ratios. Under a simplified model where the$$\textrm{LQ}$$$\text{LQ}$masses and couplings are free parameters, we focus on cases where the$$\textrm{LQ}$$$\text{LQ}$decays to a$$\tau $$$\tau$lepton and a$$\textrm{b}$$$\text{b}$quark, and study how the results are affected by different assumptions about chiral currents and interference effects with other BSM processes with the same final states, such as diagrams with a heavy vector boson,$$\textrm{Z}^{\prime }$$${\text{Z}}^{\prime }$. The analysis is performed using machine learning techniques, resulting in an increased discovery reach at the LHC, allowing us to probe new physics phase space which addresses the$$\textrm{B}$$$\text{B}$-meson anomalies, for$$\textrm{LQ}$$$\text{LQ}$masses up to$$5.00\, \textrm{TeV}$$$5.00\text{TeV}$, for the high luminosity LHC scenario.

    

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2. Probing a $$\textrm{Z}^{\prime }$$ with non-universal fermion couplings through top quark fusion, decays to bottom quarks, and machine learning techniques

   https://doi.org/10.1140/epjc/s10052-023-11506-x  

   Barbosa, Diego ; Díaz, Felipe ; Quintero, Liliana ; Flórez, Andrés ; Sanchez, Manuel ; Gurrola, Alfredo ; Sheridan, Elijah ; Romeo, Francesco ( May 2023 , The European Physical Journal C)

   Abstract The production of heavy neutral mass resonances, $$\text {Z}^{\prime }$$ Z ′ , has been widely studied theoretically and experimentally. Although the nature, mass, couplings, and associated quantum numbers of this hypothetical particle are yet to be determined, current LHC experimental results have set strong constraints assuming the simplest beyond Standard Model (SM) hypotheses. We present a new feasibility study on the production of a $$\text {Z}^{\prime }$$ Z ′ boson at the LHC, with family non-universal couplings, considering proton–proton collisions at $$\sqrt{s} = 13$$ s = 13 and 14 TeV. Such a hypothesis is well motivated theoretically and it can explain observed differences between SM predictions and experimental results, as well as being a useful tool to further probe recent results in searches for new physics considering non-universal fermion couplings. We work under two simplified phenomenological frameworks where the $$\textrm{Z}^{\prime }$$ Z ′ masses and couplings to the SM particles are free parameters, and consider final states of the $$\text {Z}^{\prime }$$ Z ′ decaying to a pair of $$\textrm{b}$$ b quarks. The analysis is performed using machine learning techniques to maximize the sensitivity. Despite being a well motivated physics case in its own merit, such scenarios have not been fully considered in ongoing searches at the LHC. We note the proposed search methodology can be a key mode for discovery over a large mass range, including low masses, traditionally considered difficult due to experimental constrains. In addition, the proposed search is complementary to existing strategies. 

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3. Free Energy Wells and Overlap Gap Property in Sparse PCA

   Ben Arous, Gerard ; Wein, Alexander S ; Zadik, Ilias ( July 2020 , Proceedings of Thirty Third Conference on Learning Theory)

   Abernethy, Jacob ; Agarwal, Shivani (Ed.)

   We study a variant of the sparse PCA (principal component analysis) problem in the “hard” regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio, has conjectured a precise expression for the best possible (sub-exponential) runtime throughout the hard regime. Following instead a statistical physics inspired point of view, we show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. These free energy wells imply hitting time lower bounds that corroborate the low-degree conjecture: we show that a class of natural MCMC (Markov chain Monte Carlo) methods (with worst-case initialization) cannot solve sparse PCA with less than the conjectured runtime. These lower bounds apply to a wide range of values for two tuning parameters: temperature and sparsity misparametrization. Finally, we prove that the Overlap Gap Property (OGP), a structural property that implies failure of certain local search algorithms, holds in a significant part of the hard regime. 

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4. Data Augmentation MCMC for Bayesian Inference from Privatized Data

   Ju, Nianqiao ; Awan, Jordan ; Gong, Ruobin ; Rao, Vinayak ( December 2022 , Advances in neural information processing systems)

   Koyejo, Sanmi ; Mohamed, Shakir (Ed.)

   Differentially private mechanisms protect privacy by introducing additional randomness into the data. Restricting access to only the privatized data makes it challenging to perform valid statistical inference on parameters underlying the confidential data. Specifically, the likelihood function of the privatized data requires integrating over the large space of confidential databases and is typically intractable. For Bayesian analysis, this results in a posterior distribution that is doubly intractable, rendering traditional MCMC techniques inapplicable. We propose an MCMC framework to perform Bayesian inference from the privatized data, which is applicable to a wide range of statistical models and privacy mechanisms. Our MCMC algorithm augments the model parameters with the unobserved confidential data, and alternately updates each one conditional on the other. For the potentially challenging step of updating the confidential data, we propose a generic approach that exploits the privacy guarantee of the mechanism to ensure efficiency. In particular, we give results on the computational complexity, acceptance rate, and mixing properties of our MCMC. We illustrate the efficacy and applicability of our methods on a na\"ive-Bayes log-linear model as well as on a linear regression model. 

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5. Data Augmentation MCMC for Bayesian Inference from Privatized Data

   Ju, Nianqiao ; Awan, Jordan ; Gong, Ruobin ; Rao, Vinayak ( January 2022 , Advances in neural information processing systems)

   Koyejo, S. ; Mohamed, S. ; Agarwal, A. ; Belgrave, D. ; Cho, K. ; Oh, A. (Ed.)

   Differentially private mechanisms protect privacy by introducing additional randomness into the data. Restricting access to only the privatized data makes it challenging to perform valid statistical inference on parameters underlying the confidential data. Specifically, the likelihood function of the privatized data requires integrating over the large space of confidential databases and is typically intractable. For Bayesian analysis, this results in a posterior distribution that is doubly intractable, rendering traditional MCMC techniques inapplicable. We propose an MCMC framework to perform Bayesian inference from the privatized data, which is applicable to a wide range of statistical models and privacy mechanisms. Our MCMC algorithm augments the model parameters with the unobserved confidential data, and alternately updates each one conditional on the other. For the potentially challenging step of updating the confidential data, we propose a generic approach that exploits the privacy guarantee of the mechanism to ensure efficiency. We give results on the computational complexity, acceptance rate, and mixing properties of our MCMC. We illustrate the efficacy and applicability of our methods on a naive-Bayes log-linear model and on a linear regression model. 

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