Abstract A test of lepton flavor universality in and decays, as well as a measurement of differential and integrated branching fractions of a nonresonant decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions to is determined from the measured double ratio of these decays to the respective branching fractions of the with and decays, which allow for significant cancellation of systematic uncertainties. The ratio is measured in the range , whereqis the invariant mass of the lepton pair, and is found to be , in agreement with the standard model expectation . This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the sameq2range, , is consistent with the present world-average value and has a comparable precision. 
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                    This content will become publicly available on January 28, 2026
                            
                            Existence and stability for the travelling waves of the Benjamin equation
                        
                    
    
            Abstract In the seminal work of Benjamin (1974Nonlinear Wave Motion(American Mathematical Society)), in the late 70s, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some special circumstances, it turns into the celebrated KdV or the Benjamin–Ono equation, During the 90s, there was renewed interest in it. Benjamin (1992J. Fluid Mech.245401–11; 1996Phil. Trans. R. Soc.A3541775–806) studied the problem for existence of solitary waves, followed by works of Bona–Chen (1998Adv. Differ. Equ.351–84), Albert–Bona–Restrepo (1999SIAM J. Appl. Math.592139–61), Pava (1999J. Differ. Equ.152136–59), who have showed the existence of travelling waves, mostly by variational, but also bifurcation methods. Some results about the stability became available, but unfortunately, those were restricted to either small waves or Benjamin model, close to a distinguished (i.e. KdV or BO) limit. Quite recently, in 2024 (arXiv:2404.04711 [math.AP]), Abdallahet al, proved existence, orbital stability and uniqueness results for these waves, but only for large values of . In this article, we present an alternative constrained maximization procedure for the construction of these waves, for the full range of the parameters, which allows us to ascertain their spectral stability. Moreover, we extend this construction to allL2subcritical cases (i.e. power nonlinearities , ). Finally, we propose a different procedure, based on a specific form of the Sobolev embedding inequality, which works for all powers , but produces some unstable waves, for largep. Some open questions and a conjecture regarding this last result are proposed for further investigation. 
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                            - Award ID(s):
- 2210867
- PAR ID:
- 10612420
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 38
- Issue:
- 2
- ISSN:
- 0951-7715
- Page Range / eLocation ID:
- 025020
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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