We study a family of genuinely exotic five-flavor molecular pentaquark states containing the five quark flavors u, d, s, c, b that form experimentally accessible hadrons. We construct the meson-baryon interaction from the local hidden gauge symmetry combined with heavy-quark spin symmetry, following the chiral unitary description that reproduces the LHCb hidden-charm strange pentaquarks. Heavy-quark flavor symmetry allows us to obtain the u d s c b ¯ sector by replacing the anti-charm quark in the meson with an anti-bottom quark while keeping the charm quark in the baryon. As a result, we obtain ten threshold-associated isoscalar poles with J P = 1 / 2 − , 3 / 2 − , 5 / 2 − in the range 7.72 to 7.96 GeV. They are narrow and organized into heavy-quark spin multiplets with predicted near-degeneracies. The loop subtraction constant, the single scheme parameter, is not adjusted by hand. Requiring the loop function at threshold to be independent of the heavy flavor fixes a ≃ − 3.2 to − 3.4 from the charm sector, consistent with the value a = − 3.1 used in the earlier two-sector study, and the predicted masses move by several tens of MeV when a varies between − 2.9 and − 3.2 . There are four states that overlap with the earlier two-sector study in the literature to about 2 MeV, which shows that the separate-sector treatment is recovered as a limit of this work. Moreover, the strongly coupled B *Ξ c and B s * Λ c channels support additional deeply bound poles. We show that their number and positions depend on the regularization scheme, and we quantify this dependence by comparing dimensional regularization with a cutoff scheme. The resulting states provide a signal that can be searched for at LHCb in the B c Λ and B s * Λ c invariant mass spectra in the window 7.60 to 7.77 GeV.
The QCD trace anomaly is a well-established textbook result in quantum field theory with several prominent features: (1) it arises from the quantum breaking of scale symmetry at ultraviolet (UV) scales, yet its full renormalized expression is independent of the particular UV regulator used, whether lattice or dimensional regularization; (2) although nominally of order αs, it is free of renormalization-scheme ambiguity; and (3) it is free of UV divergences and therefore scale independent. We show that renormalization in a reducible operator basis introduces additional convention dependence in its separation into quark and gluon parts, which do not share the properties of the whole anomaly itself. An irreducible decomposition instead keeps the trace anomaly as a single, convention-free component, and gives transparent physical meanings to anomaly-related nucleon physics, including the nucleon mass structure and internal forces.
A search for leptoquark signals is performed in final states with a hadronically decaying τ -lepton and missing transverse momentum, using data from proton–proton collisions at a centre-of-mass energy of s = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider during Run 2 (2015–18), corresponding to an integrated luminosity of 140 fb − 1 . The analysis is designed to probe both resonant production and non-resonant t -channel exchange of the leptoquark, covering a wide range of coupling scenarios. No excess above the Standard Model background prediction is observed. Limits are set on the couplings in the benchmark U 1 vector-leptoquark model at 95% confidence level for masses between 1.5 TeV and 3.0 TeV.
