Can the X(3872) be a 1^{++} four-quark state?

We use QCD spectral sum rules to test the nature of the meson X(3872), assumed to be an exotic four-quark (c\bar{c}q\bar{q}) state with J^{PC}=1^{++}. For definiteness, we work with the current proposed recently by Maiani et al [1], at leading order in \alpha_s, consider the contributions of higher dimension condensates and keep terms which are linear in the light quark mass m_q. We find M_X=(3925+- 127) MeV which is compatible, within the errors, with he experimental candidate X(3872), while the SU(3) breaking-terms lead to an unusual mass-splitting M_{X^{s}}-M_X=- (61+-30) MeV. The mass-difference between the neutral states due to isospin violation of about (2.6-3.9) MeV is much smaller than the value (8+-3) MeV proposed in [1]. For the b-quark, we predict M_{X_b}= (10144+-106) MeV for the X_b(b\bar{b}q \bar{q}), which is much below the {\bar B}B* threshold in contrast to the {\bar B}B* molecule prediction [2], and for the X_b^s(b\bar{b}s \bar{s}), a mass-splitting M_{X^s_{b}}-M_{X_b}=-(121+-182) MeV. Our analysis also indicates that the mass-splitting between the ground state and the radial excitation of about (225~250) MeV is much smaller than in the case of ordinary mesons and is (within the errors) flavour-independent. We also extract the decay constants, analogous to f_\pi, of such mesons, which are useful for further studies of their leptonic and hadronic decay widths. The uncertainties of our estimates are mainly due to the ones from the c and b quark masses.Comment: 16 pages, 10 figures. Version to appear in Phys. Rev.

N-Relaxion: Large Field Excursions from a Few Site Relaxion Model

Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an N-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-abelian fields, allowing for controlled high energy behaviour and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.Comment: 7 pages, 2 figures; v2: version to appear in PR

Selling a Single Item with Negative Externalities

We consider the problem of regulating products with negative externalities to a third party that is neither the buyer nor the seller, but where both the buyer and seller can take steps to mitigate the externality. The motivating example to have in mind is the sale of Internet-of-Things (IoT) devices, many of which have historically been compromised for DDoS attacks that disrupted Internet-wide services such as Twitter. Neither the buyer (i.e., consumers) nor seller (i.e., IoT manufacturers) was known to suffer from the attack, but both have the power to expend effort to secure their devices. We consider a regulator who regulates payments (via fines if the device is compromised, or market prices directly), or the product directly via mandatory security requirements. Both regulations come at a cost---implementing security requirements increases production costs, and the existence of fines decreases consumers' values---thereby reducing the seller's profits. The focus of this paper is to understand the \emph{efficiency} of various regulatory policies. That is, policy A is more efficient than policy B if A more successfully minimizes negatives externalities, while both A and B reduce seller's profits equally. We develop a simple model to capture the impact of regulatory policies on a buyer's behavior. {In this model, we show that for \textit{homogeneous} markets---where the buyer's ability to follow security practices is always high or always low---the optimal (externality-minimizing for a given profit constraint) regulatory policy need regulate \emph{only} payments \emph{or} production.} In arbitrary markets, by contrast, we show that while the optimal policy may require regulating both aspects, there is always an approximately optimal policy which regulates just one

Investigating different structures for the X(3872)X(3872)

Using the QCD spectral sum rule approach we investigate different currents with $J^{PC}=1^{++}$, which could be associated with the $X(3872)$ meson. Our results indicate that, with a four-quark or molecular structure, it is very difficult to explain the narrow width of the state unless the quarks have a special color configuration.Comment: 4 pages. Contribution to the proceedings of the 15th International QCD Conference (QCD10