Effective Field Theories for Heavy Quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field theory derived quantum mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and \als) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low energy QCD dynamics is also discussed.Comment: Invited Plenary talk at The 20th European Conference on Few-Body Problems in Physics. September 10-14 2007. Pisa, Italy. To be published on Few-Body System

Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum

We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $m\alpha_s \gg \Lambda_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation m\alpha_s^2 \simg \Lambda_{QCD}. When $\Lambda_{QCD} \ll m\alpha_s^2$, this is equivalent to obtain the whole set of $O(m\alpha_s^{(n+4)} \ln^n \alpha_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbative situation $m\alpha_s \sim \Lambda_{QCD}$ are also mentioned.Comment: 16 pages, LaTeX. Minor changes. Final versio

Effective field theories for heavy quarkonium

We review recent theoretical developments in heavy quarkonium physics from the point of view of Effective Field Theories of QCD. We discuss Non-Relativistic QCD and concentrate on potential Non-Relativistic QCD. Our main goal will be to derive QCD Schr\"odinger-like equations that govern the heavy quarkonium physics in the weak and strong coupling regime. We also discuss a selected set of applications, which include spectroscopy, inclusive decays and electromagnetic threshold production.Comment: 162 pages, 30 figures, revised version, references added. Accepted for publication in Reviews of Modern Physic

Renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions

We obtain the next-to-next-to-leading-log renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions by using potential NRQED. These results can also be applied to the computation of the muonic Hydrogen spectrum where we are able to reproduce some known double logs at O(m\alpha^6). We compare with other formalisms dealing with log resummation available in the literature.Comment: 9 pages, LaTeX. Minor changes, note added, final versio

Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium

We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We discuss the interplay of the scales arising in the Soft-Collinear Effective Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2. For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for 1-z << alpha_s^2. The S- and P-wave octet shape functions are calculated. When they are included in the analysis of the photon spectrum of the Upsilon (1S) system, the agreement with data in the end-point region becomes excellent. The NRQCD matrix elements and are also obtained.Comment: Revtex, 11 pages, 6 figures. Minor improvements and references added. Journal versio

Quarkonium spectroscopy and perturbative QCD: massive quark-loop effects

We study the spectra of the bottomonium and B_c states within perturbative QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between the static potential and the pole mass is performed in the epsilon-expansion scheme. We extend our previous analysis by including the (dominant) effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. We fix the b-quark MSbar mass $\bar{m}_b \equiv m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}})$ on Upsilon(1S) and compute the higher levels. The effect of the charm mass decreases $\bar{m}_b$ by about 11 MeV and increases the n=2 and n=3 levels by about 70--100 MeV and 240--280 MeV, respectively. We provide an extensive quantitative analysis. The size of non-perturbative and higher order contributions is discussed by comparing the obtained predictions with the experimental data. An agreement of the perturbative predictions and the experimental data depends crucially on the precise value (inside the present error) of alpha_s(M_Z). We obtain $m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}}) = 4190 \pm 20 \pm 25 \pm 3 ~ {\rm MeV}$.Comment: 33 pages, 21 figures; v2: Abstract modified; Table7 (summary of errors) added; Version to appear in Phys.Rev.

Inclusive Decays of Heavy Quarkonium to Light Particles

We derive the imaginary part of the potential NRQCD Hamiltonian up to order 1/m^4, when the typical momentum transfer between the heavy quarks is of the order of Lambda_{QCD} or greater, and the binding energy E much smaller than Lambda_{QCD}. We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to O(mv^3 x (Lambda_{QCD}^2/m^2,E/m)) and O(mv^5) times a short-distance coefficient, for S- and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown non-perturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal non-perturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal non-perturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.Comment: 61 pages, 9 figures. Minor change

The initial conditions of stellar protocluster formation. II. A catalogue of starless and protostellar clumps embedded in IRDCs in the Galactic longitude range 15<l<55

We present a catalogue of starless and protostellar clumps associated with infrared dark clouds (IRDCs) in a 40 degrees wide region of the inner Galactic Plane (b<1). We have extracted the far-infrared (FIR) counterparts of 3493 IRDCs with known distance in the Galactic longitude range 15<l<55 and searched for the young clumps using Hi-GAL, the survey of the Galactic Plane carried out with the Herschel satellite. Each clump is identified as a compact source detected at 160, 250 and 350 mum. The clumps have been classified as protostellar or starless, based on their emission (or lack of emission) at 70 mum. We identify 1723 clumps, 1056 (61%) of which are protostellar and 667 (39%) starless. These clumps are found within 764 different IRDCs, 375 (49%) of which are only associated with protostellar clumps, 178 (23%) only with starless clumps, and 211 (28%) with both categories of clumps. The clumps have a median mass of 250 M_sun and range up to >10^4$ M_sun in mass and up to 10^5 L_sun in luminosity. The mass-radius distribution shows that almost 30% of the starless clumps identified in this survey could form high-mass stars, however these massive clumps are confined in only ~4% of the IRDCs. Assuming a minimum mass surface density threshold for the formation of high-mass stars, the comparison of the numbers of massive starless clumps and those already containing embedded sources suggests an upper limit lifetime for the starless phase of 10^5 years for clumps with a mass M>500 M_sun.Comment: accepted for publication in MNRAS. Online catalogues available soon, please contact the authors if intereste

Tightening the belt: Constraining the mass and evolution in SDC335

Recent ALMA observations identified one of the most massive star-forming cores yet observed in the Milky Way; SDC335-MM1, within the infrared dark cloud SDC335.579-0.292. Along with an accompanying core MM2, SDC335 appears to be in the early stages of its star formation process. In this paper we aim to constrain the properties of the stars forming within these two massive millimetre sources. Observations of SDC335 at 6, 8, 23 and 25GHz were made with the ATCA. We report the results of these continuum measurements, which combined with archival data, allow us to build and analyse the spectral energy distributions (SEDs) of the compact sources in SDC335. Three HCHII regions within SDC335 are identified, two within the MM1 core. For each HCHII region, a free-free emission curve is fit to the data allowing the derivation of the sources' emission measure, ionising photon flux and electron density. Using these physical properties we assign each HCHII region a ZAMS spectral type, finding two protostars with characteristics of spectral type B1.5 and one with a lower limit of B1-B1.5. Ancillary data from infrared to mm wavelength are used to construct free-free component subtracted SEDs for the mm-cores, allowing calculation of the bolometric luminosities and revision of the previous gas mass estimates. The measured luminosities for the two mm-cores are lower than expected from accreting sources displaying characteristics of the ZAMS spectral type assigned to them. The protostars are still actively accreting, suggesting that a mechanism is limiting the accretion luminosity, we present the case for two different mechanisms capable of causing this. Finally, using the ZAMS mass values as lower limit constraints, a final stellar population for SDC335 was synthesised finding SDC335 is likely to be in the process of forming a stellar cluster comparable to the Trapezium Cluster and NGC6334 I(N).Comment: 10 pages, 5 figures. Accepted for publication in A&