On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is solved numerically, and the main features of the solutions are briefly discussed.Comment: Special Article - QNP2006: 4th International Conference on Quarks and Nuclear Physics, Madrid, Spain, 5-10 June 200

Effective four-fermion operators in top physics: a roadmap

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t -> d_k u_i dbar_j, t -> d_k e_i+ nu_j, t -> u_k u_i ubar_j, t -> u_k e_j+ e_i-, t -> u_k nu_j nu_i (with i,j,k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, p pbar and e+ e- collisions are calculated as well, namely u_i d_k -> d_j t, dbar_j d_k -> ubar_i t, u_i dbar_j -> dbar_k t, u_i u_k -> u_j t, u_i ubar_j -> ubar_k t, e+ e- -> ubar_k t and the charge conjugate processes. We also compute all top pair production cross sections, ubar_i u_j -> t tbar, dbar_i d_j -> t tbar, u_i u_j -> t t and e+ e- -> t tbar. Our results are completely general, without assuming any particular relation among effective operator coefficients.Comment: LaTeX 43 pages, 1 PS figure. Cross sections for uu,cc -> tt correcte

Model-independent measurement of the top quark polarisation

We introduce a new asymmetry in the decay t -> W b -> l nu b, which is shown to be directly proportional to the polarisation of the top quark along a chosen axis, times a sum of W helicity fractions. The latter have already been precisely measured at the Tevatron and the Large Hadron Collider. Therefore, this new asymmetry can be used to obtain a model-independent measurement of the polarisation of top quarks produced in any process at hadron or lepton colliders.Comment: LaTeX 12 pages. Discussion expanded with a new plot, references added. Final version to appear in PL

Anthropology of the Crowd, Blog 1

Student blog posts from the Great VCU Bike Race Book

A minimal set of top anomalous couplings

We simplify the general form of the fermion-fermion-gauge boson interactions generated by dimension-six gauge-invariant effective operators by using the equations of motion to remove redundant operators. It is found that the most general vertex for off-shell fermions fi, fj and an off-shell boson V=W,Z,gamma,g only involves gamma^mu and sigma^{mu nu} q_nu terms, with q=p_i-p_j. Examples are given for the Wtb, Ztt, gamma tt and gtt interactions, whose general expression is greatly simplified with respect to previous results in the literature. The same arguments apply to top flavour-changing neutral interactions with the Z boson, the photon or the gluon, which can also be parameterised in full generality with only gamma^mu and sigma^{mu nu} q_nu couplings. Explicit expressions are given for these vertices in terms of dimension-six gauge-invariant operators. We also discuss how effective operator coefficients might be determined from eventual measurements of anomalous couplings.Comment: LaTeX 29 pages, 3 PS figures. Minor comments added, final version to appear in NP

Non-perturbative QCD effective charges

Using gluon and ghost propagators obtained from Schwinger-Dyson equations (SDEs), we construct the non-perturbative effective charge of QCD. We employ two different definitions, which, despite their distinct field-theoretic origin, give rise to qualitative comparable results, by virtue of a crucial non-perturbative identity. Most importantly, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations. The various theoretical ingredients necessary for this construction are reviewed in detail, and some conceptual subtleties are briefly discussed.Comment: Invited talk at Light Cone 2009: Relativistic Nuclear and Particle Physics (LC2009), Sao Jose dos Campos, Brazil, 8-13 July, 200

Vacuum energy as a c-function for theories with dynamically generated masses

We argue that in asymptotically free non-Abelian gauge theories possessing the phenomenon of dynamical mass generation the $\beta$ function is negative up to a value of the coupling constant that corresponds to a non-trivial fixed point, in agreement with recent AdS/QCD analysis. This fixed point happens at the minimum of the vacuum energy ($\Omega$), which, as a characteristic of theories with dynamical mass generation, has the properties of a c-function.Comment: 12 pages, 3 figure

A minimal set of top-Higgs anomalous couplings

We use the equations of motion to simplify the general form of fermion-fermion-Higgs interactions generated by dimension-six gauge-invariant effective operators. After removing redundant operators it is found that the most general H f_i f_j vertex for off-shell fermions f_i, f_j and an off-shell Higgs boson only involves scalar and pseudo-scalar terms, without derivatives. Examples are presented for the Htt and Htq interactions, where q=u,c, giving the explicit expressions of the vertices in terms of gauge-invariant operators. The new operator equalities obtained here also reduce the number of operators relevant for the Ztq vertices, although the general form of these interactions is not simplified with respect to previous results.Comment: LaTeX 16 pages, 2 PS figures. Typos corrected. Final version which appeared on the journa