arXiv subjects
Publications and source records attributed to Antonio Vairo.
We review one of the most accurate low-energy determinations of $α_s$. Comparing at short distances the QCD static energy at three loops and resummation of the next-to-next-to leading logarithms with its determination in 2+1-flavor lattice QCD, we obtain $α_s(1.5~{\rm GeV})=0.336^{+0.012}_{-0.008}$, which corresponds to $α_s(M_Z)=0.1166^{+0.0012}_{-0.0008}$. We discuss future perspectives.
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass $m$ of the heavy quark. At order $1/m$ in the expansion, we obtain at the level of potential Non-Relativistic QCD a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as $Λ$-doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for $c\bar{c}$, $b\bar{c}$, and $b\bar{b}$ hybrids. The $Λ$-doubling effect breaks the degeneracy between opposite parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, sum rules calculations, and discuss the relation to the Born-Oppenheimer approximation.
In an effective field theory framework we review the two main mechanisms of quarkonium dissociation in a weakly coupled thermal bath.
The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson loop expectation values and correlators evaluated in the effective string theory, to compute the potential. We obtain previously unknown results for the spin and momentum-independent parts of the potential. These are linearly rising with the distance and may be interpreted as relativistic corrections to the string tension. We confirm known results for the other parts of the potential. Finally, we compute the discrete spectrum of a heavy quark-antiquark pair whose interaction is just given by the obtained potential.
We discuss divergences of loop functions in thermal QCD and compute perturbatively the Polyakov loop, the Polyakov loop correlator and the cyclic Wilson loop. We show how these functions get mixed under renormalization.
Heavy particles are a window to new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe non-relativistic particles propagating in a medium. After introducing some general features common to any non-relativistic effective field theory, we discuss two specific examples: heavy Majorana neutrinos colliding in a hot plasma of Standard Model particles in the early universe and quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.
We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.
Heavy Majorana neutrinos enter in many scenarios of physics beyond the Standard Model: in the original seesaw mechanism they provide a natural explanation for the small masses of the Standard Model neutrinos and in the simplest leptogenesis framework they are at the origin of the baryonic matter of the universe. In this paper, we develop an effective field theory for non-relativistic Majorana particles, which is analogous to the heavy-quark effective theory. Then, we apply it to the case of a heavy Majorana neutrino decaying in a hot and dense plasma of Standard Model particles, whose temperature is much smaller than the mass of the Majorana neutrino but still much larger than the electroweak scale. The neutrino width gets zero-temperature contributions that can be computed from in-vacuum matrix elements, and thermal corrections. Only the latter will be addressed. Symmetry and power counting arguments made manifest by the effective field theory restrict the form of the thermal corrections and simplify their calculation. The final result agrees with recent determinations obtained with different methods. The effective field theory presented here is suitable to be used for a variety of different models involving non-relativistic Majorana fermions.
We study the symmetries of the three heavy-quark system under exchange of the quark fields within the effective field theory framework of potential non-relativistic QCD. The symmetries constrain the form of the matching coefficients in the effective theory. We then focus on the color-singlet sector and determine the so far unknown leading ultrasoft contribution to the static potential, which is of order alpha_s^4 ln(μ), and consequently to the static energy, which is of order alpha_s^4 ln(alpha_s). Finally, in the case of an equilateral geometry, we solve the renormalization group equations and resum the leading ultrasoft logarithms for the static potential of three quarks in a color singlet, octet and decuplet representation.
In a weak-coupling effective field theory framework we study quarkonium dissociation induced by inelastic scattering with partons in the medium. This is the dominant dissociation process for temperatures such that the Debye mass is larger than the binding energy. We evaluate the dissociation cross section and the corresponding thermal decay width. At leading order we derive a convolution formula relating the two, which is consistent with the optical theorem and QCD at finite temperature. Bound state effects are systematically included. They add contributions to the cross section and width that are beyond a quasi-free approximation, whose validity is critically reviewed. For temperatures such that the Debye mass is smaller than the binding energy, the dominant dissociation mechanism is gluo-dissociation consisting in quarkonium dissociation induced by the absorbtion of a gluon from the medium. We calculate the gluo-dissociation cross section and width at next-to-leading-order accuracy.
In finite-temperature field theory, the cyclic Wilson loop is defined as a rectangular Wilson loop spanning the whole compactified time direction. In a generic non-abelian gauge theory, we calculate the perturbative expansion of the cyclic Wilson loop up to order g^4. At this order and after charge renormalization, the cyclic Wilson loop is known to be ultraviolet divergent. We show that the divergence is not associated with cusps in the contour but is instead due to the contour intersecting itself because of the periodic boundary conditions. One consequence of this is that the cyclic Wilson loop mixes under renormalization with the correlator of two Polyakov loops. The resulting renormalization equation is tested up to order g^6 and used to resum the leading logarithms associated with the intersection divergence. Implications for lattice studies of this operator, which may be relevant for the phenomenology of quarkonium at finite temperature, are discussed.
In the framework of Soft-Collinear Effective Theory, the jet quenching parameter, $\hat{q}$, has been evaluated by adding the effect of Glauber gluon interactions to the propagation of a highly-energetic collinear parton in a medium. The result, which holds in covariant gauges, has been expressed in terms of the expectation value of two Wilson lines stretching along the direction of the four-momentum of the parton. In this paper, we show how that expression can be generalized to an arbitrary gauge by the addition of transverse Wilson lines. The transverse Wilson lines are explicitly computed by resumming interactions of the parton with Glauber gluons that appear only in non-covariant gauges. As an application of our result, we discuss the contribution to $\hat{q}$ coming from transverse momenta of order $g^2T$ in a medium that is a weakly-coupled quark-gluon plasma.
We compare lattice data for the short-distance part of the static energy in 2+1 flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale r_0 with the QCD scale Lambda_{MS}. With the input of the value of r_0, this provides a determination of the strong coupling alpha_s at the typical distance scale of the lattice data. We obtain alpha_s(1.5 GeV)=0.326\pm0.019, which provides a novel determination of alpha_s at low energy and with three-loop accuracy (including resummation of the leading ultrasoft logarithms). When this value is evolved to the Z-mass scale M_Z, it corresponds to alpha_s(M_Z)=0.1156^{+0.0021}_{-0.0022}.
In the framework of the soft-collinear effective theory, we present a gauge invariant definition of the transverse momentum broadening probability of a highly-energetic collinear quark in a medium and consequently of the jet quenching parameter $\hat{q}$.
We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r_0Lambda_MS by comparison with available lattice data, where r_0 is the lattice scale and Lambda_MS is the QCD scale. We obtain r_0Lambda_MS=0.637^{+0.032}_{-0.030} for the zero-flavor case. The procedure we describe can be directly used to obtain r_0Lambda_MS in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling alpha_s as an input, the unquenched result would provide a determination of the lattice scale r_0.
The paper contains a systematic, model-independent treatment of electric dipole (E1) transitions in heavy quarkonium. Within the effective field theory framework of potential non-relativistic QCD (pNRQCD), we derive the complete set of relativistic corrections of relative order v^2 both for weakly and strongly-coupled quarkonia. The result supports and complements former results from potential model calculations.
The thermal width of heavy-quarkonium bound states in a quark-gluon plasma has been recently derived in an effective field theory approach. Two phenomena contribute to the width: the Landau damping phenomenon and the break-up of a colour-singlet bound state into a colour-octet heavy quark-antiquark pair by absorption of a thermal gluon. In the paper, we investigate the relation between the singlet-to-octet thermal break-up and the so-called gluo-dissociation, a mechanism for quarkonium dissociation widely used in phenomenological approaches. The gluo-dissociation thermal width is obtained by convoluting the gluon thermal distribution with the cross section of a gluon and a 1S quarkonium state to a colour octet quark-antiquark state in vacuum, a cross section that at leading order, but neglecting colour-octet effects, was computed long ago by Bhanot and Peskin. We will, first, show that the effective field theory framework provides a natural derivation of the gluo-dissociation factorization formula at leading order, which is, indeed, the singlet-to-octet thermal break-up expression. Second, the singlet-to-octet thermal break-up expression will allow us to improve the Bhanot--Peskin cross section by including the contribution of the octet potential, which amounts to include final-state interactions between the heavy quark and antiquark. Finally, we will quantify the effects due to final-state interactions on the gluo-dissociation cross section and on the quarkonium thermal width.
Effective field theories for quarkonium at zero and finite temperature provide an unifying description for a wide class of phenomena. As an example, we discuss physical effects induced by dipole transitions.