Nora Brambilla

Potential NRQCD: an effective theory for heavy quarkonium

Abstract Within an effective field theory framework we study heavy-quark–antiquark systems with a typical distance between the heavy quark and the antiquark smaller than 1/ Λ QCD . A suitable definition of the potential is given within this framework, while non-potential (retardation) effects are taken into account in a systematic way. We explore different physical systems. Model-independent results on the short distance behaviour of the energies of the gluonic excitations between static quarks are obtained. Finally, we show how infrared renormalons affecting the static potential get cancelled in the effective theory.

Static quark-antiquark pairs at finite temperature

In a fram ework thatm akesclosecontactwith m odern eectiveeld theoriesfornon-relativistic bound states at zero tem perature,we study the real-tim e evolution ofa static quark-antiquark pairin a m edium ofgluonsand lightquarksatnitetem perature.Fortem peraturesranging from values larger to sm aller than the inverse distance ofthe quark and antiquark,1=r,and at short distances,we derive the potentialbetween the two static sources,and calculate theirenergy and therm aldecay width.Two m echanism scontributeto thetherm aldecay width:theim aginary part ofthe gluon selfenergy induced by the Landau dam ping phenom enon,and the quark-antiquark color singletto color octettherm albreak up. Param etrically,therstm echanism dom inates for tem peraturessuch thatthe Debye m assislargerthan the binding energy,while the latter,which wequantify hereforthersttim e,dom inatesfortem peraturessuch thattheDebyem assissm aller than thebindingenergy.IftheDebyem assisofthesam eorderas1=r,ourresultsarein agreem ent with a recentcalculation ofthestaticW ilson loop atnitetem perature.Fortem peraturessm aller than 1=r,wend new contributions to the potential, both realand im aginary,which m ay be relevantto understand theonsetofheavy quarkonium dissociation in a therm alm edium .

Effective field theories for heavy quarkonium

QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. Here I summarize few relevant concepts and some of the interesting physical applications (spectrum, decays, production) of NREFT.

Infrared behavior of the static potential in perturbative QCD

The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.

The heavy quarkonium spectrum at order mαs5lnαs

Abstract We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at O ( mα s 5 ) in the heavy quarkonium spectrum. These leading logs, when Λ QCD ≪ mα s 2 , give the complete O ( mα s 5 ln α s ) corrections to the heavy quarkonium spectrum.

Quarkonium spectroscopy and perturbative QCD: a new perspective

We study the energy spectrum of bottomonium in perturbative QCD, taking alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar) and (b,cbar) states are also examined.

Model-independent study of magnetic dipole transitions in quarkonium

We study magnetic dipole (M1) transitions between two quarkonia in the framework of nonrelativistic effective field theories of QCD. Relativistic corrections of relative order v{sup 2} are investigated in a systematic fashion. Nonperturbative corrections due to color-octet effects are considered for the first time and shown to vanish at relative order v{sup 2}. Exact, all order expressions for the relevant 1/m and 1/m{sup 2} magnetic operators are derived. The results allow us to scrutinize several potential model claims. In particular, we show that QCD excludes both contributions to the anomalous magnetic moment of the quarkonium induced by low-energy fluctuations and contributions to the magnetic dipole operators of the type induced by a scalar potential. Finally, we apply our results to the transitions J/{psi}{yields}{eta}{sub c}{gamma}, {upsilon}(1S){yields}{eta}{sub b}{gamma}, {upsilon}(2S){yields}{eta}{sub b}(2S){gamma}, {upsilon}(2S){yields}{eta}{sub b}{gamma}, {eta}{sub b}(2S){yields}{upsilon}(1S){gamma}, h{sub b}(1P){yields}{chi}{sub b0,1}(1P){gamma}, and {chi}{sub b2}(1P){yields}h{sub b}(1P){gamma} by assuming these quarkonium states in the weak-coupling regime. Our analysis shows that the J/{psi}{yields}{eta}{sub c}{gamma} width is consistent with a weak-coupling treatment of the charmonium ground state, while such a treatment for the hindered transition {upsilon}(2S){yields}{eta}{sub b}{gamma} appears difficult to accommodate within the CLEO III upper limit.

Determination of

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 leadinglogarithmic 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 r0 with

\alpha_s

By analogy with potential nonrelativistic QCD, we construct effective field theories suitable to describe the heavy-quark sector of baryons made of two and three heavy quarks. A long-standing discrepancy between the hyperfine splitting of doubly heavy baryons obtained in the heavy-quark effective theory and potential models is solved. The one-loop matching of the 4-quark operators of dimension 6 is provided.

from the QCD static energy

We study the Polyakov loop and the correlator of two Polyakov loops at finite temperature in the weak-coupling regime. We calculate the Polyakov loop at order g{sup 4}. The calculation of the correlator of two Polyakov loops is performed at distances shorter than the inverse of the temperature and for electric screening masses larger than the Coulomb potential. In this regime, it is accurate up to order g{sup 6}. We also evaluate the Polyakov-loop correlator in an effective field theory framework that takes advantage of the hierarchy of energy scales in the problem and makes explicit the bound-state dynamics. In the effective field theory framework, we show that the Polyakov-loop correlator is at leading order in the multipole expansion the sum of a color-singlet and a color-octet quark-antiquark correlator, which are gauge invariant, and compute the corresponding color-singlet and color-octet free energies.