Observing string breaking with Wilson loops

An uncontroversial observation of adjoint string breaking is proposed, while measuring the static potential from Wilson loops only. The overlap of the Wilson loop with the broken-string state is small, but non-vanishing, so that the broken-string groundstate can be seen if the Wilson loop is long enough. We demonstrate this in the context of the (2 + 1)d SU(2) adjoint static potential, using an improved version of the Lüscher-Weisz exponential variance reduction. To complete the picture we perform the more usual multichannel analysis with two basis states, the unbroken-string state and the broken-string state (two so-called gluelumps). As by-products, we obtain the temperature-dependent static potential measured from Polyakov loop correlations, and the fundamental SU(2) static potential with improved accuracy. Comparing the latter with the adjoint potential, we see clear deviations from Casimir scaling. [email protected] [email protected] 1 Motivation Quarks are linearly confined inside hadrons by a force called the strong interaction. Therefore, we cannot see single quarks: This is the basis of the stability of the matter we are formed of. One can study this force by analysing the energy between a static colour charge and a static anticharge. Unlike in the case of the electromagnetic force, this energy is, as a consequence of linear confinement, squeezed into a long flux tube. This flux tube is a string-like object. Therefore, one can ask whether this string actually breaks when it reaches a certain length. This breaking of the string corresponds to the screening of the static charges by a virtual matter-antimatter pair created from that very energy stored in the string. The energy of the groundstate of the system, the so-called static potential, completely changes its qualitative behaviour as a function of the distance between the two static charges and can therefore be used to detect string breaking. There are two main situations where string breaking can be studied: (i) when one deals with static charges in the fundamental representation, which can only be screened by other fundamental particles, such as dynamical quarks or fundamental Higgs fields; (ii) when one considers static charges in the adjoint representation which can be screened by the gluons of the gauge field. To avoid the simulation of costly dynamical quarks or of Higgs fields, we simply consider here adjoint static charges. The bound state of a gluon and an adjoint static charge is called a “gluelump”. Therefore, the breaking of the adjoint string leads to the creation of two of these gluelumps. Three approaches have been used to measure the static potential and study string breaking: • Correlation of Polyakov loops, at finite temperature [1]. • Multichannel Ansatz (also known as Variational Ansatz) using two types of operators: one for the string-like state and one for the broken-string state [2, 3]. • Wilson loops [4, 5]. String breaking has been seen using the first two methods, but no clear signal has been observed using the third one. The failure of the Wilson loop method seems to be due to the poor overlap of the Wilson loop operator with the broken-string state. It has even been speculated that this overlap is exactly zero [6]. This is why we have a closer look at this problem, taking advantage of recent, improved techniques to measure long Wilson loops. Preliminary results have been presented in [7]. In the next Section we recall notions about the static potential and its relation to the Wilson loop. In Section 3, we take the three methods into more detailed