arXiv subjects

Matthias Berwein

Publications and source records attributed to Matthias Berwein.

11 recordsLinked to original sources

arXiv2024

One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schrödinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the $χ_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.

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arXiv2020

Polyakov loop correlator in perturbation theory

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order $g^7$ correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

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arXiv2019

Perturbative static quark potential in Maximal Abelian gauge

We calculate the static quark potential for an SU(N) gauge theory in the Maximal Abelian gauge as well as its Abelian projection up to two loops in perturbation theory. We discuss its renormalization properties. The result is compared with a recent lattice result at $r \lesssim 0.5$ fm.

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arXiv2018

Poincaré invariance in NRQCD and pNRQCD revisited

We investigate how fields transform under the Poincaré group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed terms. By requiring invariance of the action under these transformations, nontrivial relations between Wilson coefficients for both nonrelativistic QCD and potential nonrelativistic QCD are derived. We show explicitly how the Poincaré algebra is satisfied, and how this gives complementary information on the Wilson coefficients. We also briefly discuss the implications of our results, as well as the possibility of applying this method to other types of effective field theories.

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arXiv2016

An effective field theory approach to hybrids

Heavy quarkonium hybrids are studied in an effective field theory framework. Coupled and uncoupled Schrödinger equations are obtained for different quantum numbers of the hybrid states. The results are discussed and compared to other approaches.

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arXiv2015

The Polyakov loop at next-to-next-to leading order

We calculate the next-to-next-to-leading correction to the expectation value of the Polyakov loop or equivalently to the free energy of a static charge. This correction is of order $g^5$. We show that up to this order the free energy of the static charge is proportional to the quadratic Casimir operator of the corresponding representation. We also compare our perturbative result with the most recent lattice results in SU(3) gauge theory.

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arXiv2015

Quarkonium Hybrids with Nonrelativistic Effective Field Theories

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.

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arXiv2014

Power Divergences in Overlapping Wilson Lines

We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and factorization of power divergences for certain linear combinations of associated loop functions.

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arXiv2013

Renormalization of Loop Functions in QCD

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.

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arXiv2013

Ultraviolet divergences in the cyclic Wilson loop and their renormalization

We discuss the cyclic Wilson loop, i.e. a rectangular Wilson loop that spans the entire compactified time axis in the imaginary time formalism. The result of a perturbative calculation at $O(α_s^2)$ is given, with the main focus on the ultraviolet divergences of this operator. Based on a general analysis of divergences in loop diagrams, we find that, unlike usual Wilson loops, the cyclic loop does not have cusp divergences but intersection divergences, where the intersections arise due to the periodic boundary conditions. As a result, the cyclic Wilson loop itself is not multiplicatively renormalizable, but the difference between it and the correlator of two Polyakov loops is.

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arXiv2013

Renormalization of the cyclic Wilson loop

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.

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