| 1. |
- Alexandrou, Constantia, et al.
(author)
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Renormalization constants for 2-twist operators in twisted mass QCD
- 2011
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In: Physical Review D. Particles and fields. - 0556-2821 .- 1089-4918. ; 83:1
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Journal article (peer-reviewed)abstract
- Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a2) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a2). The renormalization conditions are defined in the RI⊃′-MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS̄ at 2 GeV using 3-loop perturbative results for the conversion factors
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| 2. |
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| 3. |
- Constantinou, Martha, et al.
(author)
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(a 2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons
- 2009
-
In: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; 10
-
Journal article (peer-reviewed)abstract
- We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form , to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and the Symanzik improved action for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, (a 2). Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in (a 1) improvement calculations; there, IR divergent terms are seen to have the same structure as in the (a 0) case, by virtue of parity under integration, and they can thus be handled by well-known techniques. We explain how to correctly extract the full (a 2) dependence; in fact, our method is generalizable to any order in a. The (a 2) corrections to the quark propagator and Green's functions computed in this paper are useful to improve the nonperturbative RI-MOM determination of renormalization constants for quark bilinear operators. Our results depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: Oa2results.m; the file is best perused as Mathematica input
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| 4. |
- Constantinou, Martha, et al.
(author)
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BK-parameter from Nf=2 twisted mass lattice QCD
- 2011
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In: Physical Review D. Particles and fields. - 0556-2821 .- 1089-4918. ; 83:1
-
Journal article (peer-reviewed)abstract
- We present an unquenched Nf=2 lattice computation of the B K parameter which controls K0-K̄0 oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder-Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the BK parameter which is both multiplicatively renormalizable and O(a) improved. Employing the nonperturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get BKRGI=0.729±0.030, a number well in line with the existing quenched and unquenched determinations.
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| 5. |
- Constantinou, Martha, et al.
(author)
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Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action
- 2010
-
In: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; 8
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Journal article (peer-reviewed)abstract
- We present results for the renormalization constants of bilinear quark operators obtained by using the tree-level Symanzik improved gauge action and the N f = 2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)-improvement. Our results are also relevant for the corresponding standard (un-twisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants Z V, Z A and the ratio Z P /Z S have been computed using the RI-MOMapproach, as well as other alternative methods. For Z A and Z P /Z S, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for Z V a Ward Identity has been used. The quark field renormalization constant Z q and the scale dependent renormalization constants Z S, Z P and Z T are determined in the RI-MOM scheme. Leading discretization effects of O(g 2a 2), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates
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| 6. |
- Constantinou, Martha, et al.
(author)
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Perturbative renormalization factors and Oða2Þ corrections for latticefour-fermion operators with improved fermion/gluon actions
- 2011
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In: Physical Review D. Particles and fields. - 0556-2821 .- 1089-4918. ; 83:7
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Journal article (peer-reviewed)abstract
- In this work we calculate the corrections to the amputated Green's functions of four-fermion operators, in 1-loop lattice perturbation theory. One of the novel aspects of our calculations is that they are carried out to second order in the lattice spacing, O(a2). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). While our Green's function calculations regard any pointlike four-fermion operators which do not mix with lower dimension ones, we pay particular attention to ΔF=2 operators, both parity conserving and parity violating (F stands for flavor: S, C, B). By appropriately projecting those bare Green's functions we compute the perturbative renormalization constants for a complete basis of four-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a0) results did not exist in the literature to date. The correction terms which we calculate (along with our previous O(a2) calculation of Z Ψ) are essential ingredients for minimizing the lattice artifacts which are present in nonperturbative evaluations of renormalization constants with the RI′-MOM method. Our perturbative results, for the matrix elements of ΔF=2 operators and for the corresponding renormalization matrices, depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m; the file is best perused as Mathematica input. The main results of this work have been applied to improve nonperturbative estimates of the BK-parameter in N F=2 twisted mass lattice QCD
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| 7. |
- Gross, Franz, et al.
(author)
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50 Years of quantum chromodynamics : Introduction and Review
- 2023
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In: European Physical Journal C. - 1434-6044. ; 83:12
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Research review (peer-reviewed)abstract
- Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, αs(Q2) , that varies with the energy scale Q2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of αs at low momentum transfers limits perturbative calculations to the high-energy region where Q2≫ΛQCD2≃ (250 MeV) 2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large Nc -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected qq¯ mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, W± or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude.
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