A
bstract
We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the ...pattern of underlying symmetries, chiral and conformal, we analyze the two-point functions theoretically and on the lattice, and determine the finite size scaling and the infinite volume fermion mass dependence of the would-be hadron masses. We show that the spectrum in the Coulomb phase of the system can be described in the context of a universal scaling analysis and we provide the nonperturbative determination of the fermion mass anomalous dimension γ
∗
= 0.235(46) at the infrared fixed point. We comment on the agreement with the four-loop perturbative prediction for this quantity and we provide a unified description of all existing lattice results for the spectrum of this system, them being in the Coulomb phase or the asymptotically free phase. Our results corroborate the view that the fixed point we are studying is not associated to a physical singularity along the bare coupling line and estimates of physical observables can be attempted on either side of the fixed point. Finally, we observe the restoration of the U(1) axial symmetry in the two-point functions.
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of ...physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
We show that the anomalous dimension γG of the scalar glueball operator contains information on the mechanism that leads to the onset of conformality at the lower edge of the conformal window in a ...non-Abelian gauge theory. In particular, it distinguishes whether the merging of an UV and an IR fixed point – the simplest mechanism associated to a conformal phase transition and preconformal scaling – does or does not occur. At the same time, we shed light on new analogies between QCD and its supersymmetric version. In SQCD, we derive an exact relation between γG and the mass anomalous dimension γm, and we prove that the SQCD exact beta function is incompatible with merging as a consequence of the a-theorem; we also derive the general conditions that the latter imposes on the existence of fixed points, and prove the absence of an UV fixed point at nonzero coupling above the conformal window of SQCD. Perhaps not surprisingly, we then show that an exact relation between γG and γm, fully analogous to SQCD, holds for the massless Veneziano limit of large-N QCD. We argue, based on the latter relation, the a-theorem, perturbation theory and physical arguments, that the incompatibility with merging may extend to QCD.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We present results of lattice QCD simulations with mass-degenerate up and down and mass-split strange and charm (
N
f
= 2 + 1 + 1) dynamical quarks using Wilson twisted mass fermions at maximal ...twist. The tuning of the strange and charm quark masses is performed at two values of the lattice spacing
a
≈ 0:078 fm and
a
≈ 0:086 fm with lattice sizes ranging from
L
≈ 1:9 fm to
L
≈ 2:8 fm. We measure with high statistical precision the light pseudoscalar mass
m
PS
and decay constant
f
PS
in a range 270 ≲
m
PS
≲ 510 MeV and determine the low energy parameters
f
0
and
of SU(2) chiral perturbation theory. We use the two values of the lattice spacing, several lattice sizes as well as different values of the light, strange and charm quark masses to explore the systematic effects. A first study of discretisation effects in light-quark observables and a comparison to
N
f
= 2 results are performed.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We present a detailed analysis of
ε′/
ε within the Standard Model, taking into account the strong enhancement through final-state interactions identified by Pallante and Pich in Phys. Rev. Lett. 84 ...(2000) 2568 and Nucl. Phys. B 592 (2000) 294. The relevant hadronic matrix elements are fixed at leading order in the 1/
N
C
expansion, through a matching procedure between the effective short-distance Lagrangian and its corresponding low-energy description in Chiral Perturbation Theory. All large logarithms are summed up, both at short and long distances. Two different numerical analyses are performed, using either the experimental or the theoretical value for
ε, with compatible results. We obtain Re(
ε′/
ε)=(1.7±0.9)×10
−3. The error is dominated by the uncertainty in the value of the strange quark mass and the estimated corrections from unknown 1/
N
C
-suppressed local contributions. A better estimate of the strange quark mass would reduce the uncertainty to about 30%. The Standard Model prediction agrees with the present experimental world average Re(
ε′/
ε)=(1.93±0.24)×10
−3.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was ...mistaken.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We present a study of the finite-volume two-pion matrix elements and correlation functions of the I=0 scalar operator, in full and partially quenched QCD, at one-loop order in chiral perturbation ...theory. In partially quenched QCD, when the sea and valence light quark masses are not equal, the lack of unitarity leads to the same inconsistencies as in quenched QCD and the matrix elements cannot be determined. It is possible, however, to overcome this problem by requiring the masses of the valence and sea quarks to be equal for the u and d quarks while keeping the strange quark (s) quenched (or partially quenched), but only in the kinematic region where the two-pion energy is below the two-kaon threshold. Although our results are obtained at NLO in chiral perturbation theory, they are more general and are also valid for non-leptonic kaon decays (we also study the matrix elements of (8,1) operators, such as the QCD penguin operator Q6). We point out that even in full QCD, where any problems caused by the lack of unitarity are clearly absent, there are practical difficulties in general, caused by the fact that finite-volume energy eigenstates are linear combination of two-pion, two-kaon and two-η states. Our Letter implies that extracting ΔI=1/2, K→ππ decay amplitudes from simulations with ms=md,u is not possible in partially quenched QCD (and is very difficult in full QCD).
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We perform a calculation in one-loop chiral perturbation theory of the two-pion matrix elements and correlation functions of an I=0 scalar operator, in finite and infinite volumes for both full and ...quenched QCD. We show that major difficulties arise in the quenched theory due to the lack of unitarity. Similar problems are expected for quenched lattice calculations of K→ππ amplitudes with ΔI=1/2. Our results raise the important question of whether it is consistent to study K→ππ amplitudes beyond leading order in chiral perturbation theory in quenched or partially quenched QCD.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
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