Lattice study of large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>QCD

DeGrand, Thomas; Liu, Yuzhi

doi:10.1103/physrevd.94.034506

Cited by 30 publications

(40 citation statements)

References 63 publications

(95 reference statements)

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“…In the fourth section we compare the sigma model action prediction to the computations of DeGrand and Liu for variable N c [2]. We find fair agreement with their results, although the quark masses considered are sufficiently large so that deviations from the naive large N c scaling predictions are small.…”

Section: Introductionsupporting

confidence: 52%

“…al. turn out to be too large to resolve the case we consider from that of the conventional large N c limit [2,3]. We argue that for quark masses m q Λ QCD /N 3/2 c , both the baryon mass and nucleon size scale as √ N c .…”

mentioning

confidence: 81%

“…This is when Using the model described in Sect. 2 we attempt to fit the dependence of the mesonic properties on the quark mass obtained from the lattice data [2] for N c = 3. We would like to point out that the model has a few parameters and fixing the parameters at the physical quark mass leaves us with only one parameter to vary -the sigma mass.…”

Section: The Low Energy Linear Pion Sigma Model As a Function Of N Cmentioning

confidence: 99%

“…In Figure 1, we show the dependence of the pion decay constant and the pion mass on the quark mass in the model; the results are compared to the lattice QCD calculations from Ref. [2]. The model results are obtained by solving the stationarity conditions, Eq.…”

Section: The Low Energy Linear Pion Sigma Model As a Function Of N Cmentioning

confidence: 99%

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The Large-$N$ Limit with Vanishing Leading Order Condensate for Zero Pion Mass

McLerran¹,

Skokov²

2018

Acta Phys. Pol. B

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It is conventionally assumed that the negative mass squared term in the linear sigma model version of the pion Lagrangian is M 2 ∼ Λ 2 QCD in powers of N c [1]. We consider the case where M 2 ∼ Λ 2 QCD /N c so that to leading order in N c this symmetry breaking term vanishes. We present some arguments why this might be plausible. One might think that such a radical assumption would contradict lattice Monte Carlo data on QCD as function of N c . We show that the linear sigma model gives a fair description of the data of DeGrand and Liu both for N c = 3, and for variable N c . The values of quark masses considered by DeGrand and Liu, and by Bali et. al. turn out to be too large to resolve the case we consider from that of the conventional large N c limit [2,3]. We argue that for quark masses m q Λ QCD /N 3/2 c , both the baryon mass and nucleon size scale as √ N c . For m q Λ QCD /N 3/2 c N c limit, where nuclear matter is bound with binding energies of order the nucleon mass and forms a Skyrme crystal.

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Section: Introductionsupporting

confidence: 52%

mentioning

confidence: 81%

Section: The Low Energy Linear Pion Sigma Model As a Function Of N Cmentioning

confidence: 99%

Section: The Low Energy Linear Pion Sigma Model As a Function Of N Cmentioning

confidence: 99%

See 2 more Smart Citations

The Large-$N$ Limit with Vanishing Leading Order Condensate for Zero Pion Mass

McLerran¹,

Skokov²

2018

Acta Phys. Pol. B

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“…Lattice studies in this direction have started to appear only quite recently. Examples of recent and current numerical work on relevant models (some of which have been reviewed in [8]) include [9][10][11][12][13][14]. In this contribution we provide the first (and still preliminary) numerical study of the Sp(4) gauge theory with N f = 2 fundamental Dirac fermions.…”

Section: Introductionmentioning

confidence: 99%

Higgs compositeness in Sp(2N) gauge theories – Determining the low-energy constants with lattice calculations

et al. 2018

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As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing.Combined contributions of B. Lucini

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Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

193

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We present an implementation of the relativistic three-particle quantization condition including both sand d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, K df,3 , about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, K 2 . Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong twoparticle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3π + system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of K df,3 . Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.F Properties of the isotropic approximation 50 G Failure of Eq. (4.34) for quadratic and cubic terms in the threshold expansion 53There is also an induced three-particle interaction due to the exchange of a virtual particle between a pair of two-particle interactions. This is included in all approaches.2 The p wave is absent due to Bose symmetry. 3 It is expected, however, that there is no barrier to extending to higher waves.-3 -Z 2 symmetry that forbids 2 ↔ 3 transitions. Another important feature of this approach is that it can be made relativistic [5], which turns out to simplify the expansion about threshold. Although we use the RFT approach, we expect that many of the technical considerations and general conclusions will apply to all three approaches to the quantization condition.The formalism of Ref.[1] is restricted to two-particle interactions that do not lead to poles in K 2 , the two-particle K matrix. If there are such poles, then one should use the generalized, and more complicated, formalism derived in Ref. [7]. For simplicity, we consider here only examples in which there are no K-matrix poles.Since our main goal is to show how the formalism works when including higher waves, our numerical examples are mainly chosen for illustrative purposes and do not represent physical systems. However, there is one case in nature for which our simplified setting applies, namely the 3π + system. Thus, in one of our examples, we set the two-particle scattering parameters to those measured experimentally for two charged pions, and illustrate the dependence of the resulting three-pion spectrum on the three-particle scattering parameters. This is similar to the study made in Ref.[15] using the FVU approach, except here we include d-wave dimers.All three-particle quantization condi...

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Lattice study of largeNcQCD

Cited by 30 publications

References 63 publications

The Large-$N$ Limit with Vanishing Leading Order Condensate for Zero Pion Mass

The Large-$N$ Limit with Vanishing Leading Order Condensate for Zero Pion Mass

Higgs compositeness in Sp(2N) gauge theories – Determining the low-energy constants with lattice calculations

Implementing the three-particle quantization condition including higher partial waves

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