Large $$N_c$$ scaling of meson masses and decay constants

Hernández, P.; Peña, Carlos; Romero-López, Fernando

doi:10.1140/epjc/s10052-019-7395-y

Cited by 34 publications

(65 citation statements)

References 72 publications

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“…The N c dependence can be studied from first-principles in lattice QCD by simply simulating at different number of colours [23][24][25][26][27]. In our previous work [6][7][8] we explored the related weak amplitudes K → π and K →K in the quenched approximation, and found no unnaturally large subleading N c corrections, although we confirmed the exact anticorrelation of these corrections in the two isospin channels.…”

Section: Introductionmentioning

confidence: 55%

“…The lattice spacing is found to be a ∼ 0.075 fm for all values of N c (see also Ref. [27]). In 7 See Ref.…”

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 77%

“…9 This differs from Ref. [27], where we picked c sw = 1.69. This value matches the one in the sea sector.…”

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 86%

“…The value of the lattice spacing is a 0.075 fm for the "A" ensembles (see Ref. [27]), whereas it is a 0.065 fm for "B" ensembles. We provide the pion mass in the valence sector, aM v π , and the PCAC mass, am v pcac .…”

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 99%

“…In Fit 1, we use all data points with N c = 3 − 6 in a simultaneous chiral and N c fit using Eqs. (23) and (27), incorporating the 1/N c Table 6 Results for Fit 1: the simultaneous chiral and N c fits for A + and A + A − . Errors are only statistical…”

Section: Extraction Of the Effective Couplings G ±mentioning

confidence: 99%

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Dissecting the $$\Delta I=1/2$$ rule at large $$N_c$$

Donini¹,

Hernández²,

Peña

et al. 2020

Eur. Phys. J. C

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We study the scaling of kaon decay amplitudes with the number of colours, $$N_c$$ N c , in a theory with four degenerate flavours, $$N_f=4$$ N f = 4 . In this scenario, two current-current operators, $$Q^\pm $$ Q ± , mediate $$\Delta S=1$$ Δ S = 1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $$K\rightarrow (\pi \pi )_{I=0,2}$$ K → ( π π ) I = 0 , 2 , $$A_0$$ A 0 and $$A_2$$ A 2 . In particular, we concentrate on the simpler $$K\rightarrow \pi $$ K → π amplitudes, $$A^\pm $$ A ± , mediated by these two operators. A diagrammatic analysis of the large-$$N_c$$ N c scaling of these observables is presented, which demonstrates the anticorrelation of the leading $${{\mathcal {O}}}(1/N_c)$$ O ( 1 / N c ) and $${{\mathcal {O}}}(N_f/N_c^2)$$ O ( N f / N c 2 ) corrections in both amplitudes. Using our new $$N_f=4$$ N f = 4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the $$\Delta I=1/2$$ Δ I = 1 / 2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $$g^\pm $$ g ± , can be determined. A NLO estimate of the $$K \rightarrow (\pi \pi )_{I=0,2}$$ K → ( π π ) I = 0 , 2 isospin amplitudes can then be derived, which is in good agreement with the experimental value.

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Section: Introductionmentioning

confidence: 55%

“…The lattice spacing is found to be a ∼ 0.075 fm for all values of N c (see also Ref. [27]). In 7 See Ref.…”

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 77%

“…9 This differs from Ref. [27], where we picked c sw = 1.69. This value matches the one in the sea sector.…”

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 86%

Section: Simulation and Matching Of Sea And Valence Sectorsmentioning

confidence: 99%

Section: Extraction Of the Effective Couplings G ±mentioning

confidence: 99%

See 3 more Smart Citations

Dissecting the $$\Delta I=1/2$$ rule at large $$N_c$$

Donini¹,

Hernández²,

Peña

et al. 2020

Eur. Phys. J. C

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Meson spectrum in the large N limit

Pérez

González-Arroyo

Okawa

2021

J. High Energ. Phys.

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We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

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A lattice study of ππ scattering at large Nc

Baeza-Ballesteros

Hernández

Romero-López

2022

J. High Energ. Phys.

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We present the first lattice study of pion-pion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc = 3 − 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for Nf≥ 4. A representative state is $$ \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} $$ D s + π + − D + K + / 2 . Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large Nc. For this, we compute the analytical U(Nf) ChPT prediction for two-pion scattering, and use the lattice results to constrain the Nc scaling of the relevant low-energy couplings.

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Large $$N_c$$ scaling of meson masses and decay constants

Cited by 34 publications

References 72 publications

Dissecting the $$\Delta I=1/2$$ rule at large $$N_c$$

Dissecting the $$\Delta I=1/2$$ rule at large $$N_c$$

Meson spectrum in the large N limit

A lattice study of ππ scattering at large Nc

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