Hamiltonian Effective Field Theory Study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>1535</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>Resonance in Lattice QCD

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B.; Stokes, Finn M.; Thomas, A. W.; Wu, Jia-Jun

doi:10.1103/physrevlett.116.082004

Cited by 73 publications

(76 citation statements)

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“…As the loop is correlated with the quarks carrying the quantum numbers of the state only via gluon exchange, resolving a nontrivial signal requires high statistics and innovative methods. While there has been recent success in isolating the relevant disconnected-loop contributions in ground-state baryon matrix elements [3,4], challenges in isolating baryon excitations in lattice QCD [10,40,[45][46][47][48][49][50][51][52][53][54][55][56][57] render the resolution of disconnected contributions elusive.Here, we draw on partially-quenched chiral effective field theory [44,[58][59][60][61][62][63][64][65][66] to understand the relative weight of these disconnected contributions to the form factors in QCD. With this insight, one can test quantitatively whether the light-quark contribution to the magnetic form factor of the Λ(1405), calculated in lattice QCD, is consistent with a molecular KN description of the internal structure.…”

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Light-quark contributions to the magnetic form factor of the Λ(1405)

et al. 2017

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In a recent study of the Λ(1405), the suppression of the strange-quark contribution to the magnetic form factor was interpreted as the discovery of a dominant antikaon-nucleon composition for this low-lying state. We confirm this result by calculating the light u-and d-quark contributions to the Λ(1405) magnetic form factor in lattice QCD in order to determine the extent to which their contributions support this exotic molecular description. Drawing on the recent graded-symmetry approach for the flavor-singlet components of the Λ(1405), the separation of connected and disconnected contributions is performed in both the flavor-octet and singlet representations. The relationship between light-quark contributions to the Λ(1405) magnetic form factor and the connected contributions of the nucleon magnetic form factors is established and compared with lattice calculations of the same quantities, confirming the KN molecular structure of the Λ(1405) in lattice QCD.Resolving and understanding the internal structure of hadronic excited states is an important contemporary problem in the field of nonperturbative QCD. While lattice QCD simulation methods are increasingly able to probe the chiral regime of ground state observables with unprecedented accuracy [1][2][3][4], the resolution of excited-baryon form factors is still at a very early stage [5][6][7][8][9][10].Interest in the Λ(1405) resonance has continued unabated for more than 50 years [10-44] because of its unusually low mass -lower even than the corresponding mass of the negative parity nucleon, despite containing a heavier strange quark. The unexpected position of the Λ(1405) in the spectrum has been explored in several studies, which typically indicate a significant contribution from a KN bound state . The πΣ channel also plays a nontrivial role. It is now widely agreed that there is a two-pole structure in this resonance region [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] stemming from attractive interactions in both the πΣ and KN channels. In making contact with results from lattice QCD [10,40,41], a description of the Λ(1405) over a range of quark masses has been developed [10,32,45], bridging constituent-quark ideas at heavy quark masses and the molecular KN dominance of the Λ(1405) at light quark masses.A recent lattice QCD study of the Λ(1405) reported evidence of a molecular KN structure [10]. There, the role of the strange quark was paramount in signaling the presence of a dominant KN structure. At heavier quark masses approaching the strange quark mass, the three quark flavors (u, d, s) are found to make approximately equal contributions to the magnetic form factor when their charges are set to unity. The underlying flavor symmetry is manifest. However, as the u and d quarks become light, flavor symmetry in the quark contributions to the magnetic form factor is found to be badly broken, and the strange-quark contribution drops by an order of magnitude from its maximum to a nearly vanishing value at the smallest quark mass. This feature h...

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Light-quark contributions to the magnetic form factor of the Λ(1405)

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“…We first apply the SL Hamiltonian to confirm the results, as established in [9][10][11][12][13][14], that the FVH method is equivalent to using Lüscher's formalism in relating the spectrum in finite volume to the scattering amplitudes in infinite volume. We then observe that the probability P ∆ (E) of finding the bare ∆ state in the πN scattering wave function contains resonance information which can be verified on the real-E axis, which is in turn accessible to experiments.…”

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confidence: 97%

“…[9][10][11][12][13][14]. This starts with the construction of a Hamiltonian to fit the data of the processes under consideration.…”

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Nucleon resonance structure in the finite volume of lattice QCD

Kamano

Lee

et al. 2017

Phys. Rev. D

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An approach for relating the nucleon resonances extracted from πN reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of πN reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance pole positions can be related to the probability P N * (E) of finding the bare state, N * , in the πN scattering states in infinite volume. We further demonstrate that the probability P V N * (E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P N * (E) as the volume increases. Our findings suggest that the comparison of P N * (E) and P V N * (E) can be used to examine whether the nucleon resonances extracted from the πN reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P V N * (E) directly from lattice QCD. The practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.

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“…For the states of zero momentum, the Hamiltonian p=0 can be expressed in terms of the undecayed state | , 0⟩ and its decay products in the form of a Lee Hamiltonian [22] (similar effective Hamiltonians are used also in quantum mechanics [6,19] and quantum field theory [9,23]):…”

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confidence: 99%

QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum

Giacosa

2018

Advances in High Energy Physics

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We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero threemomentum p. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as , to obtain the energy probability distribution, called p 푆 ( ), as the imaginary part of the propagator. The nondecay probability amplitude of the particle with momentum p turns out to be, as usual, its Fourier transform:−푖퐸푡 ( 푡ℎ is the lowest energy threshold in the rest frame of and corresponds to the sum of masses of the decay products). Upon a variable transformation, one can rewrite it asis the usual spectral function (or mass distribution) in the rest frame]. Hence, the latter expression, previously obtained by different approaches, is here confirmed in an independent and, most importantly, covariant QFT-based approach. Its consequences are not yet fully explored but appear to be quite surprising (such as the fact that the usual time-dilatation formula does not apply); thus its firm understanding and investigation can be a fruitful subject of future research.

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Hamiltonian Effective Field Theory Study of theN*(1535)Resonance in Lattice QCD

Cited by 73 publications

References 22 publications

Light-quark contributions to the magnetic form factor of the Λ(1405)

Light-quark contributions to the magnetic form factor of the Λ(1405)

Nucleon resonance structure in the finite volume of lattice QCD

QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum

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