<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>K</mml:mi></mml:math>scattering in full QCD with domain-wall valence quarks

Beane, Silas R.; Bedaque, Paulo F.; Luu, Thomas; Orginos, Konstantinos; Pallante, Elisabetta; Parreño, A.; Savage, Martin J.

doi:10.1103/physrevd.74.114503

Cited by 103 publications

(166 citation statements)

References 56 publications

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“…However, we will also estimate the impact of higher-order effects in the isospin-breaking corrections to the phase shifts by comparing the numerical results obtained using either leading-or next-to-leading-order expressions for these scattering parameters. The latter read 15) where the last term in Eq. (A.15) comes from the expansion ofJ(4M 2 π 0 ) in powers of ∆ π (see the expression of a 00 in Eq.…”

Section: ππ Scattering Amplitudesmentioning

confidence: 99%

Isospin breaking in the phases of the K e4 form factors

2013

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Isospin breaking in the K ℓ4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the K ± → π + π − e ± νe channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S-and P -wave ππ phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only ππ rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a 0 0 and a 2 0 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K ± → π + π − e ± νe form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a 0 0 and a 2 0 , as well as for low-energy constants and order parameters of two-flavour χPT.

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Section: ππ Scattering Amplitudesmentioning

confidence: 99%

Isospin breaking in the phases of the K e4 form factors

2013

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“…The S-wave quarkonium states we consider have angular momentum J = 0, 1 and define the total angular momentum of the entire system since the pion is spin-zero. Since the pion and bb states have different masses, the appropriate generalisation of the Lüscher relation to asymmetric systems [35] is required. We can define a scattering momentum p through the relation…”

Section: Quarkonium-pion Scatteringmentioning

confidence: 99%

Quarkonium at nonzero isospin density

2013

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We calculate the energies of quarkonium bound states in the presence of a medium of nonzero isospin density using lattice QCD. The medium, created using a canonical (fixed isospin charge) approach, induces a reduction of the quarkonium energies. As the isospin density increases, the energy shifts first increase and then saturate. The saturation occurs at an isospin density close to that where previously a qualitative change in the behaviour of the energy density of the medium has been observed, which was conjectured to correspond to a transition from a pion gas to a BoseEinstein condensed phase. The reduction of the quarkonium energies becomes more pronounced as the heavy-quark mass is decreased, similar to the behaviour seen in two-colour QCD at non-zero quark chemical potential. In the process of our analysis, the η b -π and Υ-π scattering phase shifts are determined at low momentum. An interpolation of the scattering lengths to the physical pion mass gives aη b ,π = 0.0025(8)(6) fm and aΥ,π = 0.0030(9)(7) fm.

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“…There have been a number of recent lattice computations [17][18][19][20][21][22][23][24][25] utilizing the scheme first developed by the LHP Collaboration [72,73] of employing domain wall valence quarks with the publicly available MILC configurations. In particular, the NPLQCD Collaboration has computed the I 2 scattering length [19], 17 f K =f [23] and determined both the I 3=2 and I 1=2 K scattering lengths through a direct determination of the I 3=2 K scattering length [25]. As we will demonstrate by explicit computation, the I 1 KK scattering length, together with the above three systems, share only two linearly independent sets of counterterms, which are the physical counterterms of interest.…”

Section: Applicationsmentioning

confidence: 99%

“…There recently has been a direct MA lattice QCD determination of the I 3=2 K scattering length, which in combination with the theoretical knowledge of the NLO PT I 1=2 and I 3=2 K scattering lengths [90 -93] has allowed a determination of both isospin scattering lengths [25]. There is additionally a two-loop computation of K scattering in SU 3 PT which studies the convergence of the theory with standard power counting [94].…”

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confidence: 99%

Two meson systems with Ginsparg-Wilson valence quarks

2007

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Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulas. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulas, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretizations, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulas do not depend on the unknown constant C Mix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I 1 KK scattering length does not depend on C Mix in contrast to the I 3=2 K scattering length. In addition, we show that these observables combined with f K =f and the I 2 scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I 1 KK scattering length.

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πKscattering in full QCD with domain-wall valence quarks

Cited by 103 publications

References 56 publications

Isospin breaking in the phases of the K e4 form factors

Isospin breaking in the phases of the K e4 form factors

Quarkonium at nonzero isospin density

Two meson systems with Ginsparg-Wilson valence quarks

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