Decay characteristics and masses of positive K Mesons produced by the Bevatron

Birge, Robert W.; Perkins, D. H.; Peterson, J.R.; Stork, D. H.; Whitehead, M

doi:10.1007/bf02746171

Cited by 77 publications

(16 citation statements)

References 13 publications

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“…An old problem in this sector, specifically in K → ππ decays, is the ∆I = 1/2 rule. This "rule" is the experimental observation, made nearly sixty years ago, that kaons (which have isospin of one-half) decay to the isospin-zero state with a much higher rate than to the isospin-two state [71,72,73]. The enhancement is measured to be [74] Re A K −→ (ππ, I=0)…”

Section: K → ππmentioning

confidence: 96%

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Hansen¹

2014

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Multi-Hadron Observables from Lattice Quantum Chromodynamics Maxwell T. HansenChair of the Supervisory Committee:Professor Stephen R. Sharpe Department of PhysicsWe describe formal work that relates the finite-volume spectrum in a quantum field theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the finite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable.In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic field theory, and summing to all orders in perturbation theory, we derive a result relating the finite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin Lüscher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the finite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin Lüscher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic field theory, we derive a relation between the spectrum and an infinite-volume three-to-three scattering quantity. This final analysis is the most complicated of the four, because the all-orders summation is more difficult for this system, and also because a number of new technical issues arise in analyzing the contributing diagrams.

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Section: K → ππmentioning

confidence: 96%

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Hansen¹

2014

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“…In on-massshell S-matrix theory the energy variable has a lower bound, the scattering threshold. If £=0 is chosen to correspond to threshold, this feature is incorporated into our model by restricting the observed input /(/) to be the positive-frequency part $ + (t) of a function $(t)&, 2 and the output 0(t) to be the Fourier transform of ^(£)/(£), where F is a tempered distribution with support [0, oo) and I is the inverse Fourier transform of #. Thus the input and the output are related by (1.1) …”

Section: Introductionmentioning

confidence: 99%

“…R. Screaton, Phys. Rev.165,1610 (1968), hereafter referred to as I 2. The symbols used for function and functional spaces are the usual ones; for definitions see Refs.…”

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Analyticity and Causality. II

Screaton

1969

Phys. Rev.

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“…Counters L and F will detect the K~ decay products with a probability that depends on the kinematics of the decay and the position along the beam where the decay occurs. Since Counter L is larger than Counter F, this correction is equivalent to a reduction of the effective value of d. With the assumption that the decay modes are the same for the Kr and the K+ meson, 5 we compute a correction for this effect of 9% to the counting rate of L and 3% to the rate of F. Therefore, we have made a net correction of -6% to the observed transmission. The uncertainty in the mean life from counting statistics is ±13%, and an additional uncertainty of tl% comes from the possible contamination due to TT~ mesons.…”

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confidence: 99%

Mean Life ofK−Mesons and Their Cross Section in Hydrogen

et al. 1957

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I N the course of experiments requiring the detection of antiprotons in a negative external beam from the Bevatron, 1 -2 it was found that K~ mesons also could be distinguished from the large background of lighter charged particles, primarily TT~ mesons. Particles of a a fixed momentum emitted in the forward direction from an internal beryllium target were channeled by a series of focusing quadrupole magnets for a distance of 100 feet from the target. In this beam, particles of a given mass were identified by velocity. The momentum was defined by the internal magnetic field of the Bevatron and an external deflecting magnet; velocity was measured by time-of-flight coincidence of six scintillation counters approximately equally spaced over the last 60 feet of the beam channel.With particles of momentum of 0.9 Bev/c, the lengths of the delay cables on the time-of-flight coincidence counters were adjusted to produce a coincidence with particles of a selected velocity. Figure 1 shows the counting rate obtained for delays in a velocity range including particles of iT~-meson mass. The presence of Kr mesons in the beam is clearly indicated. From the o 10 z > % »o" 5 l T T 0.9 Bev/C • 3-FOLD COINCIDENCE C, A 3-FOLD COINCIDENCE C2 • COINCIDENCE C, C, -4 0 4 8 CABLE DELAY FROM T 12 16 20 ' (FEET OF RG63/U) FIG. 1. Delay curve of time-of-flight selector at 0.9 Bev/c, Calculated delays for TT~ mesons, K~ mesons, and antiprotons are shown on the horizontal axis. Coincidence C1C2 is made between the outputs of the two threefold-coincidence circuits. LIQUID H2 TARGET 8"DIA. 62" LONG INCIDENT K~ MASONS F 4 M x4 ,,J SCINTILLATOR 100"-13" DIA. ^ PLASTIC SCINTILLATOR FIG. 2. Geometry of attenuation experiment with liquid hydrogen target.slope of the delay curve on either side of the "plateau" we estimate an upper limit of 5% for the contamination of the Kr beam when the delays are set for the edge of the plateau. In order to measure the Kr-p total cross section, a 62-inch long liquid hydrogen target was located after the last scintillator, F, of the time-of-flight selection system, Fig. 2. Beyond this, at a distance of 13.4 feet from F, a 13-inch-diameter scintillation counter, L, detected those particles which passed through the hydrogen target without interaction or decay. This counter was large enough to include the effects of the natural beam divergence and of the multiple Coulomb scattering in the hydrogen target.In principle, the change in transmission resulting from filling the hydrogen target is a measure of the total cross section; several corrections must be considered in this calculation, however. A large fraction of the Kr mesons (approximately 40%) decays in the interval from F to L. Decay secondaries that originate in the region ahead of the hydrogen target are only slightly attenuated in the hydrogen, and since only about 1% of these secondaries are detected by L, the net effect of decay ahead of the target is negligible in the transmission difference. In the region after the target, the rate of decay of Kr mesons is ...

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Decay characteristics and masses of positive K Mesons produced by the Bevatron

Cited by 77 publications

References 13 publications

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Analyticity and Causality. II

Mean Life ofK−Mesons and Their Cross Section in Hydrogen

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