We construct the full p 6 order chiral Lagrangians for the unitary group and special unitary groups, including n f -, three-and two-flavor cases, all bilinear currents (scalar, pseudoscalar, vector, axialvector and tensor currents) and θ parameter. The number of independent operators are 1391, 1326 and 969 for each of the flavor unitary groups. From these results, we find one extra linear relation among the traditional p 4 order low-energy constants under the U(3) group, and some more linear relations with tensor sources for the p 6 order low-energy constants in the special unitary groups. We develop a scheme to obtain the relations for the dependent operators in terms of independent operators.PACS numbers: 12.39. Fe, 11.30.Rd, 12.38.Aw, 12.38.Lg I. INTRODUCTIONIn low-energy QCD, chiral perturbation theory(ChPT) is a powerful tool to treat hadron physics. With the help of ChPT, we can describe the low-energy pseudoscalar mesons (π, K, η, η ′ ) up to a certain degree of precision. In the last three decades, ChPT has matured and can specify next-to-next-to-leading order (NNLO) processes. The first step in the ChPT is to obtain the chiral Lagrangian, where most of the difficulties and discussions arise. Conventionally, one expands the chiral Lagrangian in terms of powers of momentum (p). For the special unitary (SU) group, ChPT for the pseudoscalar meson has been improved from the leading (p 2 ) order [1], to the next-to-leading (p 4 ) order (NLO) [2,3], and the NNLO (p 6 order) [4][5][6][7][8][9][10]. At present, almost all NNLO chiral Lagrangian have been obtained, including twoand three-flavor quarks, the normal and anomalous parts, and all bilinear light-quark currents (scalar, pseudoscalar, vector, axial-vector and tensor currents), except for the θ parameter related terms. For the unitary (U) groups, the NLO results also were obtained [11]. Furthermore, one can expand the chiral Lagrangian in terms of p and 1/N c simultaneously. The results to order O(δ) have been obtained [12][13][14].At present, under the SU group, the NNLO chiral Lagrangian seems sufficient. The chiral Lagrangian at any higher order is much more complicated and without much physical interest. Even though it can be obtained, the work would be very tedious and long, because of the complexity, and the advantages of such a chiral Lagrangian would vanish. Furthermore, comparisons between theory and experiments have not reached the precision where higher-order computations are needed. Even in the NNLO, some mistakes may appear through the tedium of the calculations, raising doubts about the credibility of the evaluations. When the NNLO chiral Lagrangian was first obtained [4,9], some linear relations among low-energy constants (LECs) had been missed [5][6][7][8]10]. This poses the question: Do other hidden relations exit? We need a definite answer. If the existing LECs are not independent, they are not unique, and ChPT cannot work well. In the NNLO, when ones wants all LECs [10,15,16] or discusses some processes [17][18][19][20][21][22], one...
The complete list of electroweak chiral Lagrangian up to order of p 4 for left-right symmetric models with a neutral light higgs is provided. The connection of these operators to left and right gauge boson mixings and masses is made and their contribution to conventional generalized electroweak chiral Lagrangian with a neutral light higgs included in is estimated.
We present the first experimental evidence supported by simulations of kinetic effects launched in the interpenetration layer between the laser-driven hohlraum plasma bubbles and the corona plasma of the compressed pellet at the Shenguang-III prototype laser facility. Solid plastic capsules were coated with carbon-deuterium layers; as the implosion neutron yield is quenched, DD fusion yield from the corona plasma provides a direct measure of the kinetic effects inside the hohlraum. An anomalous large energy spread of the DD neutron signal (∼282 keV) and anomalous scaling of the neutron yield with the thickness of the carbon-deuterium layers cannot be explained by the hydrodynamic mechanisms. Instead, these results can be attributed to kinetic shocks that arise in the hohlraum-wall-ablator interpenetration region, which result in efficient acceleration of the deuterons (∼28.8 J, 0.45% of the total input laser energy). These studies provide novel insight into the interactions and dynamics of a vacuum hohlraum and near-vacuum hohlraum.
Understanding and controlling time-dependent implosion asymmetry are essential requirements to achieve ignition. In a recent symmetry tuning experiment at the 100 kJ laser facility, an effective time-dependent symmetry control was demonstrated by modifying the ratio of the inner beam power to the outer beam power. The hohlraum radiation and the P2 drive asymmetry of a shot used to measure backlit shell asymmetry have been analyzed, and the sensitivity of the P2 shell asymmetry to the drive asymmetry has been illustrated by using the two-dimensional code LARED. The variation in the shell P2 distortion, resulting from the variation in the P2 drive asymmetry due to the three-dimensional perturbing effects introduced to the hohlraum by the diagnostic windows (DWs) and the eight removed beams, has been assessed quantitatively using a three-dimensional postprocessor. It is found that the DWs and the four removed inner beams do not vary the P2 drive asymmetry, while the four removed outer beams cause a ∼−1% variation in the P2 drive asymmetry, resulting in a more prolate implosion.
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