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Register a new userOperators for scattering of particles with spin
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Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators $O_{Gamma,r,n}$ that transform according to a given irreducible representation $Gamma$ and row r. However, it gives little guidance on which continuum quantum numbers of total J, spin S, orbital momentum L or single-particle helicities $lambda_{1,2}$ will be related with a given operator. This is remedied with the helicity and partial-wave methods. There first the operators with good continuum quantum numbers $(J,P,lambda_{1,2})$ or $(J,L,S)$ are constructed and then subduced to the irreps $Gamma$ of the discrete lattice group. The results indicate which linear combinations $O_{Gamma,r,n}$ of various n have to be employed in the simulations in order to enhance couplings to the states with desired continuum quantum numbers. The total momentum of two hadrons is restricted to zero since parity P is a good quantum number in this case.
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We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.
The dark matter puzzle is one of the most important fundamental physics questions in 21 century. There is no doubt that solving the puzzle will be a new milestone for human beings in the way of deeper understanding the mother nature. Here we propose to use the Shanghai laser electron gamma source (SLEGS) to search for dark matter candidates particles, including dark pseudo scalar particles, dark scalar particles, and dark photons. Our simulations show that electron facilities like SLEGS with some upgrading could be competitive platforms in searching for light dark matter particles with mass under tens of keV.
An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra. In particular, this new formulation only requires propagator
We investigate $B_spi^+$ scattering in s-wave using lattice QCD in order to search for an exotic resonance X(5568) with flavor $bar b s bar d u$; such a state was recently reported by D0 but was not seen by LHCb. If X(5568) with $J^P=0^+$ exists, it can strongly decay only to $B_spi^+$ and lies significantly below all other thresholds, which makes a lattice search for X(5568) cleaner and simpler than for other exotic candidates. Both an elastic resonance in $B_spi^+$ as well as a deeply bound $B^+bar K^0$ would lead to distinct signatures in the energies of lattice eigenstates, which are not seen in our simulation. We therefore do not find a candidate for X(5568) with $J^P=0^+$ in agreement with the recent LHCb result. The extracted $B_spi^+$ scattering length is compatible with zero within the error.
In this paper the general form of scattering amplitudes for massless particles with equal spins s ($s s to s s$) or unequal spins ($s_a s_b to s_a s_b$) are derived. The imposed conditions are that the amplitudes should have the lowest possible dimension, have propagators of dimension $m^{-2}$, and obey gauge invariance. It is shown that the number of momenta required for amplitudes involving particles with s > 2 is higher than the number implied by 3-vertices for higher spin particles derived in the literature. Therefore, the dimension of the coupling constants following from the latter 3-vertices has a smaller power of an inverse mass than our results imply. Consequently, the 3-vertices in the literature cannot be the first interaction terms of a gauge-invariant theory. When no spins s > 2 are present in the process the known QCD, QED or (super) gravity amplitudes are obtained from the above general amplitudes.
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