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Register a new userPartially twisted boundary conditions for scalar mesons
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Authors
Dimitri Agadjanov
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The possibility of imposing partially twisted boundary conditions in the lattice study of the resonance states is investigated by using the effective field theory (EFT) methods. In particular, it is demonstrated that - in certain cases - it is possible to use partial twisting even in the presence of the quark annihilation diagrams.
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We propose a new method to evaluate the Lellouch-Luscher factor which relates the $Delta I=3/2$ $Ktopipi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $pipi$ phase shift to be computed as an almost continuous function of the centre-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.
The possibility of imposing partially twisted boundary conditions is investigated for the scalar sector of lattice QCD. According to the commonly shared belief, the presence of quark-antiquark annihilation diagrams in the intermediate state generally hinders the use of the partial twisting. Using effective field theory techniques in a finite volume, and studying the scalar sector of QCD with total isospin I=1, we however demonstrate that partial twisting can still be performed, despite the fact that annihilation diagrams are present. The reason for this are delicate cancellations, which emerge due to the graded symmetry in partially quenched QCD with valence, sea and ghost quarks. The modified Luescher equation in case of partial twisting is given.
We investigate an application of twisted boundary conditions for study of low-energy hadron-hadron interactions with Lushcers finite size method. It allows us to calculate the phase shifts for elastic scattering of two hadrons at any small value of the scattering momentum even in a finite volume. We then can extract model independent information of low-energy scattering parameters such as the scattering length, the effective range and the effective volume from the $S$-wave and $P$-wave scattering phase shifts through the effective range expansion. This approach also enables us to examine the existence of near-threshold and narrow resonance states, of which characteristic is observed in many of newly discovered charmonium-like $XYZ$ mesons. As a simple example, we demonstrate our method for low-energy $J/psi$-$phi$ scatterings to search for Y(4140) resonance using 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $m_{pi}=156$ MeV.
We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions $(1+beta_{m}n^{mu}partial_{mu})phi =0$ at $x=a_{m}$ on one ($m=1$) and two ($m=1,2$) parallel plates at a distance $aequiv a_{2}-a_{1}$ from each other. Making use of the generalized Abel-Plana formula previously established by one of the authors cite{Sahrev}, the Casimir energy densities are obtained as functions of $beta_{1}$ and of $beta_{1}$,$beta_{2}$,$a$, respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown, and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields to an interesting possibility for stabilizing the distance between the plates by using the vacuum forces.
We examine the extent to which it is possible to realize the NMSSM ideal Higgs models espoused in several papers by Gunion et al in the context of partially universal GUT scale boundary conditions. To this end we use the powerful methodology of nested sampling. We pay particular attention to whether ideal-Higgs-like points not only pass LEP constraints but are also acceptable in terms of the numerous constraints now available, including those from the Tevatron and $B$-factory data, $(g-2)_mu$ and the relic density $Omega h^2$. In general for this particular methodology and range of parameters chosen, very few points corresponding to said previous studies were found, and those that were found were at best $2sigma$ away from the preferred relic density value. Instead, there exist a class of points, which combine a mostly singlet-like Higgs with a mostly singlino-like neutralino coannihilating with the lightest stau, that are able to effectively pass all implemented constraints in the region $80<m_h<100$. It seems that the spin-independent direct detection cross section acts as a key discriminator between ideal Higgs points and the hard to detect singlino-like points.
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