Difference between revisions of "Pion-pion scattering: the rho resonance"

Revision as of 11:57, 16 December 2009

Craig Pelissier defended his proposal to measure the mass and width of the \(\rho\) resonance. You can find his proposal here.

We will generate two sets of lattices:

Here is the e-mail from Craig regarding the choice of lattice sizes:

lattice spacing \(a = 0.0997991 {\rm fm}\)
pion mass \(m_\pi = 330 {\rm MeV}\)
lattice size \(N_x=N_y=N_z = 18, 20, 22, 24, 26\) (20 is the lattice size with the smallest difference between the first excited state and the resonance).
\(N_t = 48\)

The bold numbers indicate the relevant sizes to measure \(\rho\).

lattice spacing \(a = 0.0997991 fm\)
pion mass \(m_\pi = 330 MeV\)
elongated direction \(N_z = 40, 42, 44, 46, 48, 50 ,52, 54, 56\) (48 is the lattice size set such that the first excited state equals the resonance).
\(N_t = 48\)
\(N_x=N_y= 24\)

\(m_\pi \times L_s\)	\(L_s\) [fm]	\(a\)[fm]	\(L_e\)[fm]	\(m_\pi\)[MeV]	\(m_\rho\) [MeV]
4.00572	2.39518	0.0997991	4.79036	330	838.769

E = the energy of the first excited state \(p = \frac{2\pi}{L_e}\).

The bold numbers indicate the relevant sizes to measure \(\rho\)..

To generate a lattice spacing with the right value we set \(\beta\) using the results quoted in Lattice spacing. We find the following parameters:

@@ Line 65: / Line 65: @@
 |}
-The brackets indicate the relevant sizes to measure <math>\rho</math>.
+The bold numbers indicate the relevant sizes to measure <math>\rho</math>..
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