Craig McNeile mcneile@amtp.liv.ac.uk
University of Liverpool
Staggered fermions (III) – p.1/16

I discuss some new calculations that could be done in the QCDOC era.
Strong decays
Electric dipole moment of the neutron
These projects are natural extensions of the computation of bubble diagrams. (Probably more useful than investigating the spectroscopy of penta-quarks).
Staggered fermions (III) – p.2/16

The detection of the electric dipole moment of particle such as the neutron would be a new source of CP violation. I believe that the CP violating phase in the CKM matrix element will contribute to dipole moments but at very tiny level.
The MSSM has many new CP violating terms that could potentially contribute to the electric dipole moment of the neutron.
Staggered fermions (III) – p.3/16

(1) L = X c i
M 4 − i O i i where M is the energy scale of the new physics
(GUT scale, Planck scale, whatever ..) The
“BSM” physics is in the c i
(perturbative of course).
coefficients
Examples of operators: G
ˆ
,
1
M qF σγ
5 q ,
GG
ˆ
.
1
M qGσγ
To get at the c i coefficients, hadronic matrix elements are required.
5 q ,
Staggered fermions (III) – p.4/16

The book “dynamics of the standard model” claims that the hadronic uncertainties in connecting GG to the electric dipole moment of the neutron are a factor of 50!
For example the chiral perturbation theory result is divergent and some flakey arguments have to be introduced to cut the integrals off.
There is new CERN fellow called Adam Ritz, who gives an interesting talk on hadronic matrix elements and EDMs (from a sum rule perspective).
Staggered fermions (III) – p.5/16

There has been no claim to have detected the electric dipole moments of hadron. However, the experimental limits are starting to constrain parts of the MSSM parameter space.
There is an experimental program of work into detecting EDM’s in the UK. For example at
Imperial college there is a group headed by Prof.
Hinds. Prof. Green and Prof. Mike Pendlebury at
Sussex are working on an experiment to detect the electric dipole moment of the neutron. (18 cites from 1999 theory paper).
Staggered fermions (III) – p.6/16

Aoki & Gocksch claimed to have done a calculation (Phys.Rev.Lett.63:1125,1989).
Erratum to PRL (with Steve Sharpe). That explained the previous result was a lattice artifact. Bubble diagrams are required.
There has been a recent theory paper by
Martinelli et al. (hep-lat/0210044)
There has been no recent numerical work on this topic. Martinelli’s group?
Staggered fermions (III) – p.7/16

From Martinelli et al. (hep-lat/0210044).
To compute the electric dipole moment of the neutron
(2) d
N
=
Z d 3 y~y h N | J
0
( y ) | N i
θ where θ is the coefficient of
ˆ and J
0 is the time component of the EM current. Because θ is small it makes sense to expand
~
N
= − i
32 π 2
(3) g 2
Z d 3 y~y h N | J
0
( y )
Z d 4 xG
ˆ
( x ) | N i
θ =0
Staggered fermions (III) – p.8/16

The basic strategy is to rotate the topological charge into ψγ
5
ψ .
(a) (b)
(c) (d) (e)
Staggered fermions (III) – p.9/16

We need code for
Staggered equivalents of γ
5
, γ
4 bubbles.
Nucleon operator (recoded from SZIN).
Perhaps sequential source
My main concern is getting a signal. I would start with one of the 20 3 64 MILC lattices. This would come under development time.
Staggered fermions (III) – p.10/16

Scalars (particles with possible glueball content) and hybrids decay strongly. To get a state into the PDG listings requires that the decay widths of the state have to be understood. It is very difficult to compute a decay width in Euclidean space, so methods must be tested on known cases (such as the ρ ).
Compute a hadronic transisition matrix element such as g
ρππ
.
Work in a kinematic region where the particle can decay.
Staggered fermions (III) – p.11/16

In the real world mesons not protected by some symmetry will decay strongly to ligher mesons.
For example the ρ decays to two π in the real world. Up until recently lattice QCD calculations were not in the region where the physical decays were allowed.
If a meson can decay on the lattice our standard analysis techniques of two point functions may break down. This is a “good sign” of unquenching!
Staggered fermions (III) – p.12/16

The decay of the ρ meson is a P-wave decay. So the threshold for
The MILC data at
ρ at rest is
20 3
2 q m 2
π
+ ( 2 π
L
) 2
64 a=0.13 fm has m
P S
/m
ρ of 0.39. You can then solve for aL to get 35.
(Only one direction needs to be this big).
It is instructive to look at the decay of the ρ with momentum 100 into pions with momentum 000 and 100. The box size for decay is 24.
φ → KK ???
Staggered fermions (III) – p.13/16

a
0
Decays of 0 ++ are S-wave, hence the threshold is the sum of masses. The MILC collaboration are already claiming to see the decay a
0
→ πη .
The a
0 is non-singlet 0 ++ .
Staggered fermions (III) – p.14/16

The claim of MILC to see a
0 decay is complicated by their use of quenched data. From the singlet project we will actually have the η mass, hence we could make a better comparison of the a
0 mass with the sum of the π η masses.
Another possibility is to look at the decay of the
K*(1430). This is strange-light 0 ++ decays mostly into K meson that
− π It has a large width of
294 MeV. This is where 2 + 1 flavour calculation are useful!
Staggered fermions (III) – p.15/16

Many other applications ππ scattering.
Staggered fermions (III) – p.16/16