## Wednesday, December 07, 2005 ... /////

### Electric dipole moments

Adam Ritz (CERN & Victoria) just gave a talk about the electric dipole moments of elementary particles and their constraints on new physics.

Do elementary particles have a dipole moment? Something analogous to two opposite charges separated by a distance? A dipole moment is a vector, and by rotational symmetry, the only direction that the dipole could take is the direction of the spin.

A special comment for Quantoken. By elementary particles, I mean leptons, quarks and gauge bosons (and possible the Higgs and graviton) - and their simple enough bound states that have no particle physics reason to have a significant (=beyond the CKM contribution) dipole moment, such as the neutron. More complicated structures such as molecules of course usually have a dipole moment whose origin we understand very well. That's also the case of some atomic states where the dipole arises from various relativistic corrections.

You know that the magnetic moment of a particle is always proportional to the spin with a fixed coefficient that depends on the particle type only. So if the particles also have an electric dipole, then there is some correlation between the electric moment and the magnetic moment. But which sign should this relative factor have? You know that E is a vector but B is a pseudovector, and therefore the electric dipole moments of the particles violate P (parity) much like CP (parity combined with charge conjugation).

The Standard Model predicts certain small electric dipole moments of particles such as neutron - because of the CP-violating phases in the CKM matrix used for quark masses. New theories of physics including supersymmetry typically predict more significant violations of the CP symmetry which also means significant dipole moments.

Experiments try to measure the dipole moments in various types of materials - liquid Xenon is a crazy example. No dipole moments of the elementary particles have been found so far which puts strong constraints on the parameters of new theories such as MSSM (minimal supersymmetric Standard Model) as well as baryogenesis (but no constraints on leptogenesis).

Various other experiments are underway and some of them are being prepared. One of them may cost as much as 10 million dollars, if you want to have an idea about the budget. Many of them want to access the limit

• d = 10^{-29} electron.centimeter
where "electron.centimeter" is a natural unit of the dipole moment. It is the same dipole as an electron-positron pair separated by 1 centimeter. You see that the corresponding distance "10^{-29}" centimeters is tiny; it is much shorter than the typical "radius" of the particles. Once the experiments get to this level, the subject of EDMs will be over because this is the scale of the dipole moment predicted by the Standard Model. Well, we should eventually see the basic dipole moments predicted by the Standard Model but it is virtually impossible to measure the EDMs accurately. In other words, it would be impossible to distinguish new contributions from the Standard Model background.

The negative results of the experiments looking for the dipole moments is a bad news for more or less any theory of new physics. No really convincing explanation why the CP violating terms should vanish has been given in the case of supersymmetry. It is also a bad news for the anthropic principle because the unnaturally small values of the dipole moments are apparently not required for any mechanism underlying life.

Of course, it is good news for everyone who is quite happy with the Standard Model. It is even better than we thought.

#### snail feedback (5) :

Dear Lumos,

Fundamental particles are electric monopoles with a magnetic dipole moment.

Forget electric dipole and magnetic monopole speculation. Maxwell's equations have never been violated in this sense. Gauss' law of the electric monopole applies to the electron, and at very high energy collisions you simply break through the polarised vacuum veil around the core and see more of the strong core charge.

Nobody has ever come up with evidence for it being anything other than an electric monopole with a magnetic dipole associated with spin. The Heaviside trapped TEM wave mechanism for the electron is illustrated here and in more detail for magnetic dipole mechanism here.

If you want to test something, figure out some way of testing string theory, but leave Maxwell's equations alone.

The only error Maxwell made was the subtle assumption that energy instantly spreads along a whole capacitor plate before displacement current travels between the plates. This fouls up his theory of radio waves and light and the real energy flow of displacement current is more complex, a transverse radio wave, with no need to add in Faradays law of induction to create a loop or cyclical oscillatory theory..

Best wishes,
Nigel

(I'm talking fermions when I discuss fundamental particles)

Lubos, you asked a dumb question. It all depends on how exactly you define "elementary" particles. If you define "elementary" as one that is without any intrisic internal structure, then of course there will be no electric dipole since electric dipole requires a structure. Structure-less particles so then is without electric dipole.

On another side, many particles, like netron, does not fit such a definition of "elementary" particle. Neutron has internal structure, and so it of course has electric dipole. You know what it is, quarks that carry different charges.

The very fact that neutrons do absorb and emit gamma ray photons tells you that it has dipoles, because you need dipole momentum to interact with electromagnetic waves. That basic electromagnetism, any radiation and absorption of EM waves is associated with dipole momentums. I hope you have not forgotten your physics 101.

Quantoken, for an electron, 99.884% of the magnetic dipole moment comes from the core and only 0.116% comes from the polarised vacuum which couples a virtual fermion to the core, increasing the total magnetism as Schwinger and Feynman found.

For a neutron, the contribution from the fundamental quarks is smaller, and much, much more of the magnetic dipole moment comes from the polarised vacuum. You also have complex interactions of field quanta ("gluons").

I think the key problem in electromagnetism is understanding the photon. The photon is an electric dipole, of course, but Maxwell's theory gets the angle wrong. He has the variation from positive to negative electric field taking place along the line of propagation, when in fact it is transverse to the line of propagation.

This is because of his error in assuming that displacement current has no transverse component, due to neglecting the obvious fact that electric energy takes time to spread across the capacitor plate (or radio transmitter aerial) while energy propagates from one capacitor plate to the other (or from a radio transmitter aerial to a parallel radio receiver aerial across empty space).

Best wishes,
nigel