dark matter Properties stable non-relativistic non-baryonic new bsm particles must exist!

CDM leading candidates: WIMPs~ 1 GeV. Axions ~ . ALPs Dark Photons .....

The U(1)_A Problem The light u-d quark Langrangin in the chiral limit: It has following symmetries:

The symmetry is broken due to quark pair condensation The vector symmetry is unbroken so

Three generators are broken so there are three pseudo Nambu-Goldstone bosons. What happened to the U(1)_A? It should also be broken and give the fourth pseudo Nambu-Goldstone which is not observed. Solution: U(1)_A is explicitly broken due to QCD instanton effect.

A classical field configuration of QCD vacuum: with the winding number n cannot be smoothly deformed into others with a different winding number without passing energy barriers

However these field configurations with different winding numbers can tunnel to each other due to instantons. So the physical vacuum has to include field configuration with all possible winding numbers thus has the form:

The \theta vacuum gives an additional effective interaction term:

This term violates CP invariance if The measurement of electric dipole moment of neutron gives a upper limit:

relaxes to zero during QCD phase transition. To solve the strong CP problem, one introduces the symmetry which is spontaneously broken relaxes to zero during QCD phase transition.

A example: the KSVZ axion One introduces an new complex scalar and a new heavy quark Q. =>

The ABJ anomaly gives the required effective axion-gluon-gluon coupling.

After QCD phase transition, the “PQ” Nambu-Goldstone boson acquires mass due to instanton effects, hence becoming a quasi-Nambu-Goldstone boson, the “axion”.

Axion like particles extra dimensions are universal properties of Quantum gravity superstring 10d observed universe 4d one solution is compactification another one is the brane scenario

Axion like particles interested background fields in string theory: the metric the two-form gauge antisymmetric field dilaton ...

Axion like particles alps arises due to compactification of the antisymmetric tensor fields the x are non-compact coordinate, y are compact coordinates.

Axion like particles the zero mode acquires a potential due to non-perturbative effects on the compactifying cycle. The effective Lagrangian in four dimension:

ALPs So if the string theory is true, alps exist inevitably. Question is: what is the mass?

The cold axion like parties can be a major part of dark matter. have a very small velocity V=[1/(t_1*m)]*[a(t_1)/a(t)] m<10^(-6)eV. They are ultra light non-relativistic bosons.

classical field approximation for a coherent state with phase space density N, the quantum correction is: cold alps phase space density is >10^26, so we can treat them as CLF.

cold alps The Lagrange in unperturbed flat FRW universe: We can derive the equation of motion

cold alps alps are non-relativistic, so slow varying terms are interested. We factor out terms of order , then we have a non-linear wave equation.

cold alps If we consider gravitational in-homogeneity, then we have:

perturbative regime From the wave function, we derive the generalized continuity equation: which is the same as the equation of point like CDM.

perturbative regime The first order velocity equation is different: comparing with point like CDM: we see two additional terms which are due to quantum pressure and self interaction.

perturbative regime We can always decompose the field in homogeneity back ground: which lead to equation of perturbation:

The jeans length combined all interactions (gravity, self-interactions), we find perturbation spectrum in k space:

non-perturbative regime non-perturbative effects can happen even the interaction couplings are weak. For example resonance, gravity instability et. al.

none-linear evolution occupation number change alps are boosted by small mass, long wave length, high field strengths. (a resonant phenomena)

hidden sector particles dark phtons hidden sector particles

dark photons

dark photons created from inflation fluctuation. power spectrum is dominated by adiabatic perturbations.

dark photons high phase space density，Shot noise is small

dark photons small velocity high energy spectrum density

dark photons in atomic scale，

dark photons

dark photons