1. Dark Photon Search At A Circular Collider
Xiao-Gang He, NTU/SJTU
Collaborators: Min He and Cheng-Kai Huang
arXiv:

2. The Dark Photon eeQemjmem Xm e << 1
A vector boson Xm couples to SM matter electromagnetic current Jmem as
eeQemjmem Xm
e << 1

3. Generating Dark Photon Interaction through Gauge Boson Kinetic Mixing L = - ¼ FμνFμν – ¼ XμνXμν will use X or A’ for dark photon
X and A are gauge fields of U(1)X X U(1)A
This term is renormalizable and gauge invariant
e is a unknown number in a given model.
Holdom 1986, Foot and He 1991,….

4. There are many interesting consequences
Consider U(1)A = U(1)Y and U(1)X a new gauge group: dark photon or … Dark photon connected to a hidden world (dark sector… )
e= -scW
f0-bare fields
A’ = X
L = - ¼ FμνFμν – ¼ ZμνZμν -1/4 F’μνF’μν
In the eigen-mass bases, to first order in e

5. Loop generation of photon and dark photon mixing

6. Summary of constraints on the dark photon mass and coupling
Iten et al, arXiv:

7. What a circular e+e- collider can do for dark photon
What a circular e+e- collider can do for dark photon? This talk describe: study dark photon using e+e- -> g A’ ->m+m-

8. CEPC project (Xinchou Lou)
~1010 Z bosons

10. Naïve expectation

11. Evaluation of the cross section

13. Observable
e2 is a function of mA, smm = 0.5% mA. I = integrated luminosity c=

14. Benchmark Luminosities:
CEPC: 2 × 1034cm2s-1 at √s: 240 GeV,
FCC-ee: 1.5 × 1036cm2s-1, 3.5 × 1035cm2s-1, and 8.4 × 1034cm2s-1
at √s: GeV, GeV and GeV.

16. CEPC may have advantage probing dark photon at 10 to a few 10s (<<mZ) GeV mass range.
CEPC, FCC-ee
Iten et al, arXiv:

17. There are two contributions in the SM, the intermediate γ and Z e+e− → γA′.
When the dark photon mass and also the center of mass frame energy are significantly away from the Z boson mass, the dominate contribution to the SM background is from intermediate γ.
Assuming μ+μ− invariant mass can be measured to an accuracy of 0.5%mA′
Constraints on ε2 for mA’ in the few tens of GeV range,
can be better than 3x10−6 for the proposed CEPC with a 10 year-running at 3σ (statistic) level,
better than 2 × 10−6 for FCC-ee with just one year-running at √s = 240 GeV,
better than the LHC and other facilities can do in a similar dark photon mass.
For FCC-ee, running at √s = 160 GeV, the constraint can be better. In the range of 20 GeV to 60 GeV for mA′ , the smallest σμν is 100 MeV which is reachable at the CEPC and FCC-ee.
With a smaller σμm the sensitivity can be improved.

18. Spontaneous symmetry breaking and Abelian-NonAbelian gauge fields mixing Arguelles, XG He, G. Ovanesyan, T. Peng and M. Ramsey-Mulsof, arXiv:
Assuming that there is a field Da transforming as 3 under SU(2)W, then one can make gauge singlet: Wamn X mn Da
If the VEV of <Da> = v3/sqrt(2) along a particular direction in group space is not zero, one can generate kinetic mixing term
W3mn X mn v3/sqrt(2)
Problem: not renormalizable.
If one gives up renormalizability one can write higher order operators to generate abelian and non-abelian gauge fields mixing!
In fact in the SM, one can generate such a mixing between SU(2)L and U(1)Y
Wamn X mn (H+taH)
Here H is the usual SM doublet!
Possible to have kinetic mixing between ablian and non-abelian gauge fields. Chen, Cline, and Frey, 2009; He, Ovanesyan, Ramesy-Musolf, 2014.

19. UV completion of kinetic mixing of Abeliand-NonAbelian gauge field?
Yes, they can be generated at loop level starting from a renormalizable theory. The particle in the loop carry both abelian and non-abelian charges. One can even talking about SU(N) and SU(m) kinetic mixing Wamn YbmnDab Kinetic mixing between an Abelian and a non-Abelian fields should be very common when going beyond SM.

20. A triplet Da (0,3,0) and W-B mixing
SU(2)W = SU(2)L, U(1)X = U(1)Y
Analysis the effects through S,T, U parameters

21. Some phenomenological implications