Dark Photon Search At A Circular Collider Xiao-Gang He, NTU/SJTU Collaborators: Min He and Cheng-Kai Huang arXiv: 1701.08614

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

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,….

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

Loop generation of photon and dark photon mixing

Summary of constraints on the dark photon mass and coupling Iten et al, arXiv:1603.0892

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-

CEPC project (Xinchou Lou) ~1010 Z bosons

Naïve expectation

Evaluation of the cross section

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

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: 160 GeV, 240 GeV and 350 GeV.

CEPC may have advantage probing dark photon at 10 to a few 10s (<<mZ) GeV mass range. CEPC, FCC-ee Iten et al, arXiv:1603.0892

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.

Spontaneous symmetry breaking and Abelian-NonAbelian gauge fields mixing Arguelles, XG He, G. Ovanesyan, T. Peng and M. Ramsey-Mulsof, arXiv:1604.00044 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.

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.

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

Some phenomenological implications