Spin-2 production at hadron Colliders

Many new physics scenarios predict spin-2 particles at the TeV scale. Here we summarize the theories that contains spin-2 particles implemented in MadGraph/MadEvent. They are the following:

• ADD or Large extra dimension theory;
• RS or Warped extra dimension theory;
• MGM (masseless graviton) model.

ADD theory

Theory with D = 4 + d dimensions, in which d is spatial and compactified in a sphere of radius R. Because only spin-2 particles can propagate through D dimensions, a massive KK tower of spin-2 particles appear. They can interact with the SM fields with a very weak coupling constant given by -1/L:

L = M_pl ~ 2.4 x 10¹⁸ GeV

The mass gap between neighbouring modes is proportional to 1/R, hence small for d not too large. The discrete mass spectrum can be approximated by a continuum with a integrated density of states. In other words, the 4 dimensional spin-2 appears as a infinite sum of its excited states.

Conclusion: Weak interaction between spin-2 and SM particles. Consequence: Spin-2 should not decay fast, so it is expected to be seem as missing energy @ hadron colliders.

In MadGraph/MadEvent: This model is called ADD and you can ask for processes with graviton emission using for example this proc_card.dat, and this param_card.cat.

• Model references:
  • I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali: ​hep-ph/9803315, ​hep-ph/9807344, ​hep-ph/9804398
• Implementation references:
  • K. Hagiwara, J. Kanzaki, Q. Li and K. Mawatari: ​arXiv/0805.2554
  • P. de Aquino, K. Hagiwara, Q. Li and F. Maltoni: ​arXiv/1101.5499

RS theory

Theory with D = 4 + 1 dimensions, in which the extra dimension is spatial and compactified in a sphere of radius R. Here, the total space-time has a warped metric and the size of the extra dimension can be at the order of the Planck length. Again, only spin-2 particles can propagate through 5 dimensions, therefore, a massive KK tower of spin-2 particles appear. They can interact with the SM fields with a strong coupling constant given by -1/L:

L = M_pl e^kR\pi

where k is a scale of order of the Planck scale. In this model, the mass of the nth spin-2 particle is given by:

m_n = k x_n e^-kR\pi

which can be ~ O(1 TeV), at the LHC reach.

Conclusion: Strong interaction between spin-2 and SM particles. Consequence: Spin-2 should decay very fast and it is expected to be seem as a resonance @ hadron colliders (e.g., it decays into a pair of leptons).

In MadGraph/MadEvent: This model is called RS and you can ask for processes with graviton emission using for example this proc_card.dat, and this param_card.cat.

• Model references:
  • L. Randall and R. Sundrum:​hep-ph/9905221, ​hep-ph/9906064
• Implementation references:
  • K. Hagiwara, J. Kanzaki, Q. Li and K. Mawatari: ​arXiv/0805.2554
  • P. de Aquino, K. Hagiwara, Q. Li and F. Maltoni: ​arXiv/1101.5499

MGM model

Four-dimensional model that contains a huge number of hidden sector particles that interacts only gravitationally with the Standard Model particles. It has been suggested that gravity may be interpreted as renormalization of the effective gravity coupling due to these hidden sector particles. Therefore, the existence of M_pl/TeV ~ 10³² such particles is required.

The graviton is massless in this class of theories and its coupling to the SM particles is given by -1/L:

L = M_pl(\mu*) = \mu* ~ 1 TeV.

Notice M_pl now depends on the effective energy scale.

Conclusion: Weak interaction between spin-2 and SM particles. Consequence: Spin-2 should not decay fast, so it is expected to be seem as missing energy @ hadron colliders.

In MadGraph/MadEvent: This model is called massless_grav and you can ask for processes with graviton emission using for example this proc_card.dat, and this param_card.cat.

• Model references:
  • G. R. Dvali: ​hep-ph/0106058, ​arXiv/0706.2050, ​arXiv/0710.4344
  • X. Calmet, S. D. H. Hsu and D. Reeb: ​arXiv/0711.2306, ​arXiv/0803.1836, ​arXiv/0805.0145
• Implementation references:
  • P. de Aquino, K. Hagiwara, Q. Li and F. Maltoni: ​arXiv/1101.5499