EXCITED FERMIONS

An introduction to excited fermions and an overview of our studies and main recent results on excited fermions is also given in the talk at the H1 Crosstalk'00.

If leptons and quarks are not elementary particles but are composite, excited states of these particles can exist, called excited fermions. HERA, having electron and proton in the initial state, is a good place to search for them. They are sought via the decay into an ordinary fermion and a gauge boson, e.g. e* -> e gamma.

• Production of excited fermions at HERA

  At HERA, excited electrons (e*) and excited quarks (q*) could be produced by t-channel exchange of a gamma or Z boson; similarly single excited neutrino (nu*) production could be achieved by t-channel exchange of a W boson :

                                                          / e
                / e (nu)               / nu (e)   e      /
  e         e* /          e      nu*  /           -------
  ------=======          ------=======                  |      / q
        |      \               |      \              B  | q*  /
      B |       \ B (W)      W |       \ B (W)          |=====
        |                      |                       /      \
  ---------------        --------------             q /        \ C
  Proton        X        Proton       X              /
                                                -------------
    B = gamma, Z           B = gamma, Z        Proton       X
        
                                               B = gamma, Z
                                               C = gamma, Z, W, gluon
  
   

  For e* production, the elastic contributions contributes to roughly 50% of the total. No elastic channel is possible for nu* production.

• Phenomenological Lagrangian

  A phenomenological model (Hagiwara, Komamiya, Zeppenfeld) is commonly used in experimental searches. In this model, excited fermions are spin 1/2 states. Left-handed fermions f_L couple to right-handed excited fermions f*_R, (f*_L. f*_R) being a weak-isospin doublet. The coupling of this doublet to a gauge boson is proportionnal to (f_i / Lambda) * g_i, where g_i is the group gauge constant and the f_i are unknown parameters of the model. Lambda (GeV) is the compositeness scale. Usually f parameters are labelled f' for SU(2), f for U(1) and f_s for SU(3).

  Hypothesis relating f, f' and f_s (e.g f=f'=f_s, or f=f' and f_s=0) allow to calculate branching ratios of the excited fermions, which are then independent on the model parameters. Under the same hypothesis, production cross-sections for f* only depend on one parameter, for example f/Lambda.

• Usual assumptions
  • For e* searches, the hypothesis f=f' is usually made. e* -> e + gamma is the dominant decay mode for low e* masses, while for M(e*) >> M(W) e* -> nu + W dominates.

  • For nu* searches : the hypothesis f=f' forbids the decay nu* -> nu + gamma. Limits for nu* production are hence often presented under the assumption that f=-f'. Note that f=-f' forbids the decay e* -> e + gamma.

  • For q* searches : if f_s is of same order of magnitude than f and f', q* -> q + gluon will largely dominate. In fact, as soon as f_s is not too small, contraints coming from TeVatron are very severe for q*. At HERA, q* searches are complementary : we make the hypothesis that f=f' and f_s is vanishingly small. HERA offers the best sensitivity to such excited quarks coupled electroweakly.

• Excited Fermions at LEP

  At LEP collider, excited leptons e*, mu*, tau* and nu* can be produced by pair up to the kinematical limit of sqrt(S)/2. Masses below sqrt(S)/2 have hence been excluded independly of f and f'.
  Above the kinematical limit, single production of f* is possible. The production cross-section then depends on f/Lambda. It is higher for e* production than for mu* production for example (mu* production can only proceed via the splitting of an emitted photon in a mu mu_bar pair, while for e* production t-channel boson exchange is additionnaly possible). Hence, limits above sqrt(S)/2 can be derived in the plane f/Lambda versus M(f*), these limits being more stringent for e* than for other f*.