Changes between Version 1 and Version 2 of modcolorS_trip


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Timestamp:
10/27/15 17:05:44 (2 years ago)
Author:
druekeel
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  • modcolorS_trip

    v1 v2  
    1 test 
     1 
     2= A Color Triplet Model = 
     3 
     4== Authors == 
     5 
     6* Elizabeth Drueke (Michigan State University) 
     7* Joseph Nutter (Michigan State University) 
     8* Reinhard Schwienhorst (Michigan State University) 
     9* Natascia Vignaroli (Michigan State University) 
     10* Devin G. E. Walker (SLAC National Accelerator Laboratory) 
     11* Jiang-Hao Yu (The University of Texas at Austin) 
     12* Tao Han (University of Wisconsin) 
     13* Ian Lewis (University of Wisconsin) 
     14* Zhen Liu (University of Wisconsin) 
     15 
     16== Description of the Model == 
     17 
     18The color-triplet (Phi) is a heavy hadronic resonance with fractional electric charge.  The Feynman diagram for decay to tb is below. 
     19 
     20[[Image(ColorResSig1.png)]] 
     21 
     22In particular, it is possible to produce triplet, anti-triplet, and sextet particles; but the LHC is a proton-proton machine and so the triplet production is enhanced by the parton-parton luminosity of the quark-quark initial state.  The contributing quark-quark initial states are QQ, QU, QD, and UD, where Q, U, and D denote the SM quark doublet, up-type singlet, and down-type singlet, respectively.  The diquark particles could be the spin-0 scalars with  
     23{{{ 
     24#!latex 
     25$SU(3) \times SU(2)_L \times U(1)_Y$ 
     26}}} 
     27quantum numbers 
     28{{{ 
     29#!latex 
     30$\Phi \simeq (6 \oplus \overline{3}, 3, \frac13), \quad \Phi_U \simeq (6 \oplus \overline{3}, 1, \frac13),$ 
     31}}} 
     32and the spin-1 vectors 
     33{{{ 
     34#!latex 
     35$V^\mu_U \simeq  (6 \oplus \overline{3}, 2, \frac56), \quad V^\mu_D \simeq  (6 \oplus \overline{3}, 2, -\frac16).$ 
     36}}} 
     37To produce the tb final state, the charge of the colored particle needs to be 1/3. The gauge-invariant Lagrangian can be written as: 
     38{{{ 
     39#!latex 
     40$\mathcal{L}_{\rm diquark} = K^j_{ab} [\kappa_{\alpha\beta} \overline{Q^C_{\alpha a}}i\sigma_2 \Phi^{j} Q_{\beta b} + \lambda_{\alpha\beta} \Phi_U \overline{D^C_{\alpha a}}U_{\beta b} + \lambda^U_{\alpha\beta}\ \overline{Q^C_{\alpha a}}i\sigma_2\gamma_\mu{V^{j}_U}^\mu U_{\beta b}$  
     41}}} 
     42{{{ 
     43#!latex                 
     44$ + \lambda^D_{\alpha\beta}\ \overline{Q^{C}_{\alpha a}}i\sigma_2\gamma_\mu{V^{j}_D}^\mu D_{\beta b}] + \rm{h.c.}$ 
     45}}} 
     46where  
     47{{{ 
     48#!latex 
     49$\Phi^j = {1\over 2}\sigma_{k} \Phi_{k}^{j}$  
     50}}} 
     51with the 
     52{{{ 
     53#!latex 
     54$SU(2)_{L}$  
     55}}} 
     56Pauli matrices  
     57{{{ 
     58#!latex 
     59$\sigma_{k}$ 
     60}}} 
     61and color factor 
     62{{{ 
     63#!latex 
     64$K^j_{ab}$. 
     65}}} 
     66The couplings to QQ, and to U and D, are given, respectively, by  
     67{{{ 
     68#!latex 
     69$\kappa_{\alpha\beta}$ \rm{ and } $\lambda_{\alpha\beta}$. 
     70}}} 
     71Here a, and b are quark color indices, and j is the diquark color index with 
     72{{{ 
     73#!latex 
     74$j=1-N_D$, 
     75}}} 
     76where N_D is the dimension of the (N_D=3) antitriplet or (N_D=6) sextet representation. C denotes charge conjugation, and alpha and beta are the fermion generation indices. After electroweak symmetry breaking, all of the SM fermions are in the mass eigenstates. The relevant couplings of the colored diquark to the top quark and the bottom quark are then given by 
     77{{{ 
     78#!latex 
     79$\mathcal{L}_{qqD} = K_{ab}^{j} \left[  \kappa^\prime_{\alpha\beta} \Phi \overline{u^c}_{\alpha a} P_\tau d_{\beta b} + \lambda^\prime_{\alpha\beta} V_{D}^{j\mu} \overline{u^c}_{\alpha a} \gamma_{\mu}P_\tau d_{\beta b} \right]+ \mathrm{h.c.},$ 
     80}}} 
     81where  
     82{{{ 
     83#!latex 
     84$P_\tau = \frac{1\pm \gamma_5}{2}$ 
     85}}} 
     86are the chiral projection operators. Assuming that the flavor-changing neutral coupling is small, the third-generation couplings are 
     87{{{ 
     88#!latex 
     89$\mathcal{L}_{\rm top} = K_{ab}^{j} \Phi \overline{t^c}_\alpha P_\tau b_\beta +  
     90K_{ab}^{j} V^\mu \overline{t^c}_\alpha \gamma_\mu P_\tau b_\beta + h.c.$ 
     91}}} 
     92The decay width of the color~triplet to tb is given by 
     93{{{ 
     94#!latex 
     95$\Gamma (\Phi \to t\,b ) = \frac{g_{\Phi}^2}{8\pi}(1-x_t^2)^2 + {\mathcal O}(x_f\times x_b) + {\mathcal O}(x_b^2) \;,$ 
     96}}} 
     97where  
     98{{{ 
     99#!latex 
     100$x_t=\frac{m_t}{m_\Phi}$ \rm{ and } $x_b=\frac{m_b}{m_\Phi}$ 
     101}}} 
     102and the color triplet coupling to tb is given by  
     103{{{ 
     104#!latex 
     105$g_{\Phi}$. 
     106}}} 
     107See more details in 
     108* [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] 
     109* [http://arxiv.org/pdf/1010.4309v2.pdf 1010.4309v2] 
     110 
     111== Model Files == 
     112 
     113* [wiki:proc_card_mg5.dat proc_card_mg5.dat]: for generation of 500 GeV triplet (place in Cards/) 
     114* [wiki:run_card.dat run_card.dat]: for generation of 500 GeV triplet (place in Cards/) 
     115* [wiki:resonanceWidth.C resonanceWidth.C]: macro to generate widths for triplet at different masses 
     116* [wiki:modcolorS_trip.zip modcolorS_trip.zip]: the model 
     117 
     118== Generation specifics == 
     119    
     120In [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2], the samples were generated with the mass as the scale, dsqrt_q2fact1, and dsqrt_q2fact2 in the run_card.  These samples were also generated without the pre-included MadGraph cuts as demonstrated in the run_card.dat for 500 GeV mass included above.  The specific generations run were  
     121{{{ 
     122p p > t b, t > b l+ vl  
     123p p > t~ b~, t~ > b~ l- vl~ 
     124}}} 
     125The resonanceWidth macro can be run to determine the WSIX parameter input for the parameters.py file in the model file. 
     126 
     127To generate a specific mass, change the MSIX parameter to the mass of the particle in GeV and the WSIX parameter as described above in the parameters.py file of the model.