Changes between Version 5 and Version 6 of HiggsEffective
- Timestamp:
- Apr 12, 2012, 11:09:07 AM (12 years ago)
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HiggsEffective
v5 v6 1 1 = Higgs Effective couplings to gluons (and photons) = 2 2 3 The Higgs effective field theory ({{{ 3 The Higgs effective field theory ( 4 {{{ 4 5 heft 5 }}}) model is an 'extension' of the Standard Model, where the Higgs boson couples directly to gluons (and photons). In the SM these couplings are present through a heavy (top) quark loop. For a not too heavy Higgs (m,,h,,<2 m,,t,,), it is a good approximation to take the mass of the heavy quark in the loop to infinity (For this approximation to hold, not only should the Higgs mass be smaller than twice the top mass, also all other kinematic variables, such as the transverse momentum of the Higgs boson, should be smaller than 2m,,t,,.) This results in effective couplings between gluons and Higgs bosons. 6 }}} 7 ) model is an 'extension' of the Standard Model, where the Higgs boson couples directly to gluons (and photons). In the SM these couplings are present through a heavy (top) quark loop. For a not too heavy Higgs (m,,h,,<2 m,,t,,), it is a good approximation to take the mass of the heavy quark in the loop to infinity (For this approximation to hold, not only should the Higgs mass be smaller than twice the top mass, also all other kinematic variables, such as the transverse momentum of the Higgs boson, should be smaller than 2m,,t,,.) This results in effective couplings between gluons and Higgs bosons. 6 8 7 9 The effective vertices can be derived from the effective dimension five Lagrangian: … … 16 18 $g_h=\frac{\alpha_s}{3\pi v}\Big(1+ \frac{7}{30}\tau + \frac{2}{21}\tau^2+ \frac{26}{525}\tau^3\Big),$ \texttt{{\small with}} $\tau=m_h^2/(4m_t^2)$ 17 19 }}} 18 and higher orders in τ have been neglected. Due to the non-abelian nature of the SU(3),,C,, color group the effective vertices do not only include two, but also three and four gluons coupling to the Higgs boson. Since !MadGraph can work only with three- and four-point vertices, the four-gluon interactions in the {{{ 20 and higher orders in τ have been neglected. Due to the non-abelian nature of the SU(3),,C,, color group the effective vertices do not only include two, but also three and four gluons coupling to the Higgs boson. Since !MadGraph can work only with three- and four-point vertices, the four-gluon interactions in the 21 {{{ 19 22 heft 20 }}} model are obtained by rewriting the QCD four-gluon interaction in terms of three-point vertices with an extra non-propagating internal tensor particle, T. This trick can be easily understood by noting that the usual (text-book) form of the four-gluon interaction is the sum of three terms, whose color and Lorentz structure correspond to 2 → 2 diagrams where a color octet tensor is exchanged in the s, t, u channels. With the introduction of this extra particle, the four-gluon-Higgs vertices can be reduced to diagrams with at most four-point vertices. To get the standard diagrammatic visualization of four-gluon and four-gluon-Higgs vertices it is sufficient to contract the T particle lines to a single point. 23 }}} 24 model are obtained by rewriting the QCD four-gluon interaction in terms of three-point vertices with an extra non-propagating internal tensor particle, T. This trick can be easily understood by noting that the usual (text-book) form of the four-gluon interaction is the sum of three terms, whose color and Lorentz structure correspond to 2 → 2 diagrams where a color octet tensor is exchanged in the s, t, u channels. With the introduction of this extra particle, the four-gluon-Higgs vertices can be reduced to diagrams with at most four-point vertices. To get the standard diagrammatic visualization of four-gluon and four-gluon-Higgs vertices it is sufficient to contract the T particle lines to a single point. 21 25 22 The gluon couplings to a pseudo-scalar Higgs are also implemented. The name of the pseudo-scalar Higgs in !MadGraph is {{{ 26 The gluon couplings to a pseudo-scalar Higgs are also implemented. The name of the pseudo-scalar Higgs in !MadGraph is 27 {{{ 23 28 h3 24 }}} ( i.e. , the same as in the 2HDM and MSSM models). The effective dimension five Lagrangian for the pseudo-scalar Higgs coupling to the gluons is 29 }}} 30 ( i.e. , the same as in the 2HDM and MSSM models). The effective dimension five Lagrangian for the pseudo-scalar Higgs coupling to the gluons is 25 31 {{{ 26 32 #!latex … … 32 38 $g_A=\frac{\alpha_s}{2\pi v}\Big(1+ \frac{1}{3}\tau+ \frac{8}{45}\tau^2 + \frac{4}{35}\tau^3\Big)$, 33 39 }}} 34 where the higher orders in τ have been neglected. The pseudo-scalar Higgs has only effective couplings to two or three gluons. The four-gluon-pseudo-scalar Higgs vertex is absent due to the anti-symmetry of the epsilon tensor ε^μνρσ^. If a mixed Higgs with no definite CP parity is needed, it sufficient to change the couplings of the Higgs to the gluons. First generate the process with the SM Higgs, then, after downloading the code, change the coupling in the {{{ 40 where the higher orders in τ have been neglected. The pseudo-scalar Higgs has only effective couplings to two or three gluons. The four-gluon-pseudo-scalar Higgs vertex is absent due to the anti-symmetry of the epsilon tensor ε^μνρσ^. If a mixed Higgs with no definite CP parity is needed, it sufficient to change the couplings of the Higgs to the gluons. First generate the process with the SM Higgs, then, after downloading the code, change the coupling in the 41 {{{ 35 42 ./Source/Model/couplings.f 36 }}} file. The coupling constant is defined as a two-dimensional object, where the first and second elements are the CP-even and CP-odd couplings of the Higgs to the gluons, respectively. The HELAS subroutines automatically use the correct kinematics for odd-, even- or mixed CP Higgs's coupling to the gluons. At present, the implementation allows production of only one Higgs-boson. The effective couplings of two Higgs bosons to gluons are available in HELAS, but not yet included in the HEFT model. 43 }}} 44 file. The coupling constant is defined as a two-dimensional object, where the first and second elements are the CP-even and CP-odd couplings of the Higgs to the gluons, respectively. The HELAS subroutines automatically use the correct kinematics for odd-, even- or mixed CP Higgs's coupling to the gluons. At present, the implementation allows production of only one Higgs-boson. The effective couplings of two Higgs bosons to gluons are available in HELAS, but not yet included in the HEFT model. 37 45 38 46 == The non-propagating auxiliary particle T == … … 76 84 $$L_{\textrm{heft}}=-\frac{1}{4}gF_{\mu\nu} F_{\mu\nu} H.$$ 77 85 }}} 78 Due to the abelian nature of QED there is only one effective vertex between photons and Higgs bosons. The value for the coupling constant in the {{{ 86 Due to the abelian nature of QED there is only one effective vertex between photons and Higgs bosons. The value for the coupling constant in the 87 {{{ 79 88 heft 80 }}} model is given by 89 }}} 90 model is given by 81 91 {{{ 82 92 #!latex
