Calculated width doesn't scale with a_s as expected

Asked by Calvet

Dear MG authors,

I am using a model (provided by B. Fuks) that adds a spin-1 color octet to the SM, in order to reproduce the Pythia8 KKgluon model.

As I want to validate it, I need to check the predicted width matches the one predicted by P8.

The width depends on alpha_s, which has to be evaluated at the mass of the resonance (2TeV). In P8, a_s(2TeV)=0.094, so I set it in MG2.9.5 using:
set WVo auto # width
set pdlabel lhapdf
set lhaid 247000
set use_syst False
set as 0.094

My understanding is alpha_s=0.094 is used only during the initialization, ie for the width calculation.

Strangely the obtained width does not match the one of P8.

Investigating this, I found that the dependence of width with respect to a_s is not the linear one we can expect from the formula in decays.py:
Decay_Vo = Decay(name = 'Decay_Vo',
                 particle = P.Vo,
                 partial_widths = {(P.d,P.d__tilde__):'G**2*(MVo**2*(8*gdL1x1**2*MVo**2 + 8*gdR1x1**2*MVo**2))/(384.*cmath.pi*abs(MVo)**3)',
                                   (P.s,P.s__tilde__):'G**2*(MVo**2*(8*gdL2x2**2*MVo**2 + 8*gdR2x2**2*MVo**2))/(384.*cmath.pi*abs(MVo)**3)',
                                   (P.b,P.b__tilde__):'G**2*(MVo**2*(8*gdL3x3**2*MVo**2 + 8*gdR3x3**2*MVo**2))/(384.*cmath.pi*abs(MVo)**3)',
                                   (P.u,P.u__tilde__):'G**2*(MVo**2*(8*guL1x1**2*MVo**2 + 8*guR1x1**2*MVo**2))/(384.*cmath.pi*abs(MVo)**3)',
                                   (P.c,P.c__tilde__):'G**2*(MVo**2*(8*guL2x2**2*MVo**2 + 8*guR2x2**2*MVo**2))/(384.*cmath.pi*abs(MVo)**3)',
                                   (P.t,P.t__tilde__):'G**2*((-8*guL3x3**2*MT**2 + 48*guL3x3*guR3x3*MT**2 - 8*guR3x3**2*MT**2 + 8*guL3x3**2*MVo**2 + 8*guR3x3**2*MVo**2)*cmath.sqrt(-4*MT**2*MVo**2 + MVo**4))/(384.*cmath.pi*abs(MVo)**3)'})

Here are the value of a_s and total width (after checking all the decays were opened for a_s>=0.01):
0.01, 61.57 GeV
0.02, 118.8
0.04, 221.7
0.08, 390.3
0.12, 521.7

Would you have a idea of what is going on here ?

Best,
Samuel

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Launchpad Janitor (janitor) said :
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Olivier Mattelaer (olivier-mattelaer) said :
#2

Hi,

Sorry for the late answer, looks like I missed the notification for this thread and did not notice on the website.

The reason is that the value in the param_card correspond to the value of as at MZ.
We then run alpha_s such that we evaluate it at 2 TeV.

Cheers,

Olivier

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Calvet (scalvet-t) said :
#3
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Launchpad Janitor (janitor) said :
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This question was expired because it remained in the 'Open' state without activity for the last 15 days.