weak mixing angle and tau polarization in DY->tau tau with Madgraph

Asked by Vladimir Cherepanov on 2018-11-27

Dear Madgraph experts,

I am using Madgraph of version MG5_aMC_v2_6_3_2.

I am trying to extract the weak mixing angle from the polarization of tau leptons in the process pp -> Z -> tau tau.
Further I denote N_L and N_R as a number of tau^- lepton being in a left- and right-handed states.

Exactly at the Z peak the following relation holds to a very good approximation:

 P_tau = (N_R - N_L ) / ( N_R + N_L ) = -2 + 8*sin2theta. (1)

In this notations N_R + N_L represents the total cross section. The QED term that contains initial quark couplings is negligible at the Z peak w.r.t Z boson exchange and thus in the equation above only weak tau couplings contribute.

I use the DY sample that was produced for analysis at CMS, it has been generated with the following settings:

set group_subprocesses Auto
set ignore_six_quark_processes False
set loop_optimized_output True
set complex_mass_scheme False
import model sm-ckm_no_b_mass
define p = g u c d s u~ c~ d~ s~
define j = g u c d s u~ c~ d~ s~
define l+ = ta+
define l- = ta-
define vl = vt
define vl~ =vt~
define p u c s d b u~ c~ s~ d~ b~ g
define l+ = ta+
define l- = ta-
define j = p
generate p p > l+ l- / h @0
add process p p > l+ l- j / h @1
add process p p > l+ l- j j / h @2
add process p p > l+ l- j j j / h @3
add process p p > l+ l- j j j j / h @4
output DYJets_HT-incl -nojpeg

From displaying parameters:

> set group_subprocesses Auto
> set ignore_six_quark_processes False
> set loop_optimized_output True
> set complex_mass_scheme False
> import model sm-ckm_no_b_mass
> display parameters
>
> Current model contains 73 parameters
>
> parameter type: ('external',)
> aEWM1 = 132.507
> mdl_Gf = 1.16639e-05
> aS = 0.118
> mdl_lamWS = 0.2253
> mdl_AWS = 0.808
> mdl_rhoWS = 0.132
> mdl_etaWS = 0.341
> mdl_ymt = 173.0
> mdl_ymtau = 1.777
> mdl_MZ = 91.188
> mdl_MT = 173.0
> mdl_MH = 125.0
> mdl_MTA = 1.777
> mdl_WZ = 2.441404
> mdl_WW = 2.0476
> mdl_WT = 1.4915
> mdl_WH = 0.00638233934
> mdl_WTau = 2.27e-12
>
> parameter type: ()
> mdl_CKM3x3 = 1.0
> mdl_conjg__CKM3x3 = 1.0
> ZERO = 0.0 = 0j
> mdl_lamWS__exp__2 = mdl_lamWS**2 = (0.05076009+0j)
> mdl_CKM1x1 = 1 - mdl_lamWS__exp__2/2. = (0.974619955+0j)
> mdl_CKM1x2 = mdl_lamWS = (0.2253+0j)
> mdl_complexi = complex(0,1) = 1j
> mdl_lamWS__exp__3 = mdl_lamWS**3 = (0.011436248277+0j)
> mdl_CKM1x3 =
> mdl_AWS*mdl_lamWS__exp__3*(-(mdl_etaWS*mdl_complexi) + mdl_rhoWS) =
> (0.00121974449623-0.00315100661527j)
> mdl_CKM2x1 = -mdl_lamWS = (-0.2253+0j)
> mdl_CKM2x2 = 1 - mdl_lamWS__exp__2/2. = (0.974619955+0j)
> mdl_CKM2x3 = mdl_AWS*mdl_lamWS__exp__2 = (0.04101415272+0j)
> mdl_CKM3x1 = mdl_AWS*mdl_lamWS__exp__3*(1 -
> mdl_etaWS*mdl_complexi - mdl_rhoWS) = (0.00802074411158-0.00315100661527j)
> mdl_CKM3x2 = -(mdl_AWS*mdl_lamWS__exp__2) = (-0.04101415272+0j)
> mdl_MZ__exp__2 = mdl_MZ**2 = (8315.251344+0j)
> mdl_MZ__exp__4 = mdl_MZ**4 = (69143404.9139+0j)
> mdl_sqrt__2 = cmath.sqrt(2) = (1.41421356237+0j)
> mdl_MH__exp__2 = mdl_MH**2 = (15625+0j)
> mdl_conjg__CKM1x3 = complexconjugate(mdl_CKM1x3) =
> (0.00121974449623+0.00315100661527j)
> mdl_conjg__CKM2x3 = complexconjugate(mdl_CKM2x3) =
> (0.04101415272+0j)
> mdl_conjg__CKM2x1 = complexconjugate(mdl_CKM2x1) = (-0.2253+0j)
> mdl_conjg__CKM3x1 = complexconjugate(mdl_CKM3x1) =
> (0.00802074411158+0.00315100661527j)
> mdl_conjg__CKM2x2 = complexconjugate(mdl_CKM2x2) =
> (0.974619955+0j)
> mdl_conjg__CKM3x2 = complexconjugate(mdl_CKM3x2) =
> (-0.04101415272+0j)
> mdl_conjg__CKM1x1 = complexconjugate(mdl_CKM1x1) =
> (0.974619955+0j)
> mdl_conjg__CKM1x2 = complexconjugate(mdl_CKM1x2) = (0.2253+0j)
>
> parameter type: ('aEWM1',)
> mdl_aEW = 1/aEWM1 = (0.00754677111398+0j)
> mdl_MW = cmath.sqrt(mdl_MZ__exp__2/2. +
> cmath.sqrt(mdl_MZ__exp__4/4. -
> (mdl_aEW*cmath.pi*mdl_MZ__exp__2)/(mdl_Gf*mdl_sqrt__2))) =
> (80.4190024458+0j)
> mdl_sqrt__aEW = cmath.sqrt(mdl_aEW) = (0.0868721538468+0j)
> mdl_ee = 2*mdl_sqrt__aEW*cmath.sqrt(cmath.pi) =
> (0.307953767244+0j)
> mdl_MW__exp__2 = mdl_MW**2 = (6467.21595437+0j)
> mdl_sw2 = 1 - mdl_MW__exp__2/mdl_MZ__exp__2 = (0.222246485786+0j)
> mdl_cw = cmath.sqrt(1 - mdl_sw2) = (0.881903347433+0j)
> mdl_sqrt__sw2 = cmath.sqrt(mdl_sw2) = (0.471430255484+0j)
> mdl_sw = mdl_sqrt__sw2 = (0.471430255484+0j)
> mdl_g1 = mdl_ee/mdl_cw = (0.349192196787+0j)
> mdl_gw = mdl_ee/mdl_sw = (0.653232930348+0j)
> mdl_vev = (2*mdl_MW*mdl_sw)/mdl_ee = (246.218458102+0j)
> mdl_vev__exp__2 = mdl_vev**2 = (60623.52911+0j)
> mdl_lam = mdl_MH__exp__2/(2.*mdl_vev__exp__2) =
> (0.128869106017+0j)
> mdl_yt = (mdl_ymt*mdl_sqrt__2)/mdl_vev = (0.993666145815+0j)
> mdl_ytau = (mdl_ymtau*mdl_sqrt__2)/mdl_vev = (0.0102066170007+0j)
> mdl_muH = cmath.sqrt(mdl_lam*mdl_vev__exp__2) = (88.3883476483+0j)
> mdl_I2x13 = mdl_yt*mdl_conjg__CKM3x1 =
> (0.00796994188793+0.00313104859883j)
> mdl_I2x23 = mdl_yt*mdl_conjg__CKM3x2 = (-0.0407543750572+0j)
> mdl_I2x33 = mdl_yt*mdl_conjg__CKM3x3 = (0.993666145815+0j)
> mdl_I3x31 = mdl_CKM3x1*mdl_yt =
> (0.00796994188793-0.00313104859883j)
> mdl_I3x32 = mdl_CKM3x2*mdl_yt = (-0.0407543750572+0j)
> mdl_I3x33 = mdl_CKM3x3*mdl_yt = (0.993666145815+0j)
> mdl_ee__exp__2 = mdl_ee**2 = (0.09483552276+0j)
> mdl_sw__exp__2 = mdl_sw**2 = (0.222246485786+0j)
> mdl_cw__exp__2 = mdl_cw**2 = (0.777753514214+0j)
>
> parameter type: ('aS',)
> mdl_sqrt__aS = cmath.sqrt(aS) = (0.343511280746+0j)
> G = 2*mdl_sqrt__aS*cmath.sqrt(cmath.pi) = (1.21771578478+0j)
> mdl_G__exp__2 = G**2 = (1.48283173249+0j)

I see that sin2theta has the on-shell tree level value (sw2= 1- MW^2/MZ^2 )
mdl_sw2 = 1 - mdl_MW__exp__2/mdl_MZ__exp__2 = (0.222246485786+0j)

However when I count helicities of tau^- at the Z peak and use the equation (1) I end up with sin2theta value of 0.2285. I am struggling a bit to understand this difference. Are there any weights or partial EWK higher order corrections applied to the input model (which I am probably missing) that changes the effective value of the weak mixing angle?

Many thanks in advance,
Vladimir.

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
Assignee:
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Last query:
2018-11-27
Last reply:
2018-11-27

Hi,

I'm not expert at all in those kind of measurement.

But note that
1) with that syntax it is quite likely that a significant contribution is off-shell (and some very offshell).
2) the polarization reported in the lhe file are computed in the center of mass of the (partonic) colision and not in the center of mass of the Z. Since those quantity are not boost invariant for massive particles this can also lead to a bias

Cheers,

Olivier

> On 27 Nov 2018, at 17:12, Vladimir Cherepanov <email address hidden> wrote:
>
> New question #676396 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/676396
>
> Dear Madgraph experts,
>
> I am using Madgraph of version MG5_aMC_v2_6_3_2.
>
> I am trying to extract the weak mixing angle from the polarization of tau leptons in the process pp -> Z -> tau tau.
> Further I denote N_L and N_R as a number of tau^- lepton being in a left- and right-handed states.
>
> Exactly at the Z peak the following relation holds to a very good approximation:
>
> P_tau = (N_R - N_L ) / ( N_R + N_L ) = -2 + 8*sin2theta. (1)
>
>
> In this notations N_R + N_L represents the total cross section. The QED term that contains initial quark couplings is negligible at the Z peak w.r.t Z boson exchange and thus in the equation above only weak tau couplings contribute.
>
> I use the DY sample that was produced for analysis at CMS, it has been generated with the following settings:
>
> set group_subprocesses Auto
> set ignore_six_quark_processes False
> set loop_optimized_output True
> set complex_mass_scheme False
> import model sm-ckm_no_b_mass
> define p = g u c d s u~ c~ d~ s~
> define j = g u c d s u~ c~ d~ s~
> define l+ = ta+
> define l- = ta-
> define vl = vt
> define vl~ =vt~
> define p u c s d b u~ c~ s~ d~ b~ g
> define l+ = ta+
> define l- = ta-
> define j = p
> generate p p > l+ l- / h @0
> add process p p > l+ l- j / h @1
> add process p p > l+ l- j j / h @2
> add process p p > l+ l- j j j / h @3
> add process p p > l+ l- j j j j / h @4
> output DYJets_HT-incl -nojpeg
>
>> From displaying parameters:
>
>> set group_subprocesses Auto
>> set ignore_six_quark_processes False
>> set loop_optimized_output True
>> set complex_mass_scheme False
>> import model sm-ckm_no_b_mass
>> display parameters
>>
>> Current model contains 73 parameters
>>
>> parameter type: ('external',)
>> aEWM1 = 132.507
>> mdl_Gf = 1.16639e-05
>> aS = 0.118
>> mdl_lamWS = 0.2253
>> mdl_AWS = 0.808
>> mdl_rhoWS = 0.132
>> mdl_etaWS = 0.341
>> mdl_ymt = 173.0
>> mdl_ymtau = 1.777
>> mdl_MZ = 91.188
>> mdl_MT = 173.0
>> mdl_MH = 125.0
>> mdl_MTA = 1.777
>> mdl_WZ = 2.441404
>> mdl_WW = 2.0476
>> mdl_WT = 1.4915
>> mdl_WH = 0.00638233934
>> mdl_WTau = 2.27e-12
>>
>> parameter type: ()
>> mdl_CKM3x3 = 1.0
>> mdl_conjg__CKM3x3 = 1.0
>> ZERO = 0.0 = 0j
>> mdl_lamWS__exp__2 = mdl_lamWS**2 = (0.05076009+0j)
>> mdl_CKM1x1 = 1 - mdl_lamWS__exp__2/2. = (0.974619955+0j)
>> mdl_CKM1x2 = mdl_lamWS = (0.2253+0j)
>> mdl_complexi = complex(0,1) = 1j
>> mdl_lamWS__exp__3 = mdl_lamWS**3 = (0.011436248277+0j)
>> mdl_CKM1x3 =
>> mdl_AWS*mdl_lamWS__exp__3*(-(mdl_etaWS*mdl_complexi) + mdl_rhoWS) =
>> (0.00121974449623-0.00315100661527j)
>> mdl_CKM2x1 = -mdl_lamWS = (-0.2253+0j)
>> mdl_CKM2x2 = 1 - mdl_lamWS__exp__2/2. = (0.974619955+0j)
>> mdl_CKM2x3 = mdl_AWS*mdl_lamWS__exp__2 = (0.04101415272+0j)
>> mdl_CKM3x1 = mdl_AWS*mdl_lamWS__exp__3*(1 -
>> mdl_etaWS*mdl_complexi - mdl_rhoWS) = (0.00802074411158-0.00315100661527j)
>> mdl_CKM3x2 = -(mdl_AWS*mdl_lamWS__exp__2) = (-0.04101415272+0j)
>> mdl_MZ__exp__2 = mdl_MZ**2 = (8315.251344+0j)
>> mdl_MZ__exp__4 = mdl_MZ**4 = (69143404.9139+0j)
>> mdl_sqrt__2 = cmath.sqrt(2) = (1.41421356237+0j)
>> mdl_MH__exp__2 = mdl_MH**2 = (15625+0j)
>> mdl_conjg__CKM1x3 = complexconjugate(mdl_CKM1x3) =
>> (0.00121974449623+0.00315100661527j)
>> mdl_conjg__CKM2x3 = complexconjugate(mdl_CKM2x3) =
>> (0.04101415272+0j)
>> mdl_conjg__CKM2x1 = complexconjugate(mdl_CKM2x1) = (-0.2253+0j)
>> mdl_conjg__CKM3x1 = complexconjugate(mdl_CKM3x1) =
>> (0.00802074411158+0.00315100661527j)
>> mdl_conjg__CKM2x2 = complexconjugate(mdl_CKM2x2) =
>> (0.974619955+0j)
>> mdl_conjg__CKM3x2 = complexconjugate(mdl_CKM3x2) =
>> (-0.04101415272+0j)
>> mdl_conjg__CKM1x1 = complexconjugate(mdl_CKM1x1) =
>> (0.974619955+0j)
>> mdl_conjg__CKM1x2 = complexconjugate(mdl_CKM1x2) = (0.2253+0j)
>>
>> parameter type: ('aEWM1',)
>> mdl_aEW = 1/aEWM1 = (0.00754677111398+0j)
>> mdl_MW = cmath.sqrt(mdl_MZ__exp__2/2. +
>> cmath.sqrt(mdl_MZ__exp__4/4. -
>> (mdl_aEW*cmath.pi*mdl_MZ__exp__2)/(mdl_Gf*mdl_sqrt__2))) =
>> (80.4190024458+0j)
>> mdl_sqrt__aEW = cmath.sqrt(mdl_aEW) = (0.0868721538468+0j)
>> mdl_ee = 2*mdl_sqrt__aEW*cmath.sqrt(cmath.pi) =
>> (0.307953767244+0j)
>> mdl_MW__exp__2 = mdl_MW**2 = (6467.21595437+0j)
>> mdl_sw2 = 1 - mdl_MW__exp__2/mdl_MZ__exp__2 = (0.222246485786+0j)
>> mdl_cw = cmath.sqrt(1 - mdl_sw2) = (0.881903347433+0j)
>> mdl_sqrt__sw2 = cmath.sqrt(mdl_sw2) = (0.471430255484+0j)
>> mdl_sw = mdl_sqrt__sw2 = (0.471430255484+0j)
>> mdl_g1 = mdl_ee/mdl_cw = (0.349192196787+0j)
>> mdl_gw = mdl_ee/mdl_sw = (0.653232930348+0j)
>> mdl_vev = (2*mdl_MW*mdl_sw)/mdl_ee = (246.218458102+0j)
>> mdl_vev__exp__2 = mdl_vev**2 = (60623.52911+0j)
>> mdl_lam = mdl_MH__exp__2/(2.*mdl_vev__exp__2) =
>> (0.128869106017+0j)
>> mdl_yt = (mdl_ymt*mdl_sqrt__2)/mdl_vev = (0.993666145815+0j)
>> mdl_ytau = (mdl_ymtau*mdl_sqrt__2)/mdl_vev = (0.0102066170007+0j)
>> mdl_muH = cmath.sqrt(mdl_lam*mdl_vev__exp__2) = (88.3883476483+0j)
>> mdl_I2x13 = mdl_yt*mdl_conjg__CKM3x1 =
>> (0.00796994188793+0.00313104859883j)
>> mdl_I2x23 = mdl_yt*mdl_conjg__CKM3x2 = (-0.0407543750572+0j)
>> mdl_I2x33 = mdl_yt*mdl_conjg__CKM3x3 = (0.993666145815+0j)
>> mdl_I3x31 = mdl_CKM3x1*mdl_yt =
>> (0.00796994188793-0.00313104859883j)
>> mdl_I3x32 = mdl_CKM3x2*mdl_yt = (-0.0407543750572+0j)
>> mdl_I3x33 = mdl_CKM3x3*mdl_yt = (0.993666145815+0j)
>> mdl_ee__exp__2 = mdl_ee**2 = (0.09483552276+0j)
>> mdl_sw__exp__2 = mdl_sw**2 = (0.222246485786+0j)
>> mdl_cw__exp__2 = mdl_cw**2 = (0.777753514214+0j)
>>
>> parameter type: ('aS',)
>> mdl_sqrt__aS = cmath.sqrt(aS) = (0.343511280746+0j)
>> G = 2*mdl_sqrt__aS*cmath.sqrt(cmath.pi) = (1.21771578478+0j)
>> mdl_G__exp__2 = G**2 = (1.48283173249+0j)
>
>
> I see that sin2theta has the on-shell tree level value (sw2= 1- MW^2/MZ^2 )
> mdl_sw2 = 1 - mdl_MW__exp__2/mdl_MZ__exp__2 = (0.222246485786+0j)
>
> However when I count helicities of tau^- at the Z peak and use the equation (1) I end up with sin2theta value of 0.2285. I am struggling a bit to understand this difference. Are there any weights or partial EWK higher order corrections applied to the input model (which I am probably missing) that changes the effective value of the weak mixing angle?
>
> Many thanks in advance,
> Vladimir.
>
>
>
>
>
> --
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