Electroweak NLOPS for the Higgs decay into four charged ... · CMCC et al., NPB Proc. Suppl. 157,...

Electroweak NLOPS for the Higgs decay into fourcharged leptons

C.M. Carloni CalamePavia University

HP25 workshop, Galileo Galilei Institute, Florence

in collaboration with S. Boselli, G. Montagna, O. Nicrosini, F. Piccinini

C.M. Carloni Calame H → ZZ → 4` September 3-5 2014 1 / 18

Summary

? Motivations for a detailed simulation of H → ZZ → 2`2`(′)

? Outline of the EW NLO calculation (in the SM)? Matching EW NLO with a QED Parton Shower? Comparison to independent calculations? Results? Conclusions and outlook


Motivations

• after the Higgs discovery, its nature is studied with high precision• H mass already measured at the few 0.1% level

mH = 125.36± 0.37 (stat)± 0.18 (sys) GeV [ATLAS]

125.6± 0.4 (stat)± 0.2 (sys) GeV [CMS]

arXiv:1406.3827 (submitted to PRD); PRD 89, 092007

• spin/parity consistent with the SM• next run will require high accuracy SM predictions, to test SM itself

or disentagle any deviation, firstly in the cleanest decay channels? H → γγ? H → ZZ → 4 charged leptons

• EW NLO and higher order corrections to H decay into 4` have tobe considered


Previous and independent work

• (gauge invariant) QED corrections to H → ZZ → 4` in leading-log(LL) approximation, QED Parton Shower approach

CMCC et al., NPB Proc. Suppl. 157, 73 (2006)PoS HEP 2005, 307 (2006)

? estimated impact of O(α) RC on extracted mH : O(100 MeV)? estimated impact of higher-order RC: O(few 10 MeV)

• full one-loop EW (& QCD) corrections to H → ZZ/WW → 4f ,implemented in the publicly available Prophecy4f

A. Bredenstein et al., PRD 74 (2006) 013004NPB Proc. Suppl. 160 (2006) 131

JHEP 0702 (2007)

? combination of 1-loop EW RC and QED exponentiation is adesirable feature


NLO RC: calculation approach

As usual, the partial width is split into two parts, ΓNLO = Γ1→4 + Γ1→5

IR singularities are regularized with a vanishingly small photon mass λ

• H → 4`

Γ1→4 =1

2mH

∫dΦ4(|M0|2 + 2<[M∗0 ×M1L

α (λ)])

• H → 4`+ γ

Γ1→5 =1

2mH

∫ω>λ

dΦ5|M1γα |2 = δ(λ, k0) Γ0+

1

2mH

∫ω>k0

dΦ5|M1γα |2

• matrix elements consistently evaluated including Z (and W , top)decay widths

• the integration over the 4/5-particles phase space is done with MCtechniques and fully-exclusive events are generated


NLO RC: 1-loop corrections

• the full set (vertex, box, pentagon, self-energy corrections) of1-loop EW diagrams are evaluated in the Feynman-’t Hooft gauge,in the on-shell renormalization schemeOmitted only the (negligible) diagrams where H is coupled to external fermions

• the on-shell ren. is “translated” to the complex mass scheme toconsistently treat the Z (+ W , top) widths in the loop diagramspreserving IR cancellation and gauge invariance

A. Denner et al., PLB 612, 223 (2005), ibid. 704, 667 (2011)A. Denner et al., NPB 724, 247 (2005), ibid. 854, 504 (2012)

• the 1-loop A, B, C, D, E functions and tensor coefficients areevalutated with the help of LoopTools v2.10, with complex Z,W , top masses

T. Hahn, www.feynarts.de/looptools/

• independence of UV & IR regulators checked with high numericalaccuracy


NLO cross-checks, comparison to Prophecy4f

• the calculation is implemented in the new MC EG Hto4l• numerics done in the Gµ scheme with the inputs

MLEPW = 80.398 GeV ΓLEP

W = 2.141 GeVMLEP

Z = 91.1876 GeV ΓLEPZ = 2.4952 GeV

mt = 172.5 GeV

the “on-shell” LEP MV and ΓV are converted to the “pole” (fixed-width) ones by means of

MV = MLEPV /

√1 + (ΓLEP

V /MLEPV )2 ΓV = ΓLEP

V /√

1 + (ΓLEPV /MLEP

V )2

• various lepton pairs invariant masses and the angle between the Zdecay planes are considered

cosφ ≡ [(p1 + p2)× p1] · [−(p3 + p4)× p3]

|(p1 + p2)× p1||(p3 + p4)× p3|

? cosφ is sensitive to H spin



0.11

10100

100010000

100000

ΓH→

2e2µ

(keV

)

150 200 250 300 350 4001

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

1.05

Γi/ΓLO

MH (GeV)

Prophecy2.0Hto4l EW NLO


0.010.1

110

1001000

10000

ΓH→

4µ

(keV

)

150 200 250 300 350 4001

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

1.05

Γi/ΓLO

MH (GeV)



• perfect agreement for EW NLO partial decay widths betweenHto4l and Prophecy4f

• for mH = 125 GeV, EW NLO corrected decay width is ' 1% largerthan LO



0

5

10

15

20

25

30

dΓ/dM

e+e−×

103

MH = 125 GeVH → e+e−µ+µ−

86 88 90 92 940.60.70.80.911.11.21.31.41.51.6

dΓNLO/d

ΓLO

Me+e− (GeV)

Hto4l NLO EWProphecy2.0 NLO EW

LO

Hto4lProphecy2.0

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

dΓ/dφ×

103

(GeV

/deg

) MH = 125 GeVH → e+e−µ+µ−

0 50 100 150 200 250 300 3500.980.9911.011.021.031.041.051.061.07

dΓNLO/d

ΓLO

φ (deg)

Hto4l NLO EWProphecy2.0 NLO EW

LO

Hto4lProphecy2.0

• perfect agreement also on distributions


Beyond NLO: matching with multiple photon emission

• the LL QED (PS) exponentiated width can be cast as

dΓ∞PS =1

2mHΠ(Q2, k0)

∞∑n=0

1

n!|MLL,n|2dΦ

[ωn>k0]

4+n

• which can be improved to include exact NLO EW corrections bythe master formula

dΓ∞matched =1

2mHΠ(Q2, k0) CSV

∞∑n=0

1

n!

n∏i=1

CH,i|MLLn |2dΦ4+n

with CSV = 1 +dΓNLOSV −dΓPSSV

dΓ0CH,i = 1 +

|Mex[i]|2−|MLL

[i]|2

|MLL[i]|2

CMCC et al., NPB 758, 227 (2006)CMCC et al., JHEP 0710, 109 (2007), JHEP 0612, 016 (2006)


Beyond NLO: matching properties

CSV and CH,i:• are built with up-to-1-loop “ingredients” and infrared/collinear safe• account for O(α) QED non-log & weak RC missing in the PS,

avoiding LL double counting, so that? [Γ∞matched]O(α) = ΓNLO

? the resummation of QED LL higher orders is preserved• the master formula allows for a fully exclusive generation of all f.s.

momenta (leptons and photons)• the integral over the phase space dΦ4+n is exact

• the closer |MLL[i] |2 to |M ex

[i] |2 the closer CH,i to 1.A “good” LL approximation for photon emission is required.


Radiation LL approximation

• the peaking structure is driven bysoft/collinear radiation ⊗ Z resonancesE.g. H → 2e2µ+ nγ amplitude

M peakn =

C

n!

∑P

n∑i=1

Jµ12

(P12 +QP)2 −m2z

Jµ,34

(P34 +QP ′)2 −m2z

4∏j=1

ηjpj ·ε(qi)pj ·qi

Jµij ≡ u(pi)γµ(gV − gAγ5)v(pj), Pij = pi + pj , QP =

∑i∈P

qi, m2z = M2

Z − iΓZMZ

• although approximately, radiation interferences are accounted for• |MLL

n |2 = |M peakn |2 ⊕ AP enhancement for hard-collinear radiation

(i.e. photons’ energy spectrum according to AP vertex)

• e.g., with CH,i switched on and n = 2 (H → 4`+ 2γ at LO), checksvs MadGraph and GoSam show very good agreement

thanks to F. Tramontano


Results: relative corrections

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

60 65 70 75 80 85 90 95 100

dΓi/dΓLO

Me+e− (GeV)

H → e+e−µ+µ−, MH = 125 GeV

NLO EWmatched EW

NLO QEDmatched QED

0.8

0.9

1

1.1

1.2

1.3

1.4

60 65 70 75 80 85 90 95 100

dΓi/dΓLO

Mµ+µ− (GeV)

H → e+e−µ+µ−, MH = 125 GeV

NLO EWmatched EW

NLO QEDmatched QED

• large corrections on lepton invariant masses (mainly) due to QED? up to 50% NLO correction on (bare) Me+e−

? O(10%) due to exponentiation, multiple-photon emissions


Results: relative corrections

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

0 50 100 150 200 250 300 350

dΓi/dΓLO

φ (deg)

H → e+e−µ+µ−, MH = 125 GeV NLO EWmatched EW

NLO QEDmatched QEDPS O(α) QED

PS exp QED

• interplay between non-log QED and pure weak corrections• moderate effect of exponentiation


Radiation exclusive observables

• the events are fully exclusive over emitted photonse.g. ∆R between softest γ (with Eγ > 4 GeV) and hardest `

05

1015202530354045

dΓi/d∆R

(eV

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50.6

0.8

1

1.2

1.4

1.6

1.8

dΓi/dΓ

NLO

EW

∆Rγ`l.e., m.e.

H → e+e−µ+µ−, MH = 125 GeV

NLO EWmatched EW

matched EW

? remarkable effect due to multiple photon emissions



0.001

0.01

0.1

1

10

dΓi/dM

4`

(×10

−9)

40 50 60 70 80 90 100 110 1200.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

dΓi/dΓ

NLO

EW

M4` (GeV)

H → e+e−µ+µ−, MH = 125 GeV

NLO EWmatched EW

matched EW0.0001

0.001

0.01

0.1

1

10

dΓi/dM

4`

(×10

−9)

40 50 60 70 80 90 100 110 1200.850.90.9511.051.11.151.21.251.31.35

dΓi/dΓ

NLO

EW

M4` (GeV)

H → µ+µ−µ+µ−, MH = 125 GeV

NLO EWmatched EW

matched EW

• 4-lepton invariant mass: large effect due to multiple-photonemission



00.5

11.5

22.5

33.5

44.5

5

dΓi/dp[4`]⊥

(×10−9)

5 10 15 20 25 30 35 400.870.880.890.90.910.920.930.940.950.960.97

dΓi/dΓ

NLO

EW

p[4`]⊥ (GeV)

H → e+e−µ+µ−, MH = 125 GeV

NLO EWmatched EW

matched EW0

0.20.40.60.8

11.21.41.61.8

dΓi/dp[4`]⊥

(×10−9)

5 10 15 20 25 30 35 400.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

dΓi/dΓ

NLO

EW

p[4`]⊥ (GeV)

H → µ+µ−µ+µ−, MH = 125 GeV

NLO EWmatched EW

matched EW

• 4-lepton p⊥ (i.e. pH⊥ ): large effect due to multiple-photon emission


Conclusion and outlook

• the Higgs boson will be studied with high precision, to unveil itsnature

• the new MC Hto4l has been developed for the precise simulationof the decay H → ZZ → 4`, including? full one-loop EW corrections in the SM, in the complex-mass

scheme? consistent matching with multiple photon emission? fully exclusive event generation? LHE compliant for interfacing to any EG for H production

• preliminary studies in the H rest frame show the effects areimportant in view of precise mass and spin/parity measurements

• work is in progress to study the realistic impact of the correctionsincluding H production and detector effects


Electroweak NLOPS for the Higgs decay into four charged ... · CMCC et al., NPB Proc. Suppl. 157,...

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