Coherent Showers in Decays of Coloured Resonances Helen Brooks & - - PowerPoint PPT Presentation

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Coherent Showers in Decays of Coloured Resonances Helen Brooks & - - PowerPoint PPT Presentation

Aug 18, 2022 28 likes •239 views

Coherent Showers in Decays of Coloured Resonances Helen Brooks & Peter Skands (Monash University) A new shower model based on Resonance- Final antennae (with mass- and helicity-dependence) VINCIA VINCIA log 10 ( a RF g/qq s AK ) as a

slide-1
SLIDE 1

VINCIA VINCIA

Coherent Showers in Decays of Coloured Resonances

Helen Brooks & Peter Skands (Monash University)

Parton Showers and Resummation Vienna, June 2019

45 90 135 180 225 270 315 1 2 3 4 5 6

log10(aRF

g/qqsAK) as a function of θjk in A COM frame

log(E/GeV) = 0.0 log(E/GeV) = 0.2 log(E/GeV) = 0.4 log(E/GeV) = 0.6 log(E/GeV) = 0.8 log(E/GeV) = 1.0 log(E/GeV) = 1.2 log(E/GeV) = 1.4 log(E/GeV) = 1.6 log(E/GeV) = 1.8

PRODUCTION DECAY(S) RF ANTENNA PATTERN

A new shower model based on “Resonance- Final” antennae (with mass- and helicity-dependence)

IF antenna IF antenna II antenna

⊗

R F a n t e n n a

⊗

slide-2
SLIDE 2

mt < Qevol < Qcut

Coherence in Resonance Decays

HE LEN B RO O K S & P E TE R SK A N D S

  • 2

MO NA S H U.

VINCIA

Note: interference between production and decay will

  • ccur at scales < Γ; not the topic of this talk

PRODUCTION DECAY(S)

IF antenna IF antenna II antenna

⊗

R F a n t e n n a

⊗

๏In narrow width approximation,
  • Factorise production and decay of resonances;
  • These stages are showered independently.

Goal is to shower the resonance-final antenna in decay coherently, without modifying the invariant mass of the resonance, needed for resonance-aware matching.

√s < Qevol < Qcut

slide-3
SLIDE 3

Prime Motivation: Top Quark Mass

HE LEN B RO O K S & P E TE R SK A N D S

  • 3

MO NA S H U.

VINCIA

arXiv:1801.03944 “... the very minimal message that can be drawn from our work is that, in order to assess a meaningful theoretical error in top-mass measurements, the use of different shower models, associated with different NLO+PS generators, is mandatory.”

slide-4
SLIDE 4

Dipoles vs Antennae (in resonance decays)

HE LEN B RO O K S & P E TE R SK A N D S

  • 4

MO NA S H U.

๏Dipole showers
  • Each branching has a well-defined

“radiator” and a “recoiler”, with distinct kinematics maps.

  • Neglect contribution from 


resonance as radiator (partition can even become negative).

  • In principle free to choose recoiler,

e.g. W in t → W b

๏Antenna Showers
  • Agnostic as to who is the radiator;

smooth transition in kinematics

๏

Interpolates between collinear limits

  • Coherence built in; cannot neglect

resonance’s contribution

  • Recoil strategy relates to antenna

factorisation

VINCIA

kinematics

t b ?

X b −t

t → b W : Top sits at rest (does not radiate) Bottom quark radiates; recoils against the

  • nly other final-state parton, W.

More branchings: ambiguous what recoiler to use for parton colour-connected to top t → b W: Antenna between bottom and crossed top. Kinematics map with X = W ⟹ W acquires recoil More branchings: unambiguous. Parton colour- connected to top participates in the RF antenna; rest = X collectively acquire the recoil.

*

*Note: the original dipole shower, ARIADNE, is of the type I here call “antenna shower”

slide-5
SLIDE 5

RF Showers 1: Antenna Functions

HE LEN B RO O K S & P E TE R SK A N D S

  • 5

MO NA S H U.

VINCIA

Note: defined for all helicity configurations & all shower states assigned explicit helicities throughout VINCIA; here just showing summed forms for brevity.

b∗ t b t∗ t b

+

Ant = |

|

2/ Born

pa

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pX

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pj

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pk

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pk

<latexit sha1_base64="w0EQAkNDfaLwaF7qtdIYNvQk4DI=">AB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe6ioIVFwMYyovmA5Ah7m7lkyd7esbsnhCM/wcZCEVt/kZ3/xk1yhSY+GHi8N8PMvCARXBvX/XYKa+sbm1vF7dLO7t7+QfnwqKXjVDFsljEqhNQjYJLbBpuBHYShTQKBLaD8e3Mbz+h0jyWj2aSoB/RoeQhZ9RY6SHpj/vlilt15yCrxMtJBXI0+uWv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzU6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDaz7hMUoOSLRaFqSAmJrO/yYArZEZMLKFMcXsrYSOqKDM2nZINwVt+eZW0alXvolq7v6zUb/I4inACp3AOHlxBHe6gAU1gMIRneIU3RzgvzrvzsWgtOPnMfyB8/kDVuiN0A=</latexit>

pX

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pa

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pj

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yaj ≡ saj/(sAK + sjk), µ

…

, µ2

a ≡ m2 a/(sAK + sjk),

collinear

= ⇒ zk ∼ yak = 1 − yaj (+2µ2

j) ,

za ∼ yAK = 1 − yjk

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Define dimensionless invariants:

aRF

emit =

1 sAK " (1 − yaj)2+δKg + (1 − yjk)2 yajyjk − 2µ2

a

y2

aj

− 2µ2

k

y2

jk

+ f(yaj, yjk, µ2

a, µ2 k)

#

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aRF

split =

1 m2

jk

" y2

ak + y2 aj + 2m2 j

m2

jk

#

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Polynomial(s) chosen such that all helicity components remain positive-definite Labeling: AI KF | {z }

pre-branching

→ aI jF kF | {z }

post-branching

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→ same forms as FF, IF, II :*

*: difference is 1/(sAK + sjk) normalisation and phase-space map

N.B.: sαβ ≡ 2pα · pβ throughout!

slide-6
SLIDE 6

RF Showers 2: Evolution Variables

HE LEN B RO O K S & P E TE R SK A N D S

  • 6

MO NA S H U.

VINCIA

Emissions: Q2

evol =

sajsjk sjk + sAK ζ = sjk + sAK sAK Splittings: Q2

evol = (sjk + 2m2 q)(saj − m2 q)

sAK + sjk + 2m2

q

ζ = sak sAK

Labeling: AI KF | {z }

pre-branching

→ aI jF kF | {z }

post-branching

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Same since mj = 0 for emission

Generalisation

  • f ARIADNE

pT

Resonance Mass “Dead Cone” Resonance Mass “Dead Cone” Final-state quark “Dead Cone”

N.B.: sαβ ≡ 2pα · pβ throughout!

slide-7
SLIDE 7 ๏2→3 phase-space factorisation:

RF Showers 3: Phase-Space Factorisation

HE LEN B RO O K S & P E TE R SK A N D S

  • 7

MO NA S H U.

VINCIA

dΦn+1 = dΦant × dΦn

Labeling: AI KF | {z }

pre-branching

→ aI jF kF | {z }

post-branching

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N.B.: sαβ ≡ 2pα · pβ throughout!

≡ ·

I Factorisation is exact, not just in soft, collinear limits I Preserves invariant mass of resonance: pA = pa I Preserves invariant mass of system of recoilers:

pA = pK + pX = ⇒ m2

X = (pA − pK)2 ≡ (pa − pj − pk)2 = m2 X0

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dΦa!jk+{X} = 1 (4π)5 dsajdsjkdφ m2

A

dΩK

dΦant = 1 16π2 dsajdsjk λ1/2(m2

A, m2 AK, m2 K)

dφ 2π

dΦA!K+{X} = 1 8(2π)2 λ1/2(m2

A, m2 AK, m2 K)

m2

A

dΩK

Same form as the final-final antenna phase space … with mX = mAK as one of the Born parameters

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SLIDE 8

RF Showers 4: Kinematics Map (Recoil)

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I Construct in A rest frame, and rotate such that K is along z. I Specify system X only recoils longitudinally. I Rotate about z by φ (flatly sampled). I Boost back to lab frame. I For each recoiler i, boost pi by pX0 − pX

Note!

If we fix to just one recoiler i.e. A → RKX, a → rjkX then CANNOT simulatenously preserve m2

A, m2 R and m2 AK.

Replace A → A − X everywhere.

I Antenna mass is modified! I Phase space normalisation is modified! I Mass used everywhere is (pA − pX)2 - not same as propagator!

Labeling: AI KF | {z }

pre-branching

→ aI jF kF | {z }

post-branching

<latexit sha1_base64="LW8v+2NvWNsOBoZepGIEU+knU=">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</latexit>

N.B.: sαβ ≡ 2pα · pβ throughout!

*Note the prescription defined here is similar to one recently implemented in Herwig7 by Cormier et al., arXiv:1810.06493

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SLIDE 9

Effect of Kinematics Map

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Consider average recoil |∆~ pW |, after first and second emission(s). Recoil after first:

100 101 pT evol [GeV] 20 40 60 80 |∆~ pW | [GeV] PYTHIA 8 (W recoil map) VINCIA (W recoil map) VINCIA (default map)

Recoil after second:

100 101 pT evol [GeV] 20 40 60 |∆~ pW | [GeV] PYTHIA 8 (W recoil map) VINCIA (W recoil map) VINCIA (default map)

Second branching: Collective RF map → less recoil to W First branching: there is only the W

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SLIDE 10

(Coherence In Production)

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VINCIA

50 100 150 200 250 pT (t¯ t) [GeV] 1 2 Ratio to HERWIG 7 ang −1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 0.75 1.00 AF B(pT (t¯ t)) p¯ p → t¯ t √s = 1.96 TeV PS only (no MPI) PYTHIA 8 HERWIG 7 angular HERWIG 7 dipole VINCIA

Forward-backwards asymmetry: AFB(O) =

dσ dO

  • ∆y>0 − dσ

dO

  • ∆y<0

dσ dO

  • ∆y>0 + dσ

dO

  • ∆y<0

Coherent showers include part of the real emission correction that generates a FB asymmetry that becomes negative for large pT (t¯ t). [1205.1466]

(b) _ _ _ _ q q (a) q t t t q q q q q t t q q

Well-studied effect in p-pbar collisions Top quark FB asymmetry

Skands, Webber, Winter JHEP 1207 (2012) 151

Coherent showers produce a pTdependent asymmetry Herwig7 dipole shower exhibits exactly same behaviour as VINCIA

slide-11
SLIDE 11

Coherence in Decay

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VINCIA

Plot antenna function in top centre of mass frame (b along z):

45 90 135 180 225 270 315 1 2 3 4 5 6

log10(aRF

g/qqsAK) as a function of θjk in A COM frame

log(E/GeV) = 0.0 log(E/GeV) = 0.2 log(E/GeV) = 0.4 log(E/GeV) = 0.6 log(E/GeV) = 0.8 log(E/GeV) = 1.0 log(E/GeV) = 1.2 log(E/GeV) = 1.4 log(E/GeV) = 1.6 log(E/GeV) = 1.8 45 90 135 180 225 270 315 0.2 0.4 0.6 0.8 1.0

aRF

g/qq

Pgq(z)/Q2 as a function of θjk in A COM frame

log(E/GeV) = 0.0 log(E/GeV) = 0.2 log(E/GeV) = 0.4 log(E/GeV) = 0.6 log(E/GeV) = 0.8 log(E/GeV) = 1.0 log(E/GeV) = 1.2 log(E/GeV) = 1.4 log(E/GeV) = 1.6 log(E/GeV) = 1.8

Antenna function is consistent with Altarelli-Parisi splitting function in (quasi-)collinear direction, coherence results in a suppression in the backwards direction.

Ratio to AP kernel Log of antenna function

slide-12
SLIDE 12 ๏VINCIA gives narrower b-jets than Pythia 8
  • Effect survives MPI + hadronisation

B-Jet Profiles

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VINCIA

0.0 0.1 0.2 0.3 0.4 0.5 0.6 r 0.5 1.0 1.5 Ratio to PYTHIA 8 10−2 10−1 100 101 (r) pp → t¯ t → b¯ b`+`−⌫¯ ⌫, √s = 13 TeV PS only (no MPI) pT bj ∈ [30, 50] GeV Qcut ∈ [0.5, 1.0] GeV PYTHIA 8 VINCIA 0.0 0.1 0.2 0.3 0.4 0.5 0.6 r 0.6 0.8 1.0 1.2 1.4 Ratio to PYTHIA 8 10−1 100 101 (r) pp → t¯ t → b¯ b`+`−⌫¯ ⌫, √s = 13 TeV PS + MPI + had pT bj ∈ [30, 50] GeV Qcut ∈ [0.5, 1.0] GeV PYTHIA 8 VINCIA

Shower only Shower + MPI + Hadr

Tentative conclusion: more coherence ~ more wide-angle suppression?

*Also agrees with intuition from dipole language where “top dipole” can be negative

Differential jet shape ρ(r)

slide-13
SLIDE 13

Matching with POWHEG

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VINCIA

I Use POWHEG v2 (t¯

tdec)1 (no need for exact finite width effects)

I Very similar setup to matching

with PYTHIA in 2.

I Veto hardest emission in

production with

Vincia:QmaxMatch = 1

I Veto hardest emission in decay

with UserHooks interface ATLAS dileptonic t¯ t @ 8 TeV [1709.09407]

100 150 200 250 300 350 pT e + pT µ[GeV ] 0.8 1.0 1.2 Ratio to ATLAS data 10−4 10−3 10−2

1

  • d

d(pT e+pT µ)[GeV −1]

pp → t¯ t → b¯ b`+`−⌫¯ ⌫, √s = 8 TeV PS only (no MPI) ATLAS data PY8+POWHEG VINCIA+POWHEG H7(ang)+POWHEG PYTHIA 8 @LO

1[1412.1828],[1509.0907] 2[1801.03944] 3Thanks to S. Ferrario Ravasio for providing an interface to H7

24

slide-14
SLIDE 14

168 170 172 174 176 178 mbj+[GeV ] 0.8 1.0 1.2 Ratio to PYTHIA 8 0.00 0.05 0.10 0.15 0.20 0.25 0.30

d dmbj + [pb/GeV]

pp → t¯ t → b¯ be+µ−νe¯ νµ, √s = 8 TeV PS +POWHEG v2 (no MPI) PYTHIA 8 VINCIA HERWIG 7 (ang) PYTHIA 8 (W recoil) VINCIA (W recoil)

Top Mass Profile @ 8 TeV : Parton Level

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p¯ p → t¯ t @ 8 TeV: mbj`⌫

Monte-Carlo “truth” (parton-level) analysis:

I Assumes we can reconstruct pν and match correct `, bj pair.

(“cheating” / looking under the hood)

Plot from H. Brooks

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SLIDE 15

Conclusions & Outlook

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๏VINCIA can now do

production and decay

  • f top quarks
  • With full mass and

helicity dependence

๏Based on new

“resonance-final” antennae

  • Coherent top+b (&

top+g) radiation patterns

  • Collective recoil

kinematics

VINCIA

Coming soon... PYTHIA 8.3 → Watch this space!

slide-16
SLIDE 16

Uncertainties

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๏Fixed-order accuracy (μR) + PDFs (μF) + matching/merging (e.g. hdamp) ๏Parton shower ambiguities from logarithmic accuracy
  • → Estimate by comparing different shower architectures
๏

+ systematic parametric variations

  • → To reduce, need systematic improvements:
๏

At LL / LC: coherence & “optimised” choices (for muR, evolution scale, recoil strategies, …)

๏

Beyond LL / LC: genuine subleading colour (beyond optimised LC) and higher-order corrections to shower kernels (beyond optimised LL)

๏+ Mass Effects, Finite-Width Effects, Polarisation Effects

VINCIA

๏+ Non-perturbative: Renormalon pole mass ambiguity ≲ ΛQCD ,

colour-reconnections,︎ MPI, beam remnant treatment, hadronisation, hadron rescattering, hadron and τ decays, …

( )

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SLIDE 17

Shower Architectures

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๏Sum over all dipoles / antennae should reproduce the

leading log

VINCIA

Type Singularities Coherence? No dead Examples soft collinear zones? DGLAP part. full 7 7 Angular full+veto full+veto 3 7 H7 ˜ q Dipole part. part. 7 3 Pythia 8 C-S part. part. 3 3 Sherpa, H7 dip Antenna (global) full part. 3 3 Vincia Antenna (sector) full full+veto 3 3 Vincia

Table from H. Brooks

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SLIDE 18

Current Status of Resonance Decay Showers

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Shower Type Decay shower? Coherence? Pythia 8 [hep-ph/0010012]

[hep-ph/0408302]

Dipole 3 7 Sherpa [1412.6478] Catani-Seymour 7

(production only)

(3) Herwig 7 (˜ q)

[1810.06493]

Angular-ordered 3 3 Herwig 7 (dip)

[1810.06493]

Catani-Seymour (3)

(on-shell only)

(3) Vincia - NEW! Antenna 3 3

Slide from H. Brooks

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SLIDE 19

Example: Collinear Limits

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Example: qq antenna limits

Can rewrite antenna as: aRF

g/qq =

1 sAK 2 6 6 6 4 2yak yajyjk − 2µ2

a

y2

aj

− 2µ2

k

y2

jk

| {z }

soft

+ yaj yjk + yjk yaj | {z }

collinear

+ n.s. 3 7 7 7 5 Define Q2 ≡ sjk; y ≡

Q2 sAK ;

z ≡

sak sAK

⇒

saj sAK = 1 + y − z

aRF

g/qq = 1

Q2 2z(1 + y) 1 + y − z + (1 + y − z) − 2m2

k

Q2 + O(y)

  • + n.s.

In collinear limit, y → 0 lim

y→0 aRF g/qq = 1

Q2 1 + z2 1 − z − 2m2

k

Q2

  • = 1

Q2 Pq→gq(z, ˜ µ) N.B. Need to sum over neighbouring antennae for gg collinear limit.

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SLIDE 20

Top Mass Profile @ 8 TeV

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20 40 60 80 100 120 140 160 180 200 mbjµ[GeV ] 0.8 0.9 1.0 1.1 1.2 Ratio to PYTHIA 8 10−4 10−3 10−2

dσ dmbj µ [pb/GeV]

pp → t¯ t → b¯ be+µ−νe¯ νµ, √s = 8 TeV PS+ MPI+had+POWHEG v2 PYTHIA 8 VINCIA HERWIG 7 (ang)

p¯ p → t¯ t @ 8 TeV: mbjµ

Full hadron-level analysis: choose pairing for `, bj that minimise average mass. Again, note endpoint. Note Endpoint (example of a realistic observable)

Plot from H. Brooks

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SLIDE 21

Outlook

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๏Finite-width effects
  • Baseline naive model:
  • + some alternatives (with Rob Verheyen)

VINCIA

IF antenna IF antenna II antenna

⊗

R F a n t e n n a R F a n t e n n a

⊗ Q > Γ Q > Γ Q < Γ

I F a n t e n n a

Note: we do not expect these effects to be large for top decays, cf e.g., Khoze & Sjöstrand Phys.Lett. B328 (1994) 466-476