Semi-analytic resummation in the Sherpa framework Daniel Reichelt May 25, 2021 - CERN ...
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Semi-analytic resummation in the Sherpa framework
Daniel Reichelt
May 25, 2021Analytic NLL in Sherpa [Gerwick, Höche, Marzani, Schumann 2015]
implement ingredients needed for NLL soft-gluon resummation
using the CAESAR formalism [Banfi, Salam, Zanderighi 2004] in Sherpa framework
interface to matrix element generator COMIX → ingredients for colour correlations in
multileg born configurations
immediate access to phase-space integration technology and fixed-order capabilities
completely differential in kinematics and parton flavours, can be exploited in matching
schemes
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 1/9CAESAR formalism [Banfi, Salam, Zanderighi 2004]
general formula for rIRC save observable:
Z " #
dσδ X B
Σδres = dBδ exp − Rl δ S Bδ F Bδ Hδ (Bδ )
dBδ
l∈δ
hard function H to regularise born phase space B
I implements phase space cuts in Sherpa
collinear radiators Rl
I known in relatively general form
soft function S → captures non-trivial colour correlations
I using matrix-element generator COMIX within Sherpa
multiple emission function F
I numerical evaluation of limits with multiple precision arithmetic
achieving NLL0 accuracy: ΣNLL0 = 1 + C (1),δ Σδres
P
δ
I simple to extract since full information on flavour channels δ in fixed order calculation
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 2/9CAESAR formalism: S and F functions
e + e − → jets, Q 2 = 91.2 GeV, Durham scale y45
F ( R′ ) |v̄
0.9
X Y Z
dΦn |Mn |2
b b b b b b
b b
F = lim lim
b b b b b
b b
b b b
b b
b
0.8
b
b
b
bc
v̄ →0 →0
bc bc bc
0.7
bc
n n emissions
bc
bc
bc
bc bc bc
bc
0.6
bc bc
bc
bc bc bc
qq̄gg qq̄qq̄
bc
0.5
bc
bc
F ( R′ = 8) × 100
→ pre-calculated in separate Monte
bc
0.4 bc
F ( R′ = 4) × 5
F ( R′ = 1)
Carlo 0.3
Lines: log10 (v̄) = −1500
0.2 bc bc
bc
bc bc
0.1 bc bc bc
bc bc
bc bc
0
bc
bc
100 500 1000 1500 2000
factorisation in soft limit λs → 0 − log10 v̄
2
Rs
−
e+
√e → qq̄gg(g)
s = 91.2 GeV
1.5
t † t
Tr He − 2 Γ ce − 2 Γ
1
S= Tr[cH]
0.5 P Q
→ Γ = −2 iCAESAR formalism: NLL0 accuracy
pp → Z + jet, jet angularity λ12
pT,jet ∈ [408, 1500] GeV, parton-level pT,jet ∈ [408, 1500] GeV, parton-level
(1/σ quark,(0)) dσ quark/d log λ
(1/σ gluon,(0)) dσ gluon/d log λ
1.25
full factorisation: 3.0
2.0 1.00
0.75
ΣNLL0 = δ 1 + C (1),δ Σδres
1.0
P
0.50
0.0
0.25
−1.0
LO 0.00 LO
−2.0 Gluon channel NLO −0.25 NLO
−3.0 Ungroomed exp LO exp LO Quark channel
exp NLO
−0.50 exp NLO Ungroomed
−4.0
can be included via matching scheme exp NLO + C −0.75 exp NLO + C
FO − Exp.
FO − Exp.
4.0 0.50
3.0 0.25
2.0
1.0 0.00
−0.25
→ need flavour information δ to 0.0
10−4 10−3 10−2 0.1 0.4 1 10−4 10−3 10−2 0.1 0.4 1
capture logs ∝ αS2 L2 in NLO λ12 [Thrust] λ12 [Thrust]
cumulant from [Caletti, Fedkevych, Marzani, DR, Schumann, Soyez, Theeuwes 2021]
use IR safe flavour algorithm [Banfi, Salam, Zanderighi 2006] to extract
δ,(1) δ,(1)
αS δ,(1) Σfo −Σres
2π C = limv →0 σ δ,(0)
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 4/9Beyond CAESAR: soft-drop grooming [Baron, DR, Schumann, Schwanemann,
Theeuwes 2020]
η (l)
popular jet substructure technique,
soft-quark grooming (final state)
remove radiation with
[Lakorski,
Marzani, Soyez, Thaler 2014]
min(pT ,i ,pT ,j ) β
∆R
pT ,i +pT ,j < zcut RSD
shown to reduce non-perturbative corrections
ln(kt /µQ )
also effective in event shape observables in
bl = 1
e + e − → hadrons [Baron, Marzani, Theeuwes 2018]
(l)
[Marzani, DR, Schumann, Soyez, Theeuwes 2019]
p p → hadrons [Baron, DR, Schumann, Schwanemann, Theeuwes 2020]
no soft wide-angle radiation
→ to some extend ignore S and non-global logs β=2 β=0
additional contribution to radiators if soft-drop
grooming is applied before observable calculation
can be calculated in terms of the same generic parametrisation
(+ grooming parameters zcut , β) Vl ∝ (kt,l /µQ )al exp (−bl ηl )
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 5/9Beyond CAESAR: jet observables [Caletti, Fedkevych, Marzani, DR, Schumann,
Soyez, Theeuwes 2021]
”vanilla” CAESAR: observables sensitive to radiation everywhere in phase space
jets → collinear radiation from single leg + soft radiation into the jet area
some (trivial) additions to radiators from jet
boundary conditions
soft wide-angle S(a)
global : coefficients of colour
k2
(b)
k1 in jet radius R k2
insertions Ti Tj as expansion k1
additional complication: non-global logs
a a
→ new soft contribution
b S non-global b
I existing MonteHCarlo
L
approach in large Nc H
limit
R HL HR
[Dasgupta, Salam 2001] non-global contribution, illustration from
I currently external calculation, Figure 1: Kinematic configurations of[Dasgupta,
interestSalam 2001]
parametrised/discretised
I suppressed effect in groomed observables
It is straightforward to exactly compute the first non-trivial term S2 and this is done
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 6/9Application I: multijet observables
σ d ln y56
[Baberuxki, Preuss, DR, Schumann 2019]
0.6
σ d ln y56
Durham scale y56
1 dσ
Durham scale y56
1 dσ
0.5 NLO+NLL’ √
√ s = 91.2 GeV
s = 91.2 GeV LC 0.5
Imp. LC NLO+NLL’ y45 > 0.02
0.4 y45 > 0.02
Sherpa MEPS@NLO
0.4
Sherpa MEPS@LO
0.3 e + e − → jets Vincia
√ 0.3
0.2 s = 91.2 GeV 0.2
0.1 0.1
0 0
1.4 1.4
@ NLO + NLL′
1.3
1.2
Durham scales yn,n+1 , 1.3
1.2
1.1 1.1
Ratio
1
0.9 for yn−1,n > ycut 1
0.9
0.8
0.8 0.7
0.7
0.6
FC
LC
0.6 0.5
1.4-10 -9 -7 -5 -4 -3 -10 -9 -8 -7 -6 -5 -4 -3
@ LO + NLL′
1.3 ln y56
1.2
1.1
1
0.9
0.8
0.7
LC
FC
0.6
1.4-10
1.3
-9 -7 -5 -4 -3 results at NLO + NLL0 accuracy for y34 , y45 , y56
@ NLL
1.2
1.1
1
0.9
FC
LC
0.8
0.7
0.6
-10 -9 -8 -7 -6 -5 -4 -3
non-trivial colour effects → assess finite NC effects
ln y56
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 7/9Application II: jet substructure observables [Caletti, Fedkevych, Marzani, DR, Schumann,
Soyez, Theeuwes 2021]
pT, jet ∈ [408, 1500] GeV, hadron-level
pp → Z + jet,
pT bins from 50 GeV to 408 GeV 0.30 Groomed
R0 = 0.8
corresponding to parallel CMS analysis Chr. hadrons
(λbc/σ) dσ/dλ
0.25
[CMS collaboration 2021]
0.20
0.15
angularities λ1α of leading jet
0.10
(groomed and ungroomed)
0.05 SHERPA MEPS@NLO (µR, µF )
NLO + NLL0 + NP (µR, µF , xL, δNP)
non-perturbative corrections as bin-by-bin
MC / NLO + NLL0
1.50
ratios from MC (Pythia/Herwig/Sherpa) 1.25
1.00
0.75
validation against mulit-jet merged
0.1 0.2 0.4 0.8
MEPS@NLO sample from Sherpa
λ11 [Width]
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 8/9Conclusion
establish tool for automated NLL resummation
exploiting advantages of general event generator environment in Sherpa
I easy access to fully differential phase space information
I color calculation tools transfer from fixed order
several applications executed, more to come
missing: more advanced/independent hadronisation model
I so far simple ratios from Monte Carlo generators
May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 9/9Backup May 25, 2021 D Reichelt (Göttingen University) Parton Showers and Resummation 2021 10 / 9
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