heavy quarks as partons - home | n3pdf
TRANSCRIPT
SUMMARY
• HEAVY QUARKS IN THE INITIAL STATE
– 4FS VS 5FS
– APPROXIMATE AND PHEONOMENOLOGICAL APPROACHES
• THE FONLL METHOD
– MATCHING RENORMALIZATION SCHEMES
– FONLL FOR DIS
• PARAMETRIZED HEAVY QUARKS
– INITIAL HEAVY QUARKS PDFS
– PARAMETRIZED CHARM: PHENOMENOLOGY
• HIGGS PRODUCTION IN BOTTOM FUSION
– “SANTANDER MATCHING”
– FONLL RESULTS: CONSTANTS VS LOGS
– MATCHING SCALES AND bbZ
• PARAMETRIZED B
– A MASSIVE b SCHEME
– bbH AND THE ROLE OF THE b PDF
AN OLD PROBLEM: MASSIVE QUARK SCHEMESEXAMPLE: bb→ H
LO 4 FLAVORS
LO 5 FLAVORS
• 4FS ⇒ MASSIVE B, NO b IN DGLAP EVOLUTION AND β
FUNCTION
• 5FS ⇒ Mb IN DGLAP EVOLUTION AND β FUNCTION BUT
b MASS NEGLECTED
SHOWERING BS
tt+ b-jet
(Jezo, Lindert, Moretti, Pozzorini, 2018)
• IN 5FS, B-JET MOSTLY DRIVEN BY PS, NEGLIGIBLE MATRIX ELEMENT
• IN 4FS, DOMINANT CONTRIBUTION FROM FS GLUON SPLIITING
• NEW POWHEG GENERATOR: 4FS+NLOPS ⇒ PS EFFECTS MODERATE,
∼ 10% AT LARGE pT FOR ttbb.
IS bb
b
t
t
FS b
b
b
t
t
pT OF b-JET: IS VS FS
Sherpa+OpenLoops
ttbbIS ttbbFS ttbbINT ttbbIS⊗ttFS⊗tt
10−3
10−2
pT of 1st b-jet (ttbb cuts)
dσ
/d
p T[p
b/G
eV]
0 50 100 150 200 250 300 350 400-0.5
0
0.5
1
1.5
pT [GeV]
dσ/
dσre
fpT OF b-JET: PERT. ORDERS
Powheg+OpenLoops
NLOLOLOPSNLOPS
10−4
10−3
10−2
pT of 1st b-jet (ttbb cuts)
dσ
/d
p T[p
b/G
eV]
0.5
1
1.5
2
σ/
σN
LO
PS0 50 100 150 200 250 300 350 400
0.80.91.01.11.2
pT [GeV]
δ PD
Fσ
/σ
NL
OPS
APPROXIMATE 4FS-5FS PS MATCHINGW Z production and the W mass
(Bagnaschi, Maltoni, Vicini, Zaro, 2018)
• MATCH 4FS WITH MASS EFFECTS TO 5FS PS & SUBTRACT (VETO) ALL FINAL STATE bS
• TUNE MATCHING SCHEME TO Z PRODUCTION
• USE FOR W PRODUCTION ⇒ ∆MW ∼ 5 GeV EFFECT ON MW DETERMINATION
Z: IMPROVED TUNES VS 5FS MW TEMPLATES VS. IMPROVED TUNESpT LEPTON mt
MASSIVE EVOLUTION
(Krauss, Napoletano, 2018)
• MASSIVE FIVE-FLAVOR SCHEME: MASS INCLUDED IN SPLITTING KERNELS
• +: CAN BE IMPLEMENTED IN PS (SHERPA AVAILABLE)
• +: MASSIVE CORRECTIONS EXPONENTIATED
• -: ONLY (UNIVERSAL) SUBSET OF FONLL TERMS INCLUDED
• FIRST APPLICATION TO Z + b PRODUCTION: Figueroa et al, 2018
5FS VS MFSbb → H
5FS5FMS
10−3
10−2
dσ
/d
p T(H
)[p
b/G
eV]
1 10 10.50.60.70.80.91.01.11.21.31.4
pT(H) [GeV]
Rat
io
(Krauss, Napoletano, 2018)
Z+B: pt SPECTRUM OF B JET
0
2
4
6
8
10
12
14
16
Z + 1b jet
−10
−5
0
5
10
20 40 60 80 100 120 140
dσ
dp
T(b
jet)
[pb/G
eV]
NLO QCD 5FSNLO QCD m5FS
δ(%
)
pT (b jet) [GeV]
NLO QCD (m5FS-5FS)NLO QCD, scale unc.
(Figueroa, Honeywell, Quackenbusch, Reina,
Reuschle, Wackeroth, 2018)
FONLL• ORIGINALLY DEVELOPED TO EXPLAIN THE b pt SPECTRUM (Cacciari, Greco, Nason,
1998)
• RESUM ln ptmb
BUT RETAIN mbpt
POWER CORRECTIONS
BASIC IDEA:THE PROBLEM
• TYPICAL GAUGE SELF-ENERGY Π(q2)DEPENDS ON lnM2 = ln(m2 + x(1− x)q2) ⇒
β = dd ln q2
lnM2 ∼{
1 IF q2 � m2
O( q2
m2 ) IF m2 � q2L
– MS SCHEME → ZERO-MASS SUBTRACTION, nf = 6 AT ALL SCALES
– DECOUPLING SCHEME → HEAVY-FLAVOR GRAPHS SUBTRACTED AT ZEROMOMENTUM, nf VARIABLE
THE SOLUTION
• PERFORM THE COMPUTATION IN BOTH SCHEMES: MS OR “ MASSLESS” (nf + 1) &“DECOUPLING” OR “MASSIVE” (nf )
• RE-EXPRESS MASSIVE RESULT IN TERMS OF MASSLESS PDFS & αs
• COMBINE BOTH & SUBTRACT DOUBLE-COUNTING
FONLLHOW DOES IT WORK?
MATCHING
f(nf+1)
i (x,m2) = Kij(αs)⊗ f(nf )
j (x,m2) = f(nf )
i (x,m2) + αsK(1)ij ⊗ f
(nf )
j (x,m2) + . . .
• Kij FOR i = h, q, q, g , j = qq, g AT O(α2s) ⇔ TWO-LOOP
NORMALIZATION MISMATCH BETWEEN Q AND G OPERATOR
• Khh STARTS AT O(αs) (h IN nf?? MORE LATER)
RE-EXPRESSING
• AT ANY OTHER SCALE, LHS EVOLVES WITH (nf + 1) & RHS WITH nf ALTARELLI-PARISI:e.g. GLUON
f(nf )g (x,Q2) =
[1 +
αs
2π
2TR
3lnQ2
m2h
]f(nf+1)g (x,Q2)
COMBININGσFONLL = σ(nf ) + σd; σd = σ(nf+1) − σ(nf , 0) with limmh→0 σ(nf ) − σ(nf , 0) = 0
σ(nf ) = Bij(α(nf+1)s )⊗ f (nf+1)
i ⊗ f (nf+1)
i ;
Bij(α(nf+1)s )⊗ f (nf+1)
i ⊗ f (nf+1)
i = σij(α(nf )s )⊗ f (nf )
i ⊗ f (nf )
i ⇒Bij(α
(nf+1)s ) = σabK
−1ai K
−1bj
FONLLσ(nf ) = Bij(α
(nf+1)s )⊗ f (nf+1)
i ⊗ f (nf+1)
i ;
Bij(α(nf+1)s )⊗ f (nf+1)
i ⊗ f (nf+1)
i = σij(α(nf )s )⊗ f (nf )
i ⊗ f (nf )
i
• THE MASSIVE (nf ) ⇒ mh DEPENDENCE RETAINED, MASSLESS (nf + 1) ⇒ MASSLOGS RESUMMED
• MASSIVE (nf ) AND MASSLESS (nf + 1) CAN BE PERFORMED AT DIFFERENT ORDERS& COMBINED
• COMPLEMENTARY VIEWS:
– σ(nf+1): ALL ORDERS IN α(nf+1)s TO WHICH σ(nf+1) IS KNOWN
REPLACED BY THEIR MASSIVE COUNTERPART
– MASS LOGS REMOVED FROM f(nf+1)
i , USED IN THE COMPUTATION OF σ(nf )
• σ(d) SUBLEADING WRT BOTH MASSLESS AND MASSIVE
• σ(d) IS JUNK ⇒ DAMPING
FONLL• DEVELOPED FOR HADROPRODUCTION & ELECTROPRODUCTION
(S.F., Laenen, Nason, Rojo, 2010)
• NECESSARY FOR DEEP-INELASTIC CHARM PRODUCTION
• ROUTINELY USED IN PDF FITS (SINCE NNPDF 2.1)
F c2 at Q2 = 10 GeV2
• FONLL-A: MASSIVE O(αs) (LO); MASSLESS O(αs) COEFF. FCTN, & SPLITTING FCTN (NLO)
• FONLL-B: MASSIVE O(α2) (NLO); MASSLESS O(αs) COEFF. FCTN, & SPLITTING FCTN (NLO)
• FONLL-C: MASSIVE O(α2s) (NLO); MASSLESS O(α2
s) COEFF. FCTN, & SPLITTING FCN(NNLO)
THE HEAVY QUARK PDFTHE CASE OF CHARM
• IN STANDARD FONLL, fh DETERMINED FROM MATCHING CONDITION
• AT O(αs), fh(m2h) = 0; NONTRIVIAL AT O(α2
s)
• BEST-FIT fc DEPENDS STRONGLY ON mc; SMALL UNCERTAINTY (DRIVEN BY GLUON)
NNLO PERTURBATIVE CHARMAT Q = mc DEPENDENCE ON mc
x 4−10 3−10 2−10 1−10
) [r
ef]
2 (
x, Q
+)
/ c2
( x
, Q+ c
0.9
0.95
1
1.05
1.1
1.15=1.51 GeVcm=1.38 GeVcm=1.64 GeVcm
NNPDF3.1 NNLO perturbative charm, Q = 100 GeV
FONLL WITH PARAMETRIZED HEAVY QUARK
f(nf+1)
i (x,m2) = Kij(αs)⊗ f(nf )
j (x,m2)
• MASSIVE-SCHEME fh DOES NOT EVOLVE
• SQUARE MATCHING MATRIX
• WHEN RE-EXPRESSING, EVOLUTION REMOVED UP TO FIXED-ORDER
f(nf ,NLO)h (x,Q2) =
∑i
[1−
αs
2πPhi ln
Q2
m2h
]⊗ f (nf+1,NLO)
i (x,Q2)
• THE “DIFFERENCE” TERM MOW VANISHES!!
• FONLL ⇒ MASSIVE PARTONIC XSECT WITH MASSLESS PARTONS
FFONLL(x,Q2) = C(nf )i ⊗K−1
ij ⊗ f(nf+1)j + F d(x,Q2);
F d =(C
(nf+1)j − C(nf , 0)
i ⊗K−1ij
)⊗ f (nf+1)
j = 0
PARAMETRIZED CHARM: PHENOMENOLOGYTHE CHARM PDF
• CHARM SHOULD NOT DEPEND STRONGLY ON CHARM MASS
PERTURBATIVE CHARM VS mc
x 4−10 3−10 2−10 1−10
) [r
ef]
2 (
x, Q
+)
/ c2
( x
, Q+ c
0.9
0.95
1
1.05
1.1
1.15=1.51 GeVcm=1.38 GeVcm=1.64 GeVcm
NNPDF3.1 NNLO perturbative charm, Q = 100 GeV
FITTED CHARM VS mc
x 4−10 3−10 2−10 1−10
) [r
ef]
2 (
x, Q
+)
/ c2
( x
, Q+ c
0.9
0.95
1
1.05
1.1
1.15=1.51 GeVcm=1.38 GeVcm=1.64 GeVcm
NNPDF3.1 NNLO fitted charm, Q = 100 GeVFITTED VS. PERTURBATIVE CHARM
x 4−10 3−10 2−10 1−10
)2 (
x, Q
+x
c
0.06−
0.04−
0.02−
0
0.02
0.04
0.06
Fitted charm
Fitted charm + EMC
Perturbative charm
NNPDF3.1 NNLO, Q=1.51 GeV
• ITS SHAPE SHOULD NOT BE DETERMINED BY FIRST-ORDER MATCHING(NO HIGHER NONTRIVIAL ORDERS KNOWN)
• MIGHT EVEN HAVE A NONPERTURBATIVE COMPONENT
FITTED VS. PERTURBATIVE:SUPPRESSED AT MEDIUM-SMALL x,ENHANCED AT VERY SMALL, VERY LARGE x
PARAMETRIZED CHARM: PHENOMENOLOGYIMPACT ON LIGHT QUARK PDFS
FITTED VS. PERTURBATIVE CHARMQQBAR LUMI
( GeV )XM10 210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2 fitted charm
perturbative charm
LHC 13 TeV, NNLOANTIDOWN PDF
x 4−10 3−10 2−10 1−10
) [r
ef]
2 (
x, Q
d)
/ 2
( x
, Qd
0.9
0.95
1
1.05
1.1
1.15 Fitted charm
Perturbative charm
NNPDF3.1 NNLO, Q = 100 GeVANTIDOWN PDF UNCERTAINTY
x 4−10 3−10 2−10 1−10
) [r
ef] )
2 (
x, Q
d)
/ (
2 (
x, Q
d δ
0
0.02
0.04
0.06
0.08
0.1
0.12
Fitted charm
Perturbative charm
NNPDF3.1 NNLO, Q = 100 GeV
• QUARK LUMI AFFECTED BECAUSE OF CHARM SUPPRESSION AT MEDIUM-x
• FLAVOR DECOMPOSITION ALTERED
• UNCERTAINTIES ON LIGHT QUARKS NOT SIGNIFICANTLY INCREASED
• AGREEMENT OF 13TeV W,Z PREDICTED CROSS-SECTIONS IMPROVES!
PARAMETRIZED CHARM: PHENOMENOLOGYIMPACT ON STANDARD CANDLES
DRELL-YAN XSECTS
0.85
0.90
0.95
1.00
1.05
1.10
σp
red
./σ
me
as.
ATLAS 13 TeV
Heavy: NNLO QCD + NLO EWLight: NNLO QCD
W− W+ Z
NNPDF3.1
NNPDF3.0
CT14
MMHT14
ABMP16
data ± total uncertainty
W+/W− XSECT RATIO
1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33σW+/σW−
ATLAS 13 TeV
Heavy: NNLO QCD + NLO EWLight: NNLO QCD
Ratio of W+ to W− boson
NNPDF3.1
NNPDF3.0
CT14
MMHT14
ABMP16
data ± total uncertainty
W/Z XSECT RATIO
9.8 10.0 10.2 10.4 10.6 10.8σW /σZ
Heavy: NNLO QCD + NLO EWLight: NNLO QCD
ATLAS 13 TeV
Ratio of W± to Z boson
NNPDF3.1
NNPDF3.0
CT14
MMHT14
ABMP16
data ± total uncertainty
• W , Z CROSS-SECTIONS AT 13 TEV IN PERFECT AGREEMENT WITH DATATHANKS TO FITTED CHARM!
HADROPRODUCTION:HIGGS IN BOTTOM FUSION
MASSIVE LO
MASSLESS NNLO
�bb
O(↵0s) O(↵1
s) O(↵2s)
�bg
�b⌃
• FONLL-A: MASSIVE O(α2s) (LO); MASSLESS O(α2
s) COEFF. FCTN, & SPLITTINGFCTN (NNLO)
• FONLL-B: MASSIVE O(α3) (NLO); MASSLESS O(α2s) COEFF. FCTN, & SPLITTING
FCTN (NNLO)
• FONLL-C: MASSIVE O(α3) (NLO); MASSLESS O(α3s) COEFF. FCTN, & SPLITTING
FCTN (NNLO) ⇒ COEFFICIENT FUNCTION RECENTLY COMPUTED (Duhr, Dulat,Mistlberger, 2019)
HIGGS IN BOTTOM FUSIONPROBLEMS
(HXSWG, YR4, 2017, Spira, Wiesemann et al.)
• 4FS (“MASSIVE”) AND 5FS (“MASSLESS”) GIVE RATHER DIFFERENT RESULTS
• DISCREPANCY ALLEVIATED WITH LOWER RENORMALIZATION SCALE ⇒ ARGUED THATµ3 = mh+2mb
4APPROPRIATE BASED ON TYPICAL SCALE OF COLLINEAR LOGS
(Maltoni, Ridolfi, Ubiali, 2012, + Lim, 2016): TYPICALLY Q ∼ pmaxt /2
• “SANTANDER” MATCHING: σ = σ(4)+wσ(5)
1+w, w = ln mh
mb− 2 ≈ 1.2
HIGGS IN BOTTOM FUSIONFONLL
0.1 0.2 0.3 0.4 0.5
µR/mH
0.3
0.4
0.5
0.6
0.7
σ(µR
)[p
b]
µF = (mH + 2mb)/4
µR = (mH + 2mb)/4σFONLL−BσFONLL−Aσ5FNNLO
σ4FNLO
σ4FLO
0.1 0.2 0.3 0.4 0.5
µF /mH
0.3
0.4
0.5
0.6
0.7
σ(µF
)[p
b]
µR = (mH + 2mb)/4
µF = (mH + 2mb)/4
σFONLL−BσFONLL−Aσ5FNNLO
σ4FNLO
σ4FLO
(SF, Napoletano, Ubiali, 2015-2016)
• SLOW CONVERGENCE AND STRONG µR DEPENDENCE OF MASSIVE SCHEME RESULT
• NLO MASSIVE CLOSER TO MASSLESS ⇒ ln mhmb
RESUMMATION DOMINANT
• FACTORIZATION SCALE DEP. STATIONARY FOR µf ∼ Qphys ⇒ LOW Qphys ∼ mh/4
• MODERATE “MASS” CORRECTIONS
HIGGS IN BOTTOM FUSIONFONLL
HIGGS MASS DEPENDENCE
10−4
10−3
10−2
10−1
100
101
σ(m
H)
[pb]
σ5FNNLO
σFONLL−Bσ4FNLO
200 400 600 800 1000
mH [GeV]
0.6
0.7
0.8
0.9
1.0
1.1
1.2
σ∗ /σ
5FNNLO
(SF, Napoletano, Ubiali, 2016) (HXSWG, YR4, 2017)
• FONLL QUITE CLOSE TO MASSLESS, 5FS ADEQUATE FAPP,SANTANDER BAD APPROX
• FONLL-A - FONLL-B DIFFERENCE ALMOST MASS-INDEP ⇒ (SMALL) FONLLIMPROVEMENT O(α3
s) CONSTANT (I.E. DEP ON τ = mhs
), INDEP OF mbmH
• AGREEMENT WITH SCET APPROACH (Bonvini, Papanastasiou, Tackmann, 2016)
TUNING THE MATCHING SCALE?• HIGH CHOICE OF MATCHING SCALE µm ∼ 10mh:(Mitov et al., 2017)
– INITIAL HQ PDF PERTUBATIVELY ACCURATE
– RESUMMATION OF HQ LOGS SUPPRESSED
• TOY CASE bbZ/ bbH:– 4FS & 5FS GET CLOSER AT HIGHER MATHCHING SCALE
– BUT 4FS → STRONG µr DEPENDENCE, PERT. INSTABILITY
– COMPARISON TO MATCHED: LOGS DOMINATE OVER CONST.
ZbbSCALE DEP. VS. MATCHING
0 20 40 60 80 100 120 140 160 180 200
µF [GeV]
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
bbZ production, LHC 13 TeVµb ∈ {1, 2, 4, 6, 8, 10}mb, NLO PDFsthick → thin lines: µb = mb → 10mb
5F NLO 4F NLO
(Bertone, Glazov, Mitov, Papanastasiou,
Ubiali, 2017)
DEP. ON MATCHING SCALE
0.1 0.2 0.3 0.4 0.5 0.6 0.7R / mZ
200
400
600
800
1000
1200
1400
1600
bbZ(
F=
(mZ
+2m
b)/3
,R)
F = (mZ + 2mb)/3
5FNNLO
FONLL B4FNLO5FNNLO( b = 2mb)FONLL B( b = 2mb)
(SF, Napoletano, Ubiali, 2018)
PARAMETRIZED B AS AMASSIVE SCHEME
• PARAMETRIZED b PDF ⇒ MASSIVE MATRIX ELEMENT WITH MASSLESS PDF ANDMASS LOGS REMOVED
• 4FS (MASSIVE) STARTS AT O(α0)
σFONLL =∑i,j
∑l,m
σmassiveij
(m2h
m2b
)⊗K−1
il ⊗ f(5)l
(Q2)K−1jm ⊗ f
(5)m
(Q2)
• FONLL-AP: MASSIVE O(αs) (NLO); MASSLESS O(α2s) COEFF. FCTN, & SPLITTING
FCTN (NLO)
• FONLL-BP: MASSIVE O(α) (NLO); MASSLESS O(α2s) COEFF. FCTN, & SPLITTING
FCTN (NNLO)
σFONLL-BP = σFONLL-AP +∑l,m
σ(5),(2)lm ⊗ f (5)l
(Q2)f(5)m
(Q2)
HIGGS IN BOTTOM FUSIONFONLL WITH PARAMETRIZED B
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50R/mH
0.40
0.45
0.50
0.55
0.60
(R,
F=
(mH
+2m
b)/4
) [pb
]
R=
(mH
+2m
b)/4
NNPDF31_nnlo_as_0118
5FNNLOFONLL BP5FNLOFONLL AP
FONLL B
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50F/mH
0.30
0.35
0.40
0.45
0.50
0.55
0.60
(R
=(m
H+
2mb)
/4,
F) [p
b]
R=
(mH
+2m
b)/4
NNPDF31_nnlo_as_0118
5FNNLOFONLL BP5FNLOFONLL AP
FONLL B
(SF, Giani, Napoletano, 2019)
• FONLL-B, FONLL-BP THREE CURVES SHOWN ⇒ b PDF AS IF USINGPERTURBATVE MATCHING AT mb/2, mb, 2/3Mb (bottom to top)
• FONLL-BP, FONLL-B DIRECTLY COMPARABLE: 1ST TWO MASSIVE ORDERSCOMBINE WITH MASSLESS NNLO
• FONLL-B: gg → bbH; FONLL-BP: bb→ H (ENHANCED DUE TO PHASE SPACE)
• LARGE NEGATIVE CORRECTION WHEN GOING FROM MASSLESS NLO TO NNLO
• MASS CORRECTIONS SAME SIZE AS PDF DEPENDENCE