HEAVY QUARKSAS PARTONS

STEFANO FORTEUNIVERSITA DI MILANO & INFN

MPI SEMINAR MUNCHEN, JULY 8, 2019

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

SUMMARY

•••