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Resummation in PDF fj ts Luca Rottoli Rudolf Peierls Centre for - - PowerPoint PPT Presentation

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Resummation in PDF fj ts Luca Rottoli Rudolf Peierls Centre for Theoretical Physics, University of Oxford LHC, New Physics, and the pursuit of Precision LHC as a discovery machine Higgs Boson 10 1 BSM particles (never as of

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Resummation in PDF fjts

Luca Rottoli Rudolf Peierls Centre for Theoretical Physics, University of Oxford

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Università di Cagliari, November 22, 2017

LHC, New Physics, and the pursuit of Precision

1

  • New BSM scenarios to be tested
  • New techniques to enhance signal/background ratio and

isolate tiny deviations from SM predictions

  • Development of accurate and precise theoretical predictions

A theorist’s Quest:

10−4 10−3 10−2 10−1 100 101 (1/σ)dσ/dpT RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 0.0< η <2.4, 66< mll <116 GeV NNPDF3.0 (NNLO) uncertainties with µR, µF , Q variations Fixed Order from arXiv:1610.01843

NNLO NNLO+NNLL NNLO+N3LL Data

101 102 pT 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

Goal: 1% accuracy in theoretical predictions LHC as a discovery machine

  • Higgs Boson
  • BSM particles

✓ 𐄃 (never as of today) Focus in LHC run II

  • Measurement of the Standard Model parameters with very

high precision

  • Signals of New Physics beyond the Standard Model

[Bizon,Monni,Re,LR,Torielli et al, in preparation]

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Università di Cagliari, November 22, 2017

LHC, New Physics, and the pursuit of Precision

2

A crucial ingredient in the physics precision programme at the LHC is the accurate understanding

  • f the internal structure of the initial state hadrons

Large HADRON Collider

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Università di Cagliari, November 22, 2017

Factorization

3

X

a b

proton proton

ˆ σab→X

Proton’s dynamics occurs on a timescale ~ 1fm Production of a heavy particle e.g. Higgs Production (hard process) occurs on timescale 1/MX ~ 1/100 GeV ~ 0.002 fm Large separation between scales allows to separate the hard process and treat it independently from the hadronic dynamics: collinear factorization

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Università di Cagliari, November 22, 2017

Factorization

4

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

centre-of-mass energy hard scale of the process

√

s

Q

h1

h2

X

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Università di Cagliari, November 22, 2017

Factorization

4

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

centre-of-mass energy hard scale of the process

√

s

Q

h1

X

σX(Q2, s) = ∑

a,b

fa/h1(Q2) ⊗ fb/h2(Q2) ⊗ ˆ σab→X(Q2, s)

h2

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Università di Cagliari, November 22, 2017

Factorization

5

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

partonic cross-section short-distance: perturbative centre-of-mass energy hard scale of the process

√

s

Q

h1

X

h2

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Università di Cagliari, November 22, 2017

Factorization

5

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

partonic cross-section short-distance: perturbative centre-of-mass energy hard scale of the process

√

s

Q

h1

X

ˆ σ = ˆ σ0(1 + . . .)

LO QCD at short distance is perturbative (asymptotic freedom)

h2

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Università di Cagliari, November 22, 2017

Factorization

5

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

ˆ σ = ˆ σ0(1 + αsc1 + α2

sc2 + . . .)

NLO partonic cross-section short-distance: perturbative centre-of-mass energy hard scale of the process

√

s

Q

h1

X

QCD at short distance is perturbative (asymptotic freedom)

h2

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Università di Cagliari, November 22, 2017

Factorization

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

QCD at short distance is perturbative (asymptotic freedom)

ˆ σ = ˆ σ0(1 + αsc1 + α2

sc2 + . . .)

NNLO partonic cross-section short-distance: perturbative centre-of-mass energy hard scale of the process

√

s

Q

h1

X

5

h2

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Università di Cagliari, November 22, 2017

Factorization

X

a b

ˆ σab→X

σ(s, Q2) = ∑

a,b

Z

dx1dx2 fa/h1(x1, Q2) fb/h2(x2, Q2)ˆ σab→X(Q2, x1x2s)

Parton Distribution Functions (PDFs) long-distance: non-perturbative PDFs are currently extracted from experiments centre-of-mass energy hard scale of the process

√

s

Q

h1

Parton distribution functions (PDFs) are universal objects which encode information on the substructure of the proton and which describe the dynamics of quarks and gluons (partons)

X

6

h2

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

fraction of the momentum of the proton

f (x, Q2)

PDFs depend on two kinematic variables

7

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

Scale of the process

f (x, Q2)

PDFs depend on two kinematic variables

7

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

PDFs depend on two kinematic variables

7

and are parametrized at an initial scale Q0

f (x, Q2)

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

1 10-1 10-2 10-3 10-4 10-5 10-6 1 101 102 103 104 106 107 x Q2 [GeV]

Q2 ∂ ∂Q2 fi(x, Q2) =

Z 1

x

dz z Pij ⇣ x z , αs(Q2) ⌘ fj(z, Q2)

Evolution in Q2 is encoded in DGLAP equation

f (x, Q2)

PDFs depend on two kinematic variables

7

and are parametrized at an initial scale Q0

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

splitting functions

Q2 ∂ ∂Q2 fi(x, Q2) =

Z 1

x

dz z Pij ⇣ x z , αs(Q2) ⌘ fj(z, Q2)

f (x, Q2)

PDFs depend on two kinematic variables

7

1 10-1 10-2 10-3 10-4 10-5 10-6 1 101 102 103 104 106 107 x Q2 [GeV]

Evolution in Q2 is encoded in DGLAP equation

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Università di Cagliari, November 22, 2017

Parton Distribution Functions

splitting functions

Q2 ∂ ∂Q2 fi(x, Q2) =

Z 1

x

dz z Pij ⇣ x z , αs(Q2) ⌘ fj(z, Q2)

f (x, Q2)

PDFs depend on two kinematic variables

Pij ⇣ x, αs(Q2) ⌘

= P(0)

ij (x) + αsP(1) ij (x) + α2 s P(2) ij (x) + . . .

7

1 10-1 10-2 10-3 10-4 10-5 10-6 1 101 102 103 104 106 107 x Q2 [GeV]

Evolution in Q2 is encoded in DGLAP equation

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Università di Cagliari, November 22, 2017

DGLAP equation

8

2nf + 1 coupled differential equation However, strong interactions do not tell apart quarks and antiquarks (charge conjugation and SU(nf) fmavour symmetry) Only singlet combination couples to gluon

Pqiqj = P¯

qi ¯ qj,

Pqi ¯

qj = P¯ qiqj,

Pqig = P¯

qig ≡ Pqg,

Pgqi = Pg ¯

qi ≡ Pgq

Σ(x, Q2) = ∑

i

[qi(x, t) + ¯

qi(x, t)]

Q2 ∂ ∂ ln Q2 ✓ Σ g ◆

=

✓ Pqq Pqg Pgq Pgg ◆

⊗

✓ Σ g ◆ Q2 ∂ ∂Q2 fi(x, Q2) =

Z 1

x

dz z Pij ⇣ x z , αs(Q2) ⌘ fj(z, Q2)

number of (active) fmavours

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Università di Cagliari, November 22, 2017

DGLAP equation

x

3 −

10

2 −

10

1 −

10 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 g/10

v

u

v

d d u s c b )

2

GeV

4

=10

2

µ xf(x, x

3 −

10

2 −

10

1 −

10 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 g/10

v

u

v

d d c s u NNPDF3.1 (NNLO) )

2

=10 GeV

2

µ xf(x,

Q2 evolution Parton lose momentum and shifts at smaller values of x growth of small-x gluon

9

Q2 = 10 GeV2 Q2 = 104 GeV2

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Università di Cagliari, November 22, 2017

Parton Distribution Function Fits

σX(Q2, s) = ∑

a,b

fa/h1(Q2) ⊗ fb/h2(Q2) ⊗ ˆ σab→X(Q2, s)

Q2 d dQ2 fi(Q2) = Pij(αs(Q2)) ⊗ fj(Q2)

theoretical input theoretical prediction (to be compared with data)

10

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Università di Cagliari, November 22, 2017

Parton Distribution Function Fits

10

PDF fjts are typically based on fjxed-order theory…

ˆ σ = ˆ σ0(1 + αsc1 + α2

sc2 + . . .)

Pij ⇣ x, αs(Q2) ⌘

= P(0)

ij (x) + αsP(1) ij (x) + α2 s P(2) ij (x) + . . .

…but is fjxed-order theory always good enough?

σX(Q2, s) = ∑

a,b

fa/h1(Q2) ⊗ fb/h2(Q2) ⊗ ˆ σab→X(Q2, s)

Q2 d dQ2 fi(Q2) = Pij(αs(Q2)) ⊗ fj(Q2)

theoretical prediction (to be compared with data) theoretical input

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Università di Cagliari, November 22, 2017

Single (double) logarithmic enhancement Perturbative convergence is spoiled when e.g. small-x behaviour of splitting functions

αk

s lnj

0 ≤ j ≤ (2)k αs ln(2) ∼ 1

Large logarithms

11

xP(x, αs) =

∞

∑

n=0

⇣ αs 2π ⌘n "

n

∑

m=1

A(n)

m−1lnm−1 1

x + x ¯ P(n)(x) #

Finite in the limit x→0

Instability at small-x

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Università di Cagliari, November 22, 2017

Single (double) logarithmic enhancement Perturbative convergence is spoiled when e.g. small-x behaviour of splitting functions

αk

s lnj

0 ≤ j ≤ (2)k αs ln(2) ∼ 1

Large logarithms

Finite in the limit x→0

Instability at small-x

All-order resummation of the logarithmically enhanced terms

(n ≥ 0, m=n) leading-logarithm (LLx), (n ≥ 0, m=n,n-1) next-to-leading-logarithm (NLLx), etc.

12

xP(x, αs) =

∞

∑

n=0

⇣ αs 2π ⌘n "

n

∑

m=1

A(n)

m−1lnm−1 1

x + x ¯ P(n)(x) #

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Università di Cagliari, November 22, 2017

Including resummation in PDF fjts:

  • provides consistent predictions when resummed computations are used
  • improves the quality of the PDF fjts
  • helps in investigating the impact of missing higher orders

… it brings us closer to ‘all-order’ PDFs

Resummation in PDF fjts

13

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Università di Cagliari, November 22, 2017

Global PDF fjts

Processes used in global PDF fjts

14

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Università di Cagliari, November 22, 2017

Global PDF fjts

Processes used in global PDF fjts Collider Deep-Inelastic Scattering Fixed-Target Deep-Inelastic Scattering Collider Drell-Yan Jets Z differential top production Fixed-Target Drell-Yan

14

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Università di Cagliari, November 22, 2017

Large x: threshold resummation

  • lnk(1 − x)

(1 − x)

  • +

double logs due to soft gluon emission

[Bonvini,Marzani,Rojo,LR,Ubiali,Ball,Bertone, Carrazza,Hartland 1507.01006]

Resummation in global PDF fjts

15

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Università di Cagliari, November 22, 2017

Small x: high-energy resummation single logs due to high-energy gluon emission

1 x lnk x

Resummation in global PDF fjts

[Ball,Bertone,Bonvini,Marzani,Rojo,LR 1710.05935]

15

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Università di Cagliari, November 22, 2017

Resummation affects: Observable (coefficient functions) Evolution (splitting functions)

σ = σ0C(αs(µ) ⊗ f (µ) [⊗ f (µ)] µ2 d dµ2 f (µ) = P(αs(µ)) ⊗ f (µ)

  • bservable

(coefficient function) evolution (splitting function) small x NLLx* NLLx large x (N)NNLL — *starts at NLLx

16

Resummation in global PDF fjts

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Università di Cagliari, November 22, 2017

PDFs with large-x resummation

[Bonvini,Marzani,Rojo,LR,Ubiali,Ball,Bertone, Carrazza,Hartland 1507.01006]

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Università di Cagliari, November 22, 2017

[Bonvini,Marzani,Rojo,LR,Ubiali,Ball,Bertone, Carrazza,Hartland 1507.01006]

process

  • bservable

included? DIS dσ/(dxdQ2) (NC, CC, F2c…) ✔ DY Z/γ dσ/(dydM2) ✔ DY W differential in lepton kinematics ✘ tt total σ ✔ jets inclusive dσ/(dydpT) ✘

Datasets considered in NNPDF3.0res

NLL known to be poor no public code available yet

Accuracy is competitive with global fjt, except for large-x gluon (jets not included) Resummation is included supplementing fjxed-order computations with K-factors

KNkLO+NkLL = σNkLO+NkLL σNkLO

17

PDFs with large-x resummation: NNPDF3.0res

public code TROLL

www.ge.infn.it/∼bonvini/troll

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Università di Cagliari, November 22, 2017

0.6 0.8 1 1.2 1.4 1.6 1.8 125 600 2000 ratio to central NNLO (with baseline PDFs) mH [GeV] Higgs cross section: gluon fusion LHC 13 TeV NNLO, fixed order PDFs NNLO+NNLL, fixed order PDFs NNLO+NNLL, resummed PDFs

Higgs Production mH ~600 GeV cancellation

  • f 1/2 of the enhancement

NNPDF3.0res: Impact on phenomenology

SM Higgs is not affected by resummation of PDFs mH~2 TeV NNLO+NNLL with resummed PDFs is similar to FO PDFs (larger uncertainty)

18

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Università di Cagliari, November 22, 2017

19

m˜

q = m˜ g = m [GeV] Global fit NLL/NLO DIS+DY+top Prescription (1) Prescription (2)

0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1000 1500 2000 2500 3000 3500 KNLO+NLL(pp → ˜ g˜ g + X) √ S = 13 TeV

[Beenakker,Borschensky,Krämer,Kulesza,Laenen,Marzani,Rojo 1510.00375]

Susy particles Predictions for MSSM particles are modifjed when using resummed PDFs

NNPDF3.0res: Impact on phenomenology

However, PDF errors are very large

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Università di Cagliari, November 22, 2017

  • First ever global fjt of PDFs with threshold resummation
  • PDFs are suppressed in the large-x region; at intermediate values of x quark PDFs are slightly enhanced

(sum rule); negligible effects at x<0.01

  • Inclusion of resummation compensates the enhancement from resummation in partonic cross sections
  • Consistent resummed calculations might be closer to fjxed order results

Limitations: larger uncertainties due to reduced dataset. Methodology enables to have truly global resummed PDFs when calculations for missing processes will be available. New processes to be included: DY Z/γ (ZpT), tt (differential)…

Outlook

20

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Università di Cagliari, November 22, 2017

PDFs with small-x resummation

[Ball,Bertone,Bonvini,Marzani,Rojo,LR 1710.05935]

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Università di Cagliari, November 22, 2017

H1 and ZEUS

x = 0.00005, i=21 x = 0.00008, i=20 x = 0.00013, i=19 x = 0.00020, i=18 x = 0.00032, i=17 x = 0.0005, i=16 x = 0.0008, i=15 x = 0.0013, i=14 x = 0.0020, i=13 x = 0.0032, i=12 x = 0.005, i=11 x = 0.008, i=10 x = 0.013, i=9 x = 0.02, i=8 x = 0.032, i=7 x = 0.05, i=6 x = 0.08, i=5 x = 0.13, i=4 x = 0.18, i=3 x = 0.25, i=2 x = 0.40, i=1 x = 0.65, i=0

Q2/ GeV2 σr,NC(x,Q2) x 2i

+

HERA I NC e+p Fixed Target HERAPDF1.0

10

  • 3

10

  • 2

10

  • 1

1 10 10 2 10 3 10 4 10 5 10 6 10 7 1 10 10

2

10

3

10

4

10

5

Deep Inelastic Scattering HERA dataset data collected down to very small x Very good agreement

  • ver vast range of x

and Q2

Need for small-x resummation?

21

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Università di Cagliari, November 22, 2017

Fixed order theory could be not sufficient to describe data points at small x and/or small Q2 Description of HERA data poorer when data points at smaller values of x are included and fjxed-order theory is used

Courtesy of Juan Rojo

Effect is more pronounced if NNLO theory is used

This may indicate the need for small-x resummation

Need for small-x resummation?

more points at small x included

22

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Università di Cagliari, November 22, 2017

Small-x resummation based on kt-factorization and BFKL. Developed mostly in the 90s-00s Affects both evolution (LLx, NLLx) and coefficient functions (NLLx, lowest logarithmic order) in the singlet sector

[Catani,Ciafaloni,Colferai,Hautmann,Salam, Stasto][Altarelli,Ball,Forte] [Thorne,White]

Splitting functions are resummed using ABF (Altarelli,Ball,Forte) procedure New formalism for coefficient function [Bonvini,Marzani,Peraro 1607.02153] and further improvements on the ABF formalism [Bonvini,Marzani,Muselli,Peraro 1708.07510] Resummed splitting functions and coefficient functions available through public code HELL

www.ge.infn.it/∼bonvini/hell

Use in PDF fjts possible thanks to the interface with APFEL

apfel.hepforge.org

(very brief) Overview of small-x resummation

23

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Università di Cagliari, November 22, 2017

All ingredients for a PDF fjt to DIS data are now available In principle, one should add additional processes:

  • DY
  • Jets
  • top
  • …

Ongoing work in this direction However, a global fjt is possible if conservatives cuts

  • n hadronic data are applied and points which may

feature small-x enhancement are excluded

(temporary) Exclusion region for hadronic data

αs(Q2) log 1 x ≥ c ∼ 1 Q2x1/(β0c) ≥ Λ2

Value of c (slope of the line) selects the exclusion region

Towards a global small-x resummed fjt

24

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Università di Cagliari, November 22, 2017

25

10−6 10−5 10−4 10−3 10−2 10−1 100 x 0.7 0.8 0.9 1.0 1.1 1.2 1.3 g(x, Q2) / g(x, Q2)[ref]

NNPDF31sx DIS only, Q = 100 GeV

NLO NNLO NNLO+NLLx

NNPDF31sx: impact on PDFs

stabilization of the gluon with respect to the perturbative order PDFs compatible within error at medium and large x

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Università di Cagliari, November 22, 2017

𝜓2NNLO+NLLx smallest

χ2/Ndat ∆χ2 χ2/Ndat ∆χ2 NLO NLO+NLLx NNLO NNLO+NLLx NMC 1.35 1.35 +1 1.30 1.33 +9 SLAC 1.16 1.14 −1 0.92 0.95 +2 BCDMS 1.13 1.15 +12 1.18 1.18 +3 CHORUS 1.07 1.10 +20 1.07 1.07 −2 NuTeV dimuon 0.90 0.84 −5 0.97 0.88 −7 HERA I+II incl. NC 1.12 1.12

  • 2

1.17 1.11 −62 HERA I+II incl. CC 1.24 1.24

  • 1.25

1.24 −1 HERA σNC

c

1.21 1.19 −1 2.33 1.14 −56 HERA F b

2

1.07 1.16 +3 1.11 1.17 +2 DY E866 σd

DY/σp DY

0.37 0.37

  • 0.32

0.30

  • DY E886 σp

1.06 1.10 +3 1.31 1.32

  • DY E605 σp

0.89 0.92 +3 1.10 1.10

  • CDF Z rap

1.28 1.30

  • 1.24

1.23

  • CDF Run II kt jets

0.89 0.87 −2 0.85 0.80 −4 D0 Z rap 0.54 0.53

  • 0.54

0.53

  • D0 W → eν asy

1.45 1.47

  • 3.00

3.10 +1 D0 W → µν asy 1.46 1.42

  • 1.59

1.56

  • ATLAS total

1.18 1.16 −7 0.99 0.98 −2 ATLAS W, Z 7 TeV 2010 1.52 1.47

  • 1.36

1.21 −1 ATLAS HM DY 7 TeV 2.02 1.99

  • 1.70

1.70

  • ATLAS W, Z 7 TeV 2011

3.80 3.73 −1 1.43 1.29 −1 ATLAS jets 2010 7 TeV 0.92 0.87 −4 0.86 0.83 −2 ATLAS jets 2.76 TeV 1.07 0.96 −6 0.96 0.96

  • ATLAS jets 2011 7 TeV

1.17 1.18

  • 1.10

1.09 −1 ATLAS Z pT 8 TeV (pll

T , Mll)

1.21 1.24 +2 0.94 0.98 +2 ATLAS Z pT 8 TeV (pll

T , yll)

3.89 4.26 +2 0.79 1.07 +2 ATLAS σtot

tt

2.11 2.79 +2 0.85 1.15 +1 ATLAS t¯ t rap 1.48 1.49

  • 1.61

1.64

  • CMS total

0.97 0.92 −13 0.86 0.85 −3 CMS Drell-Yan 2D 2011 0.77 0.77

  • 0.58

0.57

  • CMS jets 7 TeV 2011

0.88 0.82 −9 0.84 0.81 −3 CMS jets 2.76 TeV 1.07 0.98 −7 1.00 1.00

  • CMS Z pT 8 TeV (pll

T , yll)

1.49 1.57 +1 0.73 0.77

  • CMS σtot

tt

0.74 1.28 +2 0.23 0.24

  • CMS t¯

t rap 1.16 1.19

  • 1.08

1.10

  • Total

1.117 1.120 +11 1.130 1.100 −121

NNPDF31sx: fjt quality

26

1.10 vs ~1.12 (NLO & NLO+NLLx), 1.13 (NNLO)

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Università di Cagliari, November 22, 2017

χ2/Ndat ∆χ2 χ2/Ndat ∆χ2 NLO NLO+NLLx NNLO NNLO+NLLx NMC 1.35 1.35 +1 1.30 1.33 +9 SLAC 1.16 1.14 −1 0.92 0.95 +2 BCDMS 1.13 1.15 +12 1.18 1.18 +3 CHORUS 1.07 1.10 +20 1.07 1.07 −2 NuTeV dimuon 0.90 0.84 −5 0.97 0.88 −7 HERA I+II incl. NC 1.12 1.12

  • 2

1.17 1.11 −62 HERA I+II incl. CC 1.24 1.24

  • 1.25

1.24 −1 HERA σNC

c

1.21 1.19 −1 2.33 1.14 −56 HERA F b

2

1.07 1.16 +3 1.11 1.17 +2 DY E866 σd

DY/σp DY

0.37 0.37

  • 0.32

0.30

  • DY E886 σp

1.06 1.10 +3 1.31 1.32

  • DY E605 σp

0.89 0.92 +3 1.10 1.10

  • CDF Z rap

1.28 1.30

  • 1.24

1.23

  • CDF Run II kt jets

0.89 0.87 −2 0.85 0.80 −4 D0 Z rap 0.54 0.53

  • 0.54

0.53

  • D0 W → eν asy

1.45 1.47

  • 3.00

3.10 +1 D0 W → µν asy 1.46 1.42

  • 1.59

1.56

  • ATLAS total

1.18 1.16 −7 0.99 0.98 −2 ATLAS W, Z 7 TeV 2010 1.52 1.47

  • 1.36

1.21 −1 ATLAS HM DY 7 TeV 2.02 1.99

  • 1.70

1.70

  • ATLAS W, Z 7 TeV 2011

3.80 3.73 −1 1.43 1.29 −1 ATLAS jets 2010 7 TeV 0.92 0.87 −4 0.86 0.83 −2 ATLAS jets 2.76 TeV 1.07 0.96 −6 0.96 0.96

  • ATLAS jets 2011 7 TeV

1.17 1.18

  • 1.10

1.09 −1 ATLAS Z pT 8 TeV (pll

T , Mll)

1.21 1.24 +2 0.94 0.98 +2 ATLAS Z pT 8 TeV (pll

T , yll)

3.89 4.26 +2 0.79 1.07 +2 ATLAS σtot

tt

2.11 2.79 +2 0.85 1.15 +1 ATLAS t¯ t rap 1.48 1.49

  • 1.61

1.64

  • CMS total

0.97 0.92 −13 0.86 0.85 −3 CMS Drell-Yan 2D 2011 0.77 0.77

  • 0.58

0.57

  • CMS jets 7 TeV 2011

0.88 0.82 −9 0.84 0.81 −3 CMS jets 2.76 TeV 1.07 0.98 −7 1.00 1.00

  • CMS Z pT 8 TeV (pll

T , yll)

1.49 1.57 +1 0.73 0.77

  • CMS σtot

tt

0.74 1.28 +2 0.23 0.24

  • CMS t¯

t rap 1.16 1.19

  • 1.08

1.10

  • Total

1.117 1.120 +11 1.130 1.100 −121

NNPDF31sx: fjt quality

sensible improvement in the 𝜓2…

26

(𝜓2NNLO-𝜓2NNLO+NLLx)= -121

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Università di Cagliari, November 22, 2017

26

χ2/Ndat ∆χ2 χ2/Ndat ∆χ2 NLO NLO+NLLx NNLO NNLO+NLLx NMC 1.35 1.35 +1 1.30 1.33 +9 SLAC 1.16 1.14 −1 0.92 0.95 +2 BCDMS 1.13 1.15 +12 1.18 1.18 +3 CHORUS 1.07 1.10 +20 1.07 1.07 −2 NuTeV dimuon 0.90 0.84 −5 0.97 0.88 −7 HERA I+II incl. NC 1.12 1.12

  • 2

1.17 1.11 −62 HERA I+II incl. CC 1.24 1.24

  • 1.25

1.24 −1 HERA σNC

c

1.21 1.19 −1 2.33 1.14 −56 HERA F b

2

1.07 1.16 +3 1.11 1.17 +2 DY E866 σd

DY/σp DY

0.37 0.37

  • 0.32

0.30

  • DY E886 σp

1.06 1.10 +3 1.31 1.32

  • DY E605 σp

0.89 0.92 +3 1.10 1.10

  • CDF Z rap

1.28 1.30

  • 1.24

1.23

  • CDF Run II kt jets

0.89 0.87 −2 0.85 0.80 −4 D0 Z rap 0.54 0.53

  • 0.54

0.53

  • D0 W → eν asy

1.45 1.47

  • 3.00

3.10 +1 D0 W → µν asy 1.46 1.42

  • 1.59

1.56

  • ATLAS total

1.18 1.16 −7 0.99 0.98 −2 ATLAS W, Z 7 TeV 2010 1.52 1.47

  • 1.36

1.21 −1 ATLAS HM DY 7 TeV 2.02 1.99

  • 1.70

1.70

  • ATLAS W, Z 7 TeV 2011

3.80 3.73 −1 1.43 1.29 −1 ATLAS jets 2010 7 TeV 0.92 0.87 −4 0.86 0.83 −2 ATLAS jets 2.76 TeV 1.07 0.96 −6 0.96 0.96

  • ATLAS jets 2011 7 TeV

1.17 1.18

  • 1.10

1.09 −1 ATLAS Z pT 8 TeV (pll

T , Mll)

1.21 1.24 +2 0.94 0.98 +2 ATLAS Z pT 8 TeV (pll

T , yll)

3.89 4.26 +2 0.79 1.07 +2 ATLAS σtot

tt

2.11 2.79 +2 0.85 1.15 +1 ATLAS t¯ t rap 1.48 1.49

  • 1.61

1.64

  • CMS total

0.97 0.92 −13 0.86 0.85 −3 CMS Drell-Yan 2D 2011 0.77 0.77

  • 0.58

0.57

  • CMS jets 7 TeV 2011

0.88 0.82 −9 0.84 0.81 −3 CMS jets 2.76 TeV 1.07 0.98 −7 1.00 1.00

  • CMS Z pT 8 TeV (pll

T , yll)

1.49 1.57 +1 0.73 0.77

  • CMS σtot

tt

0.74 1.28 +2 0.23 0.24

  • CMS t¯

t rap 1.16 1.19

  • 1.08

1.10

  • Total

1.117 1.120 +11 1.130 1.100 −121

NNPDF31sx: fjt quality

sensible improvement in the 𝜓2… mostly driven by HERA DIS data

slide-44
SLIDE 44

Università di Cagliari, November 22, 2017

27

Small-x resummation and HERA data

Compute the 𝜓2 removing data points in the region where resummation effects are expected fjxed-order description should be good here resummation effects might be important here cuts on DIS data

αs(Q2) ln ✓ 1 x ◆

≥ Dcut

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Università di Cagliari, November 22, 2017

28

NNLO+NLLx 𝜓2 fmattens at larger values of Dcut

1.6 1.8 2 2.2 2.4 2.6 2.8 3

cut

D

1.04 1.06 1.08 1.1 1.12 1.14 1.16

dat

/N

2

χ

NNPDF3.1sx, HERA NC inclusive data

NNLO NNLO+NLLx NLO NLO+NLLx

NNPDF3.1sx, HERA NC inclusive data

NNLO+NLLx offers the best description NNLO worsens if small-x data are included

Small-x resummation and HERA data

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Università di Cagliari, November 22, 2017

improved description of data at small-x and their slope

Small-x resummation and HERA data

101 102 103 Q2 [GeV2] −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 FL(x, Q2)

x =8.8e-5 x =1.3e-4 x =1.7e-4 x =2.2e-4 x = 3.2e-4 x = 4.0e-4 x = 5.4e-4 x = 6.9e-4 x = 9.6e-4 x = 1.2e-3 x = 1.6e-3 x = 2.4e-3 x = 3.0e-3 x = 4.0e-3 x = 5.4e-3 x = 7.4e-3 x = 9.9e-3 x = 1.8e-2

NNPDF3.1sx

NNLO NNLO+NLLx H1

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 σr,NC

HERA NC √s = 920 GeV, Q2 = 4.5 GeV2

NNLO NNLO+NLLx HERA data

10−4 10−3 10−2 x 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Ratio to data

29

slide-47
SLIDE 47

Università di Cagliari, November 22, 2017

Small-x resummation and collider processes

Need to include small-x resummation in hadronic cross section (especially DY) First estimate of impact of resummation can be obtained by computing approximate results with resummation only in PDF evolution

σX(Q2, s) = ∑

a,b

fa/h1(Q2) ⊗ fb/h2(Q2) ⊗ ˆ σab→X(Q2, s)

Q2 d dQ2 fi(Q2) = Pij(αs(Q2)) ⊗ fj(Q2)

30

slide-48
SLIDE 48

Università di Cagliari, November 22, 2017

0.5 1.0 1.5 2.0 Dilepton rapidity yll 0.94 0.96 0.98 1.00 1.02 1.04 1.06 Ratio to NNLO

NNPDF31sx, CMS DY @ 7 TeV, 20 GeV < Mll < 30 GeV

NNLO NNLO+NLLx

Small-x resummation and collider processes

Need to include small-x resummation in hadronic cross section (especially DY) First estimate of impact of resummation can be obtained by computing approximate results with resummation only in PDF evolution

precision LHC phenomenology in extreme kinematic regions would require small-x resummed PDFs

31

slide-49
SLIDE 49

Università di Cagliari, November 22, 2017

  • First global fjt with small-x resummation in the NNPDF framework
  • Evidence that NNLO+NLLx improves with respect to NNLO
  • Description of the data at small x/small Q2 signifjcantly improves when resummation effects are included
  • Potential for reducing uncertainties for processes not necessarily related to small-x physics
  • Computation of small-x resummation for other processes needed
  • Motivation to explore further probes of small-x dynamics at the LHC, such as low-mass DY at LHCb
  • PDF sets with joint (large-x + small-x) resummation?

Conclusions & outlook

32

slide-50
SLIDE 50

Università di Cagliari, November 22, 2017

Backup

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Università di Cagliari, November 22, 2017

Convolution integral diagonalise in Mellin space

σ(x, Q2) = x

1

x

dz z L x z , Q2 ˆ σ(z, Q2) z

Double logarithmic enhancement due to soft gluon emission

N-soft

Exponentiation The functions gi resum αsklnkN to all orders LL

NLL

NNLL

σ(N, Q2) = L(N, Q2)σ0(N, Q2)C(N) C(N) = 1 +

∞

∑

n=1

αs

2n

∑

k=0

cnklnk N + O(1/N) C(N) = g0(αs) exp 1 αs g1(αsln N) + g2(αsln N) + αsg3(αsln N) + . . .

  • Tireshold resummation in a nutshell
slide-52
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Università di Cagliari, November 22, 2017

x

1 −

10

) [ref]

2

) [new] / g ( x, Q

2

g ( x, Q

0.8 0.9 1 1.1 1.2 1.3

NLO NLO+NLL

2

GeV

4

=10

2

NNPDF3.0 DIS+DY+Top, Q

x

1 −

10

) [ref]

2

( x, Q Σ ) [new] /

2

( x, Q Σ

0.8 0.9 1 1.1 1.2 1.3

NLO NLO+NLL

2

GeV

4

=10

2

NNPDF3.0 DIS+DY+Top, Q

x

1 −

10

) [ref]

2

) [new] / g ( x, Q

2

g ( x, Q

0.8 0.9 1 1.1 1.2 1.3

NNLO NNLO+NNLL

2

GeV

4

=10

2

NNPDF3.0 DIS+DY+Top, Q

x

1 −

10

) [ref]

2

( x, Q Σ ) [new] /

2

( x, Q Σ

0.8 0.9 1 1.1 1.2 1.3

NNLO NNLO+NNLL

2

GeV

4

=10

2

NNPDF3.0 DIS+DY+Top, Q

NLO+NLL NNLO+NNLL

Impact on PDFs

slide-53
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Università di Cagliari, November 22, 2017

Parton Distribution Functions

f (x, Q2)

Evolution in x2 is encoded in BFKL equation

−x ∂

∂x f+(x, Q2) =

Z ∞

dν2 ν K ✓µ2 ν2 , αs(Q2) ◆ f+(x, ν2)

PDFs depend on two kinematic variables

1 10-1 10-2 10-3 10-4 10-5 10-6 1 101 102 103 104 106 107 x Q2 [GeV]

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Università di Cagliari, November 22, 2017

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x Pgg(x) x αs = 0.20, nf = 4, Q0MS ‾‾‾ LO NLO NNLO

Courtesy of Marco Bonvini

0.05 0.1 0.15 0.2 0.25 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x Pqg(x) x αs = 0.20, nf = 4, Q0MS ‾‾‾ LO NLO NNLO

Small-x resummation of DGLAP evolution

ABF procedure based on

  • duality with BFKL evolution
  • symmetry of the BFKL kernel
  • momentum conservation
  • resummation of (subleading, but fundamental) running coupling effects
slide-55
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Università di Cagliari, November 22, 2017

Now matching at NNLO available!

ABF procedure based on

  • duality with BFKL evolution
  • symmetry of the BFKL kernel
  • momentum conservation
  • resummation of (subleading, but fundamental) running coupling effects

Courtesy of Marco Bonvini ‘dip’ [Ciafaloni,Colferai,Salam,Stasto]

Small-x resummation of DGLAP evolution

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x Pgg(x) x αs = 0.20, nf = 4, Q0MS ‾‾‾ LO NLO NNLO LO+LL NLO+NLL NNLO+NLL 0.05 0.1 0.15 0.2 0.25 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x Pqg(x) x αs = 0.20, nf = 4, Q0MS ‾‾‾ LO NLO NNLO NLO+NLL NNLO+NLL

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Università di Cagliari, November 22, 2017

  • massive DIS coefficient functions available and implemented in HELL
  • VFNS (FONLL = S-ACOT) implementation
  • resummed matching conditions in HELL

C

[n f +1]

L,g

(m) = C

[n f ]

L,g (m),

C

[n f +1]

2,g

(m) = C

[n f ]

2,g (m) − Khg(m)

f

[n f +1]

i

(m) =

∑

j=g,qi...qn f

Kij(m) f

[n f ]

j

, i = g, q, . . . qn f +1 Courtesy of Marco Bonvini See also [Thorne,White]

Small-x resummation of coefficient functions

  • 0.02

0.02 0.04 0.06 0.08 0.1 0.12 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x C2,g(x,αs) x αs = 0.20, nf = 4, Q0MS ‾‾‾ NLO NLO+NLL NNLO NNLO+NLL N3LO

  • 0.02

0.02 0.04 0.06 0.08 0.1 0.12 0.14 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 x CL,g(x,αs) x αs = 0.20, nf = 4, Q0MS ‾‾‾ NLO NLO+NLL NNLO NNLO+NLL N3LO