Resummation of transverse observables in momentum space: - - PowerPoint PPT Presentation

Resummation of transverse observables in momentum space: phenomenology

Emanuele Re CERN & LAPTh Annecy Resummation, Evolution, Factorization 2017

Madrid, 13 November 2017

plan of the talk

◮ previous talk: theoretical explanation of method used to perform resummation of

transverse observables in direct space, up to N3LL accuracy.

◮ we have implemented it into a numerical code, named RadISH. ◮ this talk: present results for pT,H and for Drell-Yan (pT,ℓℓ and φ∗), giving also some

details about matching to fixed-order:

• 1. Higgs transverse momentum
• 2. Drell-Yan

◮ All results obtained in collaboration with W. Bizon, P

.F. Monni, L. Rottoli and P . Torrielli [arXiv:1705.09127, arXiv:1604.02191, and work in progress]

1 / 17

Higgs transverse momentum

Higgs pT: data vs theory

◮ pT,H is one of the more important

• bservables for current Higgs studies at

the LHC

• large luminosity ⇒ precision studies

(“not limited” by stat. uncertainty)

• large pT,H: probe heavy degrees of

freedom

• medium-low pT,H: large cross section

& probe of Higgs couplings (next slide)

◮ Fully exclusive (N)NLOPS Monte-Carlo

tools heavily used by EXP . Logarithmic accuracy is limited.

◮ accurate logarithmic resummation (matched to fixed order) is important, both for

data/TH comparison, as well as to provide accurate MC tools.

2 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

∼ α3

S κc

mc mH

• 2

log2 p2

T

m2

c

• ∼ α2

S κ2 c

mc mh

• 2

. one power of αS from charm PDF . c¯ c → hg also included

• different κc scaling + log scaling ⇒ shape distorsion

3 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

∼ α3

S κc

mc mH

• 2

log2 p2

T

m2

c

• ∼ α2

S κ2 c

mc mh

• 2

. one power of αS from charm PDF . c¯ c → hg also included

• different κc scaling + log scaling ⇒ shape distorsion

3 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

∼ α3

S κc

mc mH

• 2

log2 p2

T

m2

c

• . non-Sudakov double log for mc<pT< mH

∼ α2

S κ2 c

mc mh

• 2

. one power of αS from charm PDF . c¯ c → hg also included

• different κc scaling + log scaling ⇒ shape distorsion

3 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

20 40 60 80 100 0.8 1.0 1.2 1.4 pT,h [GeV] (1/σ dσ/dpT,h)/(1/σ dσ/dpT,h)SM

κc = -10 κc = -5 κc = 0 κc = 5

• different κc scaling + log scaling ⇒ shape distorsion
• use normalized distribution to reduce uncertainties

3 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

20 40 60 80 100 0.8 1.0 1.2 1.4 pT,h [GeV] (1/σ dσ/dpT,h)/(1/σ dσ/dpT,h)SM

κc = -10 κc = -5 κc = 0 κc = 5

results: + ATLAS data & ≤ 10 % TH uncertainty

• κc ∈ [−16, 18]

+ 300 fb−1, assuming syst (exp) 3% & theory 5%

• κc ∈ [−1.4, 3.8]
• different κc scaling + log scaling ⇒ shape distorsion
• use normalized distribution to reduce uncertainties

3 / 17

Higgs pT and light-quarks Yukawa

◮ differential distributions affected by interference among top and light-quarks loops

• medium-to-low pT,H spectrum ⇒ bounds on charm Yukawa

[Bishara,Haisch,Monni,ER ’16]

[& similar ideas in [Soreq et al. ’16]]

20 40 60 80 100 0.8 1.0 1.2 1.4 pT,h [GeV] (1/σ dσ/dpT,h)/(1/σ dσ/dpT,h)SM

κc = -10 κc = -5 κc = 0 κc = 5

results: + ATLAS data & ≤ 10 % TH uncertainty

• κc ∈ [−16, 18]

+ 300 fb−1, assuming syst (exp) 3% & theory 5%

• κc ∈ [−1.4, 3.8]
• different κc scaling + log scaling ⇒ shape distorsion
• use normalized distribution to reduce uncertainties
• method mainly limited by TH precision

3 / 17

Higgs pT and Monte Carlo tools

10−3 10−2 10−1 100 dσ/dpH

T [pb/GeV]

Ratio pH

T [GeV]

dσ/dpH

T [pb/GeV]

Ratio

NNLOPS HQT

0.6 1.0 1.4 50 100 150 200 250 300 10−3 10−2 10−1 100 dσ/dpH

T [pb/GeV]

Ratio pH

T [GeV]

dσ/dpH

T [pb/GeV]

Ratio

NNLOPS HQT

0.6 1.0 1.4 50 100 150 200 250 300

◮ known how to match parton-showers to F.O. computations, at NLO, and, for color-singlet, at

NNLO

◮ logarithmic accuracy is limited, though ◮ some choices are made by comparing with more precise resummed results

◮ when matching POWHEG+MiNLO NLO results to NNLO, there’s a (partially arbitrary)

parameter.

◮ plots above show that comparison with resummation was used as a guiding principle

to fix it.

◮ RIGHT: “best result”. Better agreement with NNLL+NLO resummation.

[HqT, Bozzi et al.]

4 / 17

Higgs pT at N3LL+NNLO

◮ In arXiv:1705.09127 and arXiv:1604.02191 we have developed a new method to resum

transverse observables in momentum space, as explained in the previous talk.

◮ Obtained NNLL and N3LL results matched to NNLO for pT,H. Total normalization: N3LO.

RadISH+NNLOJET, 13 TeV, mH = 125 GeV µR = µF = mH, Q = mH/2 PDF4LHC15 (NNLO) uncertainties with µR, µF, Q variations (x 3/2)

dσ/d pt

H [pb/GeV]

NLO NNLO N3LL+NNLO 0.5 1 1.5 2 2.5 ratio to N3LL+NNLO pt

H [GeV]

0.7 0.8 0.9 1 1.1 1.2 1.3 10 20 30 40 50 60 70 80 90 100

◮ rest of the talk: results, (some) technical details, some open questions

5 / 17

Multiplicative vs Additive Matching

Σ(pT, ΦB) = pT dp′

T

dσ dp′

TdΦB

→ Σres if pT ≪ MB → ΣF.O. if pT MB additive matching Σadd

matched(pT) =

Σres(pT) + ΣF.O.(pT) − Σres,exp(pT) multiplicative matching Σmult

matched(pT) =

Σres(pT) ΣF.O.(pT) Σres,exp(pT)

◮ there’s no rigorous theory argument to favour a prescription over the other

• additive: probably the more natural choice,

simpler and clear

• numerically delicate when pT → 0

(F .O. result needs to be extremely stable)

• multiplicative: numerically more stable, as

physical suppression at small pT fixes potentially unstable F .O. results

• allows to include constant terms from F

.O.

6 / 17

Multiplicative vs Additive Matching

◮ for pT,H at N3LL, used mult. matching: constant terms at O(α3

S) recovered without the need

• f knowing analytically coefficient and hard functions.

ΣF.O. = σN3LO

pp→H −

• pT

dp′

T

dσNNLO

pp→Hj

dp′

T

◮ in additive matching, one would instead need C(3) and H(3) in effective luminosity LN3LL ◮ in mult. scheme, matching can generate higher-order subleading terms at high pT. Can be

large if K-factor large.

◮ To suppress them:

Z =

• 1 −

pT/M v0 uh Θ(v0 − pT/M) ⇒ Σmat = (Σres)Z ΣF.O. (Σres,exp)Z

◮ Z → 1 at small pT, Z → 0 at large pT ⇒ resummation turned off smoothly ◮ Used v0 = 1/2, h = 3, checked stability with v0 = 1, h = 1, 2. ◮ At small pT, Z introduces power suppressed terms (pT/M)u. Can use u to make them

arbitrarily small (although they are already suppressed). In our results, used u = 1.

7 / 17

Resummation scale

◮ to estimate higher-order logarithmic corrections, introduce resummation scale Q:

L ≡ ln M kT,1 = ln Q kT,1 − ln Q M and then vary Q, making sure that the first term is larger than the second, as we are in fact expanding about ln(Q/kT,1).

◮ in resummation formula, use replacement above in Sudakov and parton densities. Expand

about ln Q/kT,1 and reabsorb ln Q/M in H and C functions, entering the generalized luminosities

H(1)(µR) → ˜ H(1)(µR, xQ) = H(1)(µR) +

• − 1

2 A(1) ln x2

Q + B(1)

• ln x2

Q,

xQ = Q/M. C(1)

ij (z) → ˜

C(1)

ij (z, µF , xQ) = C(1) ij (z) + ˆ

P (0)

ij (z) ln

x2

QM 2

µ2

F

◮ similar, but more complicated, in H(2) and C(2).

8 / 17

Impact of N3LL resummation

RadISH, 13 TeV, mH = 125 GeV µR = µF = mH, Q = mH/2 PDF4LHC15 (NNLO) uncertainties with µR, µF, Q variations (x 3/2)

1/σ dσ/d pt

H [1/GeV]

NNLL N3LL 0.005 0.01 0.015 0.02 0.025 0.03 ratio to N3LL pt

H [GeV]

0.7 0.8 0.9 1 1.1 1.2 1.3 5 10 15 20 25 30 35 40

RadISH, 13 TeV, mH = 125 GeV µR = µF = mH, Q = mH/2 PDF4LHC15 (NNLO) uncertainties with µR, µF, Q variations (x 3/2)

1/σ dσ/d pt

H [1/GeV]

NNLL+NLO N3LL+NLO 0.005 0.01 0.015 0.02 0.025 0.03 0.035 ratio to central pt

H [GeV]

0.7 0.8 0.9 1 1.1 1.2 1.3 20 40 60 80 100 120 140

◮ here Q = mH/2 ◮ LEFT: pure resummation at N3LL vs NNLL

◮ pure N3LL correction amounts to 10-15% (partially due to inclusion of C(2) and H(2),

which, in this plot, are not included in NNLL).

◮ more importantly: reduction of theoretical uncertainty from NNLL to N3LL.

◮ RIGHT: NLO matching (σNNLO pp→H, dσNLO pp→Hj/dpT)

◮ N3LL+NLO correction: about 10% at peak, a bit larger below. ◮ perturbative uncertainty halved below 10 GeV, unchanged elsewhere. 9 / 17

N3LL+NNLO

RadISH, 13 TeV, mH = 125 GeV µR = µF = mH, Q = mH/2 PDF4LHC15 (NNLO) uncertainties with µR, µF, Q variations (x 3/2) Fixed order from PRL 115 (2015) 082003

1/σ dσ/d pt

H [1/GeV]

pt

H [GeV]

NNLO NNLL+NNLO N3LL+NNLO 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 10 20 30 40 50 60 70 80 90 100 110 120

◮ NNLO matching (σN3LO pp→H, dσNNLO pp→Hj/dpT) ◮ N3LO from Anastasiou et al., ’15 ◮ pp → Hj at NNLO from Boughezal, Caola,

et al., ’15

◮ anomalous dimension from Li, Zhu ’16,

Vladimirov ’16

◮ N3LL+NNLO corrections: few percent at peak, more sizeable below ◮ deviations from NNLO below 30 GeV ◮ after matching at NNLO, only moderate reduction in uncertainty from NNLL to N3LL.

Precise quantitative statement needs very stable NNLO distributions below peak.

◮ phenomenology: with this precision, perturbative uncertainty from resummation seems to

saturate; including quark mass effects will be relevant to improve further.

[Melnikov,Penin ’16; Melnikov et al. ’16; Lindert et al. ’17] ◮ details of matching in intermediate region might also deserve more studies (see discussion

for Drell-Yan)

10 / 17

Drell-Yan: φ∗ and pT,ℓℓ

Drell-Yan: data vs theory

◮ Drell-Yan is the best measured process at the LHC. Many applications (PDFs, ...) ◮ An example where extreme precision is relevant: extraction of the W mass

[slide from talk by M. Boonekamp, December ’16] 11 / 17

Drell-Yan: data vs theory and W mass extraction

◮ sensitive final state distributions: pT,ℓ, mT , pT,miss ◮ measured using template fits to lepton observable. Modelling of pT,W and pT,Z is crucial ◮ fit predictions to Z data, apply to W

12 / 17

Drell-Yan: data vs theory and W mass extraction

◮ sensitive final state distributions: pT,ℓ, mT , pT,miss ◮ measured using template fits to lepton observable. Modelling of pT,W and pT,Z is crucial ◮ fit predictions to Z data, apply to W ◮ using state-of-the-art pQCD predictions is not enough: doesn’t match precision of data. [ATLAS 1701.07240] ◮ at the end, LO MC(!) are used: calibration (→tune) on Z data, obtain W template

distributions.

◮ certainly it’d be more appealing to use a more accurate TH prediction

12 / 17

Matching ambiguities in Drell-Yan

◮ we have performed a resummation at N3LL+NNLO for Drell-Yan observables [Bizon et al., in progress]

RadISH, 8 TeV µR = µF = mll/2, Q = mll/4 NNPDF3.0 (NNLO) uncertainties with µR, µF, Q variations

1/σ dσ/d pt

Z [pb/GeV]

N3LL+NLO (R) N3LL+NLO (mult) ATLAS 0.01 0.02 0.03 0.04 0.05 0.06 0.07 ratio to N3LL+NLO pt

Z [GeV]

0.9 0.95 1 1.05 1.1 10 20 30 40 50 60 70 80 90

◮ data is very precise; details of matching choices can be important. Shown here at

N3LL+NLO

◮ in soft/collinear, and in hard regions, differences among matching schemes are moderate,

as expected.

◮ they are visible in the regions where fixed-order and resummation contribute similarly, i.e. in

the “matching region”.

◮ here used (→ chosen) h = 5, Q = mZ/4

13 / 17

pT,ℓℓ at N3LL+NNLO

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 <0.4, 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 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 <0.4, 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

pp → Zj at NNLO from NNLOJET, Gehrmann-De Ridder et al., ’16 ◮ LEFT: Q = mZ/2, RIGHT: Q = mZ/4. Chosen h = 5. ◮ these choices are not strictly dictated by theory. For instance, h = 5 was chosen to

“maximize” agreement with data in a “control region”:

• select only one fiducial region, and focus on interval where we can be confident that

we are not absorbing in our “tune” effects other than those genuinely due to matching ambiguities.

• pT,Z ∼ 10 GeV: far from non-perturbative region.

14 / 17

pT,ℓℓ at N3LL+NNLO

◮ then look at other regions

10−4 10−3 10−2 10−1 100 101 (1/σ)dσ/dpT RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 2.0< 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 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, 46< mll <66 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

◮ LEFT: large rapidities, RIGHT: low invariant mass. ◮ what we did here (preliminary!) is “data driven”: probably can be done better ◮ for instance: matching ambiguities are related to “power suppressed” effects. Can the

inclusion of next-to-eikonal/power corrections make transition more reliable?

15 / 17

pT,ℓℓ at N3LL+NNLO

◮ then look at other regions

10−4 10−3 10−2 10−1 100 101 (1/σ)dσ/dpT RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 2.0< 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 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, 46< mll <66 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

◮ to preserve total cross section when matching to F.O., resummation should be switched off

when radiation approaches the hard scale: modified logarithms,... ln(1/v) → 1 p ln

• 1 + 1

vp

• ≃ ln 1

v + vp p v = pT/M

◮ - progress in the computation of power corrections might help here

• relax strict unitary request ? [for MC’s, accepted in some NLOPS merging/matching schemes]

15 / 17

pT,ℓℓ at N3LL+NNLO

◮ then look at other regions

10−4 10−3 10−2 10−1 100 101 (1/σ)dσ/dpT RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 2.0< 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 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, 46< mll <66 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

◮ with the current and future precision in theory and data, these issues might start to be

relevant also for phenomenological applications. The mW extraction is such an example.

15 / 17

φ∗ at N3LL+NNLO

◮ as explained in previous talk, our approach can be used to resum all transverse

• bservables. We looked at φ∗:

φ∗ = tan π − ∆φ 2

• sin θ∗
• θ∗: angle between electron and beam axis, in Z

boson rest frame

• ATLAS uses slightly different definition:

cos θ∗ = tanh((yl− − yl+)/2)

10−2 10−1 100 101 102 (1/σ)dσ/dφ∗ RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 0.0< η <0.4, 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

10−2 10−1 100 φ∗ 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 10−2 10−1 100 101 102 (1/σ)dσ/dφ∗ RadISH 2.0 8 TeV, pp → Z(→ l+l−) + X 1.2< η <1.6, 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

10−2 10−1 100 φ∗ 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

◮ LEFT: central rapidities, RIGHT: large rapidities ◮ following the previous considerations, here used the exact same choices for the matching

as fixed using pT,Z results.

16 / 17

conclusions

◮ shown some results at N3LL+NNLO for pT,H, pT,ℓℓ and φ∗ ◮ results are encouraging. The RadISH code will be made fully available soon.

ATLAS/CMS have already started using it.

◮ at this level of accuracy, several subleading effects start to play an important role,

as the details of matching scheme, etc.

◮ issues that were usually considered of academic interest might soon become

relevant also for LHC phenomenology.

17 / 17

conclusions

◮ shown some results at N3LL+NNLO for pT,H, pT,ℓℓ and φ∗ ◮ results are encouraging. The RadISH code will be made fully available soon.

ATLAS/CMS have already started using it.

◮ at this level of accuracy, several subleading effects start to play an important role,

as the details of matching scheme, etc.

◮ issues that were usually considered of academic interest might soon become

relevant also for LHC phenomenology. Thanks for your attention!

17 / 17