Alessandro Vicini University of Milano, INFN Milano CERN, - - PowerPoint PPT Presentation

Alessandro Vicini - University of Milano CERN, December 16th 2013

The Higgs transverse momentum distribution in Shower Montecarlo codes for pp→H+X

Alessandro Vicini

University of Milano, INFN Milano

CERN, December 16th 2013

in collaboration with: E. Bagnaschi, G. Degrassi important discussions with: S. Frixione, M. Grazzini, F. Maltoni, P . Nason, C. Oleari

Alessandro Vicini - University of Milano CERN, December 16th 2013

Basic references for the Higgs ptH spectrum, including multiple parton emissions

• quark mass effects

Bagnaschi, Degrassi, Slavich, Vicini, arXiv:1111.2854 Mantler, Wiesemann, arXiv:1210.8263

• S. Frixione, talk at Higgs Cross Section Working Group meeting, December 7th 2012

Grazzini, Sargsyan, arXiv:1306.4581

• S. Frixione, talk at the HXSWG meeting, July 23rd 2013

A. Vicini, talk at the HXSWG meeting, July 23rd 2013 Banfi, Monni, Zanderighi, arXiv:1308.4634

• Analytical resummation of the Higgs ptH spectrum in HQET

Balazs, Yuan, arXiv:hep-ph/0001103 Bozzi, Catani, De Florian, Grazzini, arXiv:hep-ph/0508068 De Florian, Ferrera, Grazzini, Tommasini, arXiv:1109.2109

• Shower Montecarlo description of the Higgs ptH spectrum in HQET

Frixione, Webber, arXiv:hep-ph/0309186 Alioli, Nason, Oleari, Re, arXiv:0812.0578 Hamilton, Nason, Re, Zanderighi, arXiv:1309.0017

Alessandro Vicini - University of Milano CERN, December 16th 2013

Outline

• matching NLO matrix elements for inclusive Higgs production and Parton Shower
• quark mass effects in the SM
• two-scales vs one-scale description of the Higgs ptH distribution

in presence of quark mass effects

• tuning the POWHEG parameter h to mimic the HRes shape
• uncertainty band computed with a variation of the parameter h

Alessandro Vicini - University of Milano CERN, December 16th 2013

Higgs transverse momentum distribution in the HQET (heavy top limit)

• the Higgs transverse momentum is due to its recoil against QCD radiation
• at low ptH, the fixed order ptH distribution diverges for ptH → 0 (both at LO and at NLO)
• the resummation to all orders of the divergent log(ptH) terms yields a regular distribution

in the limit ptH → 0 different approaches: analytical (up to NLO+NNLL), via Parton Shower (up to LO+NLL)

Bozzi Catani De Florian Grazzini, arXiv:hep-ph/0508068

Alessandro Vicini - University of Milano CERN, December 16th 2013

Quark mass effects at fixed order (no resummation, no Parton Shower)

0.7 0.8 0.9 1 1.1 1.2 1.3 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 R pt

H (GeV)

LHC 7 TeV SM - mh = 120 GeV NLO R=ratio to (mtop with LO rescaling) mtop with LO rescaling mtop exact mass dependence mtop, mbot exact mass dependence

• very good agreement between independent codes

0.0001 0.001 0.01 0.1 1 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 (d/dpt

H)(pb/GeV)

pt

H (GeV)

LHC 7 TeV SM - mH = 120 GeV NLO-QCD, no EW mtop with LO rescaling exact mt mb dependence

H t, b g g

• every diagram is proportional to the corresponding Higgs-fermion

Yukawa coupling → the bottom diagrams have a suppression factor mb/mt ~1/36 w.r.t. the corresponding top diagrams → the squared bottom diagrams are negligible (in the SM) the bottom effects are due to the top-bottom interference terms (genuine quantum effects)

|M(gg → gH)|2 = |Mt + Mb|2 = |Mt|2 + 2Re(MtM†

b) + |Mb|2

Alessandro Vicini - University of Milano CERN, December 16th 2013

Quark mass effects after the resummation of multiple gluon emissions (beginning 2013)

• ./!01234

POWHEG MC@NLO

0.7 0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300

pH

T [GeV]

(dσ

LO+NLL/dpH

T ) / (dσhtl

LO+NLL/dpH

T )

htl t t+b

LHC@8 TeV, mH = 125 GeV

µF = µR = QRes = mH / 2

• H. Mantler, M. Wiesemann, arXiv:1210.8263

ratio of distributions ratio of shapes ratio of shapes

• different impact of the quark-mass effects after the matching with Parton Shower
• r after the analytical resummation
• MC@NLO and Mantler-Wiesemann share an additive matching approach

POWHEG has a different Sudakov form factor

Alessandro Vicini - University of Milano CERN, December 16th 2013

Matching NLO matrix elements and Parton Shower

Alessandro Vicini - University of Milano CERN, December 16th 2013

Matching NLO matrix elements and Parton Shower

¯ Bs = B(ΦB) +

• V (ΦB) +
• dΦR|BRs(ΦR|B)
• dσNLO+PS = dΦB ¯

Bs(ΦB)

• ∆s(pmin

⊥ ) + dΦR|B

Rs(ΦR) B(ΦB) ∆s(pT(Φ))

• + dΦRRf(ΦR),+dΦRRreg(ΦR)

Alessandro Vicini - University of Milano CERN, December 16th 2013

Matching NLO matrix elements and Parton Shower

¯ Bs = B(ΦB) +

• V (ΦB) +
• dΦR|BRs(ΦR|B)
• dσNLO+PS = dΦB ¯

Bs(ΦB)

• ∆s(pmin

⊥ ) + dΦR|B

Rs(ΦR) B(ΦB) ∆s(pT(Φ))

• + dΦRRf(ΦR),+dΦRRreg(ΦR)

is the sum of all the real emission squared matrix elements, with a regular (divergent) behavior in the collinear limit

R = Rreg + Rdiv Rs

enters in the Sudakov form factor ∆s(pT (Φ))

Rdiv = Rs + Rf

the collinear divergent matrix elements can be split in the sum of their singular part plus a finite remainder

Alessandro Vicini - University of Milano CERN, December 16th 2013

Matching NLO matrix elements and Parton Shower

¯ Bs = B(ΦB) +

• V (ΦB) +
• dΦR|BRs(ΦR|B)
• dσNLO+PS = dΦB ¯

Bs(ΦB)

• ∆s(pmin

⊥ ) + dΦR|B

Rs(ΦR) B(ΦB) ∆s(pT(Φ))

• + dΦRRf(ΦR),+dΦRRreg(ΦR)

is the sum of all the real emission squared matrix elements, with a regular (divergent) behavior in the collinear limit

R = Rreg + Rdiv Rs

enters in the Sudakov form factor ∆s(pT (Φ))

Rdiv = Rs + Rf

the collinear divergent matrix elements can be split in the sum of their singular part plus a finite remainder at low ptH, the damping factor → 1, R_div tends to its collinear approximation, at large ptH, the damping factor → 0 and suppresses R_div in the Sudakov and in the square bracket the scale h fixes the upper limit for the Sudakov form factor to play a role, effectively is the upper limit for the inclusion of multiple parton emissions the total cross section does NOT depend on the value of h

Rs = h2 h2 + p2

T

Rdiv Rf = p2

T

h2 + p2

T

Rdiv

Rf = R − Rs Rs ∝ αs t Pij(z)B(ΦB)

MC@NLO POWHEG

Alessandro Vicini - University of Milano CERN, December 16th 2013

Quark mass effects after the resummation of multiple gluon emissions (end 2013)

0.6 0.64 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 1 1.04 1.08 1.12 1.16 1.2 1.24 1.28 20 40 60 80 100 R pH

⊥ (GeV)

quark mass effects: POWHEG vs Hres LHC 8 TeV, mH = 125 GeV R =

σ(t,h=mH/1.2)+σ(t+b,h)−σ(t,h) σHQET (h=mH/1.2)

h=4.75 GeV h=9.5 GeV h=19 GeV Hres Q2 = mb

• HRes: two different resummation scales (Q1 and Q2)

POWHEG: two different values of the parameter h (ht and hb) MC@NLO: two different scales at which the shower is switched off

• good agreement in the comparison of (MC@NLO, POWHEG) vs HRes
• the “old” differences between MC@NLO and POWHEG apparently stem from the region of

intermediate ptH, together with the unitarity constraint

• the Higgs ptH spectrum, with quark masses, is a 3 scales problem (mb, MH, mt),

the first “threshold” of the hard scattering process is at ptH ~ mb

high scale low scale

• M. Grazzini, H. Sargsyan, arXiv:1306.4581

|M(t + b)|2 = |M(t)|2 + ⇥ 2ReM(t)M†(b) + |M(b)|2⇤

MC@NLO HRes

Q2=mb Q2=MH

Alessandro Vicini - University of Milano CERN, December 16th 2013

Exact matrix elements and collinear limit

|M(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3

div

(m)/pH

⊥ + Mλ1,λ2,λ3 reg

(m)|2

C(pH

⊥) =

|Mexact(pH

⊥)|2

|Mdiv(pH

⊥)/pH ⊥|2

• we discuss the validity of the collinear approximation of the amplitude,

to find the value of ptH where the non-factorizable terms become important; a 10% deviation is considered relevant

• the breaking of the collinear approximation signals that

the log(ptH) resummation formalism, which is based on the collinear factorization hypothesis can not be applied in a fully justified way

Alessandro Vicini - University of Milano CERN, December 16th 2013

Exact matrix elements and collinear limit

|M(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3

div

(m)/pH

⊥ + Mλ1,λ2,λ3 reg

(m)|2

C(pH

⊥) =

|Mexact(pH

⊥)|2

|Mdiv(pH

⊥)/pH ⊥|2

• we discuss the validity of the collinear approximation of the amplitude,

to find the value of ptH where the non-factorizable terms become important; a 10% deviation is considered relevant

• the breaking of the collinear approximation signals that

the log(ptH) resummation formalism, which is based on the collinear factorization hypothesis can not be applied in a fully justified way

• 8 helicity amplitudes:

related by parity (4+4) and by the symmetry of the process

• we discuss, at fixed partonic s , the 3 amplitudes

with a soft+collinear or only collinear divergence for u→0

• dominance of the amplitudes with soft+collinear divergence

50 100 150 200 250 300 ptH HGeVL 50 100 150 200 »M»^2

|M+++|2

|M++−|2

|M−++|2

• the results depend on partonic s; the choice of the smallest possible s allowed value guarantees

that the contribution under study has the largest PDF weight at hadron level (small changes when using other choices of s)

Alessandro Vicini - University of Milano CERN, December 16th 2013

Deviation from the collinear approximation of the exact squared helicity amplitudes

50 100 150 200 250 300 ptH 0.2 0.4 0.6 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 ptH 0.2 0.4 0.6 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 ptH 0.2 0.4 0.6 0.8 1.0 1.2 1.4 C

|M−++|2 |M++−|2 |M+++|2

ratio of squared amplitudes evaluated with: only top, only bottom, top+bottom

• only top amplitudes are well approximated by the collinear part up to ptH ~ O(50-60)
• only bottom amplitudes are well approximated by the collinear part up to ptH ~ 20 GeV
• top+bottom results are modified by regular terms starting from ptH ~ 50 GeV
• the top-bottom interference reduces the range of validity of the “only-top” collinear approximation
• since the resummation is applied on the squared matrix elements summed over helicities,

we need to identify one single scale valid for all the helicities

• the scale can be read combining the information from individual amplitudes and from their sum

Alessandro Vicini - University of Milano CERN, December 16th 2013

POWHEG comparison of two-scales vs one-scale approaches

• ht: 50 GeV (from helicity analysis) and 90 (from tuning with HRes)

hb: 4 mb (from helicity analysis) and mb (as in HRes)

• in the SM the top-quark amplitude is dominant and thus the choice of ht is crucial for the shape
• differences appear in the low (ptH<10 GeV) and in the intermediate (20<ptH<50 GeV) regions
• setting hb=4 mb obviously reduces the difference between the two approaches
• in the intermediate ptH region, the differences do not exceed the 5% level

0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD 50 50, mb 50,4 mb 90 90, mb 90, 4 mb

• 40
• 30
• 20
• 10

10 20 30 40 50 100 150 200 δ(%) pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD δ = two-scale approach vs the one-scale (same ht) 50 50, mb 50,4 mb 90 90, mb 90, 4 mb

POWHEG

Alessandro Vicini - University of Milano CERN, December 16th 2013

POWHEG comparison of PYTHIA 6 vs PYTHIA 8 effects

• starting from the same LHEF events, shower with PYTHIA8 AU2 CTEQ6L

PYTHIA6.4

• important change (-7%) of the height of the peak of the distribution (from PY6 to PY8)
• unitarity forces the high-ptH tail of the distribution to increase, by +7%, for ptH>70 GeV
• the effect is almost independent of the chosen value of h
• the tuning of h is affected by the change of the shower (PYTHIA6 h = MH/1.2 ~105 GeV,

PYTHIA8 h = ~90 GeV )

0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD PYTHIA 8 tune AU2-CTEQ6L1 vs PYTHIA 6.4 h = 50 PYTHIA 6 h = 50 PYTHIA 8 h = 100 PYTHIA 6 h = 100 PYTHIA 8

• 10
• 5

5 10 15 20 50 100 150 200 δ(%) pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD δ = PYTHIA8

PYTHIA6 − 1

• ∗ 100

PYTHIA 8 tune AU2-CTEQ6L1 vs PYTHIA 6.4 h = 50 h = 100

Alessandro Vicini - University of Milano CERN, December 16th 2013

Tuning POWHEG to mimic the HRes shape

• HRes scales fixed at: Q1=MH/2, Q2=mb

POWHEG scales scanned over: 50 < ht < 150 GeV (5 GeV steps), mb/2 < hb < 2 mb (1 GeV steps)

• for each scale choice in POWHEG, compute χ²; look for the global minimum
• two χ² definitions: w(i) constant, w(i) proportional to the xsec

(prop. to xsec → more importance to the peak, constant → more importance to the tail)

• the comparison of the shapes allows to apply a global rescaling factor

K_NNLO = σ_NNLO / σ_NLO = 1.254

χ2 = X

i∈bins

w(i)  1 σHRes

tot

dσHRes

i

dpH

⊥

− 1 σP OW HEG

tot

dσP OW HEG

i

dpH

⊥

2

Alessandro Vicini - University of Milano CERN, December 16th 2013

Tuning POWHEG to mimic the HRes shape at LO+NLL

0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD HRes POWHEG (55,2 mb) POWHEG h = 55

• 30
• 20
• 10

10 20 30 50 100 150 200 δ(%) pH

⊥ (GeV)

LHC 14 TeV LO+NLL QCD δ = POWHEG

HRes − 1

• ∗ 100

HRes POWHEG (55,2 mb) POWHEG h = 55

• at LO+NLL the result does not depend on w(i)

the preferred ht ~ Q1, a variation of hb modifies χ² at the percent level

• the preferred h is close the Q1=MH/2
• ne scale fit h=55 GeV

two scales fit ht=55 GeV, hb=2 mb

Alessandro Vicini - University of Milano CERN, December 16th 2013

Tuning POWHEG to mimic the HRes shape at NLO+NNLL

0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

LHC 14 TeV NLO+NNLL QCD HRes POWHEG (85,2mb) POWHEG h = 85 POWHEG h = 95

• 30
• 20
• 10

10 20 30 50 100 150 200 δ(%) pH

⊥ (GeV)

LHC 14 TeV NLO+NNLL QCD δ = POWHEG

HRes − 1

• ∗ 100

HRes POWHEG (85,2mb) POWHEG h = 85 POWHEG h = 95

• HRes predictions computed with Q1=MH/2 and Q2=mb
• a large value of h forces POWHEG to mimic the large ptH tail of the HRes NLO+NNLL
• the best fit mimics the shape at the ±5% level for ptH<100 GeV
• the fit results depends on the importance ( w(i) ) that we give to the tail of the distribution
• the use of PYTHIA8 forces the tuning towards smaller values of ht (w.r.t. PYTHIA6)

POWHEG rescaled by K_NNLO

• ne scale fit h=85 GeV w(i) prop.to xsec

h=95 GeV w(i) constant two scales fit ht=85 GeV, hb=2 mb

POWHEG rescaled by K_NNLO

Alessandro Vicini - University of Milano CERN, December 16th 2013

POWHEG resummation uncertainty band compared to HRes

0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

LHC 14 TeV (NLO+NNLL)-QCD Q1,2 vs ht,b uncertainty bands HRes min-max POWHEG min-max POWHEG (80,2mb) POWHEG (150,mb/2)

• the lower (upper) edge of the (rescaled) POWHEG envelope

has an integrated xsec compatible with the corresponding HRes lower (upper) edge integrated xsec at the 6% (2%) level scale variation HRes at NLO+NNLL: MH/4 < Q1<MH, mb/2 < Q2 < 2 mb POWHEG: 50 < ht < 150 GeV, mb/2 < hb < 2 mb for fixed renormalization and factorization scales μR=μF=MH min-max envelope: in each bin consider the minimum and the maximum values

• the POWHEG predictions, rescaled by a global factor K_NNLO, are compatible with the HRes results

the POWHEG uncertainty band, varying ht and hb, is comparable in width with the one by HRes for ptH<200 GeV, there is not a clear need for a differential reweighting for ptH>200 GeV the NLO+NNLL HRes results or the merging of H and HJ sample (cfr. NNLOPS) are necessary

Alessandro Vicini - University of Milano CERN, December 16th 2013

Conclusions

• the scales Q and h set the low-ptH region where resummation (PS) effects are included;

low- and high-ptH regions are correlated by unitarity;

• analysis with helicity amplitudes → Ansatz for the scale where the collinear approximation fails
• nly-top, only-bottom and top+bottom cases have different typical scales
• a comparison at LO+NLL between the one-scale and two-scales approaches shows differences

at most at the 5% level in the intermediate (15< ptH <50 GeV) region and at percent level above; the role of the bottom is crucial for ptH<10 GeV, with larger differences

• the impact of the Parton Shower formulation and tune is important (±7% PY6 vs PY8)
• the scale h can be chosen with two different attitudes:

1) following the fixed-order helicity amplitudes analysis ( relevant in BSM studies! cfr 2HDM talk) 2) as a tool to mimic the NLO+NNLL shape by HRes ( larger value than from helicity analysis )

• the usage of POWHEG-H, rescaled by K_NNLO, provides

results compatible with HRes for ptH< 200 GeV → no clear need for differential reweighting; for ptH>200 GeV a full NLO+NNLL analysis (HRes) or the merging of H and HJ samples (cfr. NNLOPS) is necessary

Alessandro Vicini - University of Milano CERN, December 16th 2013

Back-up

Alessandro Vicini - University of Milano CERN, December 16th 2013 0.001 0.01 0.1 1 50 100 150 200 dσ/dpH

⊥ (pb/GeV)

pH

⊥ (GeV)

HRes LHC 14 TeV mH/4 ≤ Q1 ≤ mH mb/2 ≤ Q2 ≤ 2mb envelope of min-max predictions LO+NLL NLO+NNLL 10 20 30 40 50 50 100 150 200 δ(%) pH

⊥ (GeV)

HRes LHC 14 TeV δ = max−min

max+min ∗ 100

size of the envelope of min-max predictions LO+NLL NLO+NNLL

HRes uncertainty bands at LO+NLL and at NLO+NNLL

Alessandro Vicini - University of Milano CERN, December 16th 2013

Collinear approximation of the full amplitude summed over helicities

50 100 150 200 250 300 ptH HGeVL 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 ptH HGeVL 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 ptH HGeVL 0.8 1.0 1.2 1.4 C

|M(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3(m)|2 = X

λ1,λ2,λ3=±1

|Mλ1,λ2,λ3

div

(m)/pH

⊥ + Mλ1,λ2,λ3 reg

(m)|2

C(pH

⊥) =

|Mexact(pH

⊥)|2

|Mdiv(pH

⊥)/pH ⊥|2

sum over helicities of the amplitudes evaluated with:

• nly top, only bottom, top+bottom