Precise theoretical predictions for Large Hadron Collider physics
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1 Precise theoretical predictions for Large Hadron Collider physics Giancarlo Ferrera Milan University & INFN, Milan Milan June 28th 2017
2 Precise theoretical predictions for LHC physics 1/20 TIF LAB: particle physics phenomenology group Members: S. Forte (Head) G. Sborlini (Postdoc) A. Vicini Z. Kassabov (PhD) G. Ferrera C. Muselli (PhD) Strong connections with scientific activities at CERN. Interactions with the local particle physics experimental groups (in particular ATLAS and LHCb).
3 Precise theoretical predictions for LHC physics 2/20 High Energy Physics and the LHC Explore elementary constituents of matter and energy, their interactions. The Standard Model (SM) of elementary particles describes strong (QCD) and electroweak (EW) interactions. The Large Hadron Collider (LHC) at CERN is the world s largest particle accelerator ( ). It explores the unknown region of the TeV energy frontier (i.e m). The LHC is addressing many fundamental questions in High Energy Physics: What is the origin of the masses of the elementary particles? What is the nature of dark matter? Why is there a large matter and anti-matter asymmetry in the Universe? Do extra spatial dimensions exist? What is the connection between Higgs field and cosmological inflation?
4 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
5 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
6 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
7 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
8 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
9 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
10 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
11 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
12 Precise theoretical predictions for LHC physics 3/20 From Maxwell equations to Higgs boson E=ρ, B=0, E= B t, B= E t +j or µfµν =j ν (F µν = µ A ν ν A µ, j ν =(ρ,j)) L 0 = 1 4 Fµν F µν QED (massless photons) local gauge invariant (A µ A µ + µ λ(x)) How to describe massive vector bosons (e.g. weak interactions)? L m= 1 4 Fµν F µν+ m 2 2 Aµ A µ forbidden by gauge invariance (cannot quantize the theory!) How to add a mass term preserving gauge invariance? The Higgs mechanism (1964): L H = 1 4 Fµν F µν+ ( µ+iqa µ)φ 2 V(φ), φ complex scalar field (L H gauge inv. φ e θ(x) φ) V(φ)=α φ 2 +β φ 4, α<0, β>0, φ 0 = α 2β, φ=φ 0+h+iπ L H = 1 4 Fµν F µν+( µh) 2 q2 α 4β Aµ A µ+2αh 2 + Gauge invariance preserved! (Gauge bosons acquire mass through spontaneous symmetry breaking). It may look like a kind of magic, however extra massive scalar particle (h) appears: the Higgs boson! After a 50-year hunt...
13 Precise theoretical predictions for LHC physics 4/20 The Higgs boson discovery ( see M. Fanti talk) [ATLAS and CMS Coll. PLB716 ( 12)] On July 2012 the discovery of the Higgs boson at CERN: most important breakthrough in particle physics of the last 30 years. Understanding the electroweak symmetry breaking and the origin of the masses of the elementary particles. Next LHC goal: detailed measurement of the Higgs boson properties. Key to unravel deviation from Standard Model predictions. Besides Higgs boson discovery many outstanding results obtained by the LHC, and new discoveries are within the LHC reach in the next years.
14 Precise theoretical predictions for LHC physics 5/20 LHC key results: Higgs boson and much more Standard Model Production Cross Section Measurements Status: August 2016 σ [pb] total (x2) ATLAS Preliminary inelastic Theory nj 1 0.1<pT <2TeV nj 2 0.3<mjj <5 TeV pt>25 GeV pt >100GeV nj 0 nj 0 nj 1 nj 0 nj 2nj 1 nj 1 nj 3nj 2 nj 2 nj 3 nj 4 nj 3 nj 4 nj 5 nj 4 nj 5 nj 6 nj 5 nj 6 nj 7 nj 6 nj 7 nj 7 total nj 4 nj 5 nj 6 nj 7 nj 8 Run 1,2 t-chan Wt s-chan s = 7, 8, 13 TeV WW WZ ZZ WW WZ ZZ WW WZ ZZ total ggf H WW H ττ VBF H WW H γγ H ZZ 4l Zγ Wγ Zγ LHC pp s = 7 TeV Data fb 1 LHC pp s = 8 TeV Data 20.3 fb 1 LHC pp s = 13 TeV Data fb W ± W ± WZ pp Jets R=0.4 γ fid. W fid. Z fid. t t fid. t tot. VV tot. γγ fid. H fid. Vγ t tw t tz t tγ Zjj WW Zγγ WγγVVjj EWK Excl. EWK fid. tot. tot. fid. fid. tot. fid. fid. fid. Very good agreement between experimental results and SM theoretical predictions of the high-q 2 processes
15 Precise theoretical predictions for LHC physics 6/20 How to increase the discovery power of the LHC? The LHC is a hadron collider machine: all the interesting reactions initiate by QCD hard scattering of partons: a good control of the QCD processes is necessary. To fully exploit the information contained in the LHC experimental data, precise theoretical predictions of the Standard Model cross sections are needed.
16 Precise theoretical predictions for LHC physics 7/20 Theoretical predictions at the LHC F(Q) Parton densities (PDFs) Partonic hard cross section Parton Shower Jets (of hadrons)
17 Precise theoretical predictions for LHC physics 8/20 Theoretical predictions at the LHC F(Q) Parton densities (PDFs) Partonic hard cross section Parton Shower Jets (of hadrons)
18 Theoretical predictions at the LHC h 1 + h 2 F(Q) + X h 1 (p 1 ) > f a/h1 (x 1,µ 2 F ). a(x 1 p 1 ) F(Q) ˆσ ab The asymptotically free QCD coupling α S (Q) > h 2 (p 2 ) f b/h2 (x 2,µ 2 F ) b(x 2 p 2 )... X The framework: QCD factorization formula σh F 1 h 2 (p 1,p 2) = 1 1 ( dx 1 dx 2f a/h1 (x 1,µ 2 F)f b/h2 (x 2,µ 2 F)ˆσ ab(x F 1p 1,x 2p 2;µ 2 ΛQCD ) p F)+O a,b 0 0 Q f a/h (x,µ 2 F ): Non perturbative universal parton densities (PDFs), µ F Q. ˆσ ab : Hard scattering cross section. Process dependent, calculable with a perturbative expansion i the strong coupling α S (Q) (Q Λ QCD 1GeV). ( ) ΛQCD p Q (with p 1): Non perturbative power-corrections. Precise predictions for σ depend on good knowledge of both ˆσ ab and f a/h (x,µ 2 F) Precise theoretical predictions for LHC physics 9/20
19 Precise theoretical predictions for LHC physics 10/20 PDFs Parton densities (PDFs) Partonic hard cross section Parton Shower Jets (of hadrons)
20 Precise theoretical predictions for LHC physics 11/20 Fit of PDFs Method: typical parametrization of parton densities f a(x,µ 2 0) at input scale µ GeV 2. Parameters constrained by imposing momentum sum rules: 1 a dx x 0 fa(x,µ2 0) = 1, then adjust parameters to fit data. Typical constraining process: DIS (fixed target exp. and HERA): sensitive to quark densities. Jet data (HERA and Tevatron): sensitive to high-x gluon density. Drell-Yan (low energy and Tevatron data): sensitive to (anti-)quark densities. Evolution µ 0 µ using DGLAP equations: f a(x,µ 2 ) = α S(µ 2 ) 1 dξ lnµ 2 2π x ξ P ab(x/ξ)f b (ξ,µ 2 ) AP kernels calculable in pqcd P ab (z) = P (0) ab (z)+α SP (1) ab (z)+α2 S P(2) ab (z)+
21 Precise theoretical predictions for LHC physics 11/20 Fit of PDFs Method: typical parametrization of parton densities f a(x,µ 2 0) at input scale µ GeV 2. Parameters constrained by imposing momentum sum rules: 1 a dx x 0 fa(x,µ2 0) = 1, then adjust parameters to fit data. Typical constraining process: DIS (fixed target exp. and HERA): sensitive to quark densities. Jet data (HERA and Tevatron): sensitive to high-x gluon density. Drell-Yan (low energy and Tevatron data): sensitive to (anti-)quark densities. Evolution µ 0 µ using DGLAP equations: f a(x,µ 2 ) = α S(µ 2 ) 1 dξ lnµ 2 2π x ξ P ab(x/ξ)f b (ξ,µ 2 ) AP kernels calculable in pqcd P ab (z) = P (0) ab (z)+α SP (1) ab (z)+α2 S P(2) ab (z)+
22 Precise theoretical predictions for LHC physics 12/20 Recent results on PDFs xγ(x,q 2 ) Photon PDF comparison at 10 GeV x MRST2004QED NNPDF2.3QED average NNPDF2.3QED replicas NNPDF 1σ NNPDF 68% c.l Some recent developments: inclusion of LHC experimental data (W, Z/γ (at low/high invariant mass), isolated γ, jets, t t production). and inclusion of QED corrections and extraction of photon PDF (with uncertainty) from data NNPDF Coll. [Forte,Kassabov et al. ( 13, 14, 17)] (N3PDF ERC project). Photon PDF has to be consistently combined with the Altarelli-Parisi splitting functions with mixed QCD-QED corrections [de Florian,Rodrigo, Sborlini( 16)].
23 Precise theoretical predictions for LHC physics 12/20 Recent results on PDFs xγ(x,q 2 ) !"#$!%#$ 4 2 Photon PDF comparison at 10 GeV x MRST2004QED NNPDF2.3QED average NNPDF2.3QED replicas NNPDF 1σ NNPDF 68% c.l Some recent developments: inclusion of LHC experimental data (W, Z/γ (at low/high invariant mass), isolated γ, jets, t t production). and inclusion of QED corrections and extraction of photon PDF (with uncertainty) from data NNPDF Coll. [Forte,Kassabov et al. ( 13, 14, 17)] (N3PDF ERC project). Photon PDF has to be consistently combined with the Altarelli-Parisi splitting functions with mixed QCD-QED corrections [de Florian,Rodrigo, Sborlini( 16)].!&#$
24 Precise theoretical predictions for LHC physics 13/20 Partonic Hard Cross Section F(Q) Parton densities (PDFs) Partonic hard cross section Parton Shower Jets (of hadrons)
25 Precise theoretical predictions for LHC physics 14/20 Higher-order calculations Parton densities (PDFs) F Partonic cross section ˆσ X Factorization theorem σ= ( Λ f a(m 2 ) f b (M 2 ) ˆσ ab (α S ) + O M) a,b Perturbation theory at leading order (LO): ˆσ(α S) = ˆσ (0) + α S ˆσ (1) + α 2 S ˆσ (2) + O(α 3 S) LO result: only order of magnitude estimate. NLO: first reliable estimate. NNLO: precise prediction & robust uncertainty. Higher-order calculations not an easy task due to infrared (IR) singularities: impossible direct use of numerical techniques. (alternatives to standard techniques being explored [Rodrigo, Sborlini et al. ( 15, 16, 17)])
26 Precise theoretical predictions for LHC physics 14/20 Higher-order calculations Parton densities (PDFs) F Partonic cross section ˆσ X Factorization theorem σ= ( Λ f a(m 2 ) f b (M 2 ) ˆσ ab (α S ) + O M) a,b Perturbation theory at next order (NLO): ˆσ(α S) = ˆσ (0) + α S ˆσ (1) + α 2 S ˆσ (2) + O(α 3 S) LO result: only order of magnitude estimate. NLO: first reliable estimate. NNLO: precise prediction & robust uncertainty. Higher-order calculations not an easy task due to infrared (IR) singularities: impossible direct use of numerical techniques. (alternatives to standard techniques being explored [Rodrigo, Sborlini et al. ( 15, 16, 17)])
27 Precise theoretical predictions for LHC physics 14/20 Higher-order calculations Parton densities (PDFs) F Partonic cross section ˆσ X Factorization theorem σ= ( Λ f a(m 2 ) f b (M 2 ) ˆσ ab (α S ) + O M) a,b Perturbation theory at NNLO: ˆσ(α S) = ˆσ (0) + α S ˆσ (1) + α 2 S ˆσ (2) + O(α 3 S) LO result: only order of magnitude estimate. NLO: first reliable estimate. NNLO: precise prediction & robust uncertainty. Higher-order calculations not an easy task due to infrared (IR) singularities: impossible direct use of numerical techniques. (alternatives to standard techniques being explored [Rodrigo, Sborlini et al. ( 15, 16, 17)])
28 Precise theoretical predictions for LHC physics 14/20 Higher-order calculations Parton densities (PDFs) F Partonic cross section ˆσ X Factorization theorem σ= ( Λ f a(m 2 ) f b (M 2 ) ˆσ ab (α S ) + O M) a,b Perturbation theory at NNLO: ˆσ(α S) = ˆσ (0) + α S ˆσ (1) + α 2 S ˆσ (2) + O(α 3 S) LO result: only order of magnitude estimate. NLO: first reliable estimate. NNLO: precise prediction & robust uncertainty. Higher-order calculations not an easy task due to infrared (IR) singularities: impossible direct use of numerical techniques. (alternatives to standard techniques being explored [Rodrigo, Sborlini et al. ( 15, 16, 17)]) Drell-Yan process LO Drell,Yan (1974) NLO Altarelli,Ellis,Greco Martinelli,( ) NNLO Catani,Cieri,deFlorian, G.F.,Grazzini (2009)
29 Precise theoretical predictions for LHC physics 15/20 NNLO QCD predictions compared with LHC data pp W + X lν l + X pp γγ + X A l Data 2010 ( s = 7 TeV) MSTW08 HERAPDF1.5 ABKM09 JR09 Stat. uncertainty Total uncertainty [pb/rad] γγ dσ/d φ 10 2 ATLAS s = 7 TeV -1 Data 2011, Ldt = 4.9 fb DIPHOX+GAMMA2MC (CT10) 2γNNLO (MSTW2008) L dt = pb ATLAS η l Lepton charge asymmetry. Comparison between experimental data and NNLO predictions (DYNNLO [Catani,Cieri,deFlorian, G.F.,Grazzini ( 09),( 10)]) using various PDFs (from [ATLAS Coll.( 12)]). data/diphox data/2γnnlo Azimuthal diphoton separation. Comparison between exp. data, NLO and NNLO predictions (2γNNLO[Catani,Cieri,de Florian,G.F., Grazzini( 12)]) (from [ATLAS Coll.( 13)]). φ γγ [rad]
30 Precise theoretical predictions for LHC physics 16/20 NNLO QCD predictions at the LHC pp W + H + X l + νb b + X pp t t + X d /dp bb T [fb/gev] pp W + H+X l bb _ +X full NNLO NNLO(prod)+NLO(dec) s=13 TeV, m H=125 GeV 350 Renormalization Scale Variation: LHC 8 TeV µ R = µ F = M WH µ r = m H (pb) (full NNLO)/(NNLO(prod)+NLO(dec)) p bb T [GeV] 100 LO NLO 50 NNLO NNNLO NNLO+NNLL µ R/m Left panel: transverse momentum of the Higgs boson in production in NNLO (HVNNLO [G.F., Grazzini,Tramontano ( 11),( 14),( 15),( 17)]). Right panel: Total cross section for (dependence on unphysical renormalization scale) [Muselli,Bonvini,Forte,Marzani,Ridolfi( 15)].
31 Precise theoretical predictions for LHC physics 17/20 Parton Shower and Hadronization Parton densities (PDFs) Partonic hard cross section Parton Shower Jets (of hadrons)
32 Precise theoretical predictions for LHC physics 18/20 Parton Shower and Hadronization Complete description of a hadron scattering event. QCD parton shower (PS): Starting from LO QCD, inclusion of dominant collinear and soft-gluon emissions to all order in a approximate way as a Markov process (probabilistic picture). No analytic solution but simple iterative structure of coherent parton branching. Implemented in numerical Monte Carlo programs. QCD parton cascade matched with hadronization model for conversion of partons into hadrons (and model for resonance decay) QCD event generators. Scheme of QCD Parton Shower and hadronization in hadron collisions.
33 % 2 2 Precise theoretical predictions for LHC physics 19/20 Parton shower at NLO pp W + X lν + X pp Z/γ + X l + l + X (pb/gev) W dm d 1 2 d d PWG EW w shower - 2. PWG w shower EW NLO - 2. BORN M W (GeV) d d PWG EW w PYTHIA+PHOTOS PWG w PYTHIA EW NLO BORN Transverse mass (left panel) and lepton transverse momentum (right panel) distribution in vector boson production. Parton shower predictions at NLO QCD EW accuracy. Relative size of EW and QCD EW corrections (lower panels) [Vicini et al.( 12, 13, 17)].
34 Precise theoretical predictions for LHC physics 20/20 Conclusions The LHC is exploring the unknown region of the TeV energy frontier, trying to address many fundamental questions in High Energy Physics. Main message: to increase the LHC discovery power, accurate theoretical predictions are necessary precise parton density (PDFs) determinations and higher-order perturbative calculations in QCD (and EW theory). The members (including the younger ones) of TIF Lab obtained significant results relevant to the physics program of the LHC.
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