C1 s } 1 C b Ca } } 2 Soft-Collinear Effective Field Theory } Thomas Becher Bern University CUSOC Graduate2 Course, EPFL, Nov. 2015 Tools for QFT computations Expansion Expansion in in the interaction scale ratios: strength: Effective Field perturbation Theories theory Toy models: Numerical solvable models methods: SUSY theories lattice simulations AdS/CFT Jet physics at the LHC Many scale hierarchies! ps pT M E m ⇤ Jet Jet out proton ⇠ QCD → Soft-Collinear Effective Theory (SCET) Outline of the course • Invitation: perturbative QCD and effective field theory • The method of regions • a simple example • Scalar Sudakov form factor • Introduction to perturbative QCD / introduction to EFT • Scalar SCET • factorization for the scalar Sudakov form factor in d=6 • Generalization to QCD Outline […] • Sudakov form factor in QCD • Resummation by RG evolution • Drell-Yan process near partonic threshold • Factorization for generic Drell-Yan • Factorization constraints on infrared divergences in n-point amplitudes • Factorization and resummation for cone-jet processes (1508.06645 with Neubert, Rothen and Shao). Literature A few selected original references are: Original SCET papers (using the label formalism): • C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, PRD 63, 114020 (2001) [hep-ph/0011336] • C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, Soft-Collinear Factorization in Effective Field Theory, PRD 65, 054022 (2002) [hep-ph/0109045] SCET in position space: • M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann,``Soft- collinear effective theory and heavy-to-light currents beyond leading power,'' Nucl. Phys. B643, 431 (2002) [arXiv:hep-ph/ 0206152] Sample collider physics applications: Factorization analysis for DIS, Drell-Yan and other processes • C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, PRD 66, 014017 (2002) [hep-ph/0202088]. Threshold resummation in momentum space using RG evolution, threshold resummation for Drell-Yan • TB and M. Neubert, Threshold resummation in momentum space from effective field theory, PRL 97, 082001 (2006), [hep-ph/0605050] • TB, M. Neubert and G. Xu, Dynamical Threshold Enhancement and Resummation in Drell-Yan Production,’' JHEP 0807, 030 (2008) [0710.0680] EFT analysis of the IR structure of gauge theory amplitudes • TB and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, PRL 102, 162001 (2009) [0901.0722]; On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP 0906, 081 (2009) [0903.1126]; Infrared singularities of QCD amplitudes with massive partons, PRD 79, 125004 (2009) [0904.1021] Factorization for cone-jet processes • TB, M. Neubert, L. Rothen and D.Y. Shao, An effective field theory for jet processes 1508.06645 Lecture Notes in Physics 896 Thomas Becher Alessandro Broggio Andrea Ferroglia Introduction to Soft-Collinear Ef ective Theory arXiv:1410.1892 Will follow this book for parts of the lecture, in particular for the construction of the EFT. The book also contains a chapter with a review of the many application of SCET • Heavy-quark physics • B-physics, top physics, unstable particle EFT • Collider physics • Event shapes, jets, threshold resummation, transverse momentum resummation, electroweak Sudakov resummation • Others: Heavy-ion collisions, soft-collinear gravity, … and a guide to the associated literature. Alternative SCET introduction edX online course on effective field theory by Iain Stewart, see https://www.edx.org/course/effective-field- theory-mitx-8-eftx • Video lectures on SCET and other EFTs • includes a set of TASI lecture notes on SCET by Christian Bauer and Iain Stewart • Uses and introduces the label formalism. R-ratio 6 46. Plots of cross sections and related quantities + σ and R in e e− Collisions -2 10 ω φ / -3 J ψ 10 ψ(2S) ρ′ Υ -4 ρ 10 Z -5 10 [mb] σ -6 10 6 46. Plots of cross sections and related quantities -7 10 + − -8e e → hadrons:σ and R in e+e crossCollisions section 10 − 2 -2 1 10 10 10 ω φ J/ψ -3 Υ 10 3 / 10 J ψ ψψ(2S)) ρ′ Υ Z -4 ρ 10 Z 10 2 -5 φ 10 ω R [mb] σ 10 -6 10 ρ′ -7 101 -8 ρ 10 -1 10 2 1 10 10 2 1 10 10 √s [GeV] 3 Υ 10 J/ψ Figure 46.6: World data on the total cross section of e+e−ψ(2hadronsS) and the ratio R(s)=σ(e+e− hadrons, s)/σ(e+e− µ+µ−,s). σ(e+e− hadrons, s)istheexperimentalcrosssectioncorrectedforinitialst→ ate radiation and electron-positron→ Z vertex loops,→σ(e+e− µ+µ−,s)=4→ πα2(s)/3s.Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV.Thecurvesareaneducativeguide:thebrokenone→ (green) is a naive2 quark-parton model prediction, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” section of this Review,Eq.(910 .7) or, for more details, K. G. Chetyrkin et al.,Nucl.Phys.B586,56(2000)(Erratumibid. B634,413(2002)).Breit-Wigner parameterizations of J/ψ, ψ(2S), and Υφ(nS),n =1, 2, 3, 4arealsoshown.Thefulllistofreferencestotheoriginaldata and the details of the R ratio extraction from themω can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are available at http://pdg.lbl.gov/current/xsect/R .(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups, May 2010.) 10 ρ′ 1 ρ -1 10 2 1 10 10 √s [GeV] Figure 46.6: World data on the total cross section of e+e− hadrons and the ratio R(s)=σ(e+e− hadrons, s)/σ(e+e− µ+µ−,s). σ(e+e− hadrons, s)istheexperimentalcrosssectioncorrectedforinitialst→ ate radiation and electron-positron→ vertex loops,→σ(e+e− µ+µ−,s)=4→ πα2(s)/3s.Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV.Thecurvesareaneducativeguide:thebrokenone→ (green) is a naive quark-parton model prediction, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” section of this Review,Eq.(9.7) or, for more details, K. G. Chetyrkin et al.,Nucl.Phys.B586,56(2000)(Erratumibid. B634,413(2002)).Breit-Wigner parameterizations of J/ψ, ψ(2S), and Υ(nS),n =1, 2, 3, 4arealsoshown.Thefulllistofreferencestotheoriginaldata and the details of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are available at http://pdg.lbl.gov/current/xsect/.(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups, May 2010.) 6 46. Plots of cross sections and related quantities + σ and R in e e− Collisions -2 10 ω φ / -3 J ψ 10 ψ(2S) ρ′ Υ -4 ρ 10 Z -5 10 [mb] σ -6 10 -7 10 -8 10 R-ratio 2 1 10 10 Υ 3 / 10 J ψ ψ(2S) Z 10 2 φ R ω 10 ρ′ 1 ρ -1 10 2 1 10 10 √s [GeV] Figure 46.6: World data on the total cross section of e+e− hadrons and the ratio R(s)=σ(e+e− hadrons, s)/σ(e+e− µ+µ−,s). σ(e+e− Thehadrons, green s)istheexperimentalcrosssectioncorrectedforinitialst dashed line is our LO→ predictionate radiation after and inclusion electron-positron→ of vertex quark loops,→σ (e+e− µ+µ−,s)=4→ πα2(s)/3s.Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV.Thecurvesareaneducativeguide:thebrokenone→ (green) ismasses a naive quark-parton and Z model-exchange. prediction, and Red the solid line one (red) includes is 3-loop pQCD NNLO prediction (seeQCD “Quantum corrections. Chromodynamics” section of this Review,Eq.(9.7) or, for more details, K. G. Chetyrkin et al.,Nucl.Phys.B586,56(2000)(Erratumibid. B634,413(2002)).Breit-Wigner parameterizations of J/ψ, ψ(2S), and Υ(nS),n =1, 2, 3, 4arealsoshown.Thefulllistofreferencestotheoriginaldata and the details of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are available at http://pdg.lbl.gov/current/xsect/.(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups, May 2010.) 46. Plots of cross sections and related quantities 7 R in Light-Flavor, Charm, and Beauty Threshold Regions 10 2 φ u, d, s ω 3looppQCD 10 Naive quark model ρ ρ′ 46. Plots of cross sections and related quantities 7 1 Sum of exclusive Inclusive R in Light-Flavor,measurements Charm, and Beauty Thresholdmeasurements Regions -1 10 0.5 1 1.5 2 2.5 3 1072 ψ(2S) J/ψ φ u, d,ψ s4160 c 6 ωMark-I Mark-I + LGW 3looppQCD ψ4415 Mark-II ψ4040 5 Naive quark model 10 PLUTO ψ3770 R ρ DASP ρ′ 4 Crystal Ball BES 13 b-quark threshold region 2 Sum of exclusive Inclusive measurements measurements -1 10 3 3.5 4 4.5 5 0.5 1 1.5 2 2.5 3 78 Υ(1S) ψ(2S) Υ(3S) b 7 J/ψ Υ(2S) ψ4160 c 6 Mark-I Υ(4S) 6 Mark-I + LGW ψ4415 Mark-II ψ4040 5 ψ3770 5 PLUTO R DASP 44 Crystal Ball BES 3 ARGUS CLEO CUSB DHHM 3 MD-1 2 Crystal Ball CLEO II DASP LENA 2 9.5 10 10.5 11 3 3.5√s [GeV] 4 4.5 5 Figure 46.7: 8R in the light-flavor, charm, and beauty threshold regions. Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV. The curves are the same as in Fig. 46.6.Υ(1Note:S) CLEO data above Υ(4S)werenotfullycorrectedforradiativeeΥ(3S) ffects,b and we retain them on the plot7 only for illustrative purposes with a normalΥ(2izationS) factor of 0.8. The full list of references to the original data and the details of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114].Thecomputer-readabledataareavailableatΥ(4S) http://pdg.lbl.gov/current/xsect/.(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups, May 2010.) 6 5 4 3 ARGUS CLEO CUSB DHHM MD-1 2 Crystal Ball CLEO II DASP LENA 9.5 10 10.5 11 √s [GeV] Figure 46.7: R in the light-flavor, charm, and beauty threshold regions.