Advances in QCD Theory Christopher Lee Los Alamos National - PowerPoint PPT Presentation

Advances in QCD Theory Christopher Lee 
 Los Alamos National Laboratory 
 Theoretical Division August 3, 2017

A handful of Advances in QCD Theory Christopher Lee 
 Los Alamos National Laboratory 
 Theoretical Division August 3, 2017

Fermi and Los Alamos Valles Caldera, near Los Alamos, May 8, 1945

Fermilab and Los Alamos • Drell-Yan: E772/E789/E866 (NuSea)/E906 (SeaQuest), E1039 Geoff Mills, 1955-2017

My charge “ QCD theory developments 
 over the last ~2 years”

Two years ago Christopher Lee, 
 May 27, 1922 
 — June 7, 2015 750 GeV , 3 . 6 σ December 2015 
 — August 2016

Historic Day: July 4

Historic Day: July 4 2012 m H = 125 GeV /c 2 San Diego 
 “Big Bay Boom”

Historic Day: July 4 2012 2017 Andreas Maria Lee, 
 m H = 125 GeV /c 2 Los Alamos, NM m AML San Diego 
 = 1 . 813 × 10 27 GeV /c 2 “Big Bay Boom”

EFTs 
 SCET, NRQCD, 
 pQCD 
 HQET, χ PT N k LO, factorization, Parton resummation showers, Monte Carlo Unitarity, PDFs 
 QCD Amplitudes quasi-PDFs, nPDFs AdS/CFT 
 AdS/QCD Lattice QCD Phases of QCD 
 Confinement, QGP … New observables 
 Jet algorithms, substrucure, grooming

Outline • Soft Collinear Effective Theory • N -Jettiness, SCET I, N 3 LL resummation • SCET II and N 3 LL resummed TMD distributions • Subtractions and NNLO cross sections • Non-Global Logarithms, fixed order and resummed • Jet substructure and SCET + • Outlook

Formation of Jets in QCD Hadronization at late time Perturbative soft and at low energy scale Λ QCD collinear splittings happen p α s � 1 at intermediate time K α s . 1 α s . 1 π π 1 probability of splitting ∼ E g (1 − cos θ ) ρ θ E g soft and collinear enhancements • Need to resum large perturbative logs e or p • Separate pert. and non-pert. physics • Both are problems of scale separation: a job for EFT Production of a new jet suppressed by α s ⌧ 1 e or p

History of Jets in QCD • Existence of gluons: • Measurements of strong coupling: event shapes 10 PDG, RPP (2015-16) • Boosted heavy particles in SM and BSM b Top Jets b H b W t Higgs Jets

Separation of scales • Large logs in QCD arise from large ratios of physical scales defining the measurement or degree of exclusivity of a jet cross section. • For jet cross sections, these are precisely ratios of hard to soft scales and ratios of collinear momentum components. ⇣ m 2 Q , m 2 Q , m 2 ⌘ • e.g. measurement of jet mass J J J p S ∼ Q J = ( p c + p s ) 2 = m 2 p 2 Q, m 2 ⇣ ⌘ J J p c ∼ Q , m J p = (¯ n · p, n · p, p ⊥ ) Hierarchy of Hard µ H = Q scales Jet Factorize cross section µ J = m J into pieces depending on only one of these µ S = m 2 Soft scales at a time. J Q

Soft Collinear Effective Theory • Modern tools for high precision resummation, factorization of Bauer, Fleming, Luke, Pirjol, Stewart perturbative and nonperturbative effects (1999-2001) QCD: SCET: collinear to n 1 ⊗ C ( Q, µ ) × Power hard expansion decoupled collinear collinear matching decoupled soft jet/beam functions to n 2 coefficient function • RG Evolution • Resummation of large logs α s (ln 2 τ + ln τ ) µ H = Q ln σ ( τ ) ∼ hard scale s (ln 3 τ + ln 2 τ + ln τ ) + α 2 s (ln 4 τ + ln 3 τ + ln 2 τ + ln τ ) + α 3 µ J,B = Q √ τ jet/beam scale . . . . . . . . + . . . . µ S = Q τ soft scale Leading 
 Next-to- 
 N 3 LL NNLL Log (LL) Leading Log 
 (NLL)

Bauer, Fleming, Luke (2000) 
 Bauer, Fleming, Pirjol, Stewart (2001) Bauer, Fleming, Pirjol, Rothstein, Stewart (2002) Soft Collinear Effective Theory • SCET I • SCET II Theory for jets constrained by mass Theory for jets constrained by transverse momentum 
 or for exclusive collinear hadrons Remove Remove hard modes hard modes a = 0 E + p z from theory E + p z a = 0 collinear hard collinear Q hard Q p 2 ∼ Q 2 p 2 ∼ Q 2 soft Q η anti-collinear anti-collinear Q η 2 Q λ 2 p 2 ∼ Q 2 λ 2 p 2 ∼ Q 2 η 2 soft p 2 ∼ Q 2 λ 4 E − p z Q η 2 Q Q η Q λ 2 E − p z Q Hard separated from coll. and soft by virtuality, • collinear & soft separated by rapidity Hard, collinear, soft all separated by virtuality • Inherits SCET I collinear-soft decoupling • Collinear/soft decoupling and factorization • Dim. Reg. regulates virtuality divergences but not • rapidity divergences need additional regulator Dim. Reg. regulates all divergences • Chiu, Jain, Neill, Rothstein (2011, 2012)

Challenges to Precision Jet Cross Sections • Jet cross sections typically depend on • choice of jet algorithm • jet sizes • jet vetoes (for exclusive jet cross sections) • These parameters generate a number of logarithms (non- global logs, logs of radii R , etc.) in perturbation theory which are challenging to resum • N -Jettiness : a global observable picking out N -jet final states by measurement of a single parameter, logs of which can be resummed in perturbation theory by standard RGE

N -jettiness Stewart, Tackmann, Waalewijn (2010) • A global event shape measuring degree to which final state is N -jet-like. 
 (small N -jettiness vetoes events with more than N jets.) τ N = 2 X min { q A · p k , q B · p k , q 1 · p k , . . . , q N · p k } Q 2 # beams # jets k groups particles into regions, q 1 according to which vector q i is closest. p p q B q A Factorization and Resummation-friendly q N

N 3 LL resummation with SCET e + e - Thrust 
 d σ 1 Abbate, Fickinger, Hoang, d σ 1 Compare fixed order: (2-Jettiness) Mateu, Stewart (2010) d τ d τ σ σ 1.4 mod 1.4 Q = m Z Sum Logs, with S + gap Q = m Z Fixed Order 3 ’ 1.2 N LL O ( α 3 1.2 s ) 3 N LL O ( α 2 s ) 1.0 ’ 1.0 NNLL O ( α s ) NNLL 0.8 0.8 ’ NLL 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 τ τ e + e - Hemisphere Jet Mass e + e - C Parameter DIS ep 1-Jettiness 1.5 NLL Q = 100 GeV NNLL x = 0.1 N 3 LL � / d a τ 1 1.0 τ 1 d σ 0.5 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 τ 1 Chien, Schwartz (2010) Hoang, Kolodrubetz, Mateu, Stewart (2014) Kang, CL, Stewart (preliminary, 2017)

High precision strong coupling present extractions from SCET predictions for e + e - 
 event shapes PDG, RPP (2015) Hoang, Kolodrubetz, Mateu, Stewart (2015)

NNLL resummation for generic observables • We do not always have a factorization theorem available to make SCET and its RG evolution to achieve resummation • Monte Carlo implementation ARES (successor to NLL CAESAR) of emission amplitudes needed for NNLL Cambridge /Durham Jet Rates Banfi, LoopFest 2017 Banfi, McAslan, Monni, Zanderighi (2016)

High precision p T resummation at LHC d � Z 2 − | ~ T dy = � 0 H ( Q 2 , µ ) d 2 ~ q T s d 2 ~ q T 1 d 2 ~ q T 2 | 2 ) q T 2 � ( ~ q T s + ~ q T 1 + ~ q T dq 2 1 ( x 1 = Q 2 ( x 2 = Q q T s , µ, ⌫ ) f ⊥ √ se y , Q, ~ q T 1 , µ, ⌫ ) f ⊥ √ se − y , Q, ~ × S ( ~ q T 2 , µ, ⌫ ) • SCET II • Rapidity Renormalization Group a = 0 E + p z collinear hard Q p 2 ∼ Q 2 soft Q η anti-collinear Q η 2 p 2 ∼ Q 2 η 2 E − p z Q η 2 Q Q η Chiu, Jain, Neill, Rothstein (2011, 2012)

New rapidity regulator and 3-loop anomalous dimension Z d σ db bJ 0 ( bq T ) e S ( b, µ, ν ) e 1 ( b, Q, x 1 , µ, ν ) e T dy = σ 0 π (2 π ) 2 H ( Q 2 , µ ) f ⊥ f ⊥ 2 ( b, Q, x 2 , µ, ν ) dq 2 Z d 2 q T b ) ≡ 1 (2 ⇡ ) 2 e i ~ q T f ( ~ f ( ~ e e b ≡ | ~ f ( ~ e b · ~ b ) ≡ q T ) f ( b ) , b | 2 ⇡ Computation of beam or soft functions requires regulation of rapidity divergences: • Regulator: shift separation of soft Wilson lines defining soft function in Euclidean time • Li, Neill, Zhu (2016)

N 3 LL resummed p T spectrum • 3-loop soft function diagrams: • N 3 LL resummed results: resummed • 3-loop rapidity anomalous dimension: envelope Li, Neill, Schulze, Stewart, Zhu 
 (SCET2016, Argonne Advances in QCD 2016)

NNLO Subtractions Moult (LoopFest 2017)

N-Jettiness Subtractions • Exploit factorization and 2-loop computations of ingredients for small τ N Boughezal, Liu, Focke, Petriello (2015) 
 Gaunt, Stahlhofen, Tackmann, Walsh (2015) • High precision, numerical stability requires power corrections:

Subleading Power Corrections Moult, Rothen, Stewart, • SCET well formulated to compute power corrections: Tackmann, Zhu (2016) • Also computable in fixed-order QCD, dramatic improvement in independence: τ cut Boughezal, Liu, Petriello (2016)

NNLO Results V +jet • vs. data: • N -jettiness subtraction method vs. antenna subtraction: Boughezal, Liu, Petriello (2016)

NNLO Revolution X. Liu DPF 2017

Non-global logs • Global observable: 
 (thrust, N-jettiness) • Non-global observable: 
 (double hemisphere mass, 
 jet vetoes) D. Neill SCET 2017

Non-global logs Dasgupta, Salam (2001) • Start to spoil “global” resummation at 2 loops: α 2 π 2  � 3 ln 2 m H s σ ( m H /m L ) = σ gl ( m H /m L ) 1 + (2 π ) 2 C F C A + · · · m L Conjecture / fit to Monte Carlo resummation (large N c ): π 2 ✓ 1 + ( at ) 2  ◆ � t 2 S ng = exp − C F C A 1 + ( bt ) c 3 L = ln m H 1 1 t = ln m L 4 πβ 0 1 − 2 β 0 α s L a = 0 . 85 C A , b = 0 . 86 C A , c = 1 . 33 Dasgupta, Salam (2002)