Logarithmic accuracy of parton showers Mrinal Dasgupta University

Logarithmic accuracy of parton showers Mrinal Dasgupta University of Manchester LHCP 2019, Puebla, Mexico Based on JHEP 1809 (2018) with Frederic Dreyer, Keith Hamilton, Pier Francesco Monni and Gavin Salam

Outline • • • Parton showers and their accuracy Transverse momentum ordered dipole showers. Issues with recoil attribution Issues with colour factor treatment Consequences for standard observables What may we expect in the near future?

Parton showers Elements of GPMC for LHC • Core component of all GPMCs used in virtually all high energy collider analyses. • Beyond SM hard process the only component directly connected to SM (QCD) Lagrangian. Holds the key to precision in MC approach.

Showers and multiple scales • Any LHC process involves huge scale hierarchy. • Showers describe evolution from Te. V scale of hard process down to ~ 1 Ge. V. • Many observables sensitive to multiple disparate scales.

Logarithmic accuracy Single scale observable. Accuracy specified by maximum n. Multiscale observable. Accuracy specified by n and m. • g 1 is leading log (LL). Controls all double log (m= 2 n) terms in expansion. • Including g 2 gives NLL and g 3 is NNLL. • NLL is a must for accurate pheno. Multiscale observable with exponentiation. Accuracy depends on gn Catani, Trentadue, Turnock and Webber 1992

Logarithmic accuracy and showers But what do we know about shower accuracy? Widespread belief showers certainly give LL accuracy. Common belief that showers in practice NLL accurate for several important observables. Based on inclusion of NLL ingredients in shower : hard-collinear splittings, running coupling effects, control over coupling scheme etc. Resummation is a delicate BEWARE ! business. Long history of Widespread belief Proof mistakes. NLL ingredients NLL result MISSING: a framework to evaluate shower accuracy let alone improve it.

Dipole showers Angular ordered parton shower (HERWIG) : starting point is collinear limit and fixes soft limit accounting for coherence. But misses a class of single logarithms : non-global logarithms. Dipole showers start from soft limit. Sequence of 2 to 3 soft splittings. Comes with question : how to assign recoil? Formulated in large Nc limit for simplicity. Partially corrected by using right colour factor e. g. CF for emission off quark leg.

Dipole branching Note use of CA/2 colour factor. Large Nc limit Represented by Lund “Origami” diagrams Emissions are ordered in suitable evolution variable

Pythia and Di. Re showers Studied 2 dipole showers: • Pythia 8 shower since most widely used • Di. Re available in both Pythia and Sherpa MC Both are ordered in type of dipole. Sjostrand Skands 2004 Hoeche and Prestel 2015 and keep recoil local within emitting First soft gluon emission from hard dipole correct in both.

Partitioning dipole emission MD, Dreyer, Hamilton, Monni and Salam 2018 • Dipole emission split into two “halves” with one leg acting as emitter with other as spectator. • The crossover happens at frame. in dipole rest • Transverse recoil taken by emitter. Bad choice beyond 1 st emission !

Issues with 2 emissions Double strong ordered config : Emits with weight Transition from CA/2 to CF in wrong place! Radiation collinear to quark has CA/2 component, Emits with weight

Issues with 2 emissions Single strong ordered config : k 1 takes transverse recoil from k 2 although k 2 collinear to quark. MD, Dreyer, Monni, Hamilton and Salam 2018 Example with

Double emission matrix element Recoil issue has impact on shower matrix element. QCD result for emissions widely separated in rapidity is independent emission : MD, Dreyer, Hamilton, Monni and Salam 2018 Shower matrix element reveals enhancement and depletion including dead zones. Possible problem for observables sensitive to correlations between emissions e. g. in ML.

Impact on logarithmic accuracy Issue in double strong-ordered limit points to problems with leading double logarithms. MD, Dreyer, Hamilton, Monni and Salam 2018 Example : Thrust distribution at order Correct result : Shower result : Effect is colour suppressed Showers spoil simple double log exponentiation

Impact on logarithmic accuracy Problem originates in wrong colour factor issue General form of resummable observables in soft collinear limit Issue applies for observables with Examples : thrust, jet masses, C-parameter, angularities, Nsubjettiness variants etc.

Impact on logarithmic accuracy Issue in single strong ordered configuration : recoil issue. Expected to give NLL or single logarithmic issues. Can give up to 10 to 20 percent effects in pheno. Effect should be more pronounced for observables sensitive to between emissions or defined in azimuthal strip. E. g. missing ET isolation cuts in both ATLAS and CMS.

Conclusions • Multiple issues in Pythia 8 and Di. Re that prevent LL and NLL accuracy. • Comments apply to transverse momentum ordered dipole showers with local recoil. • Angular ordered showers free from some of these issues e. g. colour factor problem. But don’t get NLL for many observables (missing nonglobal logs). See also new work : ar. Xiv: 1904. 11866 • Solutions possible but require to reformulate showers. Aim to have showers with guaranteed NLL accuracy and then look beyond.