Max Hansen Patrick Fritzsch Anthony Francis Mattia Bruno
Philippe De Forcrand Martin Lüscher (long-time visitor) (emeritus) Lattice field theory a A non-perturbative regularization of QFT. The lattice spacing, a, is the UV cutoff Numerical calculations are also restricted to a finite spacetime volume T x L3 Then the task is to evaluate a high-dimension integral numerically N (T/a) (L/a)3 108 dim ⇠ ⇥ ⇠ L Lattice field theory a A non-perturbative regularization of QFT. The lattice spacing, a, is the UV cutoff Numerical calculations are also restricted to a finite spacetime volume T x L3 Then the task is to evaluate a high-dimension integral numerically N (T/a) (L/a)3 108 dim ⇠ ⇥ ⇠ L Only possible by Monte-Carlo sampling the Euclidean signature path integral
0.6 The area is the same 0.5 0.4 under these two curves 0.4 0.2
0.3 -10 -5 5 10
0.2 -0.2 This one is better suited 0.1 -0.4 to numerical evaluation
-0.6 -10 -5 5 10
1 dx ix2(1 i✏) 8 1 x2 Re e =1 Now repeat in 10 dimensions dx e =1 p⇡ pi p⇡ Z Z Lattice QCD A non-perturbative regularization (not a model) of QCD
The only known way to define QCD at all energy scales
Need to fix a small number of parameters (by ‘sacrificing observables’) e.g. fix m`,ms,g0 from M⇡,MK ,M⌦ Lattice QCD A non-perturbative regularization (not a model) of QCD
The only known way to define QCD at all energy scales
Need to fix a small number of parameters (by ‘sacrificing observables’) e.g. fix m`,ms,g0 from M⇡,MK ,M⌦ Main challenges Role of non-zero a, finite T x L3, Euclidean signature… (Must be addressed in an observable specific way)
M⇡ ⌧ En⌧ Calculate correlator Aµ(0)⇡p( ⌧) = pµ f⇡(a, T , L) Z⇡e + cne h i M L M T X2 Extract observable f (a, T , L)=f + c e ⇡ + c e ⇡ + c a + ⇡ ⇡ 1 2 3 ··· Lattice QCD A non-perturbative regularization (not a model) of QCD
The only known way to define QCD at all energy scales
Need to fix a small number of parameters (by ‘sacrificing observables’) e.g. fix m`,ms,g0 from M⇡,MK ,M⌦ Main challenges Role of non-zero a, finite T x L3, Euclidean signature… (Must be addressed in an observable specific way)
M⇡ ⌧ En⌧ Calculate correlator Aµ(0)⇡p( ⌧) = pµ f⇡(a, T , L) Z⇡e + cne h i M L M T X2 Extract observable f (a, T , L)=f + c e ⇡ + c e ⇡ + c a + ⇡ ⇡ 1 2 3 ··· Heavy pions (modern calculations range from M M to 5 M ) ⇡,latt ⇠ ⇡ ⇡ Reducing statistical uncertainties/achieving reliable systematics
Unlocking new observables! Challenges
lattice spacing Euclidean (also excited state masses of contamination) nucleons, nuclei heavy quark decay constants, form factors MN, MLi
fB baryonic charges
gA, gP, gS
loosely bound states deuterium
finite volume Challenges Opportunities
lattice spacing Euclidean (also excited state masses of contamination) nucleons, nuclei heavy quark decay constants, form factors MN, MLi
fB baryonic charges
gA, gP, gS
multi-hadron EW transitions K → !! multi-hadron scattering !! → !!
loosely bound states deuterium
finite volume Challenges Opportunities
lattice spacing Euclidean (also excited state masses of contamination) nucleons, nuclei heavy quark decay constants, form factors MN, MLi
fB baryonic charges
PDFs gA, gP, gS
multi-hadron EW transitions (g-2)μ K → !! multi-hadron scattering QED + QCD states !! → !! Mn - Mp
loosely bound states deuterium
finite volume Best controlled calculations Running coupling, renormalized quark masses (Patrick, Mattia) (Challenge: reaching energies where perturbative expansion applies)
HVP contribution to (g-2)μ (Mattia, Anthony) (Challenge: reaching required precision)
heavy quark decay constants (Patrick) (Challenge: heavy quark discretization) Calculations reaching maturity multi-hadron EW transitions (e.g. K→ππ) (Mattia, Max) (Challenge: renormalizing operators, long-distance Euclidean and f.v. effects)
tetra-quark spectroscopy (Anthony) (Challenge: implementing heavy quarks, isolating ground state)
QED+QCD (Patrick) (Challenge: subtle volume effects)
Lattice beyond QCD composite dark matter (Anthony) (Challenge: choosing what to simulate, starting from scratch) A bit about me Born and raised in Montana, U.S.
PhD in Seattle (2014), Postdoc in Mainz (2014-2017) Joined CERN as fellow, now a staff member
Physics interests (>2)-hadron scattering, πππ→πππ, Nπ→Nππ
Multi-hadron form factors, ππγ*→ππ
PDFs from LQCD (e.g. volume effects)
Algorithms for numerical inverse Laplace transform Multi-hadron processes from LQCD
KEY IDEA: We can use the finite volume as a tool to extract multi-hadron observables
Two-to-two scattering
E2(L)
E1(L)
E0(L)
One-to-two transitions ` `+ L 2 1 h |J | i L K ⇡⇡ ! B K⇡ L ! Two-to-three and three-to-three scattering
E2(L)
E1(L)
E0(L) E2(L)
E1(L)
E0(L)
a = 8 a = 4 a = 2 4.0 4.0 4.0 Threshold expansion requires very large L ) 3.5 ) 3.5 ) 3.5 L L L ( ( ( n n n E E E 3.0 3.0 3.0 getting better and better 5 10 15 20 5 10 15 20 5 10 15 20 a = 1 mL a = 1/2 mL a =1/2 mL 4.0 4.0 4.0
) 3.5 ) 3.5 ) 3.5 L L L ( ( ( n n n E E E 3.0 3.0 3.0 repulsive works as well
5 10 15 20 5 10 15 20 5 10 15 20 mL mL mL My other work activities Computing committee with Peter, Wolfgang, Elena
Co-organizer of the Particle & Astro seminar (Fri@2p) with Peter, Kfir
Activities of the CERN lattice group Semi-regular lattice seminars (typically Thurs@2pm) Organizing a CERN TH Institute in July 2019 Advances in lattice gauge theory Formal and numerical progress in spectroscopy, form factors and QCD+QED, Very informal ‘lattice lunch’ together
We all love nothing more than a lattice question from a non-lattice person! CERN Lattice Group
Max Hansen Patrick Fritzsch Anthony Francis Mattia Bruno
Philippe De Forcrand Martin Lüscher (long-time visitor) (emeritus)