W/Z measurements at the luminosity limit!
Luminosity measurements with 1% uncertaintyATLAS arXiv:2104.01927; CMS arXiv:2212.09379
State of the art in QCD: N$^3$LO + N$^4$LL
see Xuan Chen's talk Tuesday morning
The LHC and future colliders literally depend on us!
Precision W/Z in recent literature
- Total inclusive at N$^3$LO Duhr, Dulat, Mistlberger '20, '21; n3loxs code: Baglio, Duhr, Mistlberger, Szafron '22
- W/Z+jet at NNLO Gehrmann De-Ridder, Gehrmann, Glover, Huss, Morgan '15; Gehrmann-De Ridder, Gehrmann, Glover, Huss, Walker '17
Boughezal, Focke, Liu, Petriello; Boughezal, Campbell, Ellis, Focke, Giele, Liu, Petriello '15
- N$^3$LL' $q_T$ resummation matched to NNLO W/Z+jetMonni, Re, Torrielli '16; Bizon, Monni, Re, Rottoli, Torrielli '17; Bizon, Gehrmann-De Ridder, Gehrmann, Glover, Huss, Monni, Re, Rottoli, Walker '19; Re, Rottoli, Torrielli '21; see also Camarda, Cieri, Ferrera '21; '23
- Third order fiducial QCDX. Chen, Gehrmann, Glover, Huss, Monni, Re, Rottoli, Torrielli '22; X. Chen, Gehrmann, Glover, Huss, T.-Z. Yang, H. X. Zhu; Camarda, Cieri, Ferrera '21
- Linear power corrections and fiducial cut sensitivityEbert, Michel, Stewart, Tackmann '20; Salam, Slade '21; Billis, Dehnadi, Ebert, Michel, Tackmann '21; Catani, de Florian, Ferrera, Grazzini '15; see also Buonocore, Kallweit, Rottoli, Wiesemann '21
- Mixed QCDxEW correctionsHeller, von Manteuffel, Schabinger, Spiesberger '20; Buonocore, Grazzini, Kallweit, Savoini, Tramontano '21; Behring, Buccioni, Caola, Delto, Jaquier, Melnikov, Röntsch '20; Buccioni, Caola, Chawdhry, Devoto, Heller, von Manteuffel, Melnikov, Röntsch, Signorile-Signorile '22; Dittmaier, Schmidt, Schwarz '20; Dittmaier, Huss, Schwinn '14; '15
- QED+QCD resummationAutieri, Cieri, Ferrera, Sborlini '23
- ...
N$^3$LO+N$^4$LL W/Z: On the shoulders of giants
- Resummation and subtraction via small-$q_T$ factorization
based on formalism of Becher, Neubert '10; Becher, Neubert, Wilhelm '11; implemented to N$^3$LL Becher, Neumann '20
$q_T$ subtractions Catani, Grazzini '07
- Three-loop beam functions M.-x. Luo, T.-Z. Yang, H. X. Zhu, Y. J. Zhu '19, '20; Ebert, Mistlberger, Vita '20
- N$^4$LL: Four loop rapidity anomalous dimensionDuhr, Mistlberger, Vita '22; Moult, H.X. Zhu, Y. J. Zhu '22
- Four-loop collinear anomalous dimensionAgarwal, von Manteuffel, Panzer, Schabinger '21
- Three-loop quark form factor Gehrmann, Glover, Huber, Ikizlerli, Studerus '10; Baikov, Chetyrkin, A.V. Smirnov, V.A. Smirnov, Steinhauser '09; Lee, A.V. Smirnov, V.A. Smirnov '10
- Massive three-loop axial singlet contributions Chen, Czakon, Niggetiedt '22; see also Gehrmann, Primo '21
- Fixed-order Z+jet NNLO calculation via 1-jettiness slicing re-implementation of Boughezal, Focke, Liu, Petriello; Boughezal, Campbell, Ellis, Focke, Giele, Liu, Petriello '15
- One-jettiness soft function Campbell, Ellis, Mondini, Williams '17; Boughezal, Liu, Petriello '15
- Four-loop splitting functions (for N$^3$LO PDFs; full N$^4$LL) Moch, Ruijl, Ueda, Vermaseren, Vogt '23; Falcioni, Herzog, Moch, Vermaseren, Vogt '23;
Gehrmann, von Manteuffel, Sotnikov, T.-Z. Yang '23; ...
(see Tong-Zhi Yang and Sven-Olaf Moch, Wednesday morning)
$q_T$ subtractions (for N$^3$LO)
Legs: $ \int_{q_T^\text{cut}} \mathrm{d}q_T
|\mathcal{M}|^2 = \text{finite!}$
Loops: Factorization at small $q_T$ $$ \sigma
\sim \hat{\sigma} \otimes B \otimes B +
\mathcal{O}(q_T^\text{cut}/m_Z) = \text{finite} +
\mathcal{O}(q_T^\text{cut}/m_Z)$$
Nested slicing! NNLO W/Z+jet with 1-jettiness
Z transverse momentum distribution
(0.007 GeV 1-jettiness cutoff for Z+jet at NNLO)
W transverse momentum distribution
Fixed-order cross-sections
Fixed-order cross-sections
Fixed-order cross-sections
0.5% N$^3$LO precision: What does it cost?
About 50-150k node hours on Perlmutter at NERSC
(64-128 nodes for about 12 hours)
Comparison with CMS 13 TeV, 1909.04133
using NNPDF 4.0; Neumann, Campbell '22
Large N$^3$LO corrections (with fixed PDFs): Are we in trouble?
Fiducial Z cross-sections:
See also Duhr, Dulat, Mistlberger '20; Duhr, Mistlberger '21; X. Chen, Gehrmann, Glover, Huss, T.-Z. Yang. H. X. Zhu '22
PDF and truncation uncertainties
PDF and truncation uncertainties
Full spectrum of PDF uncertainties
Ultimately distributions will guide us..
Impact of PDFs (e.g. in the Z transverse momentum)
Impact of PDFs (e.g. in the Z transverse momentum)
Impact of PDFs (e.g. in the Z transverse momentum)
Impact of PDFs (e.g. in the Z transverse momentum)
Outlook: Towards generic and better subtractions
Which ones are most promising in moving forward?
Performance, higher orders? How to compare?
- Antenna
subtractionsGehrmann De
Ridder, Gehrmann, Glover, Heinrich et
al.
- CoLoRFul
subtractionsDel Duca,
Duhr, Kardos, Somogyi, Troscanyi et
al.
- SecToR-ImProved PhasE
space for Real radiation (STRIPPER)Czakon et al.
- Nested soft-collinear subtractionsCaola,
Melnikov,
Röntsch et
al.
- Local analytic subtractionsMagnea, Maina, Pelliccioli, Signorile-Signorile, Torrielli, Uccirati
- Projection to BornCacciari,
Salam, Zanderighi
et al.
- 4D
unsubtractions Sborlini,
Hernandez-Pinto,
Rodrigo et
al.
- Geometric
subtractionsHerzog
- $q_T$ slicingCatani,
Grazzini et
al.
- $N$-jettiness slicing Gaunt,
Stahlhofen,
Tackmann, Walsh;
Boughezal, Petriello
et al.
see talks by Andrey Pikelner and Ivan Pedron, Thursday
- $k_T$-ness slicing (NLO) Buonocore, Grazzini, Haag, Rottoli, Savoini
see talk by Flavio Guadagni, Thursday
- + many calculations of power corrections for 0/1-jettiness
Third order QCD predictions for W and Z bosons
- Completed set of W and Z at N$^3$LO/N$^4$LL as public code
Neumann, Campbell '22, '23; arXiv:2207.07056, arXiv:2308.15382
- Residual QCD truncation uncertainties of about 1-2%
- PDF uncertainties dominant, spread of up to 14% in distributions!
- Contributes to wealth of SM precision phenomenology: $\alpha_s$, PDFs, TMDs, $m_W$, ...
- Nested slicing in $q_T$ and 1-jettiness: ~3-5 GeV in qT, 0.005 GeV in 1-jettiness
0.5% numerical+slicing precision requires about 100k hours on modern CPUs
- Future needs:
- Precision proton structure
- Fourth order QCD
- More efficient subtractions in MCFM (public codes), reach out to me!
(local subtractions, slicing power corrections)
- Parton shower event generation
- Combination with EW effects in unified framework