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


W$^+$ / W$^-$ ratio


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