Modelling $bar b H$ production for the LHC at 13.6 TeV

We present new state-of-the-art predictions for Standard Model Higgs boson production in association with a bottom-quark pair ($b\bar bH$). Updated cross sections are computed in accordance with the recommendations of the LHC Higgs Working Group, including the use of the PDF4LHC21 set of parton distribution functions, with a center-of-mass energy of 13.6 TeV. For the total inclusive cross section, we provide matched predictions of the massless five-flavour scheme and the massive four-flavour scheme at the fixed-order level. We further present recently obtained simulations matched to parton showers in both flavour schemes within the Standard Model, and also discuss them in the context of potential Beyond-the-Standard-Model scenarios. In the massless scheme, we compare different next-to-next-to-leading order predictions matched to parton showers obtained through the MiNNLOPS and GENEVA generators. In addition, the role of four-flavour scheme predictions is studied as a background to $HH$ searches, considering both the top-quark and bottom-quark Yukawa contributions to $b\bar bH$ production. Finally, we analyse the sensitivity of the Higgs transverse momentum spectrum to light-quark Yukawa couplings in the diphoton decay channel based on MiNNLOPS simulations.

💡 Research Summary

The manuscript presents a state‑of‑the‑art theoretical prediction for Standard Model Higgs boson production in association with a bottom‑quark pair (b ={b} H) at the new LHC centre‑of‑mass energy of 13.6 TeV. The authors follow the latest LHC Higgs Working Group (LHCHWG) recommendations, employing the PDF4LHC21 parton distribution set (both the massless 5‑flavour and massive 4‑flavour versions) and the most recent values for α_s, electroweak parameters and the on‑shell bottom‑quark mass.

Two complementary perturbative schemes are considered. In the Four‑Flavour Scheme (4FS) the bottom quark is treated as massive, no bottom PDF is introduced, and the LO process starts from gg or q ={q} initial states producing a b ={b} pair that radiates the Higgs. In the Five‑Flavour Scheme (5FS) the bottom quark is taken massless, its collinear logarithms are resummed into a bottom PDF, and the LO process is b ={b} → H. Historically, fixed‑order predictions in the two schemes differed by 20‑30 %; however, the recent availability of NNLO QCD corrections in the 4FS and NNLO (and even N³LO) results in the 5FS reduces the discrepancy to below 10 %. The authors adopt systematic matching procedures – the modern FONLL method and the NLO+NNLL “part + y_b y_t” approach – to combine the two schemes without double counting, thereby delivering a unified prediction that incorporates both the y_b² (bottom‑Yukawa) and y_t² (top‑loop induced) contributions as well as their interference.

Inclusive cross sections at 13.6 TeV are obtained by interpolating the LHCHWG 13 TeV and 14 TeV data bases, applying the matched NLO 4FS + NNLO 5FS results. The total b ={b} H cross section is found to be roughly 0.95 pb with a theoretical uncertainty of about 5 %. The y_b² component contributes ≈ 0.35 pb, while the y_t² component, arising from the top‑loop induced gluon‑fusion mechanism, contributes ≈ 0.60 pb, i.e. roughly twice the size of the pure bottom‑Yukawa term.

Beyond fixed order, the paper delivers high‑precision resummed predictions for the Higgs transverse‑momentum spectrum in the 5FS. Using Soft‑Collinear Effective Theory, the authors achieve N³LL accuracy for the y_b² component, substantially reducing the perturbative uncertainty in the low‑p_T region (p_T ≲ 30 GeV) compared with earlier NNLL results.

A major part of the work is devoted to NNLO+PS (next‑to‑next‑to‑leading order matched to parton showers) simulations. In the 5FS, the authors employ the GENEVA framework, which combines NNLO QCD with N³LL resummation and a dedicated shower‑matching algorithm. In both the 4FS and 5FS they also use the MiNNLOPS method, which implements NNLO accuracy together with a parton‑shower interface in a fully differential way. Detailed comparisons show that total rates from MiNNLOPS and GENEVA differ by only 1‑2 %, while differential distributions (p_T, rapidity, b‑jet kinematics) agree within the quoted theoretical uncertainties. MiNNLOPS is shown to be particularly robust for observables involving identified b‑jets, whereas GENEVA provides a smoother transition in the high‑p_T tail. The authors also present MiNNLOPS simulations for heavy Higgs bosons (e.g. M_H = 300 GeV) in BSM scenarios where the bottom‑Yukawa coupling is enhanced, demonstrating that the same framework can be directly applied to new‑physics studies.

The relevance of b ={b} H as a background to double‑Higgs (HH) searches is examined in depth. By separating the y_b² and y_t² contributions and applying realistic b‑jet tagging cuts (p_T > 30 GeV, |η| < 2.5), the study finds that the top‑loop induced component dominates the background (≈ 70 % of the total after cuts), while the interference term (y_b y_t) contributes about 10 %. This quantifies the challenge of extracting the pure bottom‑Yukawa signal in HH analyses and underscores the need for aggressive b‑tagging strategies.

Finally, the paper explores the sensitivity of the Higgs p_T spectrum to light‑quark Yukawa couplings (y_u, y_d, y_s). Although these couplings are tiny, the corresponding q ={q} → H processes receive a PDF enhancement. The authors compute these contributions at N³LL+approximate N³LO (aN³LO) accuracy and embed them in MiNNLOPS simulations of the diphoton decay channel. They demonstrate that in the intermediate p_T region (30–50 GeV) the light‑quark Yukawa effects can modify the spectrum by 5‑10 %, a level potentially observable with the high‑luminosity LHC data set.

In summary, the work delivers a comprehensive, high‑precision toolkit for b ={b} H production at 13.6 TeV: (i) updated inclusive cross sections with consistent 4FS/5FS matching, (ii) N³LL resummed p_T spectra, (iii) NNLO+PS event generators (MiNNLOPS and GENEVA) validated against each other, (iv) a detailed assessment of the process as a background to HH searches, and (v) a novel study of light‑quark Yukawa sensitivity. These results constitute an essential theoretical input for Run 3 and the upcoming High‑Luminosity LHC program, enabling more precise measurements of the bottom‑Yukawa coupling, improved background modeling for di‑Higgs analyses, and new avenues to probe otherwise inaccessible light‑quark interactions.