# Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

## Abstract

We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice over the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-ordermore »

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1253091

- Report Number(s):
- SLAC-PUB-16521

Journal ID: ISSN 2470-0010; PRVDAQ; arXiv:1605.02572

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review D; Journal Volume: 94; Journal Issue: 5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Experiment-HEP; Phenomenology-HEP; HEPEX; HEPTH

### Citation Formats

```
Wang, Sheng-Quan, Wu, Xing-Gang, Brodsky, Stanley J., and Mojaza, Matin.
```*Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.94.053003.

```
Wang, Sheng-Quan, Wu, Xing-Gang, Brodsky, Stanley J., & Mojaza, Matin.
```*Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC*. United States. doi:10.1103/PhysRevD.94.053003.

```
Wang, Sheng-Quan, Wu, Xing-Gang, Brodsky, Stanley J., and Mojaza, Matin. Fri .
"Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC". United States.
doi:10.1103/PhysRevD.94.053003. https://www.osti.gov/servlets/purl/1253091.
```

```
@article{osti_1253091,
```

title = {Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC},

author = {Wang, Sheng-Quan and Wu, Xing-Gang and Brodsky, Stanley J. and Mojaza, Matin},

abstractNote = {We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice over the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.},

doi = {10.1103/PhysRevD.94.053003},

journal = {Physical Review D},

number = 5,

volume = 94,

place = {United States},

year = {Fri Sep 09 00:00:00 EDT 2016},

month = {Fri Sep 09 00:00:00 EDT 2016}

}