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SUSY QCD CORRECTIONS TO HIGGS PAIR PRODUCTION IN BOTTOM QUARK FUSION

SUSY QCD CORRECTIONS TO HIGGS PAIR PRODUCTION IN BOTTOM QUARK FUSION. Yili Wang University Of Oklahoma (in collaboration with S. Dawson and C. Kao). Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007. Introduction. Lowest Order Cross Section for bb →  in SUSY .

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SUSY QCD CORRECTIONS TO HIGGS PAIR PRODUCTION IN BOTTOM QUARK FUSION

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  1. SUSY QCD CORRECTIONS TO HIGGS PAIR PRODUCTION IN BOTTOM QUARK FUSION Yili Wang University Of Oklahoma (in collaboration with S. Dawson and C. Kao) Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  2. Introduction. • Lowest Order Cross Section for bb→ in SUSY. • Next-to-Leading Order Corrections. • αsCorrections: bb →. • virtual corrections: gluon loop and gluino loop • real gluon emission: bb → g • 1/ΛCorrections: bg →b. • bb→ production at LHC. • Conclusions. Outline  = h, H and A Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  3. Motivation The high energy and high luminosity at the LHC might provide opportunities to detect a pair of Higgs bosons in SM and in models with more Higgs bosons In SM, a pair of Higgs boson is mainly produced by gluon fusion through triangle and box diagrams. The rate for Higgs pair production at the LHC is small. In models with two Higgs doublets (like SUSY), a large value of tan greatly enhances the Higgs coupling with bottom quarks. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  4. basic Coupling in MSSM Higgs Quark Coupling Yukawa coupling of bb are enhanced by 1/cos. The cross setion for Higgs pair production is proportional to tan4. • h bb: • H bb: • A bb: In SUSY, at the large tan, bottom quark fusion become the dominant process to produce Higgs pairs. The rate for Higgs pair production at the LHC is greatly increased. Here we concentrate Higgs pair production from bottom quark fusion in SUSY. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  5. PA h h xaPA xbPB X PB Perturbative QCD does not work for physics at hadronic scale Factorization To factorize physical quantities into a short distance component and a long distance component interference between different momentum scales are power suppressed Parton distributions donot interfere with hard interaction. They are universal Yili Wang – DPF and JPS 2006, Honolulu, Hawaii - 31 October 2006

  6. Lowest Order Cross Section lowest order cross section for b b → h h: H, h Final state identical Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  7. pg parallels to one of initial b or b momentums. • αs Corrections for b b →  : Next Leading Order • Corrections from virtual diagrams. • Infrared and collinear singularity: • pg → 0, pg || pb , or pg || pb • ultra-violet singularity: pg → , • Corrections from real gluon emission Infrared singularity: pg → 0 collinear singularity: • bg →b Corrections gluon splits into a pair of collinear b only collinear singularities Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  8. Virtual Gluon LoopDiagrams Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  9. At tree level, down type quark only couples to down type Higgs. Virtual Gluino LoopDiagrams Down type squark also couple to up type Higgs via terms in superpotiential Mixing term in sbottom mass matrix Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  10. b quark Yukawa coupling is renormalized Virtual Amplitude Virtual corrections contain both UV, IR and CO divergences UV is removed by renormalization counter term. Matrix element square IR and CO divergences finite terms IR divergences will be canceled by the IR divergences from real gluon emission diagrams Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  11. We introduce a new cutoff parameter Sto separate the gluon phase space to soft and hard regions for numerical integration Real Corrections — First Cutoff • softregions: Infrared and collinear • hardregions: only collinear singularities. (mb ~0) Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  12. softregion corrections: Virtual Plus Soft We assume gluon momentum pg is zero every where in the amplitude except in the denominators Virtual diagrams plus soft contribution of real diagrams Collinear singularity from soft region, will Absorbed into PDF Finite contributions from soft region Finite virtual contributions Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  13. Hard Corrections • hardregion has collinear singularity We introduce second new cutoff parameter cto separate the hard region into hard/non-collinear and hard/collinear regions. hard/collinear regions. NLO corrections change to: Hard/non-collinear corrections are finite and can be computed easily. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  14. The initial b quark splits into a hard parton b’ and a collinear hard gluon . Hard Collinear Corrections The cross section in hard –collinear region: Absorb this into parton distribution function cancel the collinear singularity in soft region At factorization scale μf , in MS scheme Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  15. Corrections from bb → h h g negative soft collinear Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  16. s and c are arbitrary parameters, our results should not depend on their values. Predictive power s No dependences on S and C Our method is effective. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  17. only collinear singularity exists bg →bhh cutoff Gluon splits into a pair of collinear b and b this singularity is absorbed into gluon distribution function We only need one cutoff c to separate final b phase space into collinear and non-collinear regions. Corrections from bg → bhh Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  18. SM Result Yili Wang – Physics Department, University of Oklahoma - 26 October 2006

  19. Results — MA dependence In SUSY, at the large tan, rate for Higgs pair production are enhanced significantly, specially for HH and AA pair. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  20. Complete NLO QCD corrections to b b→  within SUSY. Conclusion • In SM, gluon fusion is the dominant process to Higgs pair production. The rate for Higgs pair production is very small. although the NLO corrections significantly increase this rate. • In SUSY, at the large tan, bottom quark fusion become the dominant process for Higgs pair production. The rate for Higgs pair production are enhanced dramatically. NLO QCD corrections can be negative although they increases the cross section in most range. Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  21. Yili Wang – Brookhaven National Lab - 13 September 2006

  22. Hard Collinear Corrections Replace b(x) by b(x,μf) and drop terms high order than αS Extra terms in LO contributions. To cancel the collinear singularity in soft region To cancel the collinear singularity in hard collinear region For simplification, we use μR= μf = μ Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

  23. Results — M0Mass Yili Wang – Pheno 07 Madison, Wisconsin May 7 - 9, 2007

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