Higgs production in the MSSM : Transverse momentum resummation Marius Wiesemann University of Zürich HP2 : High Precision for Hard Processes, Florence (Italy) 3-5 August, 2014
Outline 1. Transverse momentum resummation 2. SM vs. MSSM Higgs production 3. b ¯ bH : NNLO+NNLL distribution in the 5FS 4. Gluon fusion: NLO+NLL distribution in the MSSM M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 1 / 23
p T resummation ◮ production of colorless particle (mass M) ◮ problem: p T distribution diverges at p T → 0 T / M 2 for p T ≪ M ◮ reason: large logs ln p 2 ln ( p 2 T / M 2 ) , ln 2 ( p 2 T / M 2 ) α s : α 2 ln ( p 2 T / M 2 ) , ln 2 ( p 2 T / M 2 ) , ln 3 ( p 2 T / M 2 ) , ln 4 ( p 2 T / M 2 ) s : · · · � � ��� � � ����� ����� ������ ������������ ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 2 / 23
p T resummation ◮ production of colorless particle (mass M) ◮ problem: p T distribution diverges at p T → 0 T / M 2 for p T ≪ M ◮ reason: large logs ln p 2 ln ( p 2 T / M 2 ) , ln 2 ( p 2 T / M 2 ) α s : α 2 ln ( p 2 T / M 2 ) , ln 2 ( p 2 T / M 2 ) , ln 3 ( p 2 T / M 2 ) , ln 4 ( p 2 T / M 2 ) s : · · · � � ��� � � ����� ����� ◮ solution: all order resummation ������ ���������� �������� ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 2 / 23
Transverse momentum resummation ◮ developed already 30 years ago [Parisi, Petronzio ’79], [Dokshitzer, Diakonov, Troian ’80], [Curci, Greco, Srivastava ’79], [Bassetto, Ciafaloni, Marchesini ’80], [Kodaira, Trentadue ’82], [Collins, Soper, Sterman ’85] d σ (res) � db b N ∼ 2 J 0 ( b p T ) S ( b , A , B ) H N f N f N , H N = H N C N C N dp 2 T ◮ we use newer formulation including various improvements: [Catani, de Florian, Grazzini ’01], [Bozzi, Catani, de Florian, Grazzini ’06] ◮ H embodies whole process dependence ◮ L = ln ( Q 2 b 2 / b 2 0 ) → L ′ = ln ( Q 2 b 2 / b 2 0 + 1 ) → reduction of impact at high p T (low b ) → unitarity constraint M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 3 / 23
Matching ◮ matched (resummed) cross section: � � d σ = d p 2 T f.o. + l.a. � � ��� � � ����� ����� ������ ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ matched (resummed) cross section: � � � � d σ d σ = d p 2 d p 2 T T f.o. + l.a. f.o. � � ��� � � ����� ����� ������ ������������ ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ matched (resummed) cross section: � � � � � � d σ (res) d σ d σ = − d p 2 d p 2 d p 2 T T T f.o. + l.a. f.o. f.o. � � ��� � � ����� ����� ������ ������������ ���� ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ matched (resummed) cross section: � � � � � � d σ (res) d σ d σ = − d p 2 d p 2 d p 2 T T T f.o. + l.a. f.o. f.o. � � ��� � � ����� ����� ������ ���������� ���� ������������� ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ matched (resummed) cross section: � � � � � � � � d σ (res) d σ (res) d σ d σ = − + d p 2 d p 2 d p 2 d p 2 T T T T f.o. + l.a. f.o. f.o. l.a. � � ��� � � ����� ����� ������ ���������� ���� ������������� ����� ������������� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ matched (resummed) cross section: � � � � � � � � d σ (res) d σ (res) d σ d σ = − + d p 2 d p 2 d p 2 d p 2 T T T T f.o. + l.a. f.o. f.o. l.a. � � ��� � � ����� ����� ������ ���������� ���� ������������� ����� ������������� ������� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 4 / 23
Matching ◮ unitarity (due to L → L ′ ): � � � d σ � σ (tot) � d p 2 ≡ f.o. . T d p 2 T f.o.+l.a. � � ��� � � ����� ����� ������ ������������� ����������� ����� ������ �� �� ��� ��� ��� ��� ���� � � � ������ M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 5 / 23
Applications ◮ SM Higgs production through gluon fusion (heavy-top limit) [Bozzi, Catani, de Florian, Grazzini ’06] ◮ Slepton pair production [Bozzi, Fuks, Klasen ’06] ◮ Vector boson pair production: WW and ZZ [Grazzini ’06], [Grazzini, Frederix ’08] ◮ Drell-Yan [Bozzi, Catani, Ferrera, de Florian, Grazzini ’10] ◮ SM Higgs production through gluon fusion with full mass dependence [Mantler, MW ’12], [Grazzini, Sargsyan ’13] M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 6 / 23
Applications ◮ SM Higgs production through gluon fusion (heavy-top limit) [Bozzi, Catani, de Florian, Grazzini ’06] ◮ Slepton pair production [Bozzi, Fuks, Klasen ’06] ◮ Vector boson pair production: WW and ZZ [Grazzini ’06], [Grazzini, Frederix ’08] ◮ Drell-Yan [Bozzi, Catani, Ferrera, de Florian, Grazzini ’10] ◮ SM Higgs production through gluon fusion with full mass dependence [Mantler, MW ’12], [Grazzini, Sargsyan ’13] ◮ Recently: Higgs production through bottom annihilation [Harlander, Tripathi, MW ’14] ◮ new: MSSM Higgs production in gluon fusion [Harlander, Mantler, MW ’14] M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 6 / 23
1. Transverse momentum resummation 2. SM vs. MSSM Higgs production 3. b ¯ bH : NNLO+NNLL distribution in the 5FS 4. Gluon fusion: NLO+NLL distribution in the MSSM M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 7 / 23
SM vs. MSSM Higgs production 3 10 [pb] LHC HIGGS XS WG 2014 � ) W E O N L + 2 C D 10 Q L L N N O + L N N H ( � p p 10 H (NNLO QCD) H (NNLO QCD - 5FS) q q � pp WH (NNLO QCD) b b pp � ZH (NNLO QCD) � pp 1 � pp HH (NLO QCD) H (NLO QCD) � pp t t � pp -1 10 M = 125 GeV H MSTW2008 -2 10 2 7 8 9 10 20 30 40 50 60 70 80 10 s [TeV] ◮ SM: ◮ gluon fusion by far dominant ◮ b ¯ bH sizeable only with b -tagging M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 8 / 23
SM vs. MSSM Higgs production 3 10 [pb] LHC HIGGS XS WG 2014 � ) W E O N L + 2 C D 10 Q L L N N O + L N N H ( � p p 10 H (NNLO QCD) H (NNLO QCD - 5FS) q q � pp WH (NNLO QCD) b b pp � ZH (NNLO QCD) � pp 1 � pp HH (NLO QCD) H (NLO QCD) � pp t t � pp -1 10 M = 125 GeV H MSTW2008 -2 10 2 7 8 9 10 20 30 40 50 60 70 80 10 s [TeV] ◮ SM: ◮ MSSM/2HDM: ◮ gluon fusion by far ◮ 3 neutral Higgs: h , H and A dominant ◮ y b / y t enhanced by tan β ◮ b ¯ bH sizeable only with ◮ h : constrained to be SM -like b -tagging ◮ b ¯ bH / A dominant for large tan β M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 8 / 23
Associated H ( b ¯ b ) production 4-flavour scheme 5-flavour scheme M. Wiesemann (University of Zürich) Higgs p T spectrum in the MSSM September 5, 2014 9 / 23
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