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Higgs production in the MSSM : Transverse momentum resummation - - PowerPoint PPT Presentation

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Higgs production in the MSSM : Transverse momentum resummation Marius Wiesemann University of Zrich HP2 : High Precision for Hard Processes, Florence (Italy) 3-5 August, 2014 Outline 1. Transverse momentum resummation 2. SM vs. MSSM Higgs

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SLIDE 1

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

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SLIDE 2

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 pT spectrum in the MSSM September 5, 2014 1 / 23

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SLIDE 3

pT resummation

◮ production of colorless particle (mass M) ◮ problem: pT distribution diverges at pT → 0 ◮ reason: large logs ln p2 T/M2 for pT ≪ M

αs : ln(p2

T/M2), ln2(p2 T/M2)

α2

s :

ln(p2

T/M2), ln2(p2 T/M2), ln3(p2 T/M2), ln4(p2 T/M2)

· · ·

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 23

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SLIDE 4

pT resummation

◮ production of colorless particle (mass M) ◮ problem: pT distribution diverges at pT → 0 ◮ reason: large logs ln p2 T/M2 for pT ≪ M

αs : ln(p2

T/M2), ln2(p2 T/M2)

α2

s :

ln(p2

T/M2), ln2(p2 T/M2), ln3(p2 T/M2), ln4(p2 T/M2)

· · ·

◮ solution: all order resummation

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 23

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SLIDE 5

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]

dσ(res)

N

dp2

T

∼

  • db b

2 J0(b pT) S(b, A, B) HN fN fN, HN = HN CN CN

◮ 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(Q2 b2/b2

0) → L′ = ln(Q2 b2/b2 0 + 1)

→ reduction of impact at high pT (low b) → unitarity constraint

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 3 / 23

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SLIDE 6

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 7

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 8

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 9

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 10

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

+

  • dσ(res)

dp2

T

  • l.a.
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 11

Matching

◮ matched (resummed) cross section:

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

+

  • dσ(res)

dp2

T

  • l.a.
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 23

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SLIDE 12

Matching

◮ unitarity (due to L → L′):

  • dp2

T

  • dσ

dp2

T

  • f.o.+l.a.

≡

  • σ(tot)

f.o. .

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 5 / 23

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SLIDE 13

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 pT spectrum in the MSSM September 5, 2014 6 / 23

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SLIDE 14

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 pT spectrum in the MSSM September 5, 2014 6 / 23

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SLIDE 15
  • 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 pT spectrum in the MSSM September 5, 2014 7 / 23

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SLIDE 16

SM vs. MSSM Higgs production

[TeV] s

7 8 9 10 20 30 40 50 60 70 80

2

10

[pb]

  • 2

10

  • 1

10 1 10

2

10

3

10

LHC HIGGS XS WG 2014 H ( N N L O + N N L L Q C D + N L O E W )
  • p
p H (NNLO QCD) q q
  • pp
WH (NNLO QCD)
  • pp
ZH (NNLO QCD)
  • pp
H (NLO QCD) t t
  • pp
HH (NLO QCD)
  • pp
H (NNLO QCD - 5FS) b b
  • pp

= 125 GeV

H

M MSTW2008

◮ SM:

◮ gluon fusion by far

dominant

◮ b¯

bH sizeable only with b-tagging

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 23

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SLIDE 17

SM vs. MSSM Higgs production

[TeV] s

7 8 9 10 20 30 40 50 60 70 80

2

10

[pb]

  • 2

10

  • 1

10 1 10

2

10

3

10

LHC HIGGS XS WG 2014 H ( N N L O + N N L L Q C D + N L O E W )
  • p
p H (NNLO QCD) q q
  • pp
WH (NNLO QCD)
  • pp
ZH (NNLO QCD)
  • pp
H (NLO QCD) t t
  • pp
HH (NLO QCD)
  • pp
H (NNLO QCD - 5FS) b b
  • pp

= 125 GeV

H

M MSTW2008

◮ SM:

◮ gluon fusion by far

dominant

◮ b¯

bH sizeable only with b-tagging

◮ MSSM/2HDM:

◮ 3 neutral Higgs: h, H and A ◮ yb/yt enhanced by tan β ◮ h: constrained to be SM-like ◮ b¯

bH/A dominant for large tan β

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 23

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SLIDE 18

Associated H(b¯ b) production

4-flavour scheme 5-flavour scheme

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 23

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SLIDE 19

Associated H(b¯ b) production

4-flavour scheme

◮ exclusive up to NLO [Dittmaier, Krämer, Spira ’04] [Dawson, Jackson, Reina, Wackeroth ’04]

5-flavour scheme

◮ inclusive up to NNLO [Harlander, Kilgore ’03] ◮ exclusive up to NNLO [Buehler, Herzog, Lazopoulos, Mueller ’12] ◮ NLO+NLL pT resummation [Belyaev, Nadolsky, Yuan ’06]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 23

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SLIDE 20
  • 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 pT spectrum in the MSSM September 5, 2014 10 / 23

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SLIDE 21

b¯ bH: Ingredients of the calculation

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

◮ analytic pT-distribution [Ozeren ’10]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23

αs:

❜ ❜

α2

s:

❜ ❜

b b

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SLIDE 22

b¯ bH: Ingredients of the calculation

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

◮ analytic pT-distribution [Ozeren ’10] ◮ resummation coefficients from Drell-Yan

A(1), A(2), B(1) [Kodaira, Trentadue ’82], C(1) [Davies, Stirling ’84], A(3) [Becher, Neubert ’11], C(2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23

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SLIDE 23

b¯ bH: Ingredients of the calculation

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

◮ analytic pT-distribution [Ozeren ’10] ◮ resummation coefficients from Drell-Yan

A(1), A(2), B(1) [Kodaira, Trentadue ’82], C(1) [Davies, Stirling ’84], A(3) [Becher, Neubert ’11], C(2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]

◮ Hb¯ bH(1) = 3 CF ◮ new: [Harlander, Tripathi, MW ’14]

Hb¯

bH(2) = 10.47 ± 0.08 (numerical result)

Hb¯

bH(2) = CF 321 64 − 13 48π2

CF +

  • −365

288 + π2 12

  • Nf

+

  • 5269

576 − 5 12π2 − 9 4ζ3

  • CA
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23

from universal form of H(2) [Catani, Cieri, de Florian, Grazzini ’13]

→ see Leandro’s talk

b b

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SLIDE 24

b¯ bH: Ingredients of the calculation

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

◮ analytic pT-distribution [Ozeren ’10] ◮ resummation coefficients from Drell-Yan

A(1), A(2), B(1) [Kodaira, Trentadue ’82], C(1) [Davies, Stirling ’84], A(3) [Becher, Neubert ’11], C(2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]

◮ Hb¯ bH(1) = 3 CF ◮ new: [Harlander, Tripathi, MW ’14]

Hb¯

bH(2) = 10.47 ± 0.08 (numerical result)

Hb¯

bH(2) = CF 321 64 − 13 48π2

CF +

  • −365

288 + π2 12

  • Nf

+

  • 5269

576 − 5 12π2 − 9 4ζ3

  • CA
  • = 10.52 . . .
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23

from universal form of H(2) [Catani, Cieri, de Florian, Grazzini ’13]

→ see Leandro’s talk

b b

slide-25
SLIDE 25

b¯ bH: Ingredients of the calculation

  • dσ

dp2

T

  • f.o.+l.a.

=

  • dσ

dp2

T

  • f.o.

−

  • dσ(res)

dp2

T

  • f.o.

+

  • dσ(res)

dp2

T

  • l.a.

◮ analytic pT-distribution [Ozeren ’10] ◮ resummation coefficients from Drell-Yan

A(1), A(2), B(1) [Kodaira, Trentadue ’82], C(1) [Davies, Stirling ’84], A(3) [Becher, Neubert ’11], C(2) (H(2)) [Catani, Cieri, de Florian, Grazzini ’12]

◮ + Hb¯ bH(1) and Hb¯ bH(2) ◮ third term: modified version of HqT

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 23

[Bozzi, Catani, de Florian, Grazzini ’03 ’05] [de Florian, Ferrera, Grazzini, Tommasini ’11]

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SLIDE 26

b¯ bH: Checks

◮ analytic pT-distribution checked against numerical H + jet

calculation at NLO [Harlander, Ozeren, MW ’10]

◮ unitarity:

  • dσ

dpT dpT = total

◮ for various µF, µR values ◮ integral Qres-independent

◮ fixed order (pT → 0) = logs (pT → 0)

◮ for various µF, µR values ◮ independent of Qres

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 12 / 23

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SLIDE 27

b¯ bH: Results

NLO+NLL distribution:

[Harlander, Tripathi, MW ’14], [Belyaev, Nadolsky, Yuan ’06]

  • dσ

dp2

T
  • NLO+NLL

=

  • dσ

dp2

T
  • NLO

−

  • dσ(res)

dp2

T
  • NLO

+

  • dσ(res)

dp2

T
  • NLL
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 13 / 23

Q = mH/2 Q = mH/4

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SLIDE 28

b¯ bH: Results

NLO+NLL distribution:

[Harlander, Tripathi, MW ’14], [Belyaev, Nadolsky, Yuan ’06]

  • dσ

dp2

T
  • NLO+NLL

=

  • dσ

dp2

T
  • NLO

−

  • dσ(res)

dp2

T
  • NLO

+

  • dσ(res)

dp2

T
  • NLL
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 13 / 23

higher order effect! [Banfi, Monni, Zanderighi ’13] Q = mH/2 Q = mH/4

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SLIDE 29

b¯ bH: Results

NNLO+NNLL distribution:

[Harlander, Tripathi, MW ’14]

  • dσ

dp2

T
  • NNLO+NNLL

=

  • dσ

dp2

T
  • NNLO

−

  • dσ(res)

dp2

T
  • NNLO

+

  • dσ(res)

dp2

T
  • NNLL
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 14 / 23

Q = mH/4

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SLIDE 30

b¯ bH: Results

Scale uncertainties:

[Harlander, Tripathi, MW ’14]

  • dσ

dp2

T
  • NNLO+NNLL

=

  • dσ

dp2

T
  • NNLO

−

  • dσ(res)

dp2

T
  • NNLO

+

  • dσ(res)

dp2

T
  • NNLL
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 15 / 23

Q-variation Q+µF+µR- variation

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SLIDE 31

b¯ bH: Results

Comparison to 5FS NLO+PS:

[Frederix, Frixione, Maltoni, Torielli, MW]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 16 / 23

Preliminary analytic resum: µF = µR = mT/4 NLO+PS: µF = µR = HT/4

slide-32
SLIDE 32

b¯ bH: Results

Comparison to 4FS NLO+PS:

[Frederix, Frixione, Maltoni, Torielli, MW]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 17 / 23

Preliminary analytic resum: µF = µR = mT/4 NLO+PS: µF = µR = HT/4

slide-33
SLIDE 33

b¯ bH: Results

Comparison to 4FS NLO+PS:

[Frederix, Frixione, Maltoni, Torielli, MW]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 17 / 23

Preliminary → Qshower significantly lower than Higgs mass (peak around 45 GeV , similar to µF) (default shower scale in MG5_aMC distribution peaks around 190 GeV) analytic resum: µF = µR = mT/4 NLO+PS: µF = µR = HT/4

slide-34
SLIDE 34
  • 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 pT spectrum in the MSSM September 5, 2014 18 / 23

slide-35
SLIDE 35

Gluon fusion: Ingredients of the calculation

◮ NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05] ◮ MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)

dσ dpT = dσf.o. dpT − dσlogs dpT + dσres dpT

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23

slide-36
SLIDE 36

Gluon fusion: Ingredients of the calculation

◮ NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05] ◮ MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)

dσ dpT = dσf.o. dpT − dσlogs dpT + dσres dpT

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23

Amplitudes from SusHi

[Harlander, Liebler, Mantler ’12]

slide-37
SLIDE 37

Gluon fusion: Ingredients of the calculation

◮ NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05] ◮ MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)

dσ dpT = dσf.o. dpT − dσlogs dpT + dσres dpT

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23

σ(0)

t+b

Amplitudes from SusHi

[Harlander, Liebler, Mantler ’12]

slide-38
SLIDE 38

Gluon fusion: Ingredients of the calculation

◮ NNLO+NNLL in heavy-top limit [Bozzi, Catani, de Florian, Grazzini ’05] ◮ MSSM effects? → new: MoRe-SusHi (on sushi.hepforge.org)

dσ dpT = dσf.o. dpT − dσlogs dpT + dσres dpT H

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 19 / 23

, etc. σ(0)

t+b

φ φ

Amplitudes from SusHi

[Harlander, Liebler, Mantler ’12]

slide-39
SLIDE 39

Gluon Fusion: Results

NLO+NLL ratio in the MSSM/SM (light Higgs):

[Harlander, Mantler, MW ’14]

RS(pT) = dσS/dpT

dσSM/dpT

NS(pT) = dσS/dpT

dσSM/dpT · σSM σS

0.9 0.92 0.94 0.96 0.98 1 50 100 150 200 250 300 RS(pT) pT [GeV] pp @ 13 TeV tauphobic(800,16) tauphobic(800,29.5) mhmax(300,6.5) mhmodp(500,17) mhmodm(500,16.5) lightstau(500,12) 0.9 0.92 0.94 0.96 0.98 1 50 100 150 200 250 300 RS(pT) pT [GeV] pp @ 13 TeV 0.96 0.98 1 1.02 1.04 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV tauphobic(800,16) tauphobic(800,29.5) mhmax(300,6.5) mhmodp(500,17) mhmodm(500,16.5) lightstau(500,12) 0.96 0.98 1 1.02 1.04 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 20 / 23

ratio to SM shape-ratio to SM

Benchmark Scenarios from [Carena, Heinemeyer, Stål, Wagner, Weiglein ’13]

light Higgs light Higgs

slide-40
SLIDE 40

Gluon Fusion: Results

10-7 10-6 10-5 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT tauphobic, mA = 800 GeV tan(β) = 16 tan(β) = 29.5 10-6 10-5 10-4 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT tauphobic, mA = 800 GeV tan(β) = 16 tan(β) = 29.5 10-7 10-6 10-5 10-4 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT mhmodm, mA = 800 GeV tan(β) = 17 tan(β) = 40 10-7 10-6 10-5 10-4 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT [GeV] 10-6 10-5 10-4 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT mhmodm, mA = 800 GeV tan(β) = 17 tan(β) = 40 10-6 10-5 10-4 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT [GeV]
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 21 / 23

heavy Higgs pseudo-scalar heavy Higgs pseudo-scalar

slide-41
SLIDE 41

Gluon Fusion: Results

NLO+NLL distribution in the MSSM (left: heavy, right: pseudo-scalar):

[Harlander, Mantler, MW ’14]

NS(pT) = dσS/dpT

dσSM/dpT · σSM σS

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV tauphobic(800,16) tauphobic(800,29.5) mhmodp(800,17) mhmodp(800,40) mhmodm(800,16.5) mhmodm(800,40) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV tauphobic(800,16) tauphobic(800,29.5) mhmodp(800,17) mhmodp(800,40) mhmodm(800,16.5) mhmodm(800,40) 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 50 100 150 200 250 300 NS(pT) pT [GeV] pp @ 13 TeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 22 / 23

heavy Higgs pseudo-scalar

slide-42
SLIDE 42

Conclusions and Outlook

Conclusions:

◮ b¯

bH and gluon fusion crucial in MSSM/2HDM b¯ bH:

◮ missing hard coefficient at two-loop for H(b¯

b) determined

◮ first calculation of NNLL pT-effects for H(b¯

b) production

◮ strong reduction of resummation scale dependence ◮ consistent with NLO+PS results ◮ remarkable agreement of 5FS NNLO+NNLL with 4FS NLO+PS

gluon fusion:

◮ MoRe-SusHi: MSSM effects included in analytic resummation ◮ h: quite SM-like ◮ H/A: significant shape/normalization distortion from b-loop

Outlook:

◮ first NLO+PS in 4FS ◮ complete differential comparison 4FS and 5FS for H(b¯

b)

◮ inclusion of b¯

bH into MoRe-SusHi

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 23 / 23

slide-43
SLIDE 43

BackUp

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 1 / 11

slide-44
SLIDE 44

Resummation coefficients: determination of Hb¯

bH,(2) b

◮ hard-collinear function:

Hb¯

bH(2) b¯ b←b¯ b(z) = Hb¯ bH(2) b

δ(1 − z) + known

◮ use unitarity:

  • ˆ

σ(tot)

b¯ b

  • f.o. =
  • dp2

T

  

  • dσb¯

b

dp2

T

  • f.o.

−

 dσ(res)

b¯ b

dp2

T

 

f.o.

  +

  • dp2

T

 dσ(res)

b¯ b

dp2

T

 

l.a.

  • =z ˆ

σ(0)

b¯ b Hb¯ bH(2) b¯ b←b¯ b

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 11

[Catani, Cieri, de Florian, Ferrera, Grazzini ’12]

slide-45
SLIDE 45

Resummation coefficients: determination of Hb¯

bH,(2) b

◮ hard-collinear function:

Hb¯

bH(2) b¯ b←b¯ b(z) = Hb¯ bH(2) b

δ(1 − z) + known

◮ use unitarity:

  • ˆ

σ(tot)

b¯ b

  • f.o. =
  • dp2

T

  

  • dσb¯

b

dp2

T

  • f.o.

−

 dσ(res)

b¯ b

dp2

T

 

f.o.

  +

  • dp2

T

 dσ(res)

b¯ b

dp2

T

 

l.a.

  • =z ˆ

σ(0)

b¯ b Hb¯ bH(2) b¯ b←b¯ b

→ numerical result: Hb¯

bH,(2) b

= 10.47 ± 0.08

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 2 / 11

[Catani, Cieri, de Florian, Ferrera, Grazzini ’12]

slide-46
SLIDE 46

Resummation coefficients: determination of Hb¯

bH,(2) b

→ numerical result: Hb¯

bH,(2) b

= 10.47 ± 0.08

◮ recently: universal Form of H(2) determined [Catani, Cieri, de Florian, Grazzini ’13]

→ for both gg- and q¯ q-initiated processes → process dependence: finite part of virtuals

◮ anlytical result from two-loop virtuals: [Harlander, Tripathi, MW ’14]

Hb¯

bH,(2) b

= CF

321

64 − 13 48π2

  • CF +
  • −365

288 + π2 12

  • Nf

+

5269

576 − 5 12π2 − 9 4ζ3

  • CA
  • = 10.52 . . .
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 3 / 11

slide-47
SLIDE 47

Results

PDF+αs uncertainties:

[Harlander, Tripathi, MW ’14]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 4 / 11

slide-48
SLIDE 48

b¯ bH: Results

Q = mH/2 vs. Q = mH/4:

[Harlander, Tripathi, MW ’14]

  • dσ

dp2

T
  • NNLO+NNLL

=

  • dσ

dp2

T
  • NNLO

−

  • dσ(res)

dp2

T
  • NNLO

+

  • dσ(res)

dp2

T
  • NNLL
  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 5 / 11

slide-49
SLIDE 49

pT resummation

◮ determination of resummation coefficients:

◮ expand resummation formula in αs ◮ compare to small pT region of fixed order cross section ◮ Q0 ≪ M:

αs :

Q2

  • dσ(res)

dp2

T

  • NLO

dp2

T !

=

Q2

  • dσ

dp2

T

  • NLO

dp2

T

f (A(1), B(1), C(1), H(1)) = K2 ln2(Q2

0/M2) + K1 ln(Q2 0/M2) + K0

+ O(Q2

0/M2) ◮ known for Drell-Yan and gg → H up to NNLL [Kodaira, Trentadue ’82], [Davies, Stirling ’84], [Catani, D’Emilio, Trentadue ’88], [de Florian, Grazzini ’01], [Becher, Neubert ’11], [Catani, Grazzini ’11], [Catani, Cieri, de Florian, Ferrera, Grazzini ’12]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 6 / 11

slide-50
SLIDE 50

Gluon fusion: Choosing the resummation scale

◮ Qb ≡ Qtb = mb in SM suggested due to appearance of terms [Grazzini, Sargsyan ’13]

∼ ln(mb/pT)

◮ vanish as pT → 0 ⇒ no factorization breaking, no Sudakov logs ◮ directly related to ln(mb/mH) in total rate ◮ HOWEVER: could spoil collinear/soft approximation

⇒ Sudakov resummation would be unsufficient

◮ BUT: if small, treated as all other finite terms (power

corrections in pT)

◮ choosing Qb (and Qtb) – 2 proposals:

  • 1. analyze size of finite terms

[Banfi, Monni, Zanderighi ’13]

  • 2. consider validity of collinear/soft approximation

[Bagnaschi, Vicini]

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 7 / 11 2 2

H pt mb

H

slide-51
SLIDE 51

Gluon fusion: Choosing the resummation scale

◮ bad high pT matching for large Q ◮ due to unitarity: cross section will even become negative ◮ pragmatic way to determine Q: [Harlander, Mantler, MW ’14]

require that cross section remains positive for Q = 2 Q0

0.5 1 1.5 2 100 150 200 250 300 350 400 (dσres/dpT) / (dσfo/dpT) pT [GeV] Qres = 94 GeV Qres = 96 GeV Qres = 98 GeV Qres = 100 GeV Qres = 102 GeV 0.5 1 1.5 2 100 150 200 250 300
  • pT [GeV]
Qres = 42 GeV Qres = 44 GeV Qres = 46 GeV Qres = 48 GeV Qres = 50 GeV 0.5 1 1.5 2 100 150 200 250 300 350
  • pT [GeV]
Qres = 64 GeV Qres = 66 GeV Qres = 68 GeV Qres = 70 GeV Qres = 72 GeV

high pT matching → Qt = 49 GeV, Qb = 23 GeV, Qtb = 34 GeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 11

top bottom interference

slide-52
SLIDE 52

Gluon fusion: Choosing the resummation scale

◮ bad high pT matching for large Q ◮ due to unitarity: cross section will even become negative ◮ pragmatic way to determine Q: [Harlander, Mantler, MW ’14]

require that cross section remains positive for Q = 2 Q0

0.5 1 1.5 2 100 150 200 250 300 350 400 (dσres/dpT) / (dσfo/dpT) pT [GeV] Qres = 94 GeV Qres = 96 GeV Qres = 98 GeV Qres = 100 GeV Qres = 102 GeV 0.5 1 1.5 2 100 150 200 250 300
  • pT [GeV]
Qres = 42 GeV Qres = 44 GeV Qres = 46 GeV Qres = 48 GeV Qres = 50 GeV 0.5 1 1.5 2 100 150 200 250 300 350
  • pT [GeV]
Qres = 64 GeV Qres = 66 GeV Qres = 68 GeV Qres = 70 GeV Qres = 72 GeV

high pT matching → Qt = 49 GeV, Qb = 23 GeV, Qtb = 34 GeV finite terms (for pveto

T

) → Qt ∼ 60 GeV, Qb ≡ Qtb ∼ 35 GeV soft/collinear approx (10%) → Qt ∼ 55 GeV, Qb ∼ 25 GeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 8 / 11

top bottom interference

slide-53
SLIDE 53
  • 1. size of finite terms

◮ considered for pjet T,veto efficiencies [Banfi, Monni, Zanderighi ’13]

finite terms ≤ 50% → Qt ∼ 60 GeV, Qb ≡ Qtb ∼ 35 GeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 9 / 11 0.2 0.4 0.6 0.8 1 1 10 100 εremainder(pt,veto)/εremainder(pt,veto=∞) pt,veto [GeV]

mH = 125 GeV mt = 173.5 GeV; mb = 4.65 GeV

| t |2 | b |2+2 Re[b*⋅ t] | t+b |2

slide-54
SLIDE 54
  • 2. validity of collinear approximation

◮ at matrixelement level for pT Higgs → more in Alessandro’s talk [Bagnaschi, Vicini]

max 10% deviation → Qt ∼ 55 GeV, Qb ∼ 25 GeV

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 10 / 11

50 100 150 200 250 300 eVL 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 ptH HGeVL 0.8 1.0 1.2 1.4 C 50 100 150 200 250 300 eVL 0.8 1.0 1.2 1.4 C

X

λ1,λ2,λ3=±1

50 100 150 200 250 300 ptH 0.8 1.0 1.2 1.4 50 100 150 200 250 300 ptH 0.8 1.0 1.2 1.4 C

t-only b-only

slide-55
SLIDE 55

Gluon Fusion: Results

NLO+NLL distribution in the SM:

[Harlander, Mantler, MW ’14]

  • dσ

dp2

T
  • NLO+NLL

=

  • dσ

dp2

T
  • NLO

−

  • dσ(res)

dp2

T
  • NLO

+

  • dσ(res)

dp2

T
  • NLL

10-4 10-3 10-2 10-1 100 50 100 150 200 250 300 dσ/dpT [pb/GeV] pT [GeV] SM, mH = 125.6 GeV, pp @ 13 TeV SM f.o. 0.7 0.8 0.9 1 1.1 1.2 1.3 50 100 150 200 250 300 (dσx/dpT) / (dσhtl/dpT) pT [GeV] pp @ 13 TeV b+t t

  • M. Wiesemann

(University of Zürich) Higgs pT spectrum in the MSSM September 5, 2014 11 / 11