Threshold cross sections for Drell-Yan & Higgs productions in N 3 LO QCD
|
|
- Laureen Lee
- 5 years ago
- Views:
Transcription
1 Narayan Rana 20/10/2016 1/46 Threshold cross sections for Drell-Yan & Higgs productions in N 3 LO QCD Narayan Rana 20/10/2016 in collaboration with T. Ahmed, M. C. Kumar, M. Mahakhud, M. K. Mandal, P. Mathews & V. Ravindran
2 Narayan Rana 20/10/2016 2/46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
3 Prologue Narayan Rana 20/10/2016 3/46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
4 Prologue Why Drell-Yan and Higgs Drell-Yan Large production rates and clean signatures Standard candle for detector calibration Testing physics within and beyond the SM Higgs The Nobel particle The discovery put the SM in firm footing Is it the Higgs or a Higgs? Need detail info about it s quantum nature We need precise theoretical prediction Narayan Rana 20/10/2016 4/46
5 Prologue Narayan Rana 20/10/2016 5/46 State-of-the-art : DY production NNLO NNLO inclusive. Altarelli, Ellis, Martinelli (1979). Hamberg, Matsuura, van Neerven (1991). Harlander, Kilgore (2002) NNLO differential. Anastasiou, Dixon, Melnikov, Petriello (2003). Melnikov, Petriello (2006). Catani, Cieri, Ferrera, de Florian, Grazzini (2009)
6 Prologue Narayan Rana 20/10/2016 6/46 State-of-the-art : Higgs production in gluon fusion NNLO NNLO inclusive (large m t approximation). Harlander, Kilgore (2002). Anastasiou, Melnikov (2002). Ravindran, Smith, van Neerven (2003) NNLO inclusive (1/m t expansion). Marzani, Ball, Del Duca, Forte, Vicini (2008). Harlander, Ozeren (2009). Pak, Rogal, Steinhauser (2010) N 3 LO soft approximation (partial). Moch, Vogt (2005). Ravindran (2006) NNLO + NNLL resummation. de Florian, Grazzini (2012)
7 Beyond NNLO Narayan Rana 20/10/2016 7/46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
8 Beyond NNLO Narayan Rana 20/10/2016 8/46 Going beyond NNLO: Threshold approximation σ I (τ, q 2 ) = 1 S a, b 1 τ dx ( x Φ ab(x) ŝ ˆσ ab I τ x, q2) τ = q2 S, I = g, q, b
9 Beyond NNLO Going beyond NNLO: Threshold approximation σ I (τ, q 2 ) = 1 S a, b 1 τ dx ( x Φ ab(x) ŝ ˆσ ab I τ x, q2) τ = q2 S, I = g, q, b Partonic flux Φ ab (x) becomes large when x τ or z = q2 ŝ = τ x 1 Dominant contributions come from the region z 1. For DY N(N)LO SV 0.95 N(N)LO Narayan Rana 20/10/2016 8/46
10 Beyond NNLO Going beyond NNLO: Threshold approximation σ I (τ, q 2 ) = 1 S a, b 1 τ dx ( x Φ ab(x) ŝ ˆσ ab I τ x, q2) τ = q2 S, I = g, q, b Partonic flux Φ ab (x) becomes large when x τ or z = q2 ŝ = τ x 1 Dominant contributions come from the region z 1. For DY N(N)LO SV 0.95 N(N)LO z 1 is called the soft limit. Expand the partonic cross section around z = 1. Narayan Rana 20/10/2016 8/46
11 Narayan Rana 20/10/2016 9/46 Beyond NNLO Expand the partonic cross section around z = 1 σ I (z) = sv (z) + (1 z) i H,(i) i=0
12 Narayan Rana 20/10/2016 9/46 Beyond NNLO Expand the partonic cross section around z = 1 σ I (z) = sv (z) + sv,δ δ(1 z) + (1 z) i H,(i) i=0 ( ) sv,(k) ln k (1 z) 1 z k=0 + ( ) ln k (1 z) D k (z) 1 z +
13 Narayan Rana 20/10/2016 9/46 Beyond NNLO Expand the partonic cross section around z = 1 σ I (z) = sv (z) + sv,δ δ(1 z) + (1 z) i H,(i) i=0 ( ) sv,(k) ln k (1 z) 1 z k=0 + ( ) ln k (1 z) D k (z) 1 z + Different methods Matrix element square and phase space integrals in the soft limit [Catani et al., Harlander and Kilgore] Form factors and DGLAP kernels [Moch and Vogt; Ravindran, Smith, van Neerven] Soft collinear effective theory [Becher and Neubert]
14 The universal structure of QCD Narayan Rana 20/10/ /46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
15 The universal structure of QCD Narayan Rana 20/10/ /46 QCD Divergences The higher order computations in QCD contain two types of divergences Ultraviolet Infrared
16 The universal structure of QCD Narayan Rana 20/10/ /46 QCD Divergences The higher order computations in QCD contain two types of divergences Ultraviolet Infrared Removed by UV renormalization
17 The universal structure of QCD Narayan Rana 20/10/ /46 QCD Divergences The higher order computations in QCD contain two types of divergences Ultraviolet Infrared Soft divergences (k 0 0) soft emissions + IR in virtual Collinear divergences (cos θ pk 1) sum over degenerate states 1 (p k) 2 = 1 2p 0 k 0 (1 cos θ pk )
18 The universal structure of QCD Narayan Rana 20/10/ /46 QCD Factorization The hadronic cross section following parton model S σ I (τ) = a,b f B a (τ) f B b (τ) }{{} bare PDFs ŝ ˆσ B ab (τ, ɛ c ) }{{} partonic cross section
19 The universal structure of QCD QCD Factorization The hadronic cross section following parton model S σ I (τ) = a,b f B a (τ) f B b (τ) }{{} bare PDFs ŝ ˆσ B ab (τ, ɛ c ) }{{} partonic cross section The bare partonic cross section ˆσ ab B (τ, ɛ c) contains collinear divergences. ˆσ ab B (τ, ɛ c ) = ( ) ˆσ B,V ab (τ, ɛ s, ɛ c ) + ˆσ B,R ab (τ, ɛ s, ɛ c ) deg. states ɛ s : soft gluon regulator ɛ c : collinear parton regulator Narayan Rana 20/10/ /46
20 The universal structure of QCD Narayan Rana 20/10/ /46 QCD Factorization The hadronic cross section following parton model S σ I (τ) = a,b f B a (τ) f B b (τ) }{{} bare PDFs ŝ ˆσ B ab (τ, ɛ c ) }{{} partonic cross section The bare partonic cross section ˆσ ab B (τ, ɛ c) contains collinear divergences. ˆσ ab B (τ, ɛ c ) = ( ) ˆσ B,V ab (τ, ɛ s, ɛ c ) + ˆσ B,R ab (τ, ɛ s, ɛ c ) deg. states ɛ s : soft gluon regulator ɛ c : collinear parton regulator KLN theorem KLN theorem : : Summing over the degenerate final states remove the soft divergences and final state collinear divergences. Initial state collinear singularity remains
21 The universal structure of QCD Narayan Rana 20/10/ /46 Collinear singularity factorizes ˆσ B ab (τ, ɛ c ) = cd Γ ca (τ, µ F, ɛ c ) Γ db (τ, µ F, ɛ c ) ˆσ I ab (τ, µ F ) In MS scheme f a (τ, µ F ) = Γ ac (τ, µ F, ɛ c ) f B c (τ)
22 The universal structure of QCD Narayan Rana 20/10/ /46 Collinear singularity factorizes ˆσ B ab (τ, ɛ c ) = cd Γ ca (τ, µ F, ɛ c ) Γ db (τ, µ F, ɛ c ) ˆσ I ab (τ, µ F ) In MS scheme f a (τ, µ F ) = Γ ac (τ, µ F, ɛ c ) f B c (τ) Renormalized version of parton model S σ I (τ) = ab f a (τ, µ F ) f b (τ, µ F ) ab (τ, µ F )
23 The universal structure of QCD Narayan Rana 20/10/ /46 Collinear singularity factorizes ˆσ B ab (τ, ɛ c ) = cd Γ ca (τ, µ F, ɛ c ) Γ db (τ, µ F, ɛ c ) ˆσ I ab (τ, µ F ) In MS scheme f a (τ, µ F ) = Γ ac (τ, µ F, ɛ c ) f B c (τ) Renormalized version of parton model S σ I (τ) = ab f a (τ, µ F ) f b (τ, µ F ) ab (τ, µ F ) f 1(x)... f n(x) = 1 dx dx nf 1(x 1)... f n(x n)δ(x x 1... x n)
24 Threshold framework Narayan Rana 20/10/ /46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
25 Threshold framework Narayan Rana 20/10/ /46 ab (z, µ F ) can be expanded order by order in a s [ ] ab (z, µ F ) = δ(1 z) + a s (µ 2 R) a 11 δ(1 z) + a 12 D 0 + a 13 D 1 + R 1 (z) [ ] = + a 2 s(µ 2 R) a 21 δ(1 z) a 25 D 3 + R 2 (z) +...
26 Threshold framework Narayan Rana 20/10/ /46 ab (z, µ F ) can be expanded order by order in a s [ ] ab (z, µ F ) = δ(1 z) + a s (µ 2 R) a 11 δ(1 z) + a 12 D 0 + a 13 D 1 + R 1 (z) [ ] = + a 2 s(µ 2 R) a 21 δ(1 z) a 25 D 3 + R 2 (z) +... Contributions from the soft distribution functions factorizes & exponentiates [Catani, Collins, Soper, Sterman]
27 Threshold framework Narayan Rana 20/10/ /46 ab (z, µ F ) can be expanded order by order in a s [ ] ab (z, µ F ) = δ(1 z) + a s (µ 2 R) a 11 δ(1 z) + a 12 D 0 + a 13 D 1 + R 1 (z) [ ] = + a 2 s(µ 2 R) a 21 δ(1 z) a 25 D 3 + R 2 (z) +... Contributions from the soft distribution functions factorizes & exponentiates [Catani, Collins, Soper, Sterman] Due to the factorization property of UV, Soft and Collinear terms, the complete threshold part ( sv ab ) of the partonic cross section, hence, acquires the following structure ( ) sv I (z, q 2, µ 2 R, µ 2 F ) = C exp Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) ɛ=0
28 Threshold framework Narayan Rana 20/10/ /46 ab (z, µ F ) can be expanded order by order in a s [ ] ab (z, µ F ) = δ(1 z) + a s (µ 2 R) a 11 δ(1 z) + a 12 D 0 + a 13 D 1 + R 1 (z) [ ] = + a 2 s(µ 2 R) a 21 δ(1 z) a 25 D 3 + R 2 (z) +... Contributions from the soft distribution functions factorizes & exponentiates [Catani, Collins, Soper, Sterman] Due to the factorization property of UV, Soft and Collinear terms, the complete threshold part ( sv ab ) of the partonic cross section, hence, acquires the following structure ( ) sv I (z, q 2, µ 2 R, µ 2 F ) = C exp Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) ɛ=0 Ce f(z) = δ(1 z) + 1 1! f(z) + 1 f(z) f(z) + 2!
29 Threshold framework Narayan Rana 20/10/ /46 The finite distribution Ψ ( Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) = ln ˆF I (â s, Q 2, µ 2, ɛ) 2 δ(1 z) ˆF I (â s, Q 2, µ 2, ɛ) is the bare form factor
30 Threshold framework Narayan Rana 20/10/ /46 The finite distribution Ψ ( Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) = ln ˆF I (â s, Q 2, µ 2, ɛ) 2 δ(1 z) [ 2δ(1 + ln Z I (â s, µ 2 R, µ 2, ɛ)] z) ˆF I (â s, Q 2, µ 2, ɛ) is the bare form factor Z I (â s, µ 2 R, µ2, ɛ) is the overall renormalization constant
31 Threshold framework Narayan Rana 20/10/ /46 The finite distribution Ψ ( Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) = ln ˆF I (â s, Q 2, µ 2, ɛ) 2 δ(1 z) [ 2δ(1 + ln Z I (â s, µ 2 R, µ 2, ɛ)] z) 2m C ln Γ II (â s, µ 2, µ 2 F, z, ɛ) ˆF I (â s, Q 2, µ 2, ɛ) is the bare form factor Z I (â s, µ 2 R, µ2, ɛ) is the overall renormalization constant Γ II (â s, µ 2, µ 2 F, z, ɛ) is the mass factorization kernel m = 1 for Drell-Yan & Higgs, m = 1 2 for DIS
32 Threshold framework Narayan Rana 20/10/ /46 The finite distribution Ψ ( Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) = ln ˆF I (â s, Q 2, µ 2, ɛ) 2 δ(1 z) [ 2δ(1 + ln Z I (â s, µ 2 R, µ 2, ɛ)] z) 2m C ln Γ II (â s, µ 2, µ 2 F, z, ɛ) ) + 2Φ I (â s, q 2, µ 2, z, ɛ) ˆF I (â s, Q 2, µ 2, ɛ) is the bare form factor Z I (â s, µ 2 R, µ2, ɛ) is the overall renormalization constant Γ II (â s, µ 2, µ 2 F, z, ɛ) is the mass factorization kernel Φ I (â s, q 2, µ 2, z, ɛ) is the soft distribution function m = 1 for Drell-Yan & Higgs, m = 1 2 for DIS
33 Threshold framework Narayan Rana 20/10/ /46 The finite distribution Ψ ( Ψ I (z, q 2, µ 2 R, µ 2 F, ɛ) = ln ˆF I (â s, Q 2, µ 2, ɛ) 2 δ(1 z) UV, C, S [ 2δ(1 + ln Z I (â s, µ 2 R, µ 2, ɛ)] z) UV, C, S 2m C ln Γ II (â s, µ 2, µ 2 F, z, ɛ) ) + 2Φ I (â s, q 2, µ 2, z, ɛ) UV,C, S UV,C, S ˆF I (â s, Q 2, µ 2, ɛ) is the bare form factor Z I (â s, µ 2 R, µ2, ɛ) is the overall renormalization constant Γ II (â s, µ 2, µ 2 F, z, ɛ) is the mass factorization kernel Φ I (â s, q 2, µ 2, z, ɛ) is the soft distribution function m = 1 for Drell-Yan & Higgs, m = 1 2 for DIS
34 Threshold framework Narayan Rana 20/10/ /46 Form Factor & Sudakov resummation Mueller, Collins, Sen, Sudakov The bare form factors ˆF I (â s, Q 2, µ 2, ɛ) of both fermionic and gluonic operators satisfy the following integro differential equation that follows form the gauge as well as the RG invariances. Q 2 d dq 2 ln ˆF I ( â s, Q 2, µ 2, ɛ ) = 1 ( ) )] [K I â s, µ2 R 2 µ 2, ɛ + G (â I s, Q2 µ 2, µ2 R R µ 2, ɛ all the poles in ɛ terms finite as ɛ 0
35 Threshold framework Narayan Rana 20/10/ /46 Form Factor & Sudakov resummation Mueller, Collins, Sen, Sudakov The bare form factors ˆF I (â s, Q 2, µ 2, ɛ) of both fermionic and gluonic operators satisfy the following integro differential equation that follows form the gauge as well as the RG invariances. Q 2 d dq 2 ln ˆF I ( â s, Q 2, µ 2, ɛ ) = 1 ( ) )] [K I â s, µ2 R 2 µ 2, ɛ + G (â I s, Q2 µ 2, µ2 R R µ 2, ɛ µ R independence of ˆF I d µ 2 R dµ 2 R K I = µ 2 R all the poles in ɛ terms finite as ɛ 0 d dµ 2 R G I = a i s(µ 2 R)A I i i=1 A I s are cusp anomalous dimensions
36 Threshold framework Narayan Rana 20/10/ /46 We expand K I & G I ( ) K I â s, µ2 R µ 2, ɛ G I ( â s, Q2 µ 2, µ2 R R µ 2, ɛ ( ) µ = â i 2 i ɛ 2 R s µ i=1 2 Sɛ i K I,(i) (ɛ) ) = a i s (Q2 ) G I i (ɛ) + â i s i=1 i=1 ( µ 2 R µ 2 ) i ɛ ( ) 2 i Q 2 ɛ 2 µ 2 1 Sɛ i KI,(i) (ɛ) R The solutions for K I,(i) s ( ) K I,(1) (ɛ) = 1 ɛ 2A I 1 ) ( ) K I,(2) (ɛ) = (2β 1 ɛ 2 0 A I A I 2 ɛ ( ) ( ) ( ) K I,(3) (ɛ) = 1 ɛ β2 0A I 1 + 1ɛ2 2 3 β 1A I β 0A I ɛ 3 AI 3
37 Threshold framework Narayan Rana 20/10/ /46 To solve the KG equation, we expand ln ˆF I as ln ˆF I (â s, Q 2, µ 2, ɛ) = i=1 â i s Vogt, Vermaseren, Moch, Ravindran ( Q 2 µ 2 ) i ɛ 2 S i ɛ I,(i) ˆL F (ɛ)
38 Threshold framework Narayan Rana 20/10/ /46 To solve the KG equation, we expand ln ˆF I as ln ˆF I (â s, Q 2, µ 2, ɛ) = The formal solution up to three loops i=1 â i s ˆL I,(1) (ɛ) = 1 { } F ɛ 2 2A I } {G I1 (ɛ) ɛ ˆL I,(2) (ɛ) = 1 { } F ɛ 3 β 0 A I { ɛ 2 ˆL I,(3) (ɛ) = 1 { F ɛ 4 8 } β0 2 AI { 2 9 ɛ ɛ 2 { Vogt, Vermaseren, Moch, Ravindran ( Q 2 µ 2 ) i ɛ 2 S i ɛ 1 } A I 2 β 0 GI 1 (ɛ) + 1 { 1 2 ɛ I,(i) ˆL F (ɛ) } G I 2 (ɛ) 2 β 1 A I β 0 A I } β0 2 GI 1 (ɛ) A I 3 1 β 1 G I 1 (ɛ) 4 } β 0 G I 2 (ɛ) + 1 { ɛ } G I 3 (ɛ) 3 A I s are maximally non-abelian A g i = C A C F A q i
39 Threshold framework Narayan Rana 20/10/ /46 To solve the KG equation, we expand ln ˆF I as ln ˆF I (â s, Q 2, µ 2, ɛ) = The formal solution up to three loops i=1 â i s ˆL I,(1) (ɛ) = 1 { } F ɛ 2 2A I } {G I1 (ɛ) ɛ ˆL I,(2) (ɛ) = 1 { } F ɛ 3 β 0 A I { ɛ 2 ˆL I,(3) (ɛ) = 1 { F ɛ 4 8 } β0 2 AI { 2 9 ɛ ɛ 2 { Vogt, Vermaseren, Moch, Ravindran ( Q 2 µ 2 ) i ɛ 2 S i ɛ 1 } A I 2 β 0 GI 1 (ɛ) + 1 { 1 2 ɛ I,(i) ˆL F (ɛ) } G I 2 (ɛ) 2 β 1 A I β 0 A I } β0 2 GI 1 (ɛ) A I 3 1 β 1 G I 1 (ɛ) 4 } β 0 G I 2 (ɛ) + 1 { ɛ All poles except the single one can be predicted. } G I 3 (ɛ) 3 A I s are maximally non-abelian A g i = C A C F A q i
40 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i C A C F
41 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i C A C F Collinear anomalous dimensions
42 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i C A C F UV anomalous dimensions
43 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i C A C F Soft anomalous dimensions f g i = C A C F f q i
44 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i C A C F Soft C I 1 = 0 C2 I = 2β 0g I,(1) 1 ( ) C3 I = 2β 1g I,(1) 1 2β 0 g I,(1) 2 + 2β 0g I,(2) 1 ( C4 I = 2β 2g I,(1) 1 2β 1 g I,(1) 2 + 4β 0g I,(2) 1 ) 2β 0 ( ) g I,(1) 3 + 2β 0g I,(2) 2 + 4β0g 2 I,(3) 1
45 Threshold framework Narayan Rana 20/10/ /46 Ravindran, Smith, van Neerven Explicit computation of two loop ˆF g and ˆF q in SU(N) reveals a structure of G I s C A C F C I 1 = 0 G I i = 2(B I i γ I i) + f I i + C I i + k=1 ɛ k g I,(k) i The single pole can be predicted C2 I = 2β 0g I,(1) 1 ( ) C3 I = 2β 1g I,(1) 1 2β 0 g I,(1) 2 + 2β 0g I,(2) 1 ( C4 I = 2β 2g I,(1) 1 2β 1 g I,(1) 2 + 4β 0g I,(2) 1 ) 2β 0 ( ) g I,(1) 3 + 2β 0g I,(2) 2 + 4β0g 2 I,(3) 1
46 Threshold framework Narayan Rana 20/10/ /46 DGLAP equation The DGLAP kernels satisfy RG equation d µ 2 F dµ 2 F Γ(z, µ 2 F, ɛ c ) = 1 2 P (z, µ2 F ) Γ(z, µ 2 F, ɛ c ) Both the kernels Γ and the splitting functions P can be expanded in a s. The RGE can be solved to get Γ i in terms of P i 1. The diagonal terms of the splitting functions have the following structure P (i) II (z) = 2 [ B I i+1δ(1 z) + A I i+1d 0 ] + P (i) II,reg (z) P (i) II,reg (z) are regular when z 1.
47 Threshold framework Narayan Rana 20/10/ /46 An ansatz for soft distribution function Ravindran The finiteness of Ψ I demands a integro differential equation for Φ I, similar to the Form factors q 2 d ( dq 2 ΦI â s, q 2, µ 2, z, ɛ ) = 1 2 ( ) )] [K I â s, µ2 R µ, z, ɛ + G (â I s, q2, µ2 R 2 µ 2 R µ, z, ɛ 2 The solutions for Φ I can be obtained similar to ln ˆF I, by expanding Φ I ( â s, q 2, µ 2, z, ɛ ) = i=1 â i s ( q 2 µ 2 ) i ɛ 2 S i ɛ ˆΦ I,(i) (z, ɛ) ˆΦ I,(i) (ɛ) = L I,(i) F (ɛ) ( A I δ(1 z)a I,G I (ɛ) G I ) (z,ɛ)
48 Threshold framework Narayan Rana 20/10/ /46 An ansatz for soft distribution function Ravindran The finiteness of Ψ I demands a integro differential equation for Φ I, similar to the Form factors q 2 d ( dq 2 ΦI â s, q 2, µ 2, z, ɛ ) = 1 2 ( ) )] [K I â s, µ2 R µ, z, ɛ + G (â I s, q2, µ2 R 2 µ 2 R µ, z, ɛ 2 The solutions for Φ I can be obtained similar to ln ˆF I, by expanding Φ I ( â s, q 2, µ 2, z, ɛ ) = i=1 â i s ( q 2 µ 2 ) i ɛ 2 S i ɛ ˆΦ I,(i) (z, ɛ) ˆΦ I,(i) (ɛ) = L I,(i) F (ɛ) ( A I δ(1 z)a I,G I (ɛ) G I ) (z,ɛ)
49 Threshold framework Narayan Rana 20/10/ /46 Instead, observed form of soft functions suggests to expand Φ I as Φ I (â s, q 2, µ 2, z, ɛ) = i=1 â i s ( q 2 (1 z) 2m µ 2 ) i ɛ 2 ( ) S i imɛ ɛ ˆφ I,(i) (ɛ) 1 z ˆφ I,(i) (ɛ) = L I,(i) F (ɛ) (A I A I,G I (ɛ) G I (ɛ)) 1 [ K I,(i) + G I,(i)] iɛ I,(i) I G are related to G through δ(1 z) and D j (1 z) 1+nɛ = 1 nɛ δ(1 z) + D 0 + ( nɛ)d 1 + ( nɛ)2 D
50 Threshold framework Narayan Rana 20/10/ /46 Expanding in a s i=1 â i s ( ) iɛ q 2 2 z S i ɛg I,(i) = µ 2 a i s(qz)g 2 I i(ɛ) q 2 z =q 2 (1 z) 2 i=1
51 Threshold framework Narayan Rana 20/10/ /46 Expanding in a s i=1 â i s ( ) iɛ q 2 2 z S i ɛg I,(i) = µ 2 a i s(qz)g 2 I i(ɛ) q 2 z =q 2 (1 z) 2 i=1 provides a structure of G I i G I i(ɛ) = f I i + C I i + k=1 ɛ k G I,k i where C I i = Ci I ( g I,(k) i ) G I,k i and G g,k i = C A C F G q,k i Φ g = C A C F Φ q
52 Threshold framework Narayan Rana 20/10/ /46 The threshold cross section
53 Result Narayan Rana 20/10/ /46 Outline 1 Prologue 2 Beyond NNLO 3 The universal structure of QCD 4 Threshold framework 5 Result
54 Result Narayan Rana 20/10/ /46 The available ingredients 1 Form factors up to 3 loops ˆF q and ˆF g [Moch et al.; Baikov et al.; Gehrman et al.;] ˆF b [Gehrman, Kara] 2 Renormalization constant up to 3 loops Z q = 1 Z g [Chetyrkin, Kniehl, Steinhauser] Z b [van Ritbergen, Vermaseren, Larin; Czakon] 3 Splitting functions up to third order P (i) (z) [Moch, Vermaseren, Vogt] 4 Soft distribution function up to 2 loops G I,k i [de Florian, Mazzitelli] sv I,3 = sv I,3 δ δ(1 z) + sv I,3 D0 D 0 + sv I,3 D1 D sv I,4 = sv I,4 δ δ(1 z) + sv I,4 D0 D 0 + sv I,4 D1 D 1 + sv I,4 D2 D
55 Result Narayan Rana 20/10/ /46 The available ingredients 1 Form factors up to 3 loops ˆF q and ˆF g [Moch et al.; Baikov et al.; Gehrman et al.;] ˆF b [Gehrman, Kara] 2 Renormalization constant up to 3 loops Z q = 1 Z g [Chetyrkin, Kniehl, Steinhauser] Z b [van Ritbergen, Vermaseren, Larin; Czakon] 3 Splitting functions up to third order P (i) (z) [Moch, Vermaseren, Vogt] 4 Soft distribution function up to 2 loops G I,k i [de Florian, Mazzitelli] sv I,3 = sv I,3 δ δ(1 z) + sv I,3 D0 D 0 + sv I,3 D1 D sv I,4 = sv I,4 δ δ(1 z) + sv I,4 D0 D 0 + sv I,4 D1 D 1 + sv I,4 D2 D
56 Result Ahmed, Mahakhud, NR, Ravindran The complete threshold N 3 LO for Higgs production provides sv g,3 δ. We extract G g,1 3. Using the maximally non abelian nature of the soft distribution function, we obtain G q,1 3. Narayan Rana 20/10/ /46
57 Result Ahmed, Mahakhud, NR, Ravindran The complete threshold N 3 LO for Higgs production provides sv g,3 δ. We extract G g,1 3. Using the maximally non abelian nature of the soft distribution function, we obtain G q,1 3. Narayan Rana 20/10/ /46
58 Result Narayan Rana 20/10/ /46 Ahmed, Mahakhud, NR, Ravindran The complete threshold N 3 LO for Higgs production provides sv g,3 δ. We extract G g,1 3. Using the maximally non abelian nature of the soft distribution function, we obtain G q,1 3. G I,1 3 { 2 ( = C I C A ζ 2 + ζ 2 + ζ 2 ζ ζ ζ 3 ζ ( + C A n f ζ 2 ζ 2 ζ ζ ζ ζ ) ( C F n f ζ 2 88 ζ2 ζ ζ ζ ζ ) ( + n f ζ 2 ζ ζ ) } ζ ) 8748
59 Result Narayan Rana 20/10/ /46 The new results sv I,3 = sv I,3 δ δ(1 z) + sv I,3 D0 D 0 + sv I,3 D1 D sv I,4 = sv I,4 δ δ(1 z) + sv I,4 D0 D 0 + sv I,4 D1 D 1 + sv I,4 D2 D SV ( q,3 δ = C2 A C F ζ 2 + ζ 2 ζ 2 ζ ζ ζ 3 + ζ ζ ) C A CF 2 ( ζ 2 ζ 2 + ζ 2 ζ ζ ζ 3 ζ ζ ) ( + C A C F n f ζ 2 + ζ 2 ζ ζ ζ 3 8 ζ ) C F 3 ( ζ 2 + ζ ζ2 ζ ζ ζ ζ ζ ) C F 2 ( n f ζ 2 ζ 2 ζ ζ ζ ζ ) ( N 2 4 ) ( + C F n f,v 4 2 ζ ζ ζ ) ζ N C F n 2 ( f ζ 2 + ζ ζ )
60 Result Narayan Rana 20/10/ /46 The new results sv I,3 = sv I,3 δ δ(1 z) + sv I,3 D0 D 0 + sv I,3 D1 D sv I,4 = sv I,4 δ δ(1 z) + sv I,4 D0 D 0 + sv I,4 D1 D 1 + sv I,4 D2 D A I 4 and f I 4 computed by Padé approximation. SV ( q,3 δ = C2 A C F ζ 2 + ζ 2 ζ 2 ζ ζ ζ 3 + ζ ζ ) C A CF 2 ( ζ 2 ζ 2 + ζ 2 ζ ζ ζ 3 ζ ζ ) ( + C A C F n f ζ 2 + ζ 2 ζ ζ ζ 3 8 ζ ) C F 3 ( ζ 2 + ζ ζ2 ζ ζ ζ ζ ζ ) C F 2 ( n f ζ 2 ζ 2 ζ ζ ζ ζ ) ( N 2 4 ) ( + C F n f,v 4 2 ζ ζ ζ ) ζ N C F n 2 ( f ζ 2 + ζ ζ )
61 Result Narayan Rana 20/10/ /46 DY : total cross section Stable convergence in perturbation The δ contribution is almost equal and opposite in sign to the sum of the contributions from the D i s Q (GeV) δ N 3 LO D N 3 LO NNLO (SV) NNLO N 3 LO (SV) N 3 LO SV
62 Result DY : scale variation 1.15 NLO 1.1 NNLO Q = 20 GeV 3 N LO SV Reduction in scale dependence Note : Significant increase in scale uncertainties for low µ R Due to presence of large logarithms Resummation improve the scenario (i) R (i) R Q = 200 GeV µ /Q R Narayan Rana 20/10/ /46
63 Result DY : scale variation 1.15 NLO 1.1 NNLO Q = 20 GeV 3 N LO SV Reduction in scale dependence Note : Significant increase in scale uncertainties for low µ R Due to presence of large logarithms Resummation improve the scenario (i) R (i) R Q = 200 GeV µ /Q R Narayan Rana 20/10/ /46
64 Result DY : scale variation 1.15 NLO 1.1 NNLO Q = 20 GeV 3 N LO SV Reduction in scale dependence Note : Significant increase in scale uncertainties for low µ R Due to presence of large logarithms Resummation improve the scenario (i) R (i) R Q = 200 GeV µ /Q R Narayan Rana 20/10/ /46
65 Result DY : scale variation 1.15 NLO 1.1 NNLO Q = 20 GeV 3 N LO SV Reduction in scale dependence Note : Significant increase in scale uncertainties for low µ R Due to presence of large logarithms Resummation improve the scenario (i) R (i) R Q = 200 GeV µ /Q R Narayan Rana 20/10/ /46
66 Result Narayan Rana 20/10/ /46 Higgs production in bottom quark fusion Ahmed, NR, Ravindran 0.7 LO NLO NNLO 3 N LO SV 1.7 LO NLO NNLO 3 N LO SV 0.6 σ [pb] 0.5 σ [pb] µ F = M H /4 µ R = M H µ /m R H µ /m F H
67 Result Narayan Rana 20/10/ /46 Pseudo-scalar Higgs production in gluon fusion Ahmed, Kumar, Mathews, NR, Ravindran dσ (pp A) (pb) LHC 13 TeV MSTW 2008 µ R = µ F = m A K-factors dσ (pp A) (pb) LHC 13 TeV MSTW2008 µ R = µ F = m A LO NLO NNLO N 3 LO sv 1.8 K (1) K (2) 1.6 K (3) m A (GeV) m A (GeV)
68 Result Narayan Rana 20/10/ /46 Pseudo-scalar Higgs production in gluon fusion Ahmed, Kumar, Mathews, NR, Ravindran dσ (pp A) (pb) LHC 13 TeV MSTW2008 µ = µ R = µ F m A = 200 GeV dσ (pp A) (pb) LHC 13 TeV MSTW2008 µ F = m A = 200 GeV LO NLO NNLO N 3 LO (sv) 10 0 LO NLO NNLO N 3 LO (sv) µ / m A µ R / m A
69 Result Narayan Rana 20/10/ /46 Rapidity 3 LO sv Ahmed, Mandal, NR, Ravindran In the large N limit, ˆφ I,(n) d = Γ(1 + nɛ) I,(n) ˆφ Γ 2 (1 + n ɛ 2 ) DY production Higgs production in gluon fusion Higgs production in bottom quark fusion
70 Result Narayan Rana 20/10/ /46 Remarks (1) Factorization of UV, soft and collinear contributions (2) Universal structure of the Form factor singularities (3) Soft distribution is maximally non abelian (4) Inclusive cross section and rapidity distributions can be obtained up to threshold in N 3 LO
71 Result Narayan Rana 20/10/ /46 Remarks (1) Factorization of UV, soft and collinear contributions (2) Universal structure of the Form factor singularities (3) Soft distribution is maximally non abelian (4) Inclusive cross section and rapidity distributions can be obtained up to threshold in N 3 LO
72 Result Narayan Rana 20/10/ /46 Remarks (1) Factorization of UV, soft and collinear contributions (2) Universal structure of the Form factor singularities (3) Soft distribution is maximally non abelian (4) Inclusive cross section and rapidity distributions can be obtained up to threshold in N 3 LO
73 Result Narayan Rana 20/10/ /46 Remarks (1) Factorization of UV, soft and collinear contributions (2) Universal structure of the Form factor singularities (3) Soft distribution is maximally non abelian (4) Inclusive cross section and rapidity distributions can be obtained up to threshold in N 3 LO
74 Result Narayan Rana 20/10/ /46 Thanks for your patience
Threshold Corrections To DY and Higgs at N 3 LO QCD
Threshold Corrections To DY and Higgs at N 3 LO QCD Taushif Ahmed Institute of Mathematical Sciences, India July 2, 2015 Threshold Corrections To DY and Higgs at N 3 LO QCD INFN Sezione Di Torino 1 Prologue
More informationThreshold Corrections To DY and Higgs at N 3 LO QCD
Threshold Corrections To DY and Higgs at N 3 LO QCD Taushif Ahmed Institute of Mathematical Sciences, India April 12, 2016 Threshold Corrections To DY and Higgs at N 3 LO QCD Bergische Universitat Wuppertal
More informationPSEUDO SCALAR FORM FACTORS AT 3-LOOP QCD. Taushif Ahmed Institute of Mathematical Sciences, India March 22, 2016
PSEUDO SCALAR FORM FACTORS AT 3-LOOP QCD Taushif Ahmed Institute of Mathematical Sciences, India March, 016 PROLOGUE: SM & MSSM SM Complex scalar doublet (4 DOF) 3 DOF transform into longitudinal modes
More informationPrecision Higgs physics. at hadron colliders
Precision Higgs physics at hadron colliders Claude Duhr in collaboration with C. Anastasiou, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog, A. Lazopoulos, B. Mistlberger RadCor/LoopFest 2015 UCLA, 16/06/2015
More informationHigher Order Corrections to the Drell-Yan Cross Section in the Mellin Space
Higher Order Corrections to the Drell-Yan Cross Section in the Mellin Space Petra Kovačíková (DESY, Zeuthen) petra.kovacikova@desy.de Corfu Summer School 4 th September 21 Higher Order Corrections to the
More informationarxiv:hep-ph/ v1 25 Sep 2002
hep-ph/0209302 Direct Higgs production at hadron colliders arxiv:hep-ph/0209302v1 25 Sep 2002 Massimiliano Grazzini (a,b) (a) Dipartimento di Fisica, Università di Firenze, I-50019 Sesto Fiorentino, Florence,
More informationarxiv: v1 [hep-ph] 4 Aug 2014
Prepared for sumission to JHEP HRI-RECAPP-014-018 Higgs oson production through annihilation at threshold in N LO QCD arxiv:1408.0787v1 [hep-ph] 4 Aug 014 Taushif Ahmed, a Narayan Rana a and V. Ravindran
More informationUniversality of transverse-momentum and threshold resummations,
Universality of transverse-momentum and threshold resummations, 3 3 and results up to N LO and N LL Leandro Cieri La Sapienza - Università di Roma High Precision for Hard Processes Firenze, Italia September
More informationPrecision Calculations for Collider Physics
SFB Arbeitstreffen März 2005 Precision Calculations for Collider Physics Michael Krämer (RWTH Aachen) Radiative corrections to Higgs and gauge boson production Combining NLO calculations with parton showers
More informationHigher Order QCD Lecture 2
Higher Order QCD Lecture 2 Lance Dixon, SLAC SLAC Summer Institute The Next Frontier: Exploring with the LHC July 21, 2006 Lecture 2 Outline NLO NNLO L. Dixon, 7/21/06 Higher Order QCD: Lect. 2 2 What
More informationHigher order QCD corrections to the Drell-Yan process
Higher order QCD corrections to the Drell-Yan process Massimiliano Grazzini (INFN, Firenze) Milano, march 18, 2009 Outline Introduction NLL+LO resummation NNLO calculation Summary & Outlook Introduction
More informationSM Predictions for Gluon- Fusion Higgs Production
SM Predictions for Gluon- Fusion Higgs Production Massimiliano Grazzini, Frank Petriello, Jianming Qian, Fabian Stoeckli Higgs Workshop, CERN, June 5, 2010 Outline Introduction: status of ggh Three updates:
More informationFully exclusive NNLO QCD computations
Fully exclusive NNLO QCD computations Kirill Melnikov University of Hawaii Loopfest V, SLAC, June 2006 Fully exclusive NNLO QCD computations p. 1/20 Outline Introduction Technology Higgs boson production
More informationQCD threshold corrections for gluino pair production at NNLL
Introduction: Gluino pair production at fixed order QCD threshold corrections for gluino pair production at NNLL in collaboration with Ulrich Langenfeld and Sven-Olaf Moch, based on arxiv:1208.4281 Munich,
More informationPhysics at LHC. lecture one. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture one Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, October 22, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1 LHC
More informationPhysics at LHC. lecture seven. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture seven Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, December 03, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1
More informationTHE STRONG COUPLING AND LHC CROSS SECTIONS
THE STRONG COUPLING AND LHC CROSS SECTIONS Frank Petriello Argonne National Laboratory and Northwestern University Workshop on Precision Measurements of α S February 11, 2011 Outline Focus of talk: customer
More informationStudies of TMD resummation and evolution
Studies of TMD resummation and evolution Werner Vogelsang Univ. Tübingen INT, 0/7/014 Outline: Resummation for color-singlet processes Contact with TMD evolution Phenomenology Conclusions Earlier work
More informationHIGH ENERGY BEHAVIOUR OF FORM FACTORS
HIGH ENERGY BEHAVIOUR OF FORM FACTORS Taushif Ahmed Johannes Gutenberg University Mainz Germany Skype Seminar IIT Hyderabad May 10, 018 With Johannes Henn & Matthias Steinhauser Ref: JHEP 1706 (017) 15
More informationThe forward-backward asymmetry in electron-positron annihilation. Stefan Weinzierl
The forward-backward asymmetry in electron-positron annihilation Stefan Weinzierl Universität Mainz Introduction: I.: II: III: IV.: Electroweak precision physics Higher order corrections Infrared-safe
More informationTHRESHOLD LOGARITHMS BEYOND LEADING POWER
THRESHOLD LOGARITHMS BEYOND LEADING POWER Lorenzo Magnea University of Torino - INFN Torino Radcor-Loopfest, UCLA, 15/6/2015 Outline Introduction Threshold resummations at leading power Gathering evidence
More informationHigher-order QCD corrections to the Higgs-boson qt distribution
Higher-order QCD corrections to the Higgs-boson qt distribution Jun Gao Argonne National Laboratory June 5, 05 In collaboration with Radja Boughezal and Frank Petriello Radcor/Loopfest, UCLA 05 qq Motivation
More informationSOFT RADIATION BEYOND LEADING POWER
SOFT RADIATION BEYOND LEADING POWER Lorenzo Magnea University of Torino - INFN Torino WHEPP XIV - IIT Kanpur - 07/12/2015 Outline Introduction Threshold resummations at leading power Gathering evidence
More informationTHE TRANSVERSE MOMENTUM DISTRIBUTION OF THE HIGGS BOSON AT THE LHC
THE TRANSVERSE MOMENTUM DISTRIBUTION OF THE HIGGS BOSON AT THE LHC Massimiliano Grazzini (INFN, Firenze) Les Houches, may 2005 Outline Introduction The Higgs spectrum The program HqT NLL+LO and NNLL+NLO
More informationSoft Collinear Effective Theory: An Overview
Soft Collinear Effective Theory: An Overview Sean Fleming, University of Arizona EFT09, February 1-6, 2009, Valencia Spain Background Before SCET there was QCD Factorization Factorization: separation of
More informationSCET for Colliders. Matthias Neubert. Cornell University. Based on work with Thomas Becher (FNAL) and Ben Pecjak (Siegen)
SCET for Colliders Matthias Neubert Cornell University LoopFest V, SLAC June 21, 2006 Based on work with Thomas Becher (FNAL) and Ben Pecjak (Siegen) 1 2 SCET for Colliders Introduction Overview of SCET
More informationTowards Jet Cross Sections at NNLO
Towards Jet Cross Sections at HP.4, September, MPI Munich Expectations at LHC Large production rates for Standard Model processes single jet inclusive and differential di-jet cross section will be measured
More informationarxiv:hep-ph/ v1 29 Aug 2006
IPPP/6/59 August 26 arxiv:hep-ph/6837v1 29 Aug 26 Third-order QCD results on form factors and coefficient functions A. Vogt a, S. Moch b and J.A.M. Vermaseren c a IPPP, Physics Department, Durham University,
More informationNew physics effects in Higgs cross sections
New physics effects in Higgs cross sections Robert Harlander Bergische Universität Wuppertal ERC Workshop Nov 2014, Mainz supported by rescaled couplings new Higgs bosons BSM particle effects new processes
More informationPhysics at the Large Hadron Collider
Herbstschule Maria Laach, September 2005 Physics at the Large Hadron Collider Michael Krämer (RWTH Aachen) Lecture 1: Review of the Standard Model Lecture 2: SM physics at hadron colliders Lecture 3: Higgs
More informationN-jettiness as a subtraction scheme for NNLO
N-jettiness as a subtraction scheme for NNLO! Xiaohui Liu based on:! arxiv:1504.02131, Boughezal, Focke, XL and Petriello arxiv:1505.03893, Boughezal, Focke, Giele, XL and Petriello arxiv:1504.02540, Boughezal,
More informationQCD resummation for jet and hadron production
QCD resummation for jet and hadron production Werner Vogelsang Univ. Tübingen UCL, 14 Feb 2014 Outline: Introduction: QCD threshold resummation Drell-Yan process Resummation in QCD hard-scattering Hadron
More informationHigher-Order Corrections in Threshold Resummation
DESY 5-5, SFB/CPP-5-5 DCPT/5/6, IPPP/5/3 NIKHEF 5- June 5 hep-ph/5688 Higher-Order Corrections in Threshold Resummation S. Moch a, J.A.M. Vermaseren b and A. Vogt c a Deutsches Elektronensynchrotron DESY
More informationHiggs boson production at the LHC: NNLO partonic cross sections through order ǫ and convolutions with splitting functions to N 3 LO
SFB/CPP-12-93 TTP12-45 LPN12-127 Higgs boson production at the LHC: NNLO partonic cross sections through order ǫ and convolutions with splitting functions to N 3 LO Maik Höschele, Jens Hoff, Aleey Pak,
More informationAN INTRODUCTION TO QCD
AN INTRODUCTION TO QCD Frank Petriello Northwestern U. & ANL TASI 2013: The Higgs Boson and Beyond June 3-7, 2013 1 Outline We ll begin with motivation for the continued study of QCD, especially in the
More informationHiggs + Jet angular and p T distributions : MSSM versus SM
Higgs + Jet angular and p T distributions : MSSM versus SM Oliver Brein ( Institute for Particle Physics Phenomenology, Durham, UK ) in collaboration with Wolfgang Hollik e-mail: oliver.brein@durham.ac.uk
More informationggf Theory Overview For Highest Precision
ggf Theory Overview For Highest Precision Lumley Castle Franz Herzog Nikhef LHC Higgs Production in the Standard Model 2 LHC Higgs Data 3 Theoretical Formalism To compute cross sections we use the Factorisation
More informationHiggs theory. Achilleas Lazopoulos (ETH Zurich) ATLAS HSG2 meeting Athens, 7 Sep Friday, December 30, 11
Higgs theory Achilleas Lazopoulos (ETH Zurich) ATLAS HSG2 meeting Athens, 7 Sep. 2011 Why is Higgs production different In the dominant channel, gluon fusion, it starts already at second order in as, so
More informationEffects of Beyond Standard Model physics in Effective Field Theory approach on Higgs' pt spectrum
PhD Seminar 2015, PSI Effects of Beyond Standard Model physics in Effective Field Theory approach on Higgs' pt spectrum Agnieszka Ilnicka in collaboration with: M. Grazzini M. Spira M. Wiesemann Motivation
More informatione + e 3j at NNLO: Results for all QED-type Colour Factors p.1
e + e 3j at NNLO: Results for all QED-type Colour Factors Thomas Gehrmann Universität ürich UNIVERSITAS TURICENSIS MDCCC XXXIII in collaboration with A. Gehrmann De Ridder, E.W.N. Glover, G. Heinrich Loopfest
More informationTHE INFRARED SINGULARITIES OF MASSLESS GAUGE THEORIES
THE INFRARED SINGULARITIES OF MASSLESS GAUGE THEORIES Lorenzo Magnea University of Torino - INFN Torino JGU, Mainz, 07/12/11 Outline Infrared divergences to all orders Theory Practice Tools The dipole
More informationFactorization, Evolution and Soft factors
Factorization, Evolution and Soft factors Jianwei Qiu Brookhaven National Laboratory INT Workshop: Perturbative and nonperturbative aspects of QCD at collider energies University of Washington, Seattle,
More informationProgress in Sudakov resummations
Progress in Sudakov resummations Lorenzo Magnea Università di Torino I.N.F.N. Torino magnea@to.infn.it HERA LHC Workshop - March 27, 2004 Abstract Some recent developments in the field of soft gluon resummations
More informationPrecision Jet Physics At the LHC
Precision Jet Physics At the LHC Matthew Schwartz Harvard University JETS AT THE LHC An (almost) universal feature of SUSY is and Source: Atlas TDR SIGNAL VS. BACKGROUND Source: Atlas TDR Can we trust
More informationCross sections for SM Higgs boson production
Cross sections for SM Higgs boson production Massimiliano Grazzini (INFN & ETH Zurich) Higgs MiniWorkshop, Torino, november 24, 2009 Outline Introduction Total cross section: - The NNLL+NNLO calculation
More informationRecent theoretical issues in Higgs production
Recent theoretical issues in Higgs production Frank Petriello MCTP Spring Symposium on Higgs Physics April 16, 2012 The Higgs search from LEP to the LHC In early 2000: MH
More informationFOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS. Lorenzo Magnea. University of Torino - INFN Torino. Pino Day, Cortona, 29/05/12
FOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS Lorenzo Magnea University of Torino - INFN Torino Pino Day, Cortona, 29/05/12 Outline Crossing paths with Pino Cusps, Wilson lines and Factorization
More informationQCD Collinear Factorization for Single Transverse Spin Asymmetries
INT workshop on 3D parton structure of nucleon encoded in GPD s and TMD s September 14 18, 2009 QCD Collinear Factorization for Single Transverse Spin Asymmetries Iowa State University Based on work with
More informationPoS(DIS 2010)139. On higher-order flavour-singlet splitting functions and coefficient functions at large x
On higher-order flavour-singlet splitting functions and coefficient functions at large x Department of Mathematical Sciences, University of Liverpool, UK E-mail: G.N.Soar@liv.ac.uk A. Vogt Department of
More informationTMD Fragmentation Function at NNLO
TMD Fragmentation Function at NNLO Institut für Theoretische Physik, Universität Regensburg, D-9040 Regensburg, Germany E-mail: vladimirov.aleksey@gmail.com The calculation of the unpolarized non-singlet
More informationQCD and Rescattering in Nuclear Targets Lecture 2
QCD and Rescattering in Nuclear Targets Lecture Jianwei Qiu Iowa State University The 1 st Annual Hampton University Graduate Studies Program (HUGS 006) June 5-3, 006 Jefferson Lab, Newport News, Virginia
More informationResearch in QCD factorization
Research in QCD factorization Bowen Wang Southern Methodist University (Dallas TX) Jefferson Lab Newport News VA 1/1/015 My research at SMU in 011-015 Ph. D. advisor: Pavel Nadolsky Ph. D. thesis: The
More informationm H tanβ 30 LHC(40fb -1 ): LEP2: e + e Zh m A (GeV)
Charged Higgs Bosons Production in Bottom-Gluon Fusion Tilman Plehn, Madison MSSM Higgs Bosons at the LHC Why Bottom Parton Description? QCD Corrections -QCD Corrections MSSM Higgs Bosons at the LHC MSSM
More informationTop pair production near threshold at LHC (NLO/NLL analysis in NRQCD)
Top@LHC LHC TTbar-Threshold Threshold@ILC/LHC Green Functions Top pair production near threshold at LHC (NLO/NLL analysis in NRQCD) Yuichiro Kiyo TTP, Universität Karlsruhe Collaboration with: J. H. Kühn(KA),
More informationAntenna Subtraction at NNLO
Antenna Subtraction at NNLO Aude Gehrmann-De Ridder ETH Zürich in collaboration with T. Gehrmann, E.W.N. Glover Loopfest IV Snowmass 2005 Antenna Subtraction at NNLO p.1 Outline Jet observables Jets in
More informationQCD studies and Higgs searches at the LHC. part three. Sven-Olaf Moch. DESY, Zeuthen. CALC-2012, Dubna, July
QCD studies and Higgs searches at the LHC part three Sven-Olaf Moch sven-olaf.moch@desy.de DESY, Zeuthen CALC-212, Dubna, July 28-29 212 Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.1 Plan
More informationPoS(RADCOR2011)042. O(αs 2 ) QCD corrections to the resonant sneutrino / slepton production at LHC. Swapan K Majhi
O(αs ) QCD corrections to the resonant sneutrino / slepton production at LHC Indian Association for the Cultivation of Science, A&B Raja S C Mullick Road, Kolkata 70003, India E-mail: swapan.majhi@saha.ac.in
More informationNLO weighted Sivers asymmetry in SIDIS and Drell-Yan: three-gluon correlator
NLO weighted Sivers asymmetry in SIDIS and Drell-Yan: three-gluon correlator Lingyun Dai Indiana University Based on the work done with Kang, Prokudin, Vitev arxiv:1409.5851, and in preparation 1 2 Outlines
More informationHiggs Production at LHC
Higgs Production at LHC Vittorio Del Duca INFN Torino Havana 3 April 2006 1 In proton collisions at 14 TeV, and for the Higgs is produced mostly via M H > 100 GeV gluon fusion gg H largest rate for all
More informationfrom D0 collaboration, hep-ex/
At present at the Tevatron is extracted from the transverse-mass distribution Events / GeV/c 2 2000 1500 1000 500 Fit region 0 50 60 70 80 90 100 110 120 from D0 collaboration, hep-ex/0007044 Transverse
More informationPrecise theoretical predictions for Large Hadron Collider physics
Precise theoretical predictions for Large Hadron Collider physics Giancarlo Ferrera Milan University & INFN, Milan Milan June 28th 2017 Precise theoretical predictions for LHC physics 1/20 TIF LAB: particle
More informationPrecision theoretical predictions for hadron colliders
Precision theoretical predictions for hadron colliders giuseppe bozzi Università degli Studi di Milano and INFN, Sezione di Milano IPN Lyon 25.02.2010 giuseppe bozzi (Uni Milano) Precision theoretical
More informationDiphoton production at LHC
1 Diphoton production at LHC 120 GeV < M γγ < 140 GeV Leandro Cieri Universidad de Buenos Aires - Argentina & INFN Sezione di Firenze Rencontres de Moriond March 11, 2012 Outline Introduction Available
More informationGluonic Spin Orbit Correlations
Gluonic Spin Orbit Correlations Marc Schlegel University of Tuebingen in collaboration with W. Vogelsang, J.-W. Qiu; D. Boer, C. Pisano, W. den Dunnen Orbital Angular Momentum in QCD INT, Seattle, Feb.
More informationEvolution of 3D-PDFs at Large-x B and Generalized Loop Space
Evolution of 3D-PDFs at Large-x B and Generalized Loop Space Igor O. Cherednikov Universiteit Antwerpen QCD Evolution Workshop Santa Fe (NM), 12-16 May 2014 What we can learn from the study of Wilson loops?
More information2. HEAVY QUARK PRODUCTION
2. HEAVY QUARK PRODUCTION In this chapter a brief overview of the theoretical and experimental knowledge of heavy quark production is given. In particular the production of open beauty and J/ψ in hadronic
More informationAlessandro Vicini University of Milano, INFN Milano
Higgs production via gluon fusion in the POWHEG approach in the SM and in the MSSM Alessandro Vicini University of Milano, INFN Milano Padova, 15 febbraio 12 in collaboration with: E. Bagnaschi, G. Degrassi,
More informationJoão Pires Universita di Milano-Bicocca and Universita di Genova, INFN sezione di Genova. HP September 2014 Florence, Italy
Jets in pp at NNLO João Pires Universita di Milano-Bicocca and Universita di Genova, INFN sezione di Genova HP.5-5 September 014 Florence, Italy based on: Second order QCD corrections to gluonic jet production
More informationEffective-theory methods for top-quark and squark pair production at LHC and Tevatron
Effective-theory methods for top-quark and squark pair production at LHC and Tevatron Christian Schwinn Univ. Freiburg 21.10.2010 (Based on M.Beneke, P.Falgari, CS, arxiv:0907.1443 [hep-ph], arxiv:1007.5414
More informationOutline Motivations for ILC: e + e γ/z q qg LHC: pp l + l + jet (q q l + l g + qg l + l q + qg l + l q) Existing literature The complete EW one-loop c
Complete electroweak corrections to e + e 3 jets C.M. Carloni Calame INFN & University of Southampton Workshop LC08: e + e Physics at TeV scale September 22-25, 2008 in collaboration with S. Moretti, F.
More informationUnderstanding Parton Showers
Understanding Parton Showers Zoltán Nagy DESY in collaboration with Dave Soper Introduction Pile-up events 7 vertices 2009 single vertex reconstructed! 2011 2010 4 vertices 25 vertices 2012 Introduction
More informationEdinburgh Research Explorer
Edinburgh Research Explorer Higgs production via gluon-gluon fusion with finite top mass beyond next-to-leading order Citation for published version: Marzani, S, Ball, RD, Del Duca, V, Forte, S & Vicini,
More informationNNLO Phenomenology Using Jettiness Subtraction
NNLO Phenomenology Using Jettiness Subtraction Radja Boughezal Radcor/Loopfest 2015, June 15-19, UCLA 1 Outline Motivation IR subtraction schemes at NNLO (local and non-local subtractions) The N-jettiness
More informationNumerical Evaluation of Multi-loop Integrals
Numerical Evaluation of Multi-loop Integrals Sophia Borowka MPI for Physics, Munich In collaboration with: J. Carter and G. Heinrich Based on arxiv:124.4152 [hep-ph] http://secdec.hepforge.org DESY-HU
More informationA pnrqcd approach to t t near threshold
LoopFest V, SLAC, 20. June 2006 A pnrqcd approach to t t near threshold Adrian Signer IPPP, Durham University BASED ON WORK DONE IN COLLABORATION WITH A. PINEDA AND M. BENEKE, V. SMIRNOV LoopFest V p.
More informationPhysique des Particules Avancées 2
Physique des Particules Avancées Interactions Fortes et Interactions Faibles Leçon 6 Les collisions p p (http://dpnc.unige.ch/~bravar/ppa/l6) enseignant Alessandro Bravar Alessandro.Bravar@unige.ch tél.:
More informationNNLO antenna subtraction with one hadronic initial state
antenna subtraction with one hadronic initial state Alejandro Daleo, Aude Gehrmann-De Ridder Institute for Theoretical Physics, ETH Zürich E-mail: adaleo@phys.ethz.ch, gehra@phys.ethz.ch Thomas Gehrmann,
More informationAssociated Higgs Production with Bottom Quarks at Hadron Colliders
Associated Higgs Production with Bottom Quarks at Hadron Colliders Michael Krämer (RWTH Aachen) Kickoff Meeting of the working group on Higgs and heavy quarks Wuppertal 1.-2.3. 2010 1 /25 Higgs production
More informationδm W = 15 MeV δm top = 1 GeV
Precision SM physics at the LHC... what we hope to see (Bentvelsen, Grünewald) Repeat the electroweak fit changing the uncertainties δm W = 15 MeV δm top = 1 GeV same central values Michael Krämer Page
More informationTransverse Momentum Distributions: Matches and Mismatches
Transverse Momentum Distributions: Matches and Mismatches Ahmad Idilbi ECT* M.G. Echevarría, Ahmad Idilbi, Ignazio Scimemi. [arxiv:.947] MGE, AI, Andreas Schäfer, IS. [arxiv: 08.8] MGE, AI, IS. JHEP 07
More informationZhongbo Kang. QCD evolution and resummation for transverse momentum distribution. Theoretical Division, Group T-2 Los Alamos National Laboratory
QCD evolution and resummation for transverse momentum distribution Zhongbo Kang Theoretical Division, Group T-2 Los Alamos National Laboratory QCD Evolution Worshop Jefferson Lab, Newport News, VA Outline:
More informationIntroduction to High Energy Nuclear Collisions I (QCD at high gluon density) Jamal Jalilian-Marian Baruch College, City University of New York
Introduction to High Energy Nuclear Collisions I (QCD at high gluon density) Jamal Jalilian-Marian Baruch College, City University of New York Many thanks to my colleagues, A. Deshpande, F. Gelis, B. Surrow
More informationResummation in PDF fits. Luca Rottoli Rudolf Peierls Centre for Theoretical Physics, University of Oxford
Resummation in PDF fits Luca Rottoli Rudolf Peierls Centre for Theoretical Physics, University of Oxford LHC, New Physics, and the pursuit of Precision LHC as a discovery machine Higgs Boson 10 1 BSM particles
More informationINCLUSIVE D- AND B-MESON PRODUCTION
INCLUSIVE D- AND B-MESON PRODUCTION AT THE LHC Seminar Universitaet Muenster, May 7, 22 G. Kramer based on work in collaboration with B. Kniehl, I. Schienbein, H. Spiesberger G. Kramer (Universitaet Hamburg)
More informationThe package TopoID and its applications to Higgs physics
The package TopoID and its applications to Higgs physics Jens Hoff (DESY, KIT) Theory Seminar, University of Zurich 3rd of November, 2015 1 TopoID Polynomial ordering Topology classification Relations
More informationInclusive B decay Spectra by Dressed Gluon Exponentiation. Einan Gardi (Cambridge)
Inclusive B decay Spectra by Dressed Gluon Exponentiation Plan of the talk Einan Gardi (Cambridge) Inclusive Decay Spectra Why do we need to compute decay spectra? Kinematics, the endpoint region and the
More informationImplications of LHC Higgs results
Implications of LHC Higgs results Giuseppe Degrassi Universita' di Roma Tre, I.N.F.N. Sezione Roma Tre Frascati, May 17th, 2012 Outline Past and present information on the Higgs boson Discussing the hypothesis:
More informationAzimuthal decorrelations between jets in QCD
Azimuthal decorrelations between jets in QCD Andrea Banfi ETH Zurich q q p 1 p 1 Outline Azimuthal decorrelations in QCD hard processes Dijets in the back-to-back region Phenomenology of azimuthal decorrelations
More informationStatus of Higgs plus one jet at NNLO
Status of Higgs plus one jet at NNLO Matthieu Jaquier Physics Institute University of Zürich Radcor-Loopfest UCLA 7 th June 205 Based on work with X. Chen, T. Gehrmann and E.W.N. Glover Matthieu Jaquier
More informationA. Mitov 3-loop time-like splitting functions in Mellin space and NNLO fragmentation
Three-loop time-like splitting functions in Mellin space and NNLO fragmentation Alexander Mitov DESY Work in progress with: M. Cacciari; Lance Dixon; S-O. Moch Also based on: hep-ph/0604160 (with Sven
More informationTop-pair production in hadron collisions at NNLL
EPJ Web of Conferences 49, 17014 (2013) DOI: 10.1051/ epjconf/ 20134917014 C Owned by the authors, published by EDP Sciences, 2013 Top-pair production in hadron collisions at NNLL M. Beneke 1,2, P. Falgari
More informationDrell-Yan Production at Hadron Colliders
Drell-Yan Production at Hadron Colliders Radja Boughezal Argonne National Laboratory Lectures at the CTEQ School on QCD and Electroweak Phenomenology Pittsburgh, July 18-28, 2017 Topics we will cover Historical
More informationTop production measurements using the ATLAS detector at the LHC
Top production measurements using the ATLAS detector at the LHC INFN, Sezione di Bologna and University of Bologna E-mail: romano@bo.infn.it This paper is an overview of recent results on top-quark production
More informationQCD at LHC. Vittorio Del Duca INFN Torino. Napoli 15 ottobre 2004
QCD at LHC Vittorio Del Duca INFN Torino Napoli 15 ottobre 2004 QCD Premio Nobel 2004! an unbroken Yang-Mills gauge field theory featuring asymptotic freedom confinement in non-perturbative regime (low
More informationProbing nucleon structure by using a polarized proton beam
Workshop on Hadron Physics in China and Opportunities with 12 GeV Jlab July 31 August 1, 2009 Physics Department, Lanzhou University, Lanzhou, China Probing nucleon structure by using a polarized proton
More informationQCD at the LHC Joey Huston Michigan State University
QCD at the LHC Joey Huston Michigan State University Some references CHS over 1500 downloads so far arxiv:07122447 Dec 14, 2007 goal is to provide a reasonably global picture of LHC calculations (with
More informationHEAVY QUARKS FROM PHOTOPRODUCTION (AND DIS)
HEAVY QUARKS FROM PHOTOPRODUCTION (AND DIS) INT 20, Seattle EIC workshop Week 6, Oct. 22, 20 H. Spiesberger based on work in collaboration with A. Kadeer, B. Kniehl, G. Kramer, C. Pisano, I. Schienbein,
More informationQCD Precision Tests in Deeply Inelastic Scattering
QCD Precision Tests in Deeply Inelastic Scattering Johannes Blümlein DESY Introduction and Method QCD Analysis of Unpolarized Structure Functions Λ QCD and α s (M 2 Z ) What would we like to know? J. Blümlein
More informationH + jet(s) (fixed order)
Mass effects in gg H + jet(s) (fixed order) Gudrun Heinrich Max Planck Institute for Physics, Munich Higgs+jets workshop, IPPP Durham December 9, 2014 Higgs Effective Theory (HEFT) m t L eff = c 1 G µν,a
More informationTercera Sesión. XI Escuela de Física Fundamental. Universidad Veracruzana, Xalapa. 28 de Septiembre de 2016
Tercera Sesión XI Escuela de Física Fundamental Universidad Veracruzana, Xalapa. 28 de Septiembre de 2016 1 / M.E. Tejeda-Yeomans elena.tejeda@fisica.uson.mx Iniciación a la QCD 1/35 35 3 lectures: three
More information