Resolving m c and m b in precision Higgs boson analyses Zhengkang Zhang University of Michigan Based on A. A. Petrov, S. Pokorski, J. D. Wells, ZZ, Phys. Rev. D 91 , 073001 (2015) [arXiv:1501.02803 [hep-ph]] Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 1 / 16
Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 2 / 16
Introduction: the precision frontier Measure its properties very precisely! (BSM hints?) TeV ) 2 ∼ O (1%) . ◮ Theory expectation: ( v ◮ Experiment expectation: (sub)percent-level measurements of Γ H → c ¯ c , Γ H → b ¯ b at HL-LHC, ILC, FCC-ee, CEPC. [Asner et al , 1310.0763] [Peskin, 1312.4974] [Fan, Reece, Wang, 1411.1054] [Ruan, 1411.5606] Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 3 / 16
Introduction: the precision frontier Measure its properties very precisely! (BSM hints?) TeV ) 2 ∼ O (1%) . ◮ Theory expectation: ( v ◮ Experiment expectation: (sub)percent-level measurements of Γ H → c ¯ c , Γ H → b ¯ b at HL-LHC, ILC, FCC-ee, CEPC. [Asner et al , 1310.0763] [Peskin, 1312.4974] [Fan, Reece, Wang, 1411.1054] [Ruan, 1411.5606] Will future experiments be sensitive to %-level new physics effects? No, unless theory uncertainties can be reduced to below O (1%) ! Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 3 / 16
Motivation: theory uncertainties in Γ H → c ¯ c , Γ H → b ¯ b Where are the theory uncertainties from? ◮ Perturbative uncertainty well below 1%, thanks to N 4 LO calculations [Baikov, Chetyrkin, Kuhn, hep-ph/0511063] . Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 4 / 16
Motivation: theory uncertainties in Γ H → c ¯ c , Γ H → b ¯ b Where are the theory uncertainties from? ◮ Perturbative uncertainty well below 1%, thanks to N 4 LO calculations [Baikov, Chetyrkin, Kuhn, hep-ph/0511063] . ◮ Parametric uncertainties dominate, especially a few % from input quark masses m c , m b : ∆Γ H → c ¯ ≃ ∆ m c ( m c ) ∆Γ H → b ¯ ≃ ∆ m b ( m b ) c b 10 MeV × 2 . 1% , 10 MeV × 0 . 56% . Γ H → c ¯ Γ H → b ¯ c b where m Q ( m Q ) ≡ m MS Q ( µ = m Q ) . [Denner, Heinemeyer, Puljak, Rebuzzi, Spira, 1107.5909] [Almeida, Lee, Pokorski, Wells, 1311.6721] [Lepage, Mackenzie, Peskin, 1404.0319] etc. cf. PDG: m c ( m c ) = 1 . 275(25) GeV, m b ( m b ) = 4 . 18(3) GeV. Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 4 / 16
Motivation: theory uncertainties in Γ H → c ¯ c , Γ H → b ¯ b Where are the theory uncertainties from? ◮ Perturbative uncertainty well below 1%, thanks to N 4 LO calculations [Baikov, Chetyrkin, Kuhn, hep-ph/0511063] . ◮ Parametric uncertainties dominate, especially a few % from input quark masses m c , m b : ∆Γ H → c ¯ ≃ ∆ m c ( m c ) ∆Γ H → b ¯ ≃ ∆ m b ( m b ) c b 10 MeV × 2 . 1% , 10 MeV × 0 . 56% . Γ H → c ¯ Γ H → b ¯ c b where m Q ( m Q ) ≡ m MS Q ( µ = m Q ) . [Denner, Heinemeyer, Puljak, Rebuzzi, Spira, 1107.5909] [Almeida, Lee, Pokorski, Wells, 1311.6721] [Lepage, Mackenzie, Peskin, 1404.0319] etc. cf. PDG: m c ( m c ) = 1 . 275(25) GeV, m b ( m b ) = 4 . 18(3) GeV. Goal: understand this uncertainty propagation in more detail. Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 4 / 16
Precision Higgs analyses: conventional approach Use PDG quark masses or other averaged quark masses as inputs. Unsatisfactory: ◮ Correlations among the entries neglected ◮ Correlation with α s neglected ◮ Uncertainties underestimated and inflated [Dehnadi, Hoang, Mateu, Zebarjad, 1102.2264] Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 5 / 16
Precision Higgs analyses: proposed approach PDG averaged quark masses are dominated by m c , m b determinations from low-energy observables † , e.g. ◮ e + e − → Q ¯ Q cross sections; ◮ Kinematic distributions of semileptonic B decay. † For the prospect of lattice calculations see [Lepage, Mackenzie, Peskin, 1404.0319] . Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 6 / 16
Precision Higgs analyses: proposed approach PDG averaged quark masses are dominated by m c , m b determinations from low-energy observables † , e.g. ◮ e + e − → Q ¯ Q cross sections; ◮ Kinematic distributions of semileptonic B decay. A global analysis! O Higgs � � Inputs O low ( m c , m b , α s , . . . ) ( m c , m b , α s , . . . ) 1 1 m c � O Higgs O low � ( m c , m b , α s , . . . ) ( m c , m b , α s , . . . ) 2 2 m b ⇐ ⇒ � O Higgs O low � ( m c , m b , α s , . . . ) ( m c , m b , α s , . . . ) 3 α s 3 . . . . . . . . . † For the prospect of lattice calculations see [Lepage, Mackenzie, Peskin, 1404.0319] . Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 6 / 16
Precision Higgs analyses: proposed approach ... just like what we have done before! Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 7 / 16
b in terms of M c 1 , M b A first calculation: Γ H → c ¯ c , Γ H → b ¯ 2 To see the role of low-energy observables in this precision Higgs boson analyses, we will ◮ focus on Γ H → c ¯ c , Γ H → b ¯ b , and ◮ eliminate m c , m b from the input in favor of M c 1 , M b 2 . “ n th moment of R Q ”: � where R Q ≡ σ ( e + e − → Q ¯ d s QX ) M Q n ≡ s n +1 R Q ( s ) , σ ( e + e − → µ + µ − ) . Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 8 / 16
b in terms of M c 1 , M b A first calculation: Γ H → c ¯ c , Γ H → b ¯ 2 Moments of R Q are calculated by relativistic quarkonium sum rules [Novikov, Okun, Shifman, Vainshtein, Voloshin, Zakharov, Phys. Rept. 41, 1 (1978)] � d � n � � s n +1 R Q ( s ) = 12 π 2 � d s M Q Π Q ( q 2 ) � n = , where � d q 2 n ! q 2 =0 � ( q 2 g µν − q µ q ν )Π Q ( q 2 ) = − i d 4 x e iq · x � 0 | Tj µ ( x ) j † ν (0) | 0 � , via an operator product expansion (OPE) � � 2 � α s ( µ α ) � i � Q Q / (2 / 3) ln a m Q ( µ m ) 2 ln b m Q ( µ m ) 2 M Q C ( a,b ) + M Q, np n = n,i ( n f ) . � � 2 n n π µ m 2 µ α 2 2 m Q ( µ m ) i,a,b Low moments (small n ) are preferred to suppress M Q, np . n Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 9 / 16
b in terms of M c 1 , M b A first calculation: Γ H → c ¯ c , Γ H → b ¯ 2 � � 2 � α s ( µ α ) � i � ln a m Q ( µ m ) 2 ln b m Q ( µ m ) 2 Q Q / (2 / 3) C ( a,b ) + M Q, np M Q n = n,i ( n f ) . � � 2 n n µ m 2 µ α 2 π 2 m Q ( µ m ) i,a,b Best calculations available: ◮ C ( a,b ) n,i ( n f ) : up to i = 3 [Maier, Maierhofer, Marquard, Smirnov, 0907.2117] . ◮ M Q, np : up to NLO [Broadhurst, Baikov, Ilyin, Fleischer, Tarasov, Smirnov, n hep-ph/9403274] , kept only for charm. Renormalization scales: µ m for m Q , µ α for α s . Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 10 / 16
b in terms of M c 1 , M b A first calculation: Γ H → c ¯ c , Γ H → b ¯ 2 � � 2 � α s ( µ α ) � i � Q Q / (2 / 3) ln a m Q ( µ m ) 2 ln b m Q ( µ m ) 2 M Q C ( a,b ) + M Q, np n = n,i ( n f ) . � � 2 n n π µ m 2 µ α 2 2 m Q ( µ m ) i,a,b � � � α , M c, np α s , M c 1 , µ c m , µ c m c ( m c ) = m c ( m c ) , 1 ⇒ � � α s , M b 2 , µ b m , µ b m b ( m b ) = m b ( m b ) . α [Kuhn, Steinhauser, hep-ph/0109084] [Kuhn, Steinhauser, Sturm, hep-ph/0702103] [Chetyrkin, Kuhn, Maier, Maierhofer, Marquard, Steinhauser, Sturm, 0907.2110] Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 11 / 16
b in terms of M c 1 , M b A first calculation: Γ H → c ¯ c , Γ H → b ¯ 2 � � 2 � α s ( µ α ) � i � Q Q / (2 / 3) ln a m Q ( µ m ) 2 ln b m Q ( µ m ) 2 M Q C ( a,b ) + M Q, np n = n,i ( n f ) . � � 2 n n π µ m 2 µ α 2 2 m Q ( µ m ) i,a,b � � � α , M c, np α s , M c 1 , µ c m , µ c m c ( m c ) = m c ( m c ) , 1 ⇒ � � α s , M b 2 , µ b m , µ b m b ( m b ) = m b ( m b ) . α [Kuhn, Steinhauser, hep-ph/0109084] [Kuhn, Steinhauser, Sturm, hep-ph/0702103] [Chetyrkin, Kuhn, Maier, Maierhofer, Marquard, Steinhauser, Sturm, 0907.2110] Should keep µ m � = µ α , otherwise perturbative uncertainty will be underestimated (common in the literature). [Dehnadi, Hoang, Mateu, Zebarjad, 1102.2264] [Dehnadi, Hoang, Mateu, 1504.07638] Zhengkang Zhang (U Michigan) Resolving m c and m b (1501.02803) CHARM 2015, WSU, Detroit 11 / 16
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