Precision tests of SM at low energy: Hadronic structure corrections Misha Gorshteyn - Universität Mainz 56th International Winter Meeting on Nuclear Physics - Bormio - Italia
Work being done together with Chuck Horowitz Michael Ramsey-Musolf Hubert Spiesberger Xilin Zhang Chien-Yeah Seng Hiren Patel
Precision tests of SM at low energies - basis • Goal: measure parameters of the Standard Model to high precision Confront with precision calculations in SM Constrain/discover New Physics via deviations • SM parameters: charges, masses, mixing • At low energy quarks are bound in hadrons - how can we access their fundamental properties through hadronic mess? • A charge associated with a conserved current is not renormalized by strong interaction - the charge of a composite = ∑ charges of constituents • Strong interaction may modify observables at NLO in α em / π ≈ 2 ∙ 10 -3 • Experiment + pure EW RC - accuracy at 10 -4 level or better • In many low-energy tests hadron structure effects is the main limitation!
Precision measurements of weak mixing angle Weak mixing angle - mixing of the NC gauge fields WMA determines the relative strength of the weak NC vs. e.-m. interaction Q p =+1 Q pW =1-4sin 2 θ W 4
Precision measurements of weak mixing angle Weak mixing angle - mixing of the NC gauge fields WMA determines the relative strength of the weak NC vs. e.-m. interaction Q p =+1 Q pW =1-4sin 2 θ W Atomic PV Møller scattering Colliders e + q γ Z e e Z e γ Z e e - - q e Purely leptonic Z-pole measurement Coherent quarks in a nucleus e-DIS @ JLab, EIC ν -DIS @ NuTEV P2 MESA @ Mainz ν μ , ν Q-Weak @ JLab e e e e γ Z W Z γ Z p p n n Coherent quarks in p Incoherent ν -q scattering Incoherent e-q scattering 4
Weak charge of the proton from PVES Elastic scattering of polarized electrons off unpolarized protons Q 2 at low momentum transfer � = − G F Q 2 A P V = σ → − σ ← Q p W + Q 2 B ( Q 2 ) ⇥ ⇤ √ σ → + σ ← 4 2 πα � This Experiment QWEAK Data Rotated to the Forward-Angle Limit A/A ���� Q ���������� B( , � =0) ����� HAPPEX 0.4 � ���� SAMPLE ���� PVA4 ���� G0 2 � Q SM (prediction) � 0.3 Effects of hadronic structure � 2 (size, spin, strangeness) kinematically suppressed Q 0.2 � Existing hadronic data used to obtain B and δ B W p � � � 0.1 0 � � 0.0 � 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Go down to Q 2 ≤ 0.03 GeV 2 2 2 [GeV] Q Unprecedented challenge: tiny asymmetry to 1-2 % δ sin 2 θ W = 1 − 4 sin 2 θ W δ Q p W The reward: Q Wp = 1-4sin 2 θ W ~ 0.07 in SM sin 2 θ W 4 sin 2 θ W Q p W 5
SM running of the weak mixing angle � 0.245 Erler, Ramsey-Musolf QW (p) NuTeV QW (e) 0.24 P2@MESA Qweak Moller Universal quantum corrections SOLID 0.235 can be absorbed into running, QW (APV ) LEP1 scale-dependent sin 2 θ W ( μ ) ATLAS eDIS Tevatron 0.23 SLD 3 % SM uncertainty: few x 10 -4 sin 2 θ W (Q) MS CMS 0.225 hs 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 Q [GeV] 6
SM running of the weak mixing angle � 0.245 Erler, Ramsey-Musolf QW (p) NuTeV QW (e) 0.24 P2@MESA Qweak Moller Universal quantum corrections SOLID 0.235 can be absorbed into running, QW (APV ) � LEP1 scale-dependent sin 2 θ W ( μ ) �� ATLAS eDIS Tevatron 0.23 SLD 3 % SM uncertainty: few x 10 -4 sin 2 θ W (Q) MS CMS 0.225 hs �� 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 Q [GeV] Universal running - clean prediction of SM SM uncertainty = thickness of the black line (10 ) Deviation anywhere - BSM signal �� Sensitivity to light Z Marciano Mixing with New Extra Z Dark photon or Contact interaction Fermions Dark Z Heavy BSM reach: up to 49 TeV t: Sensitivity to light dark gauge sector � Complementary to colliders � 6 V
Electroweak boxes: non-universal corrections Hadronic effects under control = (1 + ∆ ρ + ∆ e )(1 − 4 sin 2 ˆ Q p , 1 � loop θ W + ∆ 0 e ) + ⇤ W W + ⇤ ZZ + ⇤ γ Z W Marciano, Sirlin ’83,84; Erler, Musolf ’05 Non-universal correction - depends on kinematics and hadronic structure Marciano and Sirlin: γ Z-box mainly universal (large log) same for PV in atoms and e-scattering 0.0037±0.0004 (5.3 ± 0.6%) Residual dependence on hadronic scale Λ Until recently: 1-loop SM result Q pW = 0.0713 ± 0.0008 This formulation was used to plan Qweak @ JLab 1.165 GeV beam; Q 2 =0.03 GeV 2 Combined Theo+Exp. uncertainty - 4% Δ sin 2 θ W /sin 2 θ W = 0.3% 7
Electroweak boxes: non-universal corrections γ Z-box from forward dispersion relation q Compute the imaginary part first p Real part from unitarity + analyticity + symmetries W 2 =(p+q) 2 MG, Horowitz ’09; MG, Horowitz, Ramsey-Musolf ‘11 Q 2 =-q 2 >0 Lower blob: γ Z-interference structure functions p µ ˆ p ν + i ✏ µ ναβ p α q β + ˆ Im W µ ν = − ˆ g µ ν F γ Z ( p · q ) F γ Z F γ Z 1 2 3 2( p · q ) Sum rule for the γ Z-box correction Known kinematical functions Z ∞ Z ∞ dW 2 h i ⇤ γ Z ( E ) = α A ( E, W, Q 2 ) F γ Z + B ( E, W, Q 2 ) F γ Z + C ( E, W, Q 2 ) F γ Z dQ 2 1 2 3 π 0 thr Inelastic PVES data Model-independent (if data available); E-dependence calculable in each exp. kinematics
Input to the dispersion integral No or very little inelastic PVES data available; Use electromagnetic data + isospin symmetry to obtain the input in the dispersion integral All kinematics contribute; not all contribute equally. Main support in the “shadow region” - Main contribution: W < 5 GeV, Q ² < 2 GeV ² 100 1 1 0 0 . 0 . 0 > < x x : S : S I D I D E E C DIS V N I E T L C A A V R F 10 F I D 2 ) 2 (GeV GVDM Resonances GVDM Q 1 RESONANCE VDM VDM Regge 0.1 REGGE 1 10 100 W (GeV)
Energy-dependent γ Z-box Q p Reference value: 1-loop SM W ( SM ) = 0 . 0713 ± 0 . 0008 MG, Horowitz, PRL 102 (2009) 091806; 7.6% of Q Wp correction in Q-Weak kinematics Nagata, Yang, Kao, PRC 79 (2009) 062501; - missed in the original analysis Tjon, Blunden, Melnitchouk, PRC 79 (2009) 055201; Zhou, Nagata, Yang, Kao, PRC 81 (2010) 035208; ⇤ γ Z ( E = 1 . 165 GeV) = (5 . 4 ± 2 . 0) × 10 − 3 Sibirtsev, Blunden, Melnitchouk, PRD 82 (2010) 013011; Rislow, Carlson, PRD 83 (2011) 113007; MG, Horowitz, Ramsey-Musolf, PRC 84 (2011) 015502; Blunden, Melnitchouk, Thomas, PRL 107 (2011) 081801; Rislow, Carlson PRD 85 (2012) 073002; Blunden, Melnitchouk, Thomas, PRL 109 (2012) 262301; Hall et al., PRD 88 (2013) 013011; Rislow, Carlson, PRD 88 (2013) 013018; Hall et al., PLB 731 (2014) 287; MG, Zhang, PLB 747 (2015) 305; Hall et al., PLB 753 (2016) 221; MG, Spiesberger, Zhang, PLB 752 (2016) 135; QWEAK collaboration recently finalized their result: Q pW = 0.0716 ± 0.0048 The error mostly experimental (6% rather than planned 4%) Steep energy dependence observed - furnished strong motivation for P2 @ MESA • ⇤ γ Z ( E = 0 . 155 GeV) = (1 . 1 ± 0 . 3) × 10 − 3 10
P2 experiment @ MESA MESA accelerator new, Mainz Energy Recovering Acc. Beam Dump Magnetic spectrometer MAGIX Parity violation experiment P2 P2 detector
P2 experiment @ MESA 155 MeV E beam ¯ θ f 35 � 200 days of data; 20 � δθ f 150 µA beam 6 ⇥ 10 � 3 (GeV/c) 2 h Q 2 i L, δθ f 85% polarization h A exp i � 39 . 94 ppb ( ∆ A exp ) T otal 0 . 68 ppb (1 . 70 %) ( ∆ A exp ) Statistics 0 . 51 ppb (1 . 28 %) ( ∆ A exp ) P olarization 0 . 21 ppb (0 . 53 %) ( ∆ A exp ) Apparative 0 . 10 ppb (0 . 25 %) ( ∆ A exp ) ⇤ γ Z 0 . 08 ppb (0 . 20 %) Additionally: A PV measurement on C-12 ( ∆ A exp ) nucl. F F 0 . 29 ppb (0 . 72 %) Asymmetry ~ 4sin 2 θ W - no gain in precision s 2 h ˆ Z i 0 . 23116 but 15 times larger than p; 3 . 34 ⇥ 10 � 4 (0 . 14 %) s 2 ( ∆ ˆ Z ) T otal Cross sections 36 times larger than p; 2 . 68 ⇥ 10 � 4 (0 . 12 %) s 2 ( ∆ ˆ Z ) Statistics 2500h data - 0.3% on sin 2 θ W possible! 1 . 01 ⇥ 10 � 4 (0 . 04 %) s 2 ( ∆ ˆ Z ) P olarization 5 . 06 ⇥ 10 � 5 (0 . 02 %) s 2 ( ∆ ˆ Z ) Apparative 4 . 16 ⇥ 10 � 5 (0 . 02 %) s 2 ( ∆ ˆ Z ) ⇤ γ Z 1 . 42 ⇥ 10 � 4 (0 . 06 %) s 2 Production: 2019-2020 ( ∆ ˆ Z ) nucl. F F
PVeS Experiment Summary % Pioneering 0 0 % 1 Strange Form Factor (1998-2009) 0 1 -4 S.M. Study (2003-2005) 10 JLab 2010-2012 Future E122 % 1 -5 PVDIS-6 10 G0 Mainz-Be H-I SAMPLE SOLID -6 10 A4 G0 ) PV MIT-12C A4 H-III (A A4 H-He -7 δ 10 H-II PREX-I E158 PREX-II -8 10 Qweak MESA-12C -9 10 Moller MESA-P2 -10 10 -8 -6 -5 -3 -7 -4 10 10 10 10 10 10 A PV
P2 @ MESA to test Standard Model Impact of Qweak and MESA on effec5ve e-q operators: √ 2) C q q γ µ q L = − ( G F / 1 ¯ e γ µ γ 5 e ¯
P2 @ MESA to test Standard Model Impact of Qweak and MESA on effec5ve e-q operators: √ 2) C q q γ µ q L = − ( G F / 1 ¯ e γ µ γ 5 e ¯ QWEAK
P2 @ MESA to test Standard Model Impact of Qweak and MESA on effec5ve e-q operators: √ 2) C q q γ µ q L = − ( G F / 1 ¯ e γ µ γ 5 e ¯ MESA QWEAK
P2 @ MESA to test Standard Model Impact of Qweak and MESA on effec5ve e-q operators: √ MESA - C12 2) C q q γ µ q L = − ( G F / 1 ¯ e γ µ γ 5 e ¯ MESA MESA - C12: a 0.3% measurement of A PV QWEAK = 0.3% meas. of sin 2 θ W Access the isoscalar combina5on of C 1 ’s
Recommend
More recommend
