BSM Physics at the EIC Mini Ad-hoc Workshop Sonny Mantry University of North Georgia December 19th, 2017 Tuesday, December 19, 17
Physics Beyond the Standard Model at the EIC • The EIC is primarily a QCD machine. But it can also provide for a vibrant program to study physics beyond the Standard Model (BSM), complementing efforts at other colliders. • The EIC can play an important role in searching/constraining various new physics scenarios that include: • Leptoquarks • R-parity violating Supersymmetry • Right-handed W-bosons • Excited leptons (compositeness) • Dark Photons • Charged Lepton Flavor Violation (CLFV) • ... • New physics can be constrained through: • Precision measurements of the electroweak parameters 10 3 Current polarized DIS data: • Such a program physics is facilitated by: CERN DESY JLab SLAC Current polarized BNL-RHIC pp data: • high luminosity PHENIX π 0 STAR 1-jet • wide kinematic range 10 2 EIC √ s= 140 GeV, 0.01 ≤ y ≤ 0.95 Q 2 (GeV 2 ) EIC √ s= 45 GeV, 0.01 ≤ y ≤ 0.95 • range of nuclear targets • polarized beams 10 ★ The addition of a polarized positron beam will enhance the BSM program at the EIC. 1 -4 -3 -2 -1 10 10 10 10 1 x Tuesday, December 19, 17
Precision Measurements of the Weak Neutral Current Couplings Tuesday, December 19, 17
Contact Interactions A V V A • For Q 2 << (M Z ) 2 limit, electron-quark scattering via the weak neutral current is mediated by contact interactions: L = G F � X C 1 q ¯ q � µ q + C 2 q ¯ q � µ � 5 q + C 3 q ¯ `� µ � 5 ` ¯ `� µ ` ¯ `� µ � 5 ` ¯ q � µ � 5 q p , 2 q • Tree-level Standard Model values: C 1 u = − 1 2 + 4 3 sin 2 ( θ W ) , C 2 u = − 1 C 3 u = 1 2 + 2sin 2 ( θ W ) , 2 , C 1 d = 1 2 − 2 C 2 d = 1 C 3 d = − 1 3 sin 2 ( θ W ) , 2 − 2sin 2 ( θ W ) , 2 ng the three terms on the r.h.s. of Eq. (3), the first two terms are parity-vio Tuesday, December 19, 17
New Physics Effects E 6 Z’ Based Extensions RPV SUSY Extensions Leptoquarks A V u e u e e u + ~ d LQ Z’ V A e u e u e u L = G F � X C 1 q ¯ q � µ q + C 2 q ¯ q � µ � 5 q + C 3 q ¯ `� µ � 5 ` ¯ `� µ ` ¯ `� µ � 5 ` ¯ q � µ � 5 q p , 2 ` , q • New physics contact interactions arise as a shift in the WNC couplings compared to the SM prediction: utions C iq = C iq (SM) + ∆ C iq , SM contribution New Physics contribution • Deviations from the SM prediction of the WNC couplings will lead to corresponding deviations in the weak mixing angle. Tuesday, December 19, 17
New Physics Effects E 6 Z’ Based Extensions RPV SUSY Extensions Leptoquarks A V u e u e e u + ~ d LQ Z’ V A e u e u e u utions C iq = C iq (SM) + ∆ C iq , • Effective Lagrangian for New Physics Contributions can be parameterized as: � L = g 2 ⇢ � X ⌘ ` q q L � µ q L + ⌘ ` q q R � µ q R + ⌘ ` q q L � µ q L + ⌘ ` q LL ¯ LR ¯ RL ¯ RR ¯ ` L � µ ` L ¯ ` L � µ ` L ¯ ` R � µ ` R ¯ ` R � µ ` R ¯ q R � µ q R , Λ 2 ` , q • Shift in the WNC couplings due to new physics contact interactions: ⌘ ` q LL + ⌘ ` q LR − ⌘ ` q RL − ⌘ ` q ∆ C 1 q = g 2 RR , Each of the WNC couplings probe a unique √ Λ 2 2 2 G F combination of chiral structures thereby ⌘ ` q LL − ⌘ ` q LR + ⌘ ` q RL − ⌘ ` q ∆ C 2 q = g 2 complementing constraints arising from other low RR , √ Λ 2 energy experiments or colliders. 2 2 G F − ⌘ ` q LL + ⌘ ` q LR + ⌘ ` q RL − ⌘ ` q ∆ C 3 q = g 2 RR . √ Λ 2 2 2 G F Tuesday, December 19, 17
A V Contact Interactions V A L = G F � X C 1 q ¯ q � µ q + C 2 q ¯ q � µ � 5 q + C 3 q ¯ `� µ � 5 ` ¯ `� µ ` ¯ `� µ � 5 ` ¯ q � µ � 5 q p , 2 q • Precision measurements of the electroweak couplings can also be translated into constraints in specific models. � � • For example, for the different LQ states only particular chiral structures arise which leads to a corresponding pattern of shifts in the WNC couplings: ⌘ ` q LL + ⌘ ` q LR − ⌘ ` q RL − ⌘ ` q ∆ C 1 q = g 2 � RR , √ � Λ 2 2 2 G F N/N ⌘ ` q LL − ⌘ ` q LR + ⌘ ` q RL − ⌘ ` q ∆ C 2 q = g 2 RR , √ Λ 2 2 2 G F − ⌘ ` q LL + ⌘ ` q LR + ⌘ ` q RL − ⌘ ` q ∆ C 3 q = g 2 RR . √ Λ 2 2 2 G F Tuesday, December 19, 17
Weak Mixing Angle Measurements at the EIC 0.244 EIC e-D: 10 GeV x 50 GeV/u Qweak(first) 0.242 EIC e-D: 10 GeV x 125 GeV/u E158 ν -DIS EIC e-D: 15 GeV x 50 GeV/u 0.24 EIC e-D: 15 GeV x 125 GeV/u Projections based on an EIC e-D: 20 GeV x 125 GeV/u 0.238 ) µ APV(Cs) ( integrated luminosity of W PVDIS 0.236 θ 267 fb^(- 1 ) per nucleon in 2 sin electron-deuteron 0.234 collisions at EIC. 0.232 LEP + APV(Ra ) P2 Qweak SLAC SoLID Moller 0.23 0.228 -3 -2 -1 0 1 2 3 Log µ [GeV] 10 [Y.X.Zhao, A.Despande, J.Huang, K.S. Kumar, S.Riordan] • Deviations from SM predictions for the WNC couplings will lead to corresponding deviations in the SM behavior of the weak mixing angle. • Wide kinematic range and high luminosity of the EIC can provide many more measurements of the weak mixing angle along this curve. Tuesday, December 19, 17
Precision Measurements of the Weak Neutral Current Couplings • New physics reach from various precision experiments and the combination of couplings they constrain: Experiment Coupling Λ Cesium APV 9.9 TeV C 1 u + C 1 d E-158 8.5 TeV C ee Qweak 11 TeV 2 C 1 u + C 1 d SoLID 8.9 TeV 2 C 2 u � C 2 d MOLLER 19 TeV C ee P2 16 TeV 2 C 1 u + C 1 d [ K.kumar, et.al . Ann.Rev.Nucl.Part.Sci. 63 (2013) 237-267 ] L = G F � X C 1 q ¯ q � µ q + C 2 q ¯ q � µ � 5 q + C 3 q ¯ `� µ � 5 ` ¯ `� µ ` ¯ `� µ � 5 ` ¯ q � µ � 5 q p , 2 q � Tuesday, December 19, 17 � � � �
Asymmetries as a Probe of Electroweak Couplings L e ff = G F � � C 1 q ¯ q γ µ q + C 2 q ¯ q γ µ γ 5 q + C 3 q ¯ � X ℓγ µ γ 5 ℓ ¯ ℓγ µ ℓ ¯ ℓγ µ γ 5 ℓ ¯ q γ µ γ 5 q p 2 ` ,q Can be further constrained by Can be further constrained by Parity-Violating eD DIS lepton charge conjugate violating (positron beams) asymmetry • Measurement of these asymmetries requires: -p, D targets -polarized electron and positron beams Tuesday, December 19, 17
Parity-Violating e-D Asymmetry e ⇥ • Parity-violating e-D asymmetry is a powerful probe of the e WNC couplings: γ , Z | A γ | ' G F Q 2 ' | A Z | A PV ⌘ σ R � σ L 4 πα ' 10 � 4 Q 2 X D σ R + σ L • Due to the isoscalar nature of the Deuteron target, the dependence of the asymmetry on the structure functions largely cancels (Cahn-Gilman formula). CG = − G F Q 2 ⇥ 1 − (1 − y ) 2 9 1 − 20 ⇧� ⌃ 9 sin 2 ⇥ W 1 − 4 sin 2 ⇥ W A RL ⇥ � + √ 10 1 + (1 − y ) 2 2 2 ⇤� Clean probe of All hadronic effects cancel! WNC • e-D asymmetry allows a precision measurement of the weak mixing angle. Tuesday, December 19, 17
Corrections to Cahn-Gilman • Hadronic effects appear as corrections to the Cahn-Gilman formula: A RL = − G F Q 2 1 − (1 − y ) 2 9 ⇧ ⌃ a 1 + ˜ ˜ a 2 , √ 1 + (1 − y ) 2 10 2 2 ⇤� a j = − 2 ⇤ ⌅ ˜ 3 (2 C ju − C jd ) 1 + R j (new) + R j (sea) + R j (CSV) + R j (TMC) + R j (HT) (12) Higher Charge symmetry New physics twist violation Sea quarks Target mass • Hadronic effects must be well understood before any claim for evidence of new physics can be made. [J.Bjorken,T.Hobbs, W. Melnitchouk; S.Mantry, M.Ramsey-Musolf, G.Sacco; A.V.Belitsky, A.Mashanov, A. Schafer; C.Seng,M.Ramsey-Musolf, ....] Tuesday, December 19, 17
e-D PVDIS at EIC a ( x )+ 1 � ( 1 � y ) 2 G F h i A PV = Q 2 10 3 Current polarized DIS data: 1 +( 1 � y ) 2 b ( x ) p CERN DESY JLab SLAC 2 2 πα Current polarized BNL-RHIC pp data: PHENIX π 0 STAR 1-jet 10 2 EIC √ s= 140 GeV, 0.01 ≤ y ≤ 0.95 Q 2 (GeV 2 ) EIC √ s= 45 GeV, 0.01 ≤ y ≤ 0.95 h i a ( x ) = 6 ( C 1 u � 1 h i 2 C 1 d )+ corrections ; 5 10 2 C 2 d ) q ( x ) � ¯ q ( x ) b ( x ) = 6 ( C 2 u � 1 h i q ( x ) + corrections q ( x )+ ¯ 5 1 -4 -3 -2 -1 10 10 10 10 1 x • EIC can make improve on the precision of the WNC couplings. G and are integrated over x in the 0.00 • • High luminosity: -allows high precision • Measurements over wide range of y: -allows clean separation of a(x) and b(x) terms -clean separation of the combinations of WNC couplings: , ly 2 C 1 u − C 1 d d 2 C 2 u − C 2 d • Region of high Q^2: 2 -larger asymmetry -suppress higher twist effects e 4-momentum • Region of high Q^2 and restrict range of Bjorken-x ge 0 . 2 < ∼ x < ∼ 0 . 5 -suppress sea quark effects Tuesday, December 19, 17
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