ISU Coloq 11-3-2014

electron scattering (collisions)

Elastic Collisions: Conserve P and E

Inelastic : Only Conserve P

Definition of Momentum Transfer

Using Ryder 4-momentum tensor convention: [math]P_{\mu} \equiv (E/c, -\vec{p}) \;\;\;\;\; P^{\mu} \equiv (E/c, \vec{p})[/math]

[math]q_\mu \equiv (\omega, \vec{q})[/math] [math]k^i_\mu \equiv (E_i, \vec{k_i})[/math] [math]k^f_\mu \equiv (E_f, \vec{k_f})[/math]

Conservation of Momentum

[math] k^i_\mu =q_\mu + k^f_\mu [/math]

Momentum Transfer

[math] q_\mu =k^i_\mu - k^f_\mu [/math]

Momentum Transfer Squared

[math] -Q^2 = q^2 = q_\mu q^{\mu} =(E_i-E_f)^2 - (\vec{k}_i - \vec{k}_f) \cdot (\vec{k}_i - \vec{k}_f) [/math]

[math]= m_i^2 + m_f^2 -2E_iE_f + 2\left | \vec{k}_i\right | \left | \vec{k}_f\right | cos(\theta)[/math]

[math]=-4E_iE_f \sin^2(\theta/2) \;\;\; m_i = m_f \ll E_i \mbox{ and } E \approx \left | \vec{k}_i\right |[/math]

[math]Q^2 =4E_iE_f \sin^2(\theta/2) \gt 0[/math] A space-like scattering event

Space-like interval: Two events are separated by a space like interval then there isn't enough time passing between them to allow a cause-effect relationship because a photon can't traverse the distance. This means that there is no reference frame that may be used to describe the event as happening at the same spatial location but there is a frame that describes them happening at the same time. If the spacetime interval between the two events is defined as s[math]^2 = (\Delta r)^2 - (c\Delta t)^2[/math] then [math]s^2 \gt 0[/math] for a space-like interval

Time-like interval: Two events are separated by a time like interval if enough time passes between them to allow a cause-effect relationship. This means that there is no reference frame that may be used to describe the event as happening at the same time but there is one that describes them happening at the same spatial location. If the spacetime interval between the two events is defined as s[math]^2 = (\Delta r)^2 - (c\Delta t)^2[/math] then [math]s^2 \lt 0[/math] for a time-like interval

The Delta Resonance

Decay Modes: [math]ep \rightarrow \;\; \left \{ {N \pi \;\;\; 99.5% \atop p \gamma \;\;\; 0.5% } \right .[/math]

[math]\sigma = \lt \Delta^+ | V_{\mu}^3| p\gt [/math]

[math]V_{\mu}^3 =[/math] Vector current of the virtual photon exchange

4-Momentum vector definition using Ryder convention

[math]P_{\mu} \equiv \left ( \frac{E}{c} , - \vec p \right )[/math]

[math]P^{\mu} \equiv \left ( \frac{E}{c} , \vec p \right )[/math]

[math]P_{\mu} P^{\mu} = \left ( \frac{E}{c}\right )^2 - \vec p^2 = E^2-p^2 = m^2[/math] if you define the speed of light as unity

Note

Other conventions used by Perkins

[math]P_{\mu} \equiv \left ( \vec p, -E \right )[/math]

[math]P^{\mu} \equiv \left ( \vec p , E\right )[/math]

or Kollen

[math]P_{\mu} \equiv \left ( \vec p, iE \right )[/math]

[math]P^{\mu} \equiv \left ( \vec p , iE\right )[/math]

Momentum transfer is defined as

[math]q_{\mu} \equiv ( \omega, \vec q) = P^i_{\mu} - P^f_{\mu}[/math] : conservation of momentum

[math]q_{\mu}q^{\mu} = (E_i - E_f)^2 - (\vec {P}_i - \vec{P}_f) \cdot (\vec {P}_i - \vec{P}_f)[/math]

[math]= m_i^2 +m_f^2 - 2E_iE_f + 2 \left | \vec {P}_i \right | \left | \vec {P}_f \right |[/math]

Definition of Missing Mass

Inelastic scattering (Energy is not conserved but absorbed from the momentum transfer)

[math]P_e^{\mu} \equiv (E_i,\vec{k}_i)[/math] [math]\left(P_e^{\mu}\right)^{\prime} \equiv (E_f,\vec{k}_f)[/math] [math]P_p^{\mu} \equiv (M_p,0)[/math] [math]\left(P_p^{\mu}\right)^{\prime} \equiv (E_X,\vec{k}_X)[/math]

4-momentum conservation

[math]P_e^{\mu} + P_p^{\mu} = \left(P_e^{\mu}\right)^{\prime} + \left(P_p^{\mu}\right)^{\prime}[/math]

[math]\left(P_p^{\mu}\right)^{\prime} \left(P_{\mu}^p\right)^{\prime} = [P_e^{\mu} + P_p^{\mu} - \left(P_e^{\mu}\right)^{\prime} ][P^e_{\mu} + P^p_{\mu} - \left(P^e_{\mu}\right)^{\prime} ][/math]

[math]E_X^2 - P_X^2 \equiv W^2 = (E_i^2 - k_i^2) + (E_f^2-k_f^2) + M_p^2 + 2M_p(E_i - E_f) -2(E_iE_f-\vec{k_i}\cdot \vec{k_f})[/math]

[math]W^2=M_p^2 + 2M_p(E_i-E_f) -Q^2 \equiv [/math]Invariant Missing Mass = mass of the intermediate state that was created.

200 px

Spin 1/2 and 3/2 final states

References

Theory

Phenomenological

NP, B291(1987)793; NP, B346(1990)1;

    Z. Phys. C56(1992)493;
    Eur. Phys. J. C44  (2005)219;
    hep-ph/0205123
    arXiV:1310.5285

QCD inspired

NP, B483(1997)291; NP, B484(1997)265;

    PRL 85(2000)3591; PRL 89(2002)162301;
    JHEP 0211(2002)44; NP, A720(2003)131; 
    Eur. Phys. J. C30(2003)213; arXiV:09073534;
    NP, A761(2005)67; PR, C81(2010)024902

Hybrids

PYTHIA + BUU simulation

     PR, C70(2004)054609; NP, A801(2008)68

Experiment

keith's 2012 talk in Italy on EG1-DVCS

Unpolarized

http://link.springer.com/article/10.1007%2FJHEP04%282014%29005

File:AndyMiller 200TalkAtDESY.pdf 2002 talk by CA Miller at DESY

File:Dueren.98.055.pdf 1998 Duren talk

2013 APS talk on EG1-DVCS

July 30,2014 talk by XingLong Li at Heremes File:XingLongLi TalkOnPACIAEmdoelForSIDIS.pdf from

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=31&ved=0CB0QFjAAOB4&url=http%3A%2F%2Fhadron2014.csp.escience.cn%2Fdct%2Fattach%2FY2xiOmNsYjpwZGY6MzAwMjA%3D&ei=UPw1VNiQAdHlsATA7IHwDw&usg=AFQjCNH5yyek_zTJ22TZq0Dw_YLUeAxe2Q

Xiangs proposal for CLAS12 measurement of SIDIS Xsections see Fig. 1

Semi-inclusive deep inelastic scattering at small transverse momentum

Naomi's SIDIS Hermes talk from 2011 at NNPSS11

1986 article ob QCD effects in semi-inclusive deep inelastic scattering from a polarized target by P. Chiappetta J. -Ph. Guillet

theses

2014 Ph.D thesis of Naomi's student Sylvester Joosten

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&cad=rja&uact=8&ved=0CFYQFjAG&url=http%3A%2F%2Fwww.nikhef.nl%2Fpub%2Fservices%2Fbiblio%2Ftheses_pdf%2Fthesis_E_Garutti.pdf&ei=Osw3VJbSAY27ogSx3IDwDQ&usg=AFQjCNENlNdgPr6dgfq9OanlL8cUnYHmMQ&bvm=bv.77161500,d.cGU

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